33916033 Financial Management Principles and Applications

CHAPTER 1

An Introduction to Financial Management CHAPTER ORIENTATION This chapter lays a foundation for what will follow. First, it focuses on the goal of the firm, followed by a review of the legal forms of business organization. Ten principles that form the foundations of financial management then follow.

CHAPTER OUTLINE I.

Goal of the firm A.

In this book we will designate maximization of shareholder wealth, by which we mean maximization of the total market value of the firm's common stock, to be the goal of the firm. To understand this goal and its inclusive nature it is first necessary to understand the difficulties involved with the frequently suggested goal of profit maximization.

B.

While the goal of profit maximization stresses the efficient use of capital resources, it assumes away many of the complexities of the real world and for this reason is unacceptable. 1.

One of the major criticisms of profit maximization is that it assumes away uncertainty of returns. That is, projects are compared by examining their expected values or weighted average profit.

2.

Profit maximization is also criticized because it assumes away timing differences of returns.

1

C. II.

III.

Profit maximization is unacceptable and a more realistic goal is needed.

Maximization of shareholder wealth A.

We have chosen the goal of shareholder wealth maximization because the effects of all financial decisions are included in this goal.

B.

In order to employ this goal we need not consider every price change to be a market interpretation of the worth of our decisions. What we do focus on is the effect that our decision should have on the stock price if everything were held constant.

C.

The agency problem is a result of the separation between the decision makers and the owners of the firm. As a result managers may make decisions that are not in line with the goal of maximization of shareholder wealth.

Legal forms of business organization A.

The significance of different legal forms 1.

B.

The predominant form of business organization in the United States in pure numbers is the sole proprietorship.

Sole proprietorship: A business owned by a single person and that has a minimum amount of legal structure. 1.

Advantages a. b. c.

2.

Disadvantages a. b. c. d.

C.

Easily established with few complications Minimal organizational costs Does not have to share profits or control with others Unlimited liability for the owner Owner must absorb all losses Equity capital limited to the owner's personal investment Business terminates immediately upon death of owner

Partnership: An association of two or more individuals coming together as coowners to operate a business for profit. 1.

Two types of partnerships a.

General partnership: Relationship between partners is dictated by the partnership agreement. l.

Advantages a. Minimal organizational requirements b. Negligible government regulations

2.

Disadvantages a. b. c.

b.

All partners have unlimited liability Difficult to raise large amounts of capital Partnership dissolved by the death or withdrawal of general partner

Limited partnership 2

l.

Advantages a. b. c.

For the limited partners, liability limited to the amount of capital invested in the company Withdrawal or death of a limited partner does not affect continuity of the business Stronger inducement in raising capital

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2.

Disadvantages a. b. c. d.

2.

D.

There is also a Limited Liability Company (LLC) form of business. This is a cross between a partnership and a corporation. It retains limited liability for its owners, but is run and taxed like a partnership.

The corporation: An "impersonal" legal entity having the power to purchase, sell, and own assets and to incur liabilities while existing separately and apart from its owners. 1.

Ownership is evidenced by shares of stock

2.

Advantages a. b. c. d.

3.

Limited liability of owners Ease of transferability of ownership, i.e., by the sale of one's shares of stock The death of an owner does not result in the discontinuity of the firm's life Ability to raise large amounts of capital is increased

Disadvantages a. b.

IV.

There must be at least one general partner who has unlimited liability in the partnership Names of limited partners may not appear in the name of the firm Limited partners may not participate in the management of the business More expensive to organize than general partnership, as a written agreement is mandatory

Most difficult and expensive form of business to establish Control of corporation not guaranteed by partial ownership of stock

The Corporation and the Financial Markets: The Interactions A. The popularity of the corporation stems from the ease in raising capital that it provides. 1. Initially, the corporation raises funds in the financial markets by selling securities. 2. The corporation then invests this cash in return generating assets. 3. The cash flow from those assets is either reinvested in the corporation, given back to the investors in the form of dividends or interest payments, or used to repurchase stock which should cause the stock price to rise, or given to the government in the form of taxes. B. A primary market is a market in which new, as opposed to previously issued, securities are traded.

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C. An initial public offering (IPO) is the first time a company’s stock is sold to the public. D. A seasoned new issue refers to a stock offering by a company that already has common stock traded. E. The secondary market is the market in which stock previously issued by the firm trades. V.

Ten Principles that form the foundation of financial management. A.

Principle 1: The risk-return tradeoff - we won't take additional risk unless we expect to be compensated with additional return. 1. Almost all financial decisions involve some sort of risk-return tradeoff.

B.

Principle 2: The time value of money - a dollar received today is worth more than a dollar received in the future.

C.

Principle 3: Cash -- Not Profits -- is King. In measuring value we will use cash flows rather than accounting profits because it is only cash flows that the firm receives and is able to reinvest.

D.

Principle 4: Incremental cash flows - it's only what changes that count. In making business decisions we will only concern ourselves with what happens as a result of that decision.

E.

Principle 5: The curse of competitive markets - why it's hard to find exceptionally profitable projects. In competitive markets, extremely large profits cannot exist for very long because of competition moving in to exploit those large profits. As a result, profitable projects can only be found if the market is made less competitive, either through product differentiation or by achieving a cost advantage.

F.

Principle 6: Efficient Capital Markets - The markets are quick and the prices are right.

G.

Principle 7: The agency problem - managers won't work for the owners unless it's in their best interest. The agency problem is a result of the separation between the decision makers and the owners of the firm. As a result managers may make decisions that are not in line with the goal of maximization of shareholder wealth.

H.

Principle 8: Taxes bias business decisions.

I.

Principle 9: All risk is not equal since some risk can be diversified away and some cannot. The process of diversification can reduce risk, and as a result, measuring a project’s or an asset's risk is very difficult.

J.

Principle 10: Ethical behavior is doing the right thing, and ethical dilemmas are everywhere in finance. Ethical behavior is important in financial management, just as it is important in everything we do. Unfortunately, precisely how we define what is and what is not ethical behavior is sometimes difficult. Nevertheless, we should not give up the quest.

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ANSWERS TO END-OF-CHAPTER QUESTIONS 1-1.

The goal of profit maximization is too simplistic in that it assumes away the problems of uncertainty of returns and the timing of returns. Rather than use this goal, we have chosen maximization of shareholders' wealth—that is, maximization of the market value of the firm's common stock—because the effects of all financial decisions are included. The shareholders react to poor investment or dividend decisions by causing the total value of the firm's stock to fall and react to good decisions by pushing the price of the stock upward. In this way all financial decisions are evaluated, and all financial decisions affect shareholder wealth.

1-2.

The major difference between the profit maximization goal and the goal of shareholder wealth maximization is that the latter goal deals with all the complexities of the operating environment, while the profit maximization goal does not. The major factors assumed away by the profit maximization goal are uncertainty and the timing of the returns.

1-3.

The goal of shareholder wealth maximization must be looked at as a long-run goal. As such, the public image of the firm may be of concern inasmuch as it may affect sales and legislation. Thus, while these actions may not directly result in increased profits, they may affect consumers' and legislators' attitudes.

1-4.

Almost all financial decisions involve some sort of risk-return tradeoff. The more risk the firm is willing to accept, the higher the expected return for the given course of action. For example, in the area of working capital management, the less inventory held, the higher the expected return, but also the greater the risk of running out of inventory. While one manager might accept a given level of risk, another more riskaverse manager may not accept that level of risk. This does not mean that one manager is correct and one is not, only that not all managers will view the risk-return trade off in the same manner.

1-5.

(a)

A sole proprietorship is a business owned by a single individual who maintains complete title to the assets, but who is also personally liable for all indebtedness incurred.

(b)

A partnership is an association of two or more individuals coming together as co-owners for the purpose of operating a business for profit. The partnership is equivalent to the sole proprietorship, except that the partnership has multiple owners.

(c).

A corporation is a legal entity functioning separate and apart from its owners. It can individually sue and be sued, purchase, sell, or own property, and be subject to criminal punishment for crimes.

(a)

The sole proprietor maintains title to the firm's assets, has unlimited liability, is entitled to the profits from the business, but must also absorb any losses realized. This form of business is easily initiated. Termination of the business comes by the owner discontinuing the business or upon his death.

1-6.

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1-7.

(b)

In a partnership, all general partners have unlimited liability. Each partner is liable for the actions of the other partners. The partnership agreement dictates the basic relationships among the partners within the firm. As with the sole proprietorship, the partnership is terminated upon the desires of any partner within the organization, or upon a partner's death. Under certain conditions a partner's liability may be restricted to the amount of capital invested in the partnership. However, at least one general partner must remain in the association for whom the privilege of limited liability does not apply.

(c)

The corporation is legally separate from its owners. Ownership of the corporation is determined by the number of shares of common stock owned by an individual. Since the shares are transferable, the ownership in a corporation may be easily transferred. Investors' liability is limited to the amount of their investment. The life of the corporation is not dependent upon the status of the investors. The death or withdrawal of an investor does not disrupt the corporate life. However, the cost of forming a corporation is more expensive than a proprietorship or partnership.

(a)

Organizational requirements and costs favor the sole proprietorship or possibly the general partnership depending upon the approach taken in forming the partnership.

(b)

The corporation minimizes the liability of the owners. Also, the limited partnership permits some of the partners the privilege of limited liability.

(c)

The corporation is definitely the most favorable form of business because it provides the continuity of the business regardless of an owner's withdrawal or death.

(d)

If ease of ownership transferability is desired, the corporation is best. However, because of certain circumstances the owners may prefer that ownership not be easily transferred, in which case the partnership would be the most desirable.

(e)

The sole proprietor is able to maintain complete and ultimate control and minimize regulations.

(f)

The corporation is the strongest form of legal entity in terms of the ease of raising capital from external investors.

(g)

In regard to income taxes, it is difficult to determine which form of business is the most advantageous. Such a selection is dependent upon individual circumstances.

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SOLUTION TO INTEGRATIVE PROBLEM 1.

The goal of profit maximization is too simplistic in that it assumes away the problems of uncertainty of returns and the timing of returns. Rather than use this goal, we have chosen maximization of shareholders' wealth—that is, maximization of the market value of the firm's common stock—because the effects of all financial decisions are included. The shareholders react to poor investment or dividend decisions by causing the total value of the firm's stock to fall and react to good decisions by pushing the price of the stock upward. In this way all financial decisions are evaluated, and all financial decisions affect shareholder wealth.

2.

Simply put, investors won't put their money in risky investments unless they are compensated for taking on that additional risk. In effect, the return investors expect is composed of two parts. First, they receive a return for delaying consumption which must be greater than the anticipated rate of inflation. Second, they receive a return for taking on added risk. Otherwise, both risky and safe investments would have the same expected return associated with them and no one would take on the risky investments.

3.

The firm receives cash flows and is able to reinvest them rather than accounting profits. In effect, accounting profits are shown when they are earned rather than when the money is actually in hand. Unfortunately, a firm's accounting profits and cash flows may not be timed to occur together. For example, capital expenses, such as the purchase of a new plant or piece of equipment, are depreciated over several years, with the annual depreciation subtracted from profits. However, the cash flow associated with these expenses generally occurs immediately. It is the cash inflows that can be reinvested and cash outflows that involve paying out money. Therefore, cash flows correctly reflect the true timing of the benefits and costs.

4.

In an efficient market, information is impounded into security prices with such speed that there are no opportunities for investors to profit from publicly available information. Actually, what types of information are immediately reflected in security prices and how quickly that information is reflected determine how efficient the market actually is. The implications for us are, first, that stock prices reflect all publicly available information regarding the value of the company. This means we can implement our goal of maximization of shareholder wealth by focusing on the effect each decision should have on the stock price all else held constant. It also means that earnings manipulations through accounting changes should not result in price changes. In effect our preoccupation with cash flows is validated.

5.

The agency problem is the result of the separation of management and the ownership of the firm. As a result managers may make decisions that are not in line with the goal of maximization of shareholder wealth. To control this problem we monitor managers and try to align the interests of shareholders and managers. The interests of shareholders and managers can be aligned by setting up stock options, bonuses, and perquisites that are directly tied to how closely management decisions coincide with the interest of shareholders.

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6.

Ethical errors are not forgiven in the business world. Business interaction is based upon trust and there is no way that trust can be eliminated quicker than through an ethical violation. The fall of Arthur Andersen, Ivan Boesky and Drexel, Burnham, Lambert and the near collapse of Salomon Brothers illustrates this fact. As a result acting in an ethical manner is not only morally correct, but it is congruent with our goal of maximization of shareholder wealth.

7.

(1)

A sole proprietorship is a business owned by a single individual who maintains complete title to the assets, but who is also personally liable for all indebtedness incurred.

(2)

A partnership is an association of two or more individuals coming together as co-owners for the purpose of operating a business for profit. The partnership is equivalent to the sole proprietorship, except that the partnership has multiple owners.

(3).

A corporation is a legal entity functioning separate and apart from its owners. It can individually sue and be sued, purchase, sell, or own property, and be subject to criminal punishment for crimes.

SOLUTION TO CASE LIVING AND DYING WITH ASBESTOS With ethics cases there are no right or wrong answers—just opinions. Try to bring out as many opinions as possible without being judgmental or allowing other students to be judgmental. Also, it is effective to try to see if the students feel there are any possible parallels between what has happened in this case and the tobacco industry.

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CHAPTER 2

Understanding Financial Statements, Taxes, and Cash Flows CHAPTER ORIENTATION In this chapter, we review the contents and meaning of a firm’s income statement and balance sheet. We also look very carefully at how to compute a firm’s cash flows from a finance perspective, which is called free cash flows.

CHAPTER OUTLINE I.

Basic Financial Statements A.

The Income Statement 1.

The income statement reports the results from operating the business for a period of time, such as a year.

2.

It is helpful to think of the income statement as comprising five types of activities:

3.

a.

Selling the product

b.

The cost of producing or acquiring the goods or services sold

c.

The expenses incurred in marketing and distributing the product or service to the customer along with administrative operating expenses

d.

The financing costs of doing business: for example, interest paid to creditors and dividend payments to the preferred stockholders

e.

The taxes owed based on a firm’s taxable income

An example of an income statement is provided in Table 2-1 for the Harley-Davidson Corporation.

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B.

The Balance Sheet 1.

The balance sheet provides a snapshot of the firm’s financial position at a specific point in time, presenting its asset holdings, liabilities, and owner-supplied capital. a.

b.

II

Assets represent the resources owned by the firm (1)

Current assets - consisting primarily of cash, marketable securities, accounts receivable, inventories, and prepaid expenses

(2)

Fixed or long-term assets – comprising equipment, buildings, and land

(3)

Other assets – all assets not otherwise included in the firm’s current assets or fixed assets, such as patents, long-term investments in securities, and goodwill

The liabilities and owners’ equity indicate how the assets are financed. (1)

The debt consists of such sources as credit extended from suppliers or a loan from a bank.

(2)

The equity includes the stockholders’ investment in the firm and the cumulative profits retained in the business up to the date of the balance sheet.

2.

The balance sheet is not intended to represent the current market value of the company, but rather reports the historical transactions recorded at their costs.

3.

Balance sheets for the Harley-Davidson Corporation are presented in Table 2-2.

Computing a Company’s Taxes A.

Types of taxpayers 1.

2.

Sole proprietors a.

Report business income on personal tax returns

b.

Pay taxes at personal tax rate

Partnerships a.

The partnership reports income but does not pay taxes

b.

Each partner reports his or her portion of income and pays the corresponding taxes.

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3.

B.

2.

III.

a.

Corporation reports income and pays taxes

b.

Owners do not report these earnings except when all or part of the profit is paid out as dividends.

c.

Our focus is on corporate taxes.

Computing Taxable Income 1.

C.

Corporations

Taxable income is based on gross income less tax-deductible expenses a.

Interest expense is tax deductible

b.

Dividend payments are not tax deductible

Depreciation a.

Modified accelerated cost recovery system used for computing depreciation for tax purposes

b.

We use straight-line depreciation to reduce complexity.

Computing Taxes Owed 1.

Taxes paid are based on corporate tax structure.

2.

Tax rates used to calculate tax liability are marginal tax rates, or the rate applicable to the next dollar of income.

3.

Average tax rate is calculated by dividing taxes owed by the firm’s total income

4.

Marginal tax rate is used in financial decision making

Measuring Free Cash Flows A.

While an income statement measures a company’s profits, profits are not the same as cash flows; profits are calculated on an accrual basis rather than a cash basis.

B.

In measuring cash flows, we could use the conventional accountant’s presentation called a statement of cash flows. However, we are more interested in considering cash flows from the perspective of the firm’s shareholders and its investors, rather than from an accounting view. We will instead measure the cash flow that is free and available to be distributed to the firm’s investors, both debt and equity investors, or what we will call free cash flows.

C.

The cash flows that are generated through a firm’s operations and investments in assets will always equal its cash flows paid to – or received from – the company’s investors (both creditors and stockholders).

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D.

Calculating Free Cash Flows: An Asset Perspective 1.

A firm's free cash flows, from an asset perspective, is the after-tax cash flows generated from operations less the firm's investments in assets. It is this same amount that will be available for distributing to the firm’s investors. That is, a firm's free cash flows for a given period is equal to: After-tax cash flow from operations less the investment (increase) in net operating working capital less investments in fixed assets (plant and equipment) and other assets.

2.

After-tax cash flows from operations as follows: Operating income (earnings before interest and taxes) + depreciation = Earnings before interest, taxes, depreciation amortization (EBITDA) cash tax payments = After-tax cash flows from operations

3.

and

The increase in net operating working capital is equal to the: change in noninteres t - bearing   change in    current assets  current liabilitie s  

4.

Investments in fixed assets includes the change in gross fixed assets and any other balance sheet assets not already considered.

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E.

Calculating Free Cash Flows: A Financing Perspective 1.

Free cash flows from a financing perspective are equal to: Interest payments to creditors + or -

decrease in debt principal increase in debt principal

plus dividends paid to stockholders + or -

IV.

decrease in stock increase in stock

2.

Free cash flow from an asset perspective must equal free cash flow from a financing perspective.

3.

Free cash flows from a financing perspective are simply the net cash flows received by the firm’s investors, or if negative, the cash flows that the investors are paying into the firm. In the latter situation where the investors are putting money into the firm, it is because the firm’s free cash flow from assets is negative, thereby requiring an infusion of capital by the investors.

Financial Statements and International Finance A.

Many countries have different guidelines for firms to use in preparing financial statements. For example, a $1 of earnings in the United States is not the same as 1.10 Euro (the equivalent of a U.S. dollar based on the exchange rate). The differences are due to the two countries having different Generally Accepted Accounting Principles which guide their firms’ financial reporting.

B.

As a result of this situation, the International Accounting Standards Committee (IASC), a private body supported by the worldwide accounting profession, is trying to develop international financial-reporting standards that will minimize the problem. In spite of the work to standardize accounting practices around the world, the U.S. accounting profession has rejected efforts toward international standards. At this time, foreign companies seeking to list their shares in the United States must follow U.S. accounting standards.

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ANSWERS TO END-OF-CHAPTER QUESTIONS 2-1.

a.

The balance sheet represents an enumeration of a firm’s resources (assets) along with its liabilities and owners’ equity at a given date. The income statement summarizes the net results of the operation of a firm over a specified time interval. The primary distinction between these two statements is that the balance sheet shows the financial condition of a firm at a given date, whereas the income statement deals with the revenues and expenses of the firm incurred during a specified period of time.

b.

The conventional cash flow statement as prepared by accountants provides the information we need to know about what has happened to the firm’s cash and why. But it does not present it in a way that makes clear the cash flows the firm’s creditors and investors are providing to or receiving from the firm. Thus, we choose to reformat the presentation to show the firm’s free cash flows—the cash available to distribute to the creditors and investors. We are more interested in considering cash flows from the perspective of the firm’s shareholders and its investors, rather than from an accounting view. We instead measure the cash flow that is free and available to be distributed to the firm’s investors, both debt and equity investors, or what we will call free cash flows. Thus, what we use is similar to a conventional cash flow statement presented as part of a company’s financial statements, but “not exactly.” We also make the distinction between the cash flows generated by the firm’s assets and the financing free cash flows. 2-2.

2-3.

Gross profits is sales less the cost of producing or acquiring the firm’s product or service. Operating profits is the gross profits less the operating expenses, which consist of distributing the product or service to the customer (namely, marketing expenses) and any general and administrative expenses in operating the business. Net income is operating profits less financing costs (interest expenses and preferred stock dividends) and less income taxes.

Interest expense is the cost of borrowing money from a banker or another lender. There typically is a fixed interest rate so that the interest expense is computed as the interest rate times the amount borrowed. If we borrow $500,000 at an interest rate of 12 percent, then our interest expense will be $60,000. While interest is paid for the use of debt capital, dividends are paid to the firm’s stockholders. Preferred stock typically has a fixed dividend rate, so that the preferred stockholder gets a constant dividend each year. Common stockholders, on the other hand, usually receive dividends only if management decides to pay a dividend instead of reinvesting the firm’s profits. However, typically once a dividend has been paid to common stockholders, management is reluctant to decrease it or cease paying a dividend.

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2-4

Once preferred shares are sold, dividends are paid or accrued each year based upon preferred dividends (i.e., the percentage of the preferred stock’s par value paid as dividends) agreed to at the selling date. However, these dividends affect the income statement only. Common stock dividends, which may vary from year to year, also affect the income statement; however, the investment of common shareholders varies with the net addition to (or reduction from) retained earnings from year to year. The net addition to retained earnings equals the difference in the period’s net income and common dividends paid. Thus, the common equity section of the balance sheet (par value of common stock, paid-in capital and retained earnings) varies from year to year due to changes in the retained earnings portion of the firm’s common equity. 2.5

Net working capital is the firm’s liquid assets (current assets) less its short-term debt. Accountants include all short-term debt when computing net working capital; however, in computing free cash flows, we only subtract the noninterest-bearing debt, such as accounts payables and accruals. With this latter method, we are only considering the assets and liabilities that are changing as a result of the normal operating cycle of the business—beginning with the time inventory is purchased on credit to the time the firm collects the cash from its customer.

Gross working capital is the sum of current assets, while net working capital is the difference between current assets and current liabilities. As already suggested, we have both interest-bearing debt and noninterest-bearing debt. The former is debt where the lender is paid interest for providing us the money. Noninterest-bearing debt charges no interest because the “lender” is really a supplier or an employee to whom we owe money, but they are not requiring the firm to pay interest. 2-6.

A firm could have positive cash flows but still be in trouble because it has negative cash flows from operations. The positive cash flows would then be the result of the firm reducing its investments in working capital or long-term assets. Such a situation means that the company is not earning a satisfactory rate of return on its investments. Another company could have very attractive rates of return on its assets, but be growing so fast that the large investments in working capital and long-term assets result in negative cash flows. In this latter case, management is simply investing in the future. As the rate of growth slows, positive cash flows will occur.

2-7.

Examining only the income statement and the balance sheet fails to tell us how the firm is using its cash, which is a critical issue for any company.

2-8.

Free cash flows from assets equal the cash flows that are generated by the company that are then distributed to (if positive) or received from (if negative) the firm’s creditors and investors. It looks at cash flows from the firm’s perspective. Free cash flows from a financing perspective looks at the cash flows from the investors’ viewpoint. It indicates how the investor received cash in the form of interest, dividends, debt repayment or stock repurchase and how the investor infused cash in the form of additional debt or stock purchase. Whatever the company does is the exact opposite of what the investor receives or pays. That is, if a company distributes $100 in cash to the investors, then the investors must receive $100 as well. They have to be equal.

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SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 2-1A.

Belmond, Inc. Balance Sheet December 31, 2003 ASSETS Current assets Cash Accounts receivable Inventory Total current assets Gross buildings & equipment Accumulated depreciation Net buildings & equipment Total assets

$ 16,550 9,600 6,500 $ 32,650 $122,000 (34,000) $ 88,000 $120,650

LIABILITIES AND EQUITY Liabilities Current Liabilities Notes payable

$

Accounts payable Total current liabilities Long-term debt Total liabilities Equity Common stock Retained earnings Total equity Total liabilities and equity

600

4,800 $ 5,400 55,000 $ 60,400 $ 45,000 15,250 $ 60,250 $120,650

Belmond, Inc. Income Statement For the Year Ended December 31, 2003 Sales Cost of goods sold Gross profits General & admin expense Depreciation expense Total operating expense Operating income (EBIT) Interest expense Earnings before taxes

$ 12,800 5,750 $ 7,050 $

850 500 $ $ $

1,350 5,700 900 4,800 17

Taxes Net income

$

2-2A.

1,440 3,360

Sharpe Mfg. Company Balance Sheet December 31, 2003 ASSETS Cash Accounts receivable Inventory Total current assets Machinery and equipment Accumulated depreciation Net fixed assets Total assets LIABILITIES & EQUITY Liabilities Current Liabilities Notes payable Accounts payable Total current liabilities Long-term debt Total liabilities Equity Common stock Retained earnings Prior year Current year Total equity Total liabilities and equity

$

96,000 120,000 110,000 $ 326,000 $ 700,000 (236,000) 464,000 $ 790,000

$ 100,000 90,000 $ 190,000 160,000 $ 350,000 $ 320,000 100,000 20,000 $ 440,000 $ 790,000

Sharpe Mfg. Company Income Statement For the Year Ended December 31, 2003 Sales Cost of goods sold Gross profits Operating expense Net income (Assume no interest accrued or taxes)

$ 800,000 500,000 $ 300,000 280,000 $ 20,000

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2-3A. Delaney, Inc. - Corporate Income Tax Sales Cost of goods sold and cash operating expenses Depreciation expense Operating profit Interest expense Taxable Income

$4,000,000 2,400,000 100,000 $1,500,000 150,000 $1,350,000

Tax Liability: $50,000 25,000 25,000 235,000 1,015,000 $1,350,000

x x x x x

0.15 0.25 0.34 0.39 0.34

= = = = =

$7,500 6,250 8,500 91,650 345,100 $459,000

2-4A. Potts, Inc. - Corporate Income Tax Sales Cost of goods sold and cash operating expenses Operating profit Interest expense Taxable Income

$ 6,000,000 5,600,000 $ 400,000 30,000 $ 370,000

Tax Liability: $50,000 25,000 25,000 235,000 35,000 $370,000

x x x x x

0.15 0.25 0.34 0.39 0.34

= = = = =

$7,500 6,250 8,500 91,650 11,900 $125,800

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2-5A. Pamplin, Inc. Free cash flows from an asset perspective: Operating income (EBIT) Depreciation EBITDA Tax expense Less change in tax payable Cash taxes After-tax cash flows from operations Change in net working capital Change in current assets: Change in cash Change in accounts receivable Change in inventory Change in current assets Change in noninterest-bearing current debt: Change in accounts payable Change in net operating working capital

$ 360,000 200,000 $ 560,000 $ 120,000 $ 120,000 $ 440,000

$ (50,000) (25,000) 75,000 $ $ (50,000) $ (50,000)

Change in long-term assets: Purchase of fixed assets Free cash flows - asset perspective

(400,000) $ (10,000)

Free cash flows from a financing perspective: Interest expense $ (60,000) Less change in interest payable Interest paid to lenders Repayment of long-term debt Increase in short-term debt Common stock dividends paid to owners Free cash flows - financing perspective

$ (60,000) 150,000 (80,000) $ 10,000

Note: The dividends were computed by comparing net income against the change in retained earnings. Net income was $180,000, but retained earnings increased only by $100,000; thus the balance was distributed in the form of dividends. Pamplin, Inc. had an after-tax operating cash flow of $440,000. Additionally, Pamplin acquired further financing though increasing short-term debt by $150,000. This cash was mainly used to purchase fixed assets of $400,000. The remainder was used to decrease payables to suppliers by $50,000, pay interest of $60,000, and pay dividends back to the investors of $80,000.

20

2-6A. T.P. Jarmon Free cash flows from an asset perspective: Step 1: Compute after-tax cash flows from operations Earnings before taxes Plus interest expense EBIT Depreciation EBITDA Tax expense $ 27,100 Less change in tax payable Cash taxes After-tax cash flows from operations Step 2: Change in net operating working capital Change in current assets: Change in cash $ (1,000) Change in accounts receivable (9,000) Change in inventory 33,000 Change in prepaid rent (100) Change in marketable securities 200 Change in current assets $ 23,100 Change in noninterest-bearing current debt: Change in accounts payable $ 9,000 Change in accrued expenses (1,000) Change in noninterest-bearing current debt: $ 8,000 Change in net operating working capital Step 3: Change in long-term assets Purchase of fixed assets $ 14,000 (Change in net fixed assets + depr. expense) Change in other assets Net cash used for investments Asset free cash flows Free cash flows from a financing perspective: Interest paid to investors $(10,000) Less change in interest payable Interest received by investors Decrease in long-term debt Decrease in notes payable Common stock dividends Financing free cash flows

$ 70,000 10,000 80,000 30,000 $ 110,000 27,100 $ 82,900

$ (15,100)

$ (14,000) $ 53,800

$ (10,000) (10,000) (2,000) (31,800) $ (53,800)

T.P. Jarmon had a successful year, generating an after-tax cash flow of $82,900. To increase cash flow further, noninterest-bearing debt increased by $8,000. Part of this cash was consumed when current assets were increased by $23,100 (of which inventory increased by $33,000). Fixed assets of $14,000 were also purchased. The substantial part of the cash flow, however, was distributed back to the investors. Debt was decreased, both long-term and short-term, by $12,000. Interest of $10,000 was also paid on this debt. Finally, investors were paid $31,800 in dividends.

21

2-7A. Abrams Manufacturing Free cash flows from an asset perspective: Step 1: Compute after-tax cash flows from operations Operating Income Depreciation EBITDA Tax expense $ 16,000 Less change in tax payable Cash taxes After-tax cash flows from operations

$ 54,000 26,000 $ 80,000 16,000 $ 64,000

Step 2: Change in net operating working capital Change in current assets: Change in cash $ 11,000 Change in accounts receivables 6,000 Change in inventories (12,000) Change in prepaid expenses Change in current assets $ 5,000 Change in noninterest-bearing current debt: Change in accounts payables $ 5,000 Change in accrued liabilities (5,000) Change in noninterest-bearing current debt: $ Change in net operating working capital

$ (5,000)

Step 3: Change in long-term assets Purchase of fixed assets Change in other assets Net cash used for investments Asset free cash flows

$ (73,000) $ (14,000)

$ 73,000 -

Free cash flows from a financing perspective: Interest paid to investors $ (4,000) Less change in interest payable Interest received by investors Decrease in long-term debt (mortgage payable) Increase in preferred stock Preferred stock dividends Common stock dividends Financing free cash flows

$ (4,000) (70,000) 120,000 (10,000) (22,000) $ 14,000

Abrams generated cash through an after-tax operating profit of $64,000 and issuing preferred stock of $120,000. This cash was primarily used to pay down debt of $70,000 and purchase fixed assets of $73,000. Investors also received cash back through dividends of $32,000 and interest of $4,000. Abrams also increased current assets in total by $5,000 by increasing cash and accounts receivable while decreasing inventory.

22

2-8A. J.T. Williams Williams generated $224,210 in after-tax operating cash flows(including other income). To further increase cash flow, accounts payable and accrued expenses were increased by $1,662 and $32,283, respectively. They also increased their short-term debt by $30,577, increased their long-term debt by $7,018 and issued more common stock for $61,806. They used the operating cash flow and increased financing to purchase $58,297 in inventory and other current assets and purchased $308,336 in fixed assets, investments, and other assets. While Williams generated a positive aftertax cash flow from operations, investors and creditors infused $99,401 into the operations to finance the increases in assets. Williams needs to analyze whether the investors are receiving an acceptable return on their investments. It should be careful not to become over-capitalized during this time of rapid growth. 2-9A. Johnson, Inc. Johnson incurred a loss of $450,571 in after-tax operating cash flows(including other losses). In addition, interest expense of $87,966 was paid to cover the company’s current debt. The company increased their cash reserve, inventory and other current assets by $587,924. Fixed assets, investments, and other assets increased in net by $1,420,113. To finance this negative free cash flow, Johnson increased their long-term debt by $1,118,198, increased short-term debt and other current liabilities by $227,607, and issued more common stock in the amount of $851,016. Accounts payable to suppliers were also increased by $349,753. While investors in Internet companies have been satisfied with repeated annual losses, Johnson should look for ways to decrease debt, produce positive future cash flows, and provide an acceptable rate of return to its investors.

SOLUTION TO INTEGRATIVE PROBLEM Davis & Howard had a successful year bringing in positive after-tax cash flows from operations(including other income) of $174,034. This money was used in part to increase current assets and fixed assets of $77,100 and $61,873, respectively. Investments also increased $2,730 and other assets were sold for $9,881. The noninterest-bearing current debt also increased by $59,062 to help finance the increase in current assets. However, the increase in current assets was substantially due to an increase of $57,467 in accounts receivable. Management should take measures to reduce the average collection period or utilize other tools to maintain control of this asset. Free cash flows of $101,274 were distributed to investors. Interest expense of $17,024 was paid for the current debt. Davis & Howard decreased their debt principal(including long-term debt, other liabilities, and notes payable) by a total of $27,380. Stockholders were paid dividends of $26,912. Finally, Davis & Howard used their free cash flows to repurchase common stock for $29,958.

23

Solutions to Problem Set B 2-1B.

Warner Company Balance Sheet December 31, 2003 ASSETS Current assets Cash Accounts receivable Inventory Prepaid expenses Total current assets Gross buildings & equipment Accumulated depreciation Net buildings & equipment Total assets

$ 225,000 153,000 99,300 14,500 $ 491,800 $ 895,000 (263,000) $ 632,000 $1,123,800

LIABILITIES AND EQUITY Liabilities Current Liabilities Accounts payable Notes payable Taxes payable Accrued expense Total current liabilities Long-term debt Total liabilities Equity Common stock Retained earnings Total equity Total liabilities and equity

$ 102,000 75,000 53,000 7,900 $ 237,900 334,000 $ 571,900 $ 289,000 262,900 $ 551,900 $1,123,800

Warner Company Income Statement For the Year Ended December 31, 2003 Sales Cost of goods sold Gross profits General & admin expense Depreciation expense Total operating expense Operating income (EBIT) Interest expense Earnings before taxes Taxes

$ $

573,000 297,000 276,000

$ 79,000 66,000 $ $ $

145,000 131,000 4,750 126,250 50,500 24

Net income

$

2-2B.

75,750

Sabine Mfg. Company Balance Sheet December 31, 2003 ASSETS Current assets Cash Accounts receivable Inventory Total current assets Machinery and Equipment Accumulated depreciation Net buildings & equipment Total assets

$

90,000 150,000 110,000 $ 350,000 $ 700,000 (236,000) $ 464,000 $ 814,000

LIABILITIES AND EQUITY Liabilities Current Liabilities Accounts payable Short-term notes payable Total current liabilities Long-term debt Total liabilities Equity Common stock Retained earnings Prior year Current year Total equity Total liabilities and equity

$

90,000 90,000 $ 180,000 160,000 $ 340,000 $ 320,000 84,000 70,000 $ 474,000 $ 814,000

Sabine Mfg. Company Income Statement For the Year Ended December 31, 2003 Net Sales Cost of goods sold Gross profits Operating expense Net income

$ $ $

900,000 550,000 350,000 280,000 70,000

25

2-3B. Cook, Inc. - Corporate Income Tax Sales Cost of goods sold and cash operating expenses Depreciation expense Operating profit Interest expense Taxable Income

$ 3,500,000 2,500,000 100,000 $ 900,000 165,000 $ 735,000

Tax Liability: $50,000 25,000 25,000 235,000 400,000 $735,000

x x x x x

0.15 0.25 0.34 0.39 0.34

= = = = =

$

7,500 6,250 8,500 91,650 136,000 $249,900

2-4B. Rose, Inc. - Corporate Income Tax Sales Cost of goods sold and cash operating expenses Operating profit Interest expense Taxable Income

$7,000,000 6,600,000 $400,000 40,000 $ 360,000

Tax Liability: $50,000 25,000 25,000 235,000 25,000 $ 360,000

x x x x x

0.15 0.25 0.34 0.39 0.34

= = = = =

$

7,500 6,250 8,500 91,650 8,500 $122,400

26

2-5B. J.B. Chavez Free cash flows from an asset perspective: Step 1: Compute after-tax cash flows from operations Earnings before taxes Plus interest expense EBIT Depreciation EBITDA Tax expense $ 108,000 Less change in tax payable Cash taxes After-tax cash flows from operations

$ 270,000 60,000 330,000 200,000 $ 530,000 108,000 $ 422,000

Step 2: Change in net operating working capital Change in current assets: Change in cash $ (50,000) Change in accounts receivable (20,000) Change in inventory 50,000 Change in current assets $ (20,000) Change in noninterest-bearing current debt: Change in accounts payable Change in accrued expenses Change in noninterest-bearing current debt:

$(135,000) $(135,000)

Change in net operating working capital Step 3: Change in long-term assets Purchase of fixed assets Change in other assets Net cash used for investments

$ (115,000) $ 300,000 $ (300,000)

Asset free cash flows

$

7,000

Free cash flows from a financing perspective: Interest expense $ (60,000) Less change in interest payable Interest paid to lenders Increase in notes payable Common stock dividends Financing free cash flows

$ (60,000) 115,000 (62,000) $ (7,000)

After-tax cash flows from operations of $422,000 and an increase in notes payable of $115,000 were used to pay down the accounts payable by $135,000 and increase our inventory and fixed assets by $50,000 and $300,000, respectively. Interest of $60,000 and common stock dividends of $62,000 were paid to investors.

27

2-6B. RPI, Inc. Free cash flows from an asset perspective: Step 1: Compute after-tax cash flows from operations Earnings before taxes Plus interest expense EBIT Depreciation EBITDA Tax expense $ 27,100 Less change in tax payable Cash taxes After-tax cash flows from operations Step 2: Change in net operating working capital Change in current assets: Change in cash $ Change in marketable securities Change in accounts receivable Change in prepaid rent Change in inventory Change in current assets $ Change in noninterest-bearing current debt: Change in accounts payable $ Change in accrued expenses Change in noninterest-bearing current debt: $ Change in net operating working capital Step 3: Change in long-term assets Purchase of fixed assets (Change in net fixed assets + depreciation expense) Change in other assets Net cash used for investments Asset free cash flows

$

$ 110,000 10,000 120,000 30,000 $ 150,000 27,100 $ 122,900

1,000 200 (4,000) (100) 43,000 40,100 7,000 (1,000) 6,000 $ (34,100) 34,000 -

Free cash flows from a financing perspective: Interest expense $ (10,000) Less change in interest payable Interest paid to lenders Decrease in notes payable Decrease in long-term debt Common stock dividends Financing free cash flows

$ (34,000) $ 54,800

$ (10,000) (3,000) (10,000) (31,800) $ (54,800)

28

RPI had positive after-tax operating cash flows of $122,900. As a result, RPI made a decision to evenly split the cash flow between distribution to investors and investing back into the company. Net operating capital increased by $34,100, mostly in the area of inventory which increased by $43,000. Fixed assets of $34,000 were also purchased. The asset free cash flow of $54,800 was distributed back to investors through interest of $10,000, debt repayments of $13,000, and dividends of $31,800. 2-7B. Cameron Co. Free cash flows from an asset perspective: Step 1: Compute after-tax cash flows from operations Earnings before taxes Plus interest expense EBIT Depreciation EBITDA Tax expense $ 30,000 Less change in tax payable Cash taxes After-tax cash flows from operations

$

72,000 5,000 77,000 26,000 $ 103,000

$

30,000 73,000

Step 2: Change in net operating working capital Change in current assets: Change in cash $ (19,000) Change in accounts receivable 6,000 Change in prepaid expenses Change in inventory (22,000) Change in current assets $ (35,000) Change in noninterest-bearing current debt: Change in accounts payable $ (5,000) Change in accrued liabilities (5,000) Change in noninterest-bearing current debt: $ (10,000) Change in net operating working capital

$

25,000

Step 3: Change in long-term assets Purchase of fixed assets Change in other assets Net cash used for investments Asset free cash flows

$ (63,000) $ 35,000

$

63,000 -

Free cash flows from a financing perspective: Interest expense $ (5,000) Less change in interest payable Interest paid to lenders Decrease in mortgage payable Increase in preferred stock Preferred stock dividends Common stock dividends Financing free cash flows

$ (5,000) (60,000) 70,000 (8,000) (32,000) $ (35,000)

29

Cameron Co. created cash flows through after-tax profits of $73,000 and issuing $70,000 of preferred stock. Cameron also decreased current assets of $35,000 through inventory and cash. This cash was used to decrease $10,000 in noninterest-bearing current debt and to purchase $63,000 in fixed assets. Cameron also eliminated $60,000 in a mortgage payable and distributed $40,000 in dividends and $5,000 in interest to investors. 2-8B

Hilary’s Ice Cream Hilary’s had a profitable year generating after-tax operating cash flows(including other losses) of $10,953. However, it should be noted that current assets increased by $5,038 of which accounts receivable increased by $7,495. This increase was offset by increasing accounts payable by $5,456. Hilary’s should be concerned with the substantial increase in payables and the even greater threat of aging receivables. Hilary’s used some of the above operating cash flow to purchase other assets for $3,060. The asset free cash flow of $9,688 was distributed to the investors in the form of $1,634 in interest, $3,822 in long-term debt principal, and repurchasing $4,593 in common stock. It is possible that Hilary’s thought it wise to lower long term debt and repurchase stock rather than make investments in further growth.

2.9B

Retail.com In need of cash, Retail.com issued common stock for $368,463 and increased current liabilities by $9,609. This cash was used, in part, to cover an after-tax operating loss(including other income) of $63,689. Retail.com mainly used the cash to increase growth by purchasing fixed assets and other investments of $31,971 and $178,108, respectively. Retail.com also sought to increase their liquidity by increasing current assets by $84,962, consisting mainly of a $76,680 increase in their cash reserve, which was offset in part by increasing payables by $4,657. The remainder of the common stock issue was paid back to investors through a dividend of $23,612. For many years, it has been fairly easy for innovative Internet companies to raise money through the stock market. It has been more important to grow quickly than to create profits. In future years, Retail.com must turn these losses into profits and create true value for their investors.

CHAPTER 3 30

Evaluating A Firm’s Financial Performance CHAPTER ORIENTATION Financial analysis can be defined as the process of assessing the financial condition of a firm. The principal analytical tool of the financial analyst is the financial ratio. In this chapter, we provide a set of key financial ratios and a discussion of their effective use.

CHAPTER OUTLINE I

Financial ratios help us identify some of the financial strengths and weaknesses of a company.

II.

The ratios give us a way of making meaningful comparisons of a firm’s financial data at different points in time and with other firms.

III.

We could use ratios to answer the following important questions about a firm’s operations. A.

B.

Question 1: How liquid is the firm? 1.

The liquidity of a business is defined as its ability to meet maturing debt obligations. That is—does or will the firm have the resources to pay the creditors when the debt comes due?

2.

There are two ways to approach the liquidity question. a.

We can look at the firm’s assets that are relatively liquid in nature and compare them to the amount of the debt coming due in the near term.

b.

We can look at how quickly the firm’s liquid assets are being converted into cash.

Question 2: Is management generating adequate operating profits on the firm’s assets? 1.

We want to know if the profits are sufficient relative to the assets being invested.

2.

We have several choices as to how we measure profits: gross profits, operating profits, or net income. Gross profits would not be acceptable because it does not include important information such as marketing and distribution expenses. Net income includes the unwanted effects of the firm’s financing policies. This leaves operating profits as our best choice in measuring the firm’s operating profitability. Thus, the

31

appropriate measure is the operating income return on investment (OIROI): OIROI = C.

D.

operating income total assets

Question 3: How is the firm financing its assets? 1.

Here we are concerned with the mix of debt and equity capital the firm is using.

2.

Two primary ratios used to answer this question are the debt ratio and times interest earned. a.

The debt ratio is the proportion of total debt to total assets.

b.

Times interest earned compares operating income to interest expense for a crude measure of the firm’s capacity to service its debt.

Question 4: Are the owners (stockholders) receiving an adequate return on their investment? 1.

We want to know if the earnings available to the firm’s owners, or common equity investors, are attractive when compared to the returns of owners of similar companies in the same industry.

2.

Return on equity (ROE) = common equity

3.

We demonstrate the effect of using debt on net income through an example showing how the use of debt affects a firm’s return on equity.

4.

Return on equity is presented as a function of:

net income

a.

the operating income return on investment less the interest rate paid, and

b.

the amount of debt used in the capital structure relative to the equity.

IV. An Integrative Approach to Ratio Analysis: The DuPont Analysis

V.

A.

The DuPont analysis is another approach used to evaluate a firm’s profitability and return on equity.

B.

Its graphic technique may be helpful in seeing how ratios relate to one another and the account balances.

C.

Return on Equity is a function of a firm’s net profit margin, total asset turnover, and debt ratio.

Limitations of Ratio Analysis A.

This list warns of the many pitfalls that may be encountered in computing and interpreting financial ratios.

B.

Ratio users should be aware of these concerns prior to making decisions based solely on ratio analysis. 32

ANSWERS TO END-OF-CHAPTER QUESTIONS 3-1.

In learning about ratios, we could simply study the different types or categories of ratios. These categories have conventionally been classified as follows: Liquidity ratios are used to measure the ability of a firm to pay its bills on time. Example ratios include the current ratio and acid-test ratio. Efficiency ratios reflect how effectively the firm has utilized its assets to generate sales. Examples of this type of ratio include accounts receivable turnover, inventory turnover, fixed asset turnover, and total asset turnover. Leverage ratios are used to measure the extent to which a firm has financed its assets with outside (non-owner) sources of funds. Example ratios include the debt ratio and times interest earned ratio. Profitability ratios serve as overall measures of the effectiveness of the firm’s management relative to sales and/or to investment. Examples of profitability ratios include the net profit margin, return on total assets, operating profit margin, operating income return on investment, and return on common equity. Instead, we have chosen to cluster the ratios around important questions that may be addressed to some extent by certain ratios. These questions, along with the related ratios may be represented as follows: 1.

How liquid is the firm? Current ratio Quick ratio Accounts receivable turnover (average collection period) Inventory turnover

2.

Is management generating adequate operating profits on the firm’s assets? Operating income return on investment Operating profit margin Gross profit margin Asset turnover ratios, such as for total assets, accounts receivable, inventory, and fixed assets

33

3.

How is the firm financing its assets? Debt to total assets Debt to equity Times interest earned

4.

Are the owners (stockholders) receiving an adequate return on their investment? Return on common equity

In answering questions 2 through 4, we can see the linkage between operating activities and financing activities as they influence return on common equity. 3-2.

The two sources of standards or norms used in performing ratio analysis consist of similar ratios for the firm being analyzed over a number of past operating periods, and similar ratios for firms which are in the same general industry or have similar product mix characteristics.

3-3.

The financial analyst can obtain norms from a variety of sources. Two of the most well known are the Dun & Bradstreet Industry Norms and Key Business Ratios and RMA’s Annual Statement Studies. Industry norms often do not come from "representative" samples, and it is very difficult to categorize firms into industry groups. In addition, the industry norm is an average ratio which may not represent a desirable standard. Thus, industry averages only provide a "rough guide" to a firm’s financial health.

3-4.

Liquidity is the ability to repay short-term debt. We measure liquidity by comparing the firm’s liquid assets—cash or assets that will be turned into cash in the operating cycle— to the amount of short-term debt outstanding, which is the measurement provided by the current ratio and the quick, or acid-test, ratio. We can also measure liquidity by computing how quickly accounts receivables turn over (how long it takes to collect them on average) and how quickly inventories turn over. The more quickly these assets can be turned over, the more liquid the firm.

3-5.

Operating income return on investment is the amount of operating income produced relative to $1 of assets invested (total assets), while operating profit margin is the amount of operating income per $1 of sales. The first ratio measures the profitability on the firm’s assets, while the latter measures the profitability on the sales.

3-6.

We can compute operating income return on investment (OIROI) as: Operating

Income

Return on Invesment

=

Operating Income Total Assets

or as: Operating Income Return on Investment

Operating = Profit Margin

X

Total Asset Turnover

Thus, we see that OIROI is a function of how well we manage the income statement, as measured by the operating profit margin, and how well we manage the balance sheet (the firm’s assets), as measured by the asset turnover ratio.

34

3-7.

Gross profit margin measures a firm’s pricing decisions and its ability to manage its cost of goods sold per dollar of sales. Operating profit margin is likewise a function of pricing and cost of goods sold, but also the amount of operating expenses (marketing expenses and general and administrative expenses) for every dollar of sales. Net profit margin builds on the above relationships, but then includes the firm’s financing costs, such as interest expense. Thus, the gross profit margin measures the firm’s pricing decisions and the ability to acquire or produce its product cheaply. The operating profit margin then adds the cost of distributing the product to the customer. Finally, the net profit margin adds the firm’s financing decisions to the operating performance.

3-8.

Return on equity is equal to net income divided by the total equity. But knowing how to compute return on equity is not the same as understanding what decisions drive return on equity. It helps to know that return on equity is driven by the spread between operating income return on investment and the interest rate paid on the firm’s debt. The greater the OIROI compared to the interest rate, the higher the return on equity will be. If OIROI is higher (lower) than the interest rate, as a firm increases its use of debt, return on equity will be higher (lower).

SOLUTIONS TO END-OF-CHAPTER PROBLEMS 3-1A. Cash Accounts Receivable * Inventory Current Assets Net Fixed Assets Total Assets

201,875 175,000 223,125 600,000 1,500,000 2,100,000

Accounts Payable Long-Term Debt Total Liabilities Common Equity

100,000 320,000 420,000 1,680,000

Total Liability & Equity

2,100,000

* Based on 360 days. Current ratio Total asset turnover Gross profit margin Inventory turnover Average collection period Debt ratio Sales Cost of goods sold Total liabilities

6 1 15% 8 30 20% 2,100,000 1,785,000 420,000

3-2A. Mitchem's present current ratio of 2.5 to 1 in conjunction with its $2.5 million investment in current assets indicates that its current liabilities are presently $1 million. Letting x represent the additional borrowing against the firm's line of credit (which also equals the addition to current assets) we can solve for that level of x which forces the firm's current ratio down to 2 to 1; i.e., 2 = ($2.5 million + x) / ($1.0 million + x)

35

x = $0.5 million, or $500,000 3-3A. Instructor’s Note: This is a very rudimentary "getting started" exercise. It requires no analysis beyond looking up the appropriate formula and plugging in the corresponding figures. =

Current ratio =

Debt ratio

current assets current liabilitie s

total debt total assets

$3,500 $2,000

=

$4,000 $8,000

=

operating income interest expense

Times interest earned = Average collection period

=

=

1.75X

=

.50 or 50%

$1,700 $367

=

accounts receivable credit sales / 365

=

4.63X

$2,000 $8,000 / 365

=

= 91

days Inventory turnover

cost of goods sold inventory

=

=

Fixed asset turnover

=

net sales = fixed assets

Total asset turnover

=

net sales total assets

Gross profit margin

=

Operating income return

=

on investment

Return on equity

=

net income common equity

= =

$800 $4,000

=

$8,000 $8,000

1.78X

=

$1,700 $8,000

=

$1,700 $8,000

=

3.3X

=

$4,700 $8,000

=

operating income net sales

operating income total assets

=

$8,000 $4,500

=

gross profit net sales

Operating profit margin =

$3,300 $1,000

1X .59 or 59% =

=

.21 or 21%

.21 or 21%

.20 or 20%

or, we can calculate return on equity as: = Return on assets ÷ (1- debt ratio) = =

Total debt  Net income   ÷ 1 − Total assets  Total assets  800 ÷ (1 - .50 ) 8,000

= .20 or 20%

36

3-4A. a. b.

Total Assets Turnover 3.5

sales = total assets

=

$10m $5m

= 2x

sales $5m

=

Sales =

$17.5m

Thus, the needed sales growth is $7.5 million ($17.5m - $10m), or an increase of 75%: $7.5m $10m

c.

=

75%

For last year, Operating Income Return on Investment

operating profit margin

= =

10%

=

20%

X

total asset turnover

X

2.0

If sales grow by 75%, then for next year-end assuming a 10% operating profit margin: Operating

Income

Return on Investment

3-5A. a.

Average Collection Period

=

=

operating profit margin

X

total asset turnover

=

10%

X

3.5

=

35%

Accounts Receivable Credit Sales/365

Avg Collection Period

=

$562,500 (.75 x $9m)/365

Avg Collection Period

=

30 days

Note that the average collection period is based on credit sales, which are 75% of total firm sales. b.

Average collection period

=

20

=

Accounts Receivable (.75 x $9m)/365

Solving for accounts receivable:

Accounts receivable

=

$369,863

Thus, Brenmar would reduce its accounts receivable by $562,500 - $369,863

=

$192,637.

37

c.

Inventory Turnover 9 Inventories

=

Cost of Goods Sold Inventorie s

=

.70 x Sales Inventorie s

=

.70 x $9m 9

=

$700,000

3-6A. a. RATIO Liquidity: Current Ratio Acid-test (Quick) Ratio Average Collection Period Inventory Turnover

2002

2003

Industry Norm

6.0x 3.25x 137 days 1.27x

4.0x 1.92x 107 days 1.36x

5.0x 3.0x 90 days 2.2x

Operating profitability: Operating Profit Margin Total Asset Turnover Average Collection Period Inventory Turnover Fixed Asset Turnover

20.8% .5x 137 days 1.27x 1.00x

24.8% .56x 107 days 1.36x 1.04x

20.0% .75x 90 days 2.2x 1.00x

Financing: Debt Ratio Times Interest Earned

0.33 5.0x

Return on common stockholders’ investment: Return on Common Equity 7.5%

b.

0.35 5.63x 10.5%

0.33 7.0x 9.0%

Regarding the firm’s liquidity in 2003, the current and acid-test (quick) ratios are both well below the industry averages and have decreased considerably from the prior year. Also, the average collection period and inventory turnover do not compare favorably against the industry averages, which suggests that accounts receivable and inventories are not of equal quality of these assets in other firms in the industry. So, we may reasonably conclude that Pamplin is less liquid than the average company in its industry.

38

c.

In evaluating Pamplin’s operating profitability relative to the average firm in the industry, we must first analyze the operating income return on investment (OIROI) both for Pamplin and the industry. From the information given, this computation may be made as follows: Operating income return on investment

=

Operating profit margin

Total asset turn over

X

Industry:

20%

X

0.75 = 15%

Pamplin 2002:

20.8%

X

0.50 = 10.4%

Pamplin 2003:

24.8%

X

0.56 = 13.9%

Thus, given the low operating income return on investment for Pamplin relative to the industry, we must conclude that management is not doing an adequate job of generating operating profits on the firm’s assets. However, they did improve between 2002 and 2003. The problem lies not with the operating profit margin, which addresses the operating costs and expenses relative to sales. Instead, the problem arises from Pamplin’s management not using the firm’s assets efficiently, as indicated by the low asset turnover ratios. Here the problem occurs in managing accounts receivable and inventories, where we see the low turnover ratios. The firm does appear to be using the fixed assets reasonably well—note the satisfactory fixed assets turnover. d.

Financing decisions A balance-sheet perspective: The debt ratio for Pamplin in 2003 is around 35%, an increase from 33% in 2002; that is, they finance slightly more than one-third of their assets with debt and a little less than two-thirds with common equity. Also, the average firm in the industry uses about the same amount of debt per dollar of assets as Pamplin. An income-statement perspective: Pamplin’s times interest earned is below the industry norm—5.0 and 5.63 in 2002 and 2003, respectively, compared to 7.0 for the industry average. In thinking about why, we should remember that a company’s times interest earned is affected by (1) the level of the firm’s operating profitability (EBIT), (2) the amount of debt used, and (3) the interest rate. Items 2 and 3 determine the amount of interest paid by the company. Here is what we know about Pamplin: 1.

The firm’s operating income return on investment is below average, but improving. Thus, we would expect this fact to contribute to a lower, but also improving, times interest earned. The evidence is consistent with this thought.

2.

Pamplin uses about the same amount of debt as the average firm, which should mean that its times interest earned, all else equal, would be about the same as for the average firm. Thus, Pamplin’s low times interest earned is not the consequence of using more debt.

39

3.

We do not have any information about Pamplin’s interest rate, so we cannot make any observation about the effect of the interest rate. But we know if Pamplin is paying a higher interest rate than its competitors, such a situation would also be contributing to the problem.

e.

Pamplin has improved its return on common equity from 7.5% in 2002 to 10.5% in 2003, compared to an industry norm of 9%. The sharp improvement has come from a significant increase in the firm’s operating income return on investment and a modest increase in the use of debt financing. It is also possible that the higher return on equity comes from Pamplin paying a lower interest rate on its debt, but we do not have enough information to know for certain. Nevertheless, Pamplin has enhanced the returns to its owners, but with a touch of additional financial risk (slightly higher debt ratio) in the process.

3-7A. a.

Salco’s total asset turnover, operating profit margin, and operating income return on investment. Total Asset Turnover

=

Sales Total Assets

=

$4,500 ,000 $2,000 ,000

=

2.25 times

Operating Profit Margin =

Operating Income Return on Investment

or

Operating Income Sales

=

$500 ,000 $4,500 ,000

=

11.11%

=

Operating Income Total Assets

=

$500 ,000 $2,000 ,000

=

25%

=

Operating Income Sales

=

.1111 X 2.25

=

25%

x

Sales Total Assets

40

b.

The new operating income return on investment for Salco after the plant renovation: Operating Income Return on Investment

c.

=

Operating Income Sales

=

.13

=

.13 x 1.5

=

19.5%

x

x

Sales Total Assets

$4,500 ,000 $3,000 ,000

Return earned on the common stockholders’ investment: Post-Renovation Analysis: Return on common equity

Net IncomeAvailable = to CommonStockholders

Common Equity =

$217 ,500 $1,000 ,000 + $500 ,000

=

14.5%

Net income available to common stockholders following the renovation was calculated as follows: Operating Income (.13 x $4.5m) Less: Interest ($100,000 + $50,000)

$ 585,000 (150,000)

Earnings Before Taxes

435,000

Less: Taxes (50%)

(217,500)

Net Income Available to Common Stockholders

$ 217,500

The increase in Common equity was calculated as follows: Total assets purchased Less: Increase in debt ($1,500,000 - $1,000,000) Increase in equity to finance purchase

$ 1,000,000 (500,000) $ 500,000

The computation above is measuring the return on equity based on the beginning-of-the-year common equity. The equity would increase $217,500 by year end.

41

Pre-renovation Analysis: The pre-renovation rate of return on common equity is calculated as follows: Return on Common Equity

=

$200 ,000 = $1,000 ,000

20%

Comparative Analysis: A comparison of the two rates of return would argue that the renovation not be undertaken. However, since investments in fixed assets generally produce cash flows over many years, it is not appropriate to base decisions about their acquisition on a single year’s ratios. There are additional problems with this approach to fixed asset decision making which we will discover when we discuss capital budgeting in a later chapter. Instructor’s Note: To help convince those students who simply cannot accept the fact that the renovation may be worthwhile even though the return on common equity falls in the first year, we note that the existing plant is recorded on the firm’s books at original cost less accounting depreciation. In a period of rising replacement costs, this means that the return on common equity of 20% without renovation may actually overstate the true return earned on a more realistic “replacement cost” common equity base. In addition, the issue is probably one of when to renovate (this year or next) rather than whether or not to renovate. That is, the existing facility may require renovation in the next two years to continue to operate. These considerations simply cannot be incorporated in the ratio analysis performed here. We find this a very useful point to make at this juncture of the course since industry practice still frequently involves use of rules of thumb and ratio guides to the analysis of capital expenditures. 3-8A. T.P. Jarmon Instructor’s note: This problem serves to integrate the use of the DuPont analysis with financial ratios. The student is guided through a thorough analysis of a loan applicant that (on the surface) appears acceptable. However, an in-depth analysis reveals that the firm is not nearly so liquid as it first appears and has used a substantial amount of current debt to finance its assets. a.

See the accompanying table.

b.

The most important ratios to consider in evaluating the firm’s credit request relate to its liquidity and use of financial leverage. However, the credit analyst can also evaluate the firm’s profitability ratios as a general indication as to how effective the firm’s management has been in managing the resources available to it. This latter analysis would be useful in evaluating the prospects for a long and fruitful relationship with the new client.

42

c.

The DuPont Analysis for Jarmon is shown in the graph on the next page. The earning power analysis provides an in-depth basis for analyzing Jarmon’s only deficiency, that relating to its relatively large investment in inventories. However, even this potential weakness is largely overcome by the firm’s strengths. The firm’s return on assets and its return on owner capital (return on common equity) both compare well with the respective industry norms. Instructor’s Note At this point, we usually note the one major deficiency of DuPont Analysis. This relates to the lack of any liquidity ratios. Thus, the analysis of earning power alone is not appropriate for credit analysis since no indicators of liquidity are calculated. This deficiency can, of course, be easily corrected by appending one or more liquidity ratios to the analysis.

43

Ratio

Formula

$138 ,300 $75 ,000

Current Ratio Acid-Test Ratio

Current Assets - Inventory Current Liabilitie s

Industry Average

Calculation = 1.84

$138 ,300 −84 ,000 $75 ,000 $225 ,000 $408 ,300

Debt Ratio $80 ,000 $10 ,000

= 8

43

Accounts Receivable Credit Sales per Day

1.8 = .72

= .55

.9 .5

10 $33 ,000 $600 ,000 / 365

=

20.1 days

20 days

Inventory Turnover

$460 ,000 $84 ,000

= 5.48

7

Operating Income Return on Investment

$80 ,000 $408 ,300

= .196

16.8%

= .133

14%

or

19.6%

$80 ,000 $600 ,000

or

13.3%

Ratio

Formula

Calculation $140 ,000 $600 ,000

or

44

Return on Assets

Net Income Total Assets

= .233

Industry Average 25%

23.3%

$600 ,000 $408 ,300

= 1.47

1.2

$600 ,000 $270 ,000

= 2.22

1.8

= .1051

6%

$42,900 $408,300

or 10.51%

Return on Equity

EarningsAvailableto Com m onStockholde rs Com m onEquity

$42 ,900 $183 ,300

= .234

or 23.4%

12%

Return on Equity 23.4%

Return on Assets 10.51%

Net Profit Margin 7.15%

Net Income

Equity Total Assets 0.45

divided by

Total Asset Turnover

multipled by

1.47

divided by

$42,900

Sales $600,000

Sales $600,000

divided by Total Assets $408,300

Sales $600,000

Fixed Assets

Current Assets $138,300

Other Assets $0

$270,000

less Fixed Assets Turnover 2.22

Total costs and expenses $557,100 Cost of goods sold $460,000

Cash and Marketable Securites $20,200

Accounts Receivable $33,000

Cash operating expenses $30,000 Depreciation $30,000

Inventory Collection Period

$84,000

÷

Fixed Assets $270,000

Other Current Assets $1,100

20.08 days

Interest Expense $10,000 Taxes $27,100

Sales $600,000

Inventory Turnover 5.48

Daily Credit Accounts Sales Receivables divided by $33,000 $1,644

Cost of Goods Sold divided by $460,000

Inventory $84,000

45

3-9A. HiTech RATIO Liquidity: Current Ratio Acid-test (Quick) Ratio Average Collection Period Accounts Receivable Turnover Inventory Turnover

2003

Industry Norm

2.51 2.30 45.95 7.94 6.13

2.01 1.66 72.64 5.02 4.42

Operating profitability: Operating Income Return on Investment Operating Profit Margin Total Asset Turnover Accounts Receivable Turnover Inventory Turnover Fixed Asset Turnover

23.2% 34.6% .67 7.94 6.13 2.51

9.0% 13.0% .69 5.02 4.42 2.27

Financing: Debt Ratio Times Interest Earned Return on common stockholders’ investment: Return on Common Equity

.26 247.78 22.4%

.44 8.87 12.0%

The above analysis of HiTech reveals a strong company in many areas. First, let’s look at the liquidity question. How liquid is HiTech’s balance sheet? The current ratio surpasses the industry, and when we subtract inventories in the acid-test ratio, HiTech still surpasses the industry. It is the same with the inventory turnover ratio. This suggests that HiTech has a lower than normal inventory level. The receivable turnover and average collection period also reveal that HiTech controls this asset better than its competitors. These ratios tell us that HiTech’s liquidity relies on assets other than inventory and receivables. When we review the balance sheet, this assumption is supported for we see that $11.8 million of the $17.8 million of HiTech’s current assets is in cash and cash equivalents alone. We next turn to the profitability question. HiTech compares impressively on the OIROI and operating profit margin ratios. The OIROI ratio tells us that either HiTech must be doing a superior job at sales, expenses, or generating greater sales from a lower asset level. When we look at the total asset turnover, HiTech rates slightly lower than normal. HiTech is generating the same proportionate level of sales from the same level of assets as its competitors. We know that HiTech is doing a good job of turning over its current assets. The fixed asset turnover tells us that part of the problem is in the level of fixed assets that HiTech is maintaining. As we look at the balance sheet, we see that HiTech also maintains a high level of “other investments”. HiTech must be doing an excellent job at controlling costs, which is supported by the excellent operating profit margin ratio. We now look at the financing question. HiTech is maintaining a low level of debt as compared to the industry and is more than able to service its interest expense. This means that HiTech is financing its assets through equity. Let’s look at the return that these owners are receiving from their investment through the final ratio. HiTech also rates favorably on return on common equity, 22.4% as compared to the 12.0% industry average. 46

INTEGRATIVE PROBLEM 1. Blake International Current ratio Acid-test ratio Average collection period Accounts receivable turnover Inventory turnover Operating income return on investment Gross profit margin Operating profit margin Total asset turnover Fixed asset turnover Debt ratio Times interest earned Return on equity

1999

2000

2001

2002

2003

3.11 1.64 53.16 6.87 3.28 0.22

2.83 1.78 62.00 5.89 3.87 0.15

2.54 1.56 56.29 6.48 4.00 0.16

2.22 1.35 58.63 6.23 3.73 0.08

1.99 1.33 52.48 6.95 4.21 0.09

0.40 0.10 2.10 18.13 0.43 14.00 0.18

0.39 0.08 1.95 18.81 0.79 6.31 0.36

0.38 0.08 2.07 23.21 0.71 4.31 0.27

0.38 0.04 1.85 18.64 0.69 2.30 0.04

0.40 0.05 1.85 16.29 0.66 2.78 0.02

Note: Above ratio calculations may be subject to rounding errors.

Question #1 It is apparent that Blake’s liquidity is decreasing over time, as the current and acid-test ratios indicate. However, the receivable turnover and average collection period stayed relatively constant while the inventory turnover actually increased. When we review the balance sheet, we note that the cash balance has actually increased while the receivable and inventory balances decreased, creating more liquidity within the total current assets, even though the net current asset balance decreased in total. The real problem lies with the increase in current liabilities over time in combination with the decrease in current assets. Question #2 Also of great concern is the decrease in operating profitability that is shown in the OIROI ratios over time. The problem does not seem to be in the cost of goods sold as 47

indicated by the gross profit margin ratio. The problem appears in the operating profit margin having also decreased over time. Upon review of the income statement, we will see that while sales have decreased, the operating expenses have stayed the same. The total asset turnover and fixed asset turnover have also decreased, although not to the same degree. Blake has lowered the asset balances as sales have lowered, but still needs to work further to lower fixed assets, decrease expenses, and increase sales. Question #3 While sales and assets have decreased over time, the level of debt to equity has increased. As of 2003, 66% of Blake’s assets are being financed through the use of debt. The company is quickly becoming over-leveraged and soon will lose its ability to pay interest as the times interest earned ratio shows.

Question #4 Return on common equity has declined, especially in the last two years. This can be the result of two factors, a lower rate of return or financing through less debt. As noted above, Blake has increased debt greatly over the last five years. As we have also noted, Blake’s operating profitability has also decreased over the last few years as a result of decreasing sales and higher interest costs. We can safely assume that the decreasing return is the result of decreasing profits. Scott Corp. Current ratio Acid-test ratio Average collection period Accounts receivable turnover Inventory turnover Operating income return on investment Gross profit margin Operating profit margin Total asset turnover Fixed asset turnover Debt ratio Times interest earned Return on equity

1999

2000

2001

2002

2003

1.85 1.28 80.75 4.52 4.45 0.21

1.86 1.22 75.92 4.81 4.11 0.24

2.05 1.33 69.69 5.24 4.01 0.25

2.07 1.25 63.96 5.71 4.21 0.16

2.26 1.43 64.71 5.64 4.42 0.16

0.41 0.14 1.51 8.58 0.37 27.54 0.20

0.41 0.14 1.64 10.06 0.38 23.45 0.23

0.42 0.15 1.71 9.96 0.41 24.73 0.25

0.38 0.09 1.77 8.28 0.40 12.60 0.12

0.40 0.10 1.67 6.93 0.36 16.41 0.14

Note: Above ratio calculations may be subject to rounding errors.

Question #1 Scott’s liquidity increased over the last five years, despite its growth. While current liabilities increased, current assets grew by over 60%. This is reflected in the positive 48

trend of the current ratio. Despite inventory growth of 90%, the acid-test ratio and inventory turnover both increased positively over time due to strong growth in other areas such as receivables and sales (which in turn impacted cost of goods sold on which the inventory turnover ratio is based). The receivable turnover ratio and average collection period also trended positively due to a slight increase in receivables as compared to an 84% increase in sales. Question #2 Operating profitability seems to have decreased slightly over the last five years. Upon review of the ratios in combination with the financial statements, this seems to be the result of two factors. One, operating expenses have grown disproportionately to sales over the years. Depreciation has grown due to the fixed asset growth, which is the second factor. The total asset turnover has increased as a result of the positive use of receivables and inventories. However, fixed assets have grown considerably, affecting both the OIROI and the fixed asset turnover.

49

Question #3 Upon initial review of the debt ratio, Scott seems to be successively financing its growth with the same proportion of debt over the last five years. However, Scott does need to be aware that the times interest earned is trending down due to the fact that the operating expenses have grown disproportionately. This will impact its ability to service debt over future years. Question #4 Scott has decreased its return on common equity especially in the last two years. Since Scott has not decreased its debt ratio, we must review the income statement for the explanation. Even though Scott has almost doubled its sales, net income has remained the same. This is the result of decreased operating profit margin and increased interest. The increased interest is either the result of increased debt or a higher cost of debt. 2.

The differences in Scott’s and Blake’s financial performance are easy to find. Scott continues to be a thriving company while Blake seems to have many financial problems. Scott’s sales have grown 84% while Blake’s sales have decreased by 17%. However, they also have many similarities. Let’s look at the differences and similarities by question. Liquidity – Both Blake and Scott have done a good job of controlling their inventories and receivables. Both had positive trends in these areas. The difference is that Scott has considerable liquidity while Blake is losing this ability due to its increasing current liabilities. Profitability – Both Scott and Blake are having problems with operating profitability. Their OIROI’s have trended downward over time due to increasing operating expenses and increasing fixed assets as compared to sales. Financing – The true differences appear in how Blake and Scott are financing their assets. While Scott’s debt ratio has stayed the same, Blake has increased its debt ratio to 66%. This has significantly increased the risk to the financial health of Blake. While both Scott’s and Blake’s times interest earned have decreased due to increasing operating expenses, Blake is dangerously close to losing its ability to service its debt. Return on Investment – Once again, Scott and Blake are more similar than different, except as to the severity of the amount. Scott and Blake have decreased their return on investment. Blake has increased its debt while Scott’s stayed the same. Both have decreased their net income as compared to sales. This is the result of increased operating and interest costs, as gross profit margins have stayed the same.

50

Solutions for Set B 3-1B. Cash Accounts Receivable * Inventory Current Assets Net Fixed Assets Total Assets

174,363 80,137 45,500 300,000 1,000,000 1,300,000

Accounts Payable Long-Term Debt Total Liabilities Common Equity

100,000 290,000 390,000 910,000

Total Liability & Equity 1,300,000

* Based on 360 days. Current ratio Total asset turnover Gross profit margin Inventory turnover Average collection period Debt ratio Sales Cost of goods sold Total liabilities

3 0.5 30% 10 45 30% 650,000 455,000 390,000

3-2B. Allandale’s present current ratio of 2.75 in conjunction with its $3.0 million investment in current assets indicates that its current liabilities are presently $1.09 million. Letting x represent the additional borrowing against the firm’s line of credit (which also equals the addition to current assets), we can solve for that level of x which forces the firm’s current ratio down to 2 to 1, i.e., 2 = ($3.0 million + x) / ($1.09 million + x) x = $.82 million 3-3B. Instructor’s Note: This is a very rudimentary "getting started" exercise. It requires no analysis beyond looking up the appropriate formula and plugging in the corresponding figures. Current Ratio

=

Debt Ratio

=

$3,500 $1,800

=

$3,900 $8,000

=

Times Interest Earned =

=

= 1.94X

$1,500 $367

Average Collection Period =

=

= .49 or 49%

= 4.09X $1,500 $7,500 ÷ 365

= 73

days Inventory Turnover =

=

Fixed Asset Turnover = = Total Asset Turnover =

$3,000 $1,000

= 3.0X

$7,500 $4,500

= 1.67X

$7,500 Net Sales = $8,000 Total Assets

= .94X 51

Gross Profit Margin = =

$4,500 Gross Profits = $7,500 Net Sales

= .60 or 60%

$1,500 $7,500

= .20 or 20%

Operating Income = Net Sales

= =

$1,500 $8,000

= .19 or 19% $680 $4,100

Return on Equity = =

=.17 or 17%

or, we can calculate return on equity as:

3-4B. a.

b.

=

Return on assets ÷ (1- debt ratio)

=

Total debt  Net income   ÷ 1 − Total assets  Total assets 

=

680 ÷ (1 - .49 ) = 8,000

Total Assets Turnover

2.5 Sales

.17 or 17%

=

Sales Total Assets

=

$11m $6m

= 1.83X

= = $15m

Thus, the needed sales growth is $4 million ($15m - $11m) or an increase of 36%: = 36%

52

c.

Last year, =

X

=

6%

=

11%

X

1.83

If sales grow by 36%, then for next year-end assuming a 6% operating profit margin: =

3-5B. a.

X

=

6%

=

15%

X

Average Collection Period

=

Avg Collection Period

=

$562,500 (.75 x $9.75m)/36

Avg Collection Period

=

28.08 days

2.5

5

Note that the average collection period is based on credit sales, which are 75% of total firm sales. b.

= 20 =

Accounts Receivable (.75 x $9.75m)/36 5

Solving for accounts receivable: Accounts = Receivable

$400,685

Thus, Brenda Smith, Inc. would reduce its accounts receivable by $562,500 - $400,685 = c.

Inventory Turnover 8 Inventories

$161,815

= = =

=

$914,062.50

53

3-6B. a. 2002

2003

5.00 2.70 131.40 1.22

5.35 2.63 108.24 1.40

5.00 3.00 90.00 2.20

Operating profitability: Operating Income Return on Investment Operating Profit Margin Total Asset Turnover Average Collection Period Inventory Turnover Fixed Asset Turnover

12.24% 24.00% .51 131.40 1.22 1.04

13.04% 22.76% .57 108.24 1.40 1.12

15.00% 20.00% .75 90.00 2.20 1.00

34.69% 6.00

32.81% 5.50

33.00% 7.00

9.53%

13.43%

Financing: Debt Ratio Times Interest Earned

Rate of return on common stockholders’ investment: Return on Common Equity 9.38% b.

Industry Norm

RATIO Liquidity: Current Ratio Acid-test (Quick) Ratio Average Collection Period Inventory Turnover

Regarding the firm’s liquidity, the acid-test (quick) ratios are below the industry average and have decreased from the prior year. Also, the average collection period and inventory turnover are well below the industry averages, which suggests that inventories and receivables are not of equal quality of these assets in other firms in the industry. Since the current ratio is satisfactory, the problem apparently lies in the management of inventories and receivables. So, we may reasonably conclude that Chavez is less liquid than the average company in its industry because it has a greater investment in inventories and receivables than the industry average.

54

c.

In evaluating Chavez’s operating profitability relative to the average firm in the industry, we must first analyze the operating income return on investment (OIROI) both for Chavez and the industry. From the information given, this computation may be made as follows: =

X

Industry:

20.00%

X

0.75 = 15.00%

Chavez 2002:

24.00%

X

0.51 = 12.24%

Chavez 2003:

22.76%

X

0.57 = 12.97%

Thus, given the low operating income return on investment for Chavez relative to the industry, we must conclude that management is not doing an adequate job of generating operating profits on the firm’s assets. However, they did improve between 2002 and 2003. The problem lies not with the operating profit margin, which addresses the operating costs and expenses relative to sales. Instead, the problem arises from Chavez’s management not using the firm’s assets efficiently, as indicated by the low asset turnover ratios. Here, the problem occurs in managing accounts receivable and inventories, where we see the low turnover ratios. The firm does appear to be using the fixed assets reasonably well—note the satisfactory fixed assets turnover. d.

Financing decisions A balance-sheet perspective: The debt ratio for Chavez in 2003 is around 33%, a decrease from 34.7% in 2002; that is, they finance about one-third of their assets with debt and a little more than two-thirds with common equity. The average firm in the industry uses about the same amount of debt per dollar of assets as Chavez. An income-statement perspective: Chavez’s times interest earned is below the industry norm—6.0 and 5.5 in 2002 and 2003, respectively, compared to 7.0 for the industry average. In thinking about why, we should remember that a company’s times interest earned is affected by (1) the level of the firm’s operating profitability (EBIT), (2) the amount of debt used, and (3) the interest rate. Items 2 and 3 determine the amount of interest paid by the company. Here is what we know about Chavez: 1.

The firm’s operating profitability is below average, but improving. Thus, we would expect this fact to contribute to a lower times interest earned. The evidence is consistent with this thought.

2.

Chavez uses about the same amount of debt as the average firm, which should mean that its times interest earned, all else equal, would be about the same as for the average firm. Thus, Chavez’s low times interest earned is not the consequence of using more debt.

3.

We do not have any information about Chavez’s interest rate, so we cannot make any observation about the effect of the interest rate. But we know if Chavez is paying a higher interest rate than its competitors, such a situation would also be contributing to the problem. 55

e.

Chavez has improved its return on common equity from 9.38% in 2000 to 9.53% in 2001, compared to an industry norm of 13.43%. The improvement has come from an increase in the firm’s operating income return on investment, despite a slight decrease in the use of debt financing. Thus, Chavez has enhanced the returns to its owners, and with a small decline of financial risk (slightly lower debt ratio) in the process.

3-7B. a.

Mel’s total asset turnover, operating profit margin, and operating income return on investment. Total Asset Turnover

= =

$5,000 ,000 $2,000 ,000

=

2.50 times

Operating Profit Margin =

Operating Income Return on Investment

or

=

$500 ,000 $5,000 ,000

=

10.00%

=

Operating Income Total Assets

=

$500,000 $2,000,000

=

25%

= =

b.

X 10%

X

2.50 = 25%

The new operating income return on investment for Mel’s after the plant renovation: =

x

=

.13 X $3,000 ,000

=

.13 X 1.67

=

21.67%

$5,000 ,000

56

c.

Return earned on the common stockholders’ investment: Post-Renovation Analysis: Return on Common Equity =

Net Income Available to Common Stockholde rs Common Equity

=

$306 ,000 $1,000 ,000 + $500 ,000

=

.204 = 20.4%

Net income available to common stockholders following the renovation was calculated as follows: Operating Income (.13 x $5m) Less: Interest ($100,000 + $40,000) Earnings Before Taxes Less: Taxes (40%) Net Income Available to Common Stockholders

$ 650,000 (140,000) 510,000 (204,000) $ 306,000

The increase in Common equity was calculated as follows: Total assets purchased

$ 1,000,000

Less: Increase in debt ($1,500,000 - $1,000,000) Increase in equity to finance purchase

(500,000) $ 500,000

The computation above is measuring the return on equity based on the beginning-of-the-year common equity. The equity would increase $217,500 by year end. Pre-renovation Analysis: The pre-renovation rate of return on common equity is calculated as follows: Return on Common Equity

=

$240 ,000 = $1,000 ,000

24%

57

Comparative Analysis: A comparison of the two rates of return would argue that the renovation not be undertaken. However, since investments in fixed assets generally produce cash flows over many years, it is not appropriate to base decisions about their acquisition on a single year’s ratios. There are additional problems with this approach to fixed asset decision making which we will discover when we discuss capital budgeting in a later chapter. Instructor’s Note: To help convince those students who simply cannot accept the fact that the renovation may be worthwhile even though the return on common equity falls in the first year, we note that the existing plant is recorded on the firm’s books at original cost less accounting depreciation. In a period of rising replacement costs, this means that the return on common equity of 24% without renovation may actually overstate the true return earned on a more realistic "replacement cost" common equity base. In addition, the issue is probably one of when to renovate (this year or next) rather than whether or not to renovate. That is, the existing facility may require renovation in the next two years to continue to operate. These considerations simply cannot be incorporated in the ratio analysis performed here. We find this a very useful point to make at this juncture of the course, since industry practice still frequently involves use of rules of thumb and ratio guides to the analysis of capital expenditures. 3-8B. a. b.

See the accompanying table. The most important ratios to consider in evaluating the firm’s credit request relate to its liquidity and use of financial leverage. However, the credit analyst can also evaluate the firm’s profitability ratios as a general indication as to how effective the firm’s management has been in managing the resources available to it. This latter analysis would be useful in evaluating the prospects for a long and fruitful relationship with the new client.

58

Ratio

Formula

Acid-Test Ratio

Calculation $156 ,300 $73 ,000

Current Ratio Current Assets − Inventory Current Li abilities

Debt Ratio

58

Operating Income Interest Expense

= 2.14

1.8

$156 ,300 −93 ,000 $73 ,000

= .87

.9

$223 ,000 $446 ,300

= .50

.5

$120 ,000 $10 ,000

= 12

10

$38 ,000 $700 ,000 / 365

Inventory Turnover

Industry Average

$500 ,000 $93 ,000

=

19.81 days

= 5.38

20 days 7

Ratio

Formula

Operating Income Return on Investment

$120 ,000 $446 ,300

or $120 ,000 $700 ,000

or $200 ,000 $700 ,000

or

59 Return on Assets

Net Income Total Assets

Return on Equity

= .2689

16.8%

26.89% = .171

14%

17.1% = .2857

25%

28.57%

$700 ,000 $446 ,300

= 1.57

1.2

$700 ,000 $290 ,000

= 2.41

1.8

$82,900 $446,300

or

EarningsAvailableto Com m onStockholde rs Com m onEquity

Industry Average

Calculation

$82 ,900 $223 ,300

or

= .1857

6.0%

18.57% =

.3712

37.12%

12%

Return on Equity 37.1%

Return on Assets 18.57%

Net Profit Margin 11.84%

Net Income

Equity Total Assets 0.50

divided by

Total Asset Turnover

multipled by

1.57

divided by

$82,900

Sales $700,000

Sales $700,000

Current Assets $156,300

less

divided by Total Assets $446,300

Sales $700,000

Fixed Assets $290,000

Total costs and expenses $617,100 Cost of goods sold $500,000

Cash and Marketable Securites $24,200

Accounts Receivable

Depreciation $30,000

Inventory Collection Period

$93,000

÷

Fixed Assets $290,000

Other Current Assets $1,100

19.81 days

Interest Expense $10,000 Taxes $27,100

Fixed Assets Turnover 2.41 Sales $700,000

$38,000

Cash operating expenses $50,000

Other Assets $0

Inventory Turnover 5.38

Daily Credit Accounts Sales Receivables divided by $38,000 $1,918

Cost of Goods Sold $500,000

61

divided by

Inventory $93,000

62

3-9B. Reynolds Computer RATIO 2003 Liquidity: Current Ratio 1.48 Acid-test (Quick) Ratio 1.40 Average Collection Period 38.69 Accounts Receivable Turnover 9.43 Inventory Turnover 50.87 Operating profitability: Operating Income Return on Investment 21.4% Operating Profit Margin 9.7% Total Asset Turnover 2.20 Accounts Receivable Turnover 9.43 Inventory Turnover 50.87 Fixed Asset Turnover 33.02 Financing: Debt Ratio .54 Times Interest Earned 72.26 Rate of return on common stockholders’ investment: Return on Common Equity 31.3%

Norm 1.49 1.36 53.38 6.84 20.87

9.0% 6.0% 1.58 6.84 20.87 13.02 .47 14.79 13.0%

Liquidity – Based on the current and acid-test ratios, Reynolds Computer is performing as well as the industry average in the area of liquidity. At a detail level, Reynolds Computer is doing much better than average in managing both receivables and inventory. As you can observe, the acid-test ratio changes little from the current ratio. Based upon the small effect that inventory has on the current ratio, we might assume that Reynolds Computer is not holding a large amount of inventory. Upon review of the balance sheet, inventory only accounts for 5% of total current assets. Cash accounts for 54% of the total current assets making Reynolds Computer much more liquid than the current ratio indicates. Profitability – Reynolds Computer seems to be doing an excellent job at operating profitability based on the OIROI ratio. Let’s break down this ratio into its two components We have already ascertained that Reynolds Computer is managing its accounts receivable and inventory effectively. From the fixed asset ratio, Reynolds Computer is also managing a much lower amount of fixed assets as compared to sales than the industry. Overall, Reynolds Computer is generating more sales from every $1 of assets than its competitors. Reynolds Computer is also doing a good job at managing its income statement. The operating profit margin shows that Reynolds Computer is controlling costs efficiently. Both the asset turnover and profit margin contribute to Reynolds Computer’s favorable operating profitability. Financing – Reynolds Computer finances more of its assets through debt than its competitors. This involves more risk, but it can also provide higher returns as we will note in the next section. Reynolds Computer must be careful not to over-leverage itself. However, Reynolds Computer’s times interest earned ratio indicates that Reynolds Computer can service its debt more easily than the average firm. Return on Investment- As noted above, Reynolds Computer finances more of its assets through debt than the industry average. With more debt and less equity, this will provide a higher return to its owners as long as the earned rate of return is higher than the cost of debt. Based on the high operating profitability and times interest earned ratios, we can assume this is the case. As a result, the common equity owners are receiving a higher return on their investment than the industry average.

63

CHAPTER 4 64

Financial Forecasting, Planning, and Budgeting CHAPTER ORIENTATION This chapter is divided into two sections. The first section includes an overview of the role played by forecasting in the firm's planning process. The second section focuses on the construction of detailed financial plans, including developing a cash budget for future periods of the firm's operations. A budget is a forecast of future events and provides the basis for taking corrective action and can also be used for performance evaluation. The cash budget also provides the necessary information to estimate future financing requirements of the firm. These estimates are the key elements in our discussion of financial planning and budgeting.

CHAPTER OUTLINE I.

Financial forecasting and planning A.

B.

The need for forecasting in financial management arises whenever the future financing needs of the firm are being estimated. There are three basic steps involved in predicting financing requirements. 1.

Project the firm's sales revenues and expenses over the planning period.

2.

Estimate the levels of investment in current and fixed assets, which are necessary to support the projected sales level.

3.

Determine the financing needs of the firm throughout the planning period.

The key ingredient in the firm's planning process is the sales forecast. This forecast should reflect (l) any past trend in sales that is expected to continue and (2) the effects of any events, which are expected to have a material effect on the firm's sales during the forecast period.

65

II.

III.

C.

The traditional problem faced in financial forecasting begins with the sales forecast and involves making forecasts of the impact of predicted sales on the firm's various expenses, assets, and liabilities. One technique that can be used to make these forecasts is the percent of sales method.

1.

The percent of sales method involves projecting the financial variable as a percent of projected sales.

2.

As sales volume changes, the level of assets required to support the firm changes. Assets are financed by liabilities and equity, so changes in assets lead to changes in liabilities and equity. Current liabilities, such as accounts payable and accrued expenses, vary spontaneously as sales change. Retained earnings are impacted by changes in net income and dividends.

3.

The difference between the projected level of assets and the projected change in liabilities and equity is the discretionary financing needed.

4

Percent of sales forecasting can give erroneous results for assets that have scale economies or assets that must be purchased in discrete quantities.

Sustainable rate of growth A.

Sustainable rate of growth indicates how fast a firm can grow without having to increase the firm’s debt ratio and without having to sell more stock.

B.

Sustainable rate of growth, g = return on equity x (1 – dividend payout ratio)

Financial planning and budgeting A.

Three functions of a budget are indicating the amount and timing of future financing needs, providing the basis for taking corrective action if actual figures do not match budget estimates, and evaluating performance of the firm.

B.

The cash budget represents a detailed plan of future cash flows and can be broken down into four components: cash receipts, cash disbursements, net change in cash for the period, and new financing needed.

C.

Although no strict rules exist, as a general rule, the budget period shall be long enough to show the effect of management policies, yet short enough so that estimates can be made with reasonable accuracy. For instance, the capital expenditure budget may be properly developed for a 10-year period while a cash budget may only cover 12 months.

66

D.

Cash budgets can be used to develop a pro forma income statement and a pro forma balance sheet.

1.

A pro forma income statement represents a statement of planned profit or loss for the future period and is based primarily on information generated in the cash budget.

2.

The pro forma balance sheet for a future date is developed by adjusting present balance sheet figures for projected information found primarily within the cash budget and pro forma income statement.

ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1.

This rather simplistic forecast method assumes no other information is available which would indicate a change in the observed relationship between sales and the expense item, asset or liability being forecast. Furthermore, the percent of sales method works best for projected sales levels that are very close to the base level sales used to determine the "percent of sales." The greater the difference in predicted and base level sales, in general, the less accurate will be the percent of sales forecast.

4-2.

In a fixed cash budget, cash flow estimates are made for a single set of sales estimates, whereas a variable budget involves the preparation of several cash flow estimates, with each estimate corresponding to a different set of sales estimates.

4.3

A flexible (or variable) cash budget gives the firm's management more information regarding the range of possible financing needs of the firm, and secondly, it provides management with a standard against which it can measure the performance of those subordinates who are responsible for the various cost and revenue items contained in the budget.

4-4.

The probable effect on cash flows would be as follows: (a) increased cash inflow from sales but increased cash outflow to finance needed increases in inventories and other assets. (b) increased supply of available cash. (c) decreased cash inflow. (d) immediate decrease in cash inflows (or a cash outflow).

4-5.

As a general rule, the budget period should be long enough to show the effect of management policies yet short enough so that estimates can be made with reasonable accuracy. Since some budgets, such as capital expenditure budgets, require longrange planning in order to be effective while other budgets are more effective for shorter periods, it would not be wise for a firm to establish a standard budget period for all budgets. Instead, firms usually have a minimum of two and sometimes three types of budgets. The short-term budget is very detailed and includes a cash budget covering 6 months to a year. The intermediate term budget will contain pro forma 67

statements and verbal descriptions of major investment/financing plans that cover 2 to 5 years. A long-term plan would involve less detailed general statements about the firm's strategic plans covering the next 3 to 10 years. 4-6.

A cash budget can also be used to determine the amount of excess cash on hand that will not be needed to finance future operations. This excess cash can then be invested in securities or other profitable alternatives.

4-7.

The careful budgeting of cash is of particular importance to a seasonal operation because cash flows are not continuous. The availability of cash resources must be carefully planned in order that the normal operation of the firm can be continued during slow periods. In addition, it is important to plan for future cash needs so that excess funds may be invested.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 4-1A. Sales Net Income Current Assets Net fixed assets Total Assets

2003 12,000,000 1,200,000

% of Sales

2004 15,000,000 2,000,000

3,000,000 6,000,000 9,000,000

25% 50%

3,750,000 7,500,000 11,250,000

Accounts payable Long-term debt Total Liabilities

3,000,000 2,000,000 5,000,000

25% NA

3,750,000 2,000,000 5,750,000

Common stock Paid-in capital Retained earnings Common equity Total Liabilities and Equity

1,000,000 1,800,000 1,200,000 4,000,000 9,000,000

NA NA

1,000,000 1,800,000 3,200,000 6,000,000 11,750,000

Liabilities and Owner's Equity

DFN =

68

(500,000)

4-2A. a.

% Credit Sales

0.5

Sales February March April (estimated)

20,000 30,000 40,000

Accounts receivable (3/31/03) 20,000 plus credit sales for April (50% x 40,000) 20,000 less collections from Feb sales (50% x 20,000 x .5) (5,000) less collections from March sales(50% x 30,000 x .5)(7,500) Accounts receivable (4/30/03) 27,500 b.

Collections From: April cash sales February credit sales March credit sales

$ 20,000 5,000 7,500 $ 32,500

4-3A. Based upon the projections made, Sambonoza can expect to have total assets next year equal to $1.8 million made up of the $1 million in fixed assets plus $800,000 (.2 x $4 million) in current assets. These assets will be financed by known sources of funding comprised of $900,000 in common equity [$800,000 + (.5)(.05)($4 million) = $900,000], plus payables and trade credit equal to 10% of projected sales ($400,000) which totals $1.3 million. This leaves $500,000 ($1.8 million - $1.3 million), which will need to be raised to meet the financing needs of the firm. 4-4A. Instructor’s Note: This is an introductory percent of sales financial forecasting problem. Students should be able to solve it after a first reading of the chapter. (a)

Projected Financing Needs = Projected Total Assets = Projected Current Assets + Projected Fixed Assets =

(b)

{ x $20 m} +{ $5m + $.1m} = $11.77m

DFN = Projected Current Assets + Projected Fixed Assets - Present LTD - Present Owner's Equity - [Projected Net Income - Dividends] - Spontaneous Financing

} + $5.1m - $2m - $6.5m - [.05 x $20m - $.5m] -{ x $20m} =

{

x $20m

DFN = $6.67m + $5.1m - $8.5m - $.5m - $2m = $.77m

69

(c)

We first solve for the maximum level of sales for which DFN = 0: DFN = (

5 1.5 - .05 ) Sales – (5.1M-2M-6.5M +.5M) 15 15

DFN = .1833 SALES - $2.9M = 0 Thus, SALES = $15.82M The largest increase in sales that can occur without a need to raise "discretionary funds" is $15.82M - $15M = $820,000. 4-5A. Cash Accounts Receivable Inventories Net Fixed Assets

$ .1m .1m 1.0m .8m $2.0m

Current Liabilities Long-Term Debt Common Stock plus Retained earnings

70

$.6m .4m 1.0m $2.0m

4-6A. (a)

The Sharpe Corporation Cash Budget Worksheet Nov $220,000

Sales Collections: Month of sale (10%) First month (60%) Second month (30%)

Total Collections 274,500 Purchases

Dec $175,000

Jan $ 90,000

Feb $120,000

Mar $135,000

Apr $240,000

May $300,000

June $270,000

July $225,000

9,000 105,000 66,000

12,000 54,000 52,500

13,500 72,000 27,000

24,000 81,000 36,000

30,000 144,000 40,500

27,000 180,000 72,000

22,500 162,000 90,000

180,000 72,000

81,000

Payments (one month lag) 72,000

67

Cash Receipts (collections) Cash Disbursements Purchases Rent Other Expenditures Tax Deposits Interest on Short-Term Borrowing Total Disbursements Net Monthly Change Beginning Cash Balance Additional Financing Needed (Repayment)

118,500

112,500

144,000

81,000

141,000

180,000

144,000

214,500

162,000

180,000

135,000

279,000

162,000

90,000

135,000

75,000

90,000

180,000

118,500

112,500

141,000

214,500

279,000

274,500

72,000 10,000 20,000

81,000 10,000 20,000

144,000 10,000 20,000 22,500

180,000 10,000 20,000

162,000 10,000 20,000

135,000 10,000 20,000 22,500

90,000 10,000 20,000

_______ $102,000 $78,000 22,000

_______ $111,000 $7,500 100,000

_______ $196,500 ($84,000) 107,500

_______ $210,000 ($69,000) 23,500

605 $192,605 $21,895 15,000

386 $187,886 $91,114 15,000

_______ $120,000 $154,500 67,509

________

_______

________

60,500

(21,895)

(38,605)

_______

Ending Cash Balance $222,009 Cumulative Borrowing 38,605 0 (b)

$100,000 $107,500 $ 23,500

$15,000

$ 15,000

0

0

0

$

$ 60,500

67,509 $

0

The firm will have sufficient funds to cover the $200,000 note payable due in July. In fact, if the firm's estimates are realized they will have $222,009 in cash by the end of July.

72

4-7A. Cash YES1 Marketable Securities NO Accounts Payable YES Notes Payable NO2 Plant and Equipment NO3 Inventories YES 1 Cash receipts follow sales with a lag related to the payment habits of the firm's customers and the firm's policy regarding payments on its accounts payables. 2 Notes payable may well follow sales if the firm uses a line of credit to finance its working capital needs (discussed later in Chapter 18). 3 The answer depends on whether or not the firm has excess capacity. If there is excess capacity, plant and equipment will not vary directly with the level of firms sales. If there is no excess capacity, plant and equipment will vary directly. 4-8A. (a) Current assets1 Net fixed assets

____________ 1 x $80m = $16m 2 x $80m = $ 8m 3 $31m - $28m = $ 3m financing needs in 2004) ____________ (b) (c)

$16m 15m $31m

Accounts payable2 Notes payable3 Bonds payable Common equity

$ 8m 3m 10m 10m $31m

(Balancing figures which equal estimated discretionary

= - - bonds = $31m - $8m - $10m - $10m = $3m See answer to question 4-1.

Instructor’s Note: This problem follows the text example very closely and provides an excellent assigned exercise to accompany a first reading of the chapter.

73

4-9A. (a)

Estimating Future Financing Needs Armadillo Dog Biscuit Co., Inc. Projected Need for Discretionary Financing

Current Assets Net Fixed Assets Total

Present Level $2.0m $3.0m $5.0m

% of Sales ($5m) = .40 or 40% = .60 or 60%

Accounts Payable

$.5m

= .10 or 10%

Accrued Expenses Notes Payable1 Current Liabilities Long-Term Debt Common Stock Retained Earnings 2 Common Equity Total

$.5m -----$1.0m $2.0m .5m 1.5m $2.0m $5.0m

= .10 or 10% -----

1

2

Projected Level (Based on $7m Sales) .40 x $7m = $ 2.8m .60 x $7m = $ 4.2m $ 7.0m .10 x 7m = .7m

.10 x 7m = .7m Plug Figure = 1.11m $ 2.51m No Change $2.00m No Change .50m $1.5m + .07 x $7m = $ 1.99m $2.49m $ 7.00m

Notes payable is a balancing figure which equals discretionary financing needed, DFN, which equals: Total Assets Accounts Payable - Accrued Expenses - Long-Term Debt - Common Stock - Retained Earnings = $7.0m - $0.7m $0.7m - $2.0m - $0.5m - $1.99m = $1.11m. The projected retained earnings is the sum of the beginning balance of $1.5m plus net income for the period (.07 x $7m).

(b) Current Ratio Debt Ratio

Before = 2 times = .60 or 60%

After = 1.12 times = .644 or 64.4%

The growth in the firm's assets (due to the projected increase in sales) was financed predominantly with notes payable (a current liability). This led to a substantial deterioration in both the firm's liquidity (as reflected in the current ratio) and an increase in its use of financial leverage.

74

(c)

The slower rate of growth in sales would have allowed Armadillo to finance a larger portion of the funds needed using retained earnings. For example, using the 7 percent net profit margin Armadillo would have .07 x $6m = $420,000 it could reinvest after one-year's operations plus .07 x $7 million = $490,000 from the second year's sales. The total amount of retained earnings over the two years then would be $910,000 rather than only $490,000 as before. This would mean that notes payable would be $380,000 after one year, and only $1.11m - . 42m = $690,000 at the end of the second year. The resulting level of current liabilities would be $2.09m. Thus, the post sales growth current ratio after two years would be 1.34 ($2.8m/2.09m = 1.34) compared to 1.12 with a one-year growth period. The debt ratio under the two-year growth period will be only 58% compared to approximately 64% with the single year growth period. The slower growth pace would allow the firm to expand its assets more gradually, thus requiring less external financing since more earnings can be retained.

4-10A. Instructor’s Note: This problem differs from the text discussion of "discretionary financing needed" in that it relies on the projected change in assets rather than the projected level of total assets. Under these circumstances DFN = ∆ TA - ∆ SL - ∆ RE where ∆ TA = the projected change in total assets, which is the amount of new financing needed (in total); ∆ SL = the projected change in spontaneous liabilities; and ∆ RE = the projected change in retained earnings that will be available to finance a portion of the firm's needs for new funds. First, we estimate that the projected change in assets during the coming year will be: ∆ TA = .30 ∆ Sales = .30 ($500,000) = $150,000 Thus, total new financing of $150,000 must be obtained during the next year to support the growth in firm sales. Next, we project the change in spontaneous liabilities (∆ SL) ∆ SL = =

.15 ∆ Sales .15 ($500,000)

=

$75,000

Finally, we project new retained earnings (∆ RE) that will be available to help finance the firm's operations during the next year, ∆ RE = = = ∆ RE =

New Income - Dividends .05 x Projected Sales - .04 x Projected Sales .01 ($5,500,000) $55,000

75

Discretionary Financing Needed (DFN) can now be calculated as follows: DFN

= = =

∆ TA - ∆ SL - ∆ RE $150,000 - 75,000 - 55,000 $20,000

Note that this problem solution works with the change in financing needs rather than totals. The same solution would result if we projected total assets, total spontaneous financing, etc. However, in this problem we do not know the existing levels of the assets, liabilities and owners' equity accounts. Thus, we cannot use this latter approach to solve the problem.

76

4-11A a.

Projections based on expected sales levels: Nov 220,000

72

Sales Collections: Month of sales (20%) First month (50%) Second month (30%) Total collections Purchases 65,000 Payments Cash Receipts Cash Disbursements -Purchases Rent Other expenditures Tax Deposits Interest on S-T borrowing Total Disbursements

Dec 175,000

78,000 65,000

Jan 100,000

Feb 120,000

Mar 150,000

Apr 300,000

May 275,000

June 200,000

July 200,000

20,000 87,500 66,000 173,500 97,500 78,000 173,500

24,000 50,000 52,500 126,500 195,000 97,500 126,500

30,000 60,000 30,000 120,000 178,750 195,000 120,000

60,000 75,000 36,000 171,000 130,000 178,750 171,000

55,000 150,000 45,000 250,000 130,000 130,000 250,000

40,000 137,500 90,000 267,500 117,000 130,000 267,500

40,000 100,000 82,500 222,500 0 117,000 222,500

78,000 10,000 20,000

97,500 10,000 20,000

195,000 10,000 20,000 22,500

178,750 10,000 20,000

130,000 10,000 20,000

117,000 10,000 20,000

610

994

130,000 10,000 20,000 22,500 104

0

108,000

127,500

247,500

209,360

160,994

182,604

147,000

Net Monthly Change

65,500

-1,000

-127,500

-38,360

89,006

84,896

75,500

Beginning Cash Balance

22,000

87,500

86,500

20,000

20,000

20,000

94,542

61,000

38,360

(89,006)

(10,354)

0

20,000

20,000

20,000

94,542

170,042

Additional Financing Needed (Repayment) Ending Cash Balance

87,500

86,500

August 180,000

Cumulative Borrowing

61,000

78

99,360

10,354

0

0

Projections based on sale 20% higher than expected Cash Budget

73

Nov Sales 220,000 Collections: Month of sales (10%) First month (60%) Second month (30%) Total collections Purchases 78,000 Payments Cash Receipts (collections) Cash Disbursements Purchases Rent Other expenditures Tax Deposits Interest on S-T

Dec 175,000

93,600 78,000

borrowing Total Disbursements

Jan 120,000

Feb 144,000

Mar 180,000

Apr 360,000

May 330,000

June 240,000

July 240,000

24,000 87,500 66,000 177,500 117,000 93,600 177,500

28,800 60,000 52,500 141,300 234,000 117,000 141,300

36,000 72,000 36,000 144,000 214,500 234,000 144,000

72,000 90,000 43,200 205,200 156,000 214,500 205,200

66,000 180,000 54,000 300,000 156,000 156,000 300,000

48,000 165,000 108,000 321,000 140,400 156,000 321,000

48,000 120,000 99,000 267,000 0 140,400 267,000

93,600 10,000 20,000

117,000 10,000 20,000

234,000 10,000 20,000 22,500

214,500 10,000 20,000

156,000 10,000 20,000

140,400 10,000 20,000

923

1,325

156,000 10,000 20,000 22,500 198

0

123,600

147,000

286,500

245,423

187,325

208,698

170,400

Net Monthly Change

53,900

-5,700

-142,500

-40,223

112,675

112,302

96,600

Beginning Cash Balance

22,000

75,900

70,200

20,000

20,000

20,000

112,454

92,300

40,223

(112,675)

(19,848)

0

20,000

20,000

20,000

112,454

209,054

Additional Financing Needed (Repayment) Ending Cash Balance

75,900

70,200

August 216,000

Cumulative Borrowing

92,300

80

132,523

19,848

0

0

Projections based on sales 20% lower than expected: Nov 220,000

74

Sales Collections: Month of sales (20%) First month (50%) Second month (30%) Total collections Purchases 52,000 Payments Cash Receipts (collections) Cash Disbursements Purchases Rent Other expenditures Tax Deposits Interest on S-T

Dec 175,000

62,400 52,000

borrowing Total Disbursements

Jan 80,000

Feb 96,000

Mar 120,000

Apr 240,000

May 220,000

June 160,000

July 160,000

16,000 87,500 66,000 169,500 78,000 62,400 169,500

19,200 40,000 52,500 111,700 156,000 78,000 111,700

24,000 48,000 24,000 96,000 143,000 156,000 96,000

48,000 60,000 28,800 136,800 104,000 143,000 136,800

44,000 120,000 36,000 200,000 104,000 104,000 200,000

32,000 110,000 72,000 214,000 93,600 104,000 214,000

32,000 80,000 66,000 178,000 0 93,600 178,000

62,400 10,000 20,000

78,000 10,000 20,000

156,000 10,000 20,000 22,500

143,000 10,000 20,000

104,000 10,000 20,000

93,600 10,000 20,000

297

662

104,000 10,000 20,000 22,500 9

0

92,400

108,000

208,500

173,297

134,662

156,509

123,600

Net Monthly Change

77,100

3,700

-112,500

-36,497

65,338

57,491

54,400

Beginning Cash Balance

22,000

99,100

102,800

20,000

20,000

20,000

76,632

29,700

36,497

(65,338)

(859)

0

20,000

20,000

20,000

76,632

131,032

Additional Financing Needed (Repayment) Ending Cash Balance

99,100

102,800

August 144,000

Cumulative Borrowing

29,700

82

66,197

859

0

0

b.

Harrison will not be able to retire the $200,000 note at the end of June. June Ending

Sales Levels

Cash Balance Expected +20% -20%

$94,542 112,454 76,632

4-12A. a.

Calculations of the sustainable rate of growth for ADP, Inc. for each of the years 1999 through 2003 :

Net Income Common Equity ROE Dividends b g* b.

2003 150 812 18.47%

2002 110 722 15.24%

2001 90 656 13.72%

2000 70 602 11.63%

1999 60 560 10.71%

60 40%

44 40%

36 40%

28 40%

24 40%

11.1%

9.1%

8.2%

7.0%

6.4%

Compare actual sales growth rates to the sustainable rate if growth for each year. 2003

2002

2001

2000

1999

Sales Sales growth rate

3,000 36.4%

2,200 22.2%

1,800 28.6%

1,400 16.7%

1,200 N/A

g*

11.1%

9.1%

8.2%

7.0%

6.4%

Difference

25.3%

13.1% 20.4% 9.7% N/A

A quick review of ADP's balance sheets over the test years reveals a growing reliance on debt financing. The firm's debt ratio in 1999 was roughly 48% while it had grown to 70% in 2003. Thus, ADP has financed its growth with increased debt financing.

83

4-13A. a.

Carrera Game Co. 2003

2002

2001

2000

1999

Liabilities Assets Debt to Assets

33,000 54,000 61.1%

31,200 50,400 61.9%

25,680 43,200 59.4%

16,320 32,400 50.4%

12,000 27,000 44.4%

Net Income Common Equity ROE

3,000 21,000 14.3%

2,800 19,200 14.6%

2,400 17,520 13.7%

1,800 16,080 11.2%

1,500 15,000 10.0%

Dividends b

1,200 40.0%

1,120 40.0%

960 40.0%

720 40.0%

600 40.0%

Sales Sales growth rate

60,000 7.1%

56,000 16.7%

48,000 33.3%

36,000 20.0%

30,000 N/A

b.

The sustainable rates of growth for each of the last five years are calculated as follows:

g* Difference 4-14A. a.

b.

8.6%

8.8%

8.2%

6.7%

6.0%

-1.5%

7.9%

25.1%

13.3%

N/A

Findlay's sales and inventory balances are plotted in the figure below. Note that the relationship between the two variables is very nearly linear. However, the intercept for the relationship is not zero, consequently the percent of sales projections are going to provide erroneous estimates of future inventories. The average of the inventories as a percent of sales ratio for the last five years was 6.39%. Thus, we project inventories for a sales level of $30 million to be $1,917,000. That is, Projected Inventories = x =

.0639 x $30 million

=

$1,917,000

Similarly, using the most recent year's percent of sales (5%) we calculate inventories to be $1,500,000. That is, 2003

Projected Inventories

=

percent

x

ofsales

=

.05 x $30 million

84

=

$1,500,000

We can make a forecast of inventories using the relationship observed between sales and inventories in part a by sketching a line through the observed relationship and extrapolating the line to sales of $30,000,000.

Inventory ( In Thousands)

1,500 1,400 1,300 1,200 1,100 1,000 10,000

15,000

20,000

25,000

30,000

35,000

Sales (In Thousands) Using this graphical technique we see that the level of inventories will probably be just over $1,300,000. The substantial difference in the percent of sales forecast and the "true relationship" forecast is a result of the implicit assumption made when using the percent of sales forecast. That is, the percent of sales forecast is simply a linear extrapolation of inventories based on sales where the intercept is assumed to be zero. As we saw in part a, above, this assumption is not valid for this problem.

85

SOLUTION TO INTEGRATIVE PROBLEM Historical data for Phillips Petroleum: 1986-92

Sales Net Income Earnings per share Dividends per share Number of Common Shares

78

Current Assets Total Assets Current Liabilities Long-term Liabilities Total Liabilities Preferred Stock Common Equity Total Liabilities and Equity Projected Sales

1986 10,018 228 0.89 2.02

1987 10,917 35 0.06 1.73

1988 11,490 650 2.72 1.34

1989 12,492 219 0.90 0.00

1990 13,975 541 2.18 1.03

1991 13,259 98 0.38 1.12

1992 12,140 270 1.04 1.12 259,615,385

2,802 12,403 2,234 8,175 10,409 270 1,724 12,403

2,855 12,111 2,402 7,887 10,289 205 1,617 12,111

3,062 11,968 2,468 7,387 9,855 0 2,113 11,968

2,876 11,256 2,706 6,418 9,124 0 2,132 11,256

3,322 12,130 2,910 6,501 9,411 0 2,719 12,130

1993 1 3,000

1994 1 3,500

1995 1 4,000

1996 1 4,500

1997 1 5,500

2,459 11,473 2,603 6,113 8,716 0 2,757 11,473

2,349 11,468 2,517 5,894 8,411 359 2,698 11,468

1.

Projected Net Income using the percent of sales method.

Sales Net Income Net Income/Sales Average Net Income/Sales

1986 10,018 228 2.28% 2.406%

1987 10,917 35 0.32%

1988 11,490 650 5.66%

1989 12,492 219 1.75%

1990 13,975 541 3.87%

Projected Sales Projected Net Income

1993 13,000 313

1994 13,500 325

1995 14,000 337

1996 14,500 349

1997 15,500 373

2.

1991 13,259 98 0.74%

1992 12,140 270 2.22%

Projected total assets and current liabilities

79

Sales Total Assets Current Liabilities TA/Sales CL/Sales

1986 10,018 12,403 2,234

1987 10,917 12,111 2,402

1988 11,490 11,968 2,468

1989 12,492 11,256 2,706

1990 13,975 12,130 2,910

1991 13,259 11,473 2,603

1992 12,140 11,468 2,517

123.81% 22.30%

110.94% 22.00%

104.16% 21.48%

90.11% 21.66%

86.80% 20.82%

86.53% 19.63%

94.46% 20.73%

1994 13,500 13,438 2,866

1995 14,000 13,936 2,972

1996 14,500 14,433 3,078

1997 15,500 15,429 3,291

Average TA/Sales Average CL/Sales

99.54% 21.23%

Projected Sales Projected Total Assets Projected C. Liabilities

1993 13,000 12,940 2,760

3.

Projected discretionary financing requirements for 1993-97. 1993 12,940

1994 13,438

1995 13,936

1996 14,433

1997 15,429

Current Liabilities Long-term Debt Preferred Stock Common Equity*

2,760 5,894 359 2,720

2,866 5,894 359 2,754

2,972 5,894 359 2,800

3,078 5,894 359 2,858

3,291 5,894 359 2,940

Discretionary Financing Needed**

1,207

1,565

1,911

2,244

2,945

Total Assets

259,615, * Common dividends = $1.12 x the number of common shares outstanding in 1992 ( 385) Thus, Common Equity (1993) = Common Equity (1992) + NI (1993) - Dividends (1993)

80

** Discretionary Financing Needed = Projected Total Assets - Current Liabilities - Long-term Debt - Preferred Stock - Common Equity

Solutions to Problem Set B 4-1B. Sales Net Income

2003 20,000,000 1,000,000

Current Assets Net fixed assets Total Assets

4,000,000 8,000,000 12,000,000

Liabilities and Owner's Equity Accounts payable 3,000,000 Long-term debt 2,000,000 Total Liabilities 5,000,000 Common stock 1,000,000 Paid-in capital 1,800,000 Retained earnings 4,200,000 Common equity 7,000,000 Total Liabilities and Equity12,000,000

% of Sales

20% 40%

5,000,000 10,000,000 15,000,000

15% NA

3,750,000 2,000,000 5,750,000 1,000,000 1,800,000 6,200,000 9,000,000 14,750,000

NA NA

DFN = 4-2B. a.

b.

% Credit Sales

2004 25,000,000 2,000,000

250,000 40%

Sales February March April (estimated)

100,000 80,000 60,000

Accounts receivable (3/31/04) plus credit sales (April) less coll. from February less coll. from March Accounts receivable (4/30/04)

52,000 24,000 (20,000) (16,000) 40,000

Cash Sales Collections from February Collections from March Realized Cash during April

36,000 20,000 16,000 72,000

4-3B. Based upon the projections made, Simpson can expect to have total assets next year equal to $1.75 million made up of the $1 million in fixed assets plus $.75 million in current assets (.15 x 5m). These assets will be financed by known sources of funding comprised of the firm's common equity, .85million ($.7 million + $.3 million. - $.15 million) plus payables and trade credit equal to 11% of projected sales ($.55 million) which totals $1.4 million. This leaves $.35 million, which will need to be raised to meet the financing needs of the firm. 81

4-4B. Instructor’s Note: This is an introductory percent of sales financial forecasting problem. Students should be able to solve it after a first reading of the chapter. (a)

Projected Financing Needs = Projected Total Assets = Projected Current Assets + Projected Fixed Assets =(

7 x 25m) + 6m + .1m 18

= $15,822,222 (b)

DFN = Projected Current Assets + Projected Fixed Assets - Present LTD - Present Owner's Equity - [Projected Net Income - Dividends] - Spontaneous Financing =(

7 1.5 x 25m) + 6m + .1m – 2m –9.5m – (.05 x 25m - .6m) – ( x 18 18

25m) DFN = $1,588,889 (c)

We first solve for the maximum level of sales where DFN = 0: DFN = (

7 1.5 -.05 ) Sales + 6.1m –2m –9.5m +.6m 18 18

= .25556 Sales -4.8 million = 0 Thus, SALES = $18,782,282 The largest increase in sales that can occur without a need to raise "discretionary funds" is $18,782,282 - $18m = $782,282. 4-5B. Cash Accounts Receivable Inventories Net Fixed Assets

$ .03m .14m 1.0m .83m $2.0m

Current Liabilities Long-Term Debt Common Equity

$.39m .81m .80m $2.0m

4-6B. (a) CASH BUDGET DATA January February March April

100,000 110,000 130,000 250,000

May June July August

82

275,000 250,000 235,000 160,000

83

The Carmel Corporation Cash Budget Worksheet Nov Dec $220,000 $175,000 Collections: Month of sale (20%) First month (60%) Second month (20%)

Jan $100,000

Feb $110,000

Mar $130,000

Apr $250,000

May $275,000

June $250,000

20,000 105,000 44,000

22,000 60,000 35,000

26,000 66,000 20,000

50,000 78,000 22,000

55,000 150,000 26,000

50,000 165,000 50,000

47,000 150,000 55,000

169,000

117,000

112,000

150,000

231,000

265,000

91,000

175,000

192,500

175,000

164,500

112,000

0

70,000

77,000

91,000

175,000

192,500

175,000

164,500

169,000

117,000

112,000

150,000

231,000

265,000

252,000

77,000 10,000 20,000

91,000 10,000 20,000

175,000 10,000 20,000 23,000

192,500 10,000 20,000

175,000 10,000 20,000

112,000 10,000 20,000

560

1,291

164,500 10,000 20,000 23,000 1,044

$223,060 ($73,060) 20,000 73,060

$206,291 $24,709 20,000 (24,709)

$218,544 $46,456 20,000 (46,456)

$142,579 $109,421 20,000 (57,895)

Total Collections

July Aug $235,000 160k

252,000 Purchases

70,000

Payments (1 mo lag) 112,000 Cash Receipts (collections)

83

Cash Disbursements Purchases Rent Other Expenditures Tax Deposits Interest on Short-Term Borrowing Total Disbursements Net Monthly Change Beginning Cash Balance Additional Financing

77,000

$107,000 $62,000 22,000

$121,000 $228,000 ($4,000) ($116,000) 84,000 80,000 56,000

579

Needed (Repayment)

Ending Cash Balance 20,000 $71,526 Cumulative Borrowing (b)

0

$84,000

$80,000

$20,000

$20,000

$20,000

56,000

$129,060

$104,351

$57,895

0

0

The firm will not have sufficient funds to cover the $250,000 note payable due in July.

85

$

4-7B.

Cash Marketable Securities Accounts Payable Notes Payable Plant and Equipment Inventories 1

4-8B. (a)

YES NO YES NO NO1 YES

The answer depends on whether or not the firm has excess capacity. If there is excess capacity, plant and equipment will not vary directly with the level of firms sales. If there is no excess capacity, plant and equipment will vary directly.

$13.33m 1.67m 10.00m 10.00m $35.00m (b) Total financing requirements = $35m--however, spontaneous financing accounts for all but the $1.67m increase in notes payable (discretionary financing needed). (c) See answer to question 4-1. 4-9B. Instructor’s Note: This problem follows the text example very closely and provides an excellent assigned exercise to accompany a first reading of the chapter. (a)

Current assets Net fixed assets

$20.00m 15.00m $35.00m

Accounts payable Notes payable Bonds payable Common equity

Estimating Future Financing Needs Symbolic Logic Corporation (SLC), Inc. Projected Need for Discretionary Financing

Current Assets Net Fixed Assets Total Assets Accounts Payable Accrued Expenses Notes Payable*

Present Level $2.5m $3.0m $5.5m $.1.0m $.5m ------

Current Liabilities $1.50m Long-Term Debt $2.00m Common Stock .50m Retained Earnings** 1.50m Common Equity $2.00m Total Liabilities and Equity

% of Sales ($5m) = 50% = 60% = 20% = 10% -------

Projected Level (Based on $8m Sales) .50 x $8m = $ 4.0m .60 x 8m = $ 4.80m $ 8.80m .20 x 8m = 1.60m .10 x 8m = .80m Plug Figure 1.84m

$ 4.24m No Change $2.00m No Change .50m $1.5m + (07 x $8m) = $ 2.06m $2.56m $5.50m $8.80m

*Notes payable is a balancing figure which equals discretionary financing needed, DFN or: Total Assets - Accounts Payable - Accrued Expenses - Long-Term Debt Common Stock - Retained Earnings = $8.80m - 1.60m - .8m – 2m - .5m – 2.06m = $1.84m.

86

**The projected level of retained earnings equals the beginning balance of $1.50m plus net income for the period (.07 x $8m). (b) Before After Current Ratio = 1.67 times = .94 times Debt Ratio = 64% = 71% The growth in the firm's assets (due to the projected increase in sales) was financed predominantly with notes payable (a current liability). This led to a substantial deterioration in the firm's liquidity (as reflected in the current ratio) and an increase in its use of financial leverage. (c) The slower rate of growth in sales would have allowed SLC to finance a larger portion of the funds needed using retained earnings. 4-10B.Instructor’s Note: This problem differs from the text discussion of "discretionary financing needed" in that it relies on the projected change in assets rather than the projected level of total assets. Under these circumstances DFN = ∆ TA - ∆ SL - ∆ RE where ∆ TA = the projected change in total assets, which is the amount of new financing needed (in total); ∆ SL = the projected change in spontaneous liabilities; and ∆ RE = the projected change in retained earnings that will be available to finance a portion of the firm's needs for new funds. First, we estimate that the projected change in assets during the coming year will be: ∆ TA

= =

.40 ∆ Sales .40 ($500,000)

=

$200,000

Thus, total new financing of $200,000 must be obtained from somewhere during the next year to support the growth in firm sales. Next, we project the change in spontaneous liabilities (∆ SL) ∆ SL

= =

.15 x ∆ Sales .15 ($500,000)

=

$75,000

Finally, we project new retained earnings (∆ RE) that will be available to help finance the firm's operations during the next year, ∆ RE ∆ RE

= = = =

New Income - Dividends .05 x Projected Sales - .04 x Projected Sales .01 ($5,500,000) $55,000

Discretionary Financing Needed (DFN) can now be calculated as follows: DFN

= = =

∆ TA - ∆ SL - ∆ RE $200,000 - 75,000 - 55,000 $70,000

Note that this problem solution works with the change in financing needs rather than totals. The same solution would result if we projected total assets, total spontaneous financing, etc. However, in this problem we do not know the existing levels of the assets, liabilities and owners' equity accounts. Thus, we cannot use this latter approach to solve this problem.

87

4-11B. Minimum Cash Balance Beginning Cash Balance

= =

25,000 28,000

Historical Sales and Base Case Sales Predictions for Future Sales January 120,000 May February 160,000 June March 140,000 July April 190,000 August Sales Expansion % = 0.00% Purchases as a % Sales = 75% Collections: Current Mo. 30%

88

225,000 250,000 200,000 220,000

Annual Interest Rate = 12.00% 1 Mo. Later 2 Mo. Later 30% 40%

Cash Budget for January thru July based on expected sales Nov Dec Jan Feb Sales 230,000 225,000 120,000 160,000 Collections: Month of sales 36,000 48,000 First month 67,500 36,000 Second month 92,000 90,000 Total Collections Purchases Payments Cash Receipts (collections)

195,500 174,000 90,000 120,000 105,000 90,000 120,000 195,500

87

Cash Disbursements Payments for Purchases Rent Other Expenditures Tax Deposits Interest on Short-Term Borrowing Total Disbursements Net Monthly Change Analysis of Borrowing Needs Beginning Cash Balance Ending Cash (No Borrow) Needed (Borrowing) Loan Repayment

120,000 12,000 20,000

Mar 140,000

Apr 190,000

May 225,000

June 250,000

July 210,000

42,000 48,000 48,000

57,000 42,000 64,000

67,500 57,000 56,000

75,000 67,500 76,000

63,000 75,000 90,000

138,000 142,500 105,000 174,000

163,000 180,500 168,750 187,500 157,500 142,500 168,750 187,500 138,000 163,000 180,500

218,500 165,000 157,500 218,500

105,000 12,000 20,000

142,500 12,000 20,000 26,500

157,500 12,000 20,000 26,500 564

168,750 12,000 20,000 0

$152,000

$137,000

$43,500

$37,000

28,000 71,500 0 0

71,500 108,500 0 0

187,500 12,000 20,000 173

228,000 165,000 228,000

165,000 12,000 20,000 545

$201,000 $200,750 $219,673 $216,564 $197,545 ($63,000) ($37,750) ($39,173) 108,500 45,500 0 0

45,500 7,750 17,250 0

25,000 (14,173) 39,173 0

August 220,000

$1,936

$30,455

25,000 26,936 0 1,936

25,000 55,455 0 30,455

Ending Cash Balance Cumulative Borrowing

$71,500 0

$108,500 0

$45,500 0

90

$25,000 $17,250

$25,000 $56,423

$ 25,000 $54,487

$25,000 24,032

Cash Budget for January thru July based on a 20% increase in sales Nov Dec Jan Feb Mar Apr Sales 230,000 225,000 144,000 192,000 168,000 228,000 Collections: Month of sales 43,200 57,600 50,400 68,400 First month 67,500 43,200 57,600 50,400 Second month 92,000 90,000 57,600 76,800 Total Collections Purchases 108,000 Payments Cash Receipts (collections)

202,700 144,000 108,000

88

Cash Disbursements Payments for Purchases Rent Other Expenditures Tax Deposits Interest on Short-Term Borrowing Total Disbursements Net Monthly Change Analysis of Borrowing Needs Beginning Cash Balance Ending Cash (No Borrow) Needed (Borrowing)

190,800

165,600

May 270,000

June 300,000

July 252,000

81,000 68,400 67,200

90,000 81,000 91,200

75,600 90,000 108,000

195,600

216,600

126,000 144,000 202,700

171,000 126,000 190,800

202,500 171,000 165,600

225,000 202,500 195,600

189,000 225,000 216,600

198,000 189,000 262,200

144,000 12,000 20,000

126,000 12,000 20,000

171,000 12,000 20,000 26,500

202,500 12,000 20,000

225,000 12,000 20,000

189,000 12,000 20,000 26,500 811

14 $176,000 $158,000

403

262,200

198,000 273,600

198,000 12,000 20,000 672

$229,500

$234,514 $257,403 $248,311 $230,672 -$38,914 -$40,803

$26,700

$32,800

-$63,900

28,000 54,700 0

54,700 87,500 0

87,500 23,600 1,400

25,000 -13,914 38,914

25,000 -15,803 40,803

$13,889

$42,928

25,000 38,889

25,000 67,928

August 264,000

273,600

Loan Repayment Ending Cash Balance Cumulative Borrowing

0 $54,700 0

0 $87,500 0

0 $25,000 1,400

0 $25,000 $40,314

92

0 $25,000 $81,117

(13,889) $ 25,000 $67,228

(42,928) $25,000 24,300

Cash Budget for January thru July based on a 20% decrease in sales Nov Dec Jan Feb Mar Apr Sales 230,000 225,000 96,000 128,000 112,000 152,000 Collections: Month of sales 28,800 38,400 33,600 45,600 First month 67,500 28,800 38,400 33,600 Second month 92,000 90,000 38,400 51,200 Total Collections Purchases 72,000 Payments Cash Receipts (collections)

188,300 96,000 72,000

89

Cash Disbursements Payments for Purchases Rent Other Expenditures Tax Deposits Interest on Short-Term Borrowing Total Disbursements Net Monthly Change Analysis of Borrowing Needs Beginning Cash Balance Ending Cash (No Borrow) Needed (Borrowing)

157,200

110,400

May 180,000

June 200,000

July 168,000

54,000 45,600 44,800

60,000 54,000 60,800

50,400 60,000 72,000

130,400

144,400

174,800

84,000 96,000 188,300

114,000 84,000 157,200

135,000 114,000 110,400

150,000 135,000 130,400

126,000 150,000 144,400

132,000 126,000 1320,000 174,800 182,400

96,000 12,000 20,000

84,000 12,000 20,000

114,000 12,000 20,000 26,500

135,000 12,000 20,000

150,000 12,000 20,000

126,000 12,000 20,000 26,500 318

$128,000 $116,000

132,000 12,000 20,000 418

$172,500

$167,000 $182,000 $184,818 $164,418 -$36,600 -$37,600 -$10,018

$60,300

$41,200

-$62,100

28,000 88,300 0

88,300 129,500 0

129,500 67,400 0

67,400 30,800 0

30,800 -6,800 31,800

25,000 14,982 10,018

$17,982 25,000 42,982

August 176,000

182,400

Loan Repayment Ending Cash Balance Cumulative Borrowing

0 0 $88,300 $129,500 0 0

0 $67,400 0

0 $30,800 0

94

0 $25,000 $31,800

0 $ 25,000 $41,818

(17,982) $25,000 23,836

b.

Halsey will not be able to retire the $200,000 note at the end of July. July Ending

Sales Levels

Cash Balance Expected +20% -20%

$25,000 25,000 25,000

250

CHAPTER 5

The Time Value of Money CHAPTER ORIENTATION In this chapter the concept of a time value of money is introduced, that is, a dollar today is worth more than a dollar received a year from now. Thus if we are to logically compare projects and financial strategies, we must either move all dollar flows back to the present or out to some common future date.

CHAPTER OUTLINE I.

Compound interest results when the interest paid on the investment during the first period is added to the principal and during the second period the interest is earned on the original principal plus the interest earned during the first period. A.

Mathematically, the future value of an investment if compounded annually at a rate of i for n years will be FVn = PV (l + i)n where n = the number of years during which the compounding occurs i = the annual interest (or discount) rate PV = the present value or original amount invested at the beginning of the first period FVn = the future value of the investment at the end of n years 1.

The future value of an investment can be increased by either increasing the number of years we let it compound or by compounding it at a higher rate.

2.

If the compounded period is less than one year, the future value of an investment can be determined as follows: FVn

=

PV

mn

where m= the number of times compounding occurs during the year

251

II.

Determining the present value, that is, the value in today's dollars of a sum of money to be received in the future, involves nothing other than inverse compounding. The differences in these techniques come about merely from the investor's point of view. A.

Mathematically, the present value of a sum of money to be received in the future can be determined with the following equation: PV where:

1.

III.

= n i PV FVn

FVn = = = =

the number of years until payment will be received, the interest rate or discount rate the present value of the future sum of money the future value of the investment at the end of n years

The present value of a future sum of money is inversely related to both the number of years until the payment will be received and the interest rate.

An annuity is a series of equal dollar payments for a specified number of years. Because annuities occur frequently in finance, for example, bond interest payments, we treat them specially. A.

A compound annuity involves depositing or investing an equal sum of money at the end of each year for a certain number of years and allowing it to grow. 1.

This can be done by using our compounding equation, and compounding each one of the individual deposits to the future or by using the following compound annuity equation: FVn where:

 n −1 t PMT   ∑ (1 + i)   t =0 

= PMT

= the annuity value deposited at the end of each year = the annual interest (or discount) rate = the number of years for which the annuity will last = the future value of the annuity at the end of the nth year

i n FVn B.

Pension funds, insurance obligations, and interest received from bonds all involve annuities. To compare these financial instruments we would like to know the present value of each of these annuities. 1.

This can be done by using our present value equation and discounting each one of the individual cash flows back to the present or by using the following present value of an annuity equation: PV

=

 n PMT  ∑  t =1

252

1 (1 + i) t

   

where:

PMT

= the annuity deposited or withdrawn at the end of each year = the annual interest or discount rate = the present value of the future annuity = the number of years for which the annuity will last

i PV n C.

IV.

This procedure of solving for PMT, the annuity value when i, n, and PV are known, is also the procedure used to determine what payments are associated with paying off a loan in equal installments. Loans paid off in this way, in periodic payments, are called amortized loans. Here again we know three of the four values in the annuity equation and are solving for a value of PMT, the annual annuity.

Annuities due are really just ordinary annuities where all the annuity payments have been shifted forward by one year. Compounding them and determining their present value is actually quite simple. Because an annuity, due merely shifts the payments from the end of the year to the beginning of the year, we now compound the cash flows for one additional year. Therefore, the compound sum of an annuity due is FVn(annuity due) A.

VI.

PMT (FVIFAi,n) (1 + i)

Likewise, with the present value of an annuity due, we simply receive each cash flow one year earlier – that is, we receive it at the beginning of each year rather than at the end of each year. Thus the present value of an annuity due is PV(annuity due)

V.

=

=

PMT (PVIFAi,n) (1 + i)

A perpetuity is an annuity that continues forever, that is every year from now on this investment pays the same dollar amount. A.

An example of a perpetuity is preferred stock which yields a constant dollar dividend infinitely.

B.

The following equation can be used to determine the present value of a perpetuity: PV = where: PV = the present value of the perpetuity pp = the constant dollar amount provided by the perpetuity i = the annual interest or discount rate

To aid in the calculations of present and future values, tables are provided at the back of Financial Management (FM). A.

To aid in determining the value of FVn in the compounding formula FVn

=

PV (1 + i)n = PV (FVIFi,n)

tables have been compiled for values of FVIFi,n or (i + 1)n in Appendix B, "Compound Sum of $1," in FM.

253

B.

To aid in the computation of present values PV

=

FVn = FVn (PVIFi,n)

tables have been compiled for values of or PVIFi,n and appear in Appendix C in the back of FM. C.

Because of the time-consuming nature of compounding an annuity, FVn

=

PMT

n −1

∑ t =0

(1 + i) t

= PMT (FVIFAi,n)

Tables are provided in Appendix D of FM for n −1

∑ t =0

(1 + i) t or FVIFAi,n

for various combinations of n and i. D.

To simplify the process of determining the present value of an annuity  n PV = PMT  ∑  t =1

  (1 + i)   1

t

= PMT (PVIFAi,n)

tables are provided in Appendix E of FM for various combinations of n and i for the value n

1

t =1

(1 +i) t

∑

or PVIFAi,n

V. Spreadsheets and the Time Value of Money. A.

While there are several competing spreadsheets, the most popular one is Microsoft Excel. Just as with the keystroke calculations on a financial calculator, a spreadsheet can make easy work of most common financial calculations. Listed below are some of the most common functions used with Excel when moving money through time:

Calculation:

Formula:

Present Value Future Value Payment

= PV(rate, number of periods, payment, future value, type) = FV(rate, number of periods, payment, present value, type) = PMT(rate, number of periods, present value, future value, type) Number of Periods = NPER(rate, payment, present value, future value, type) Interest Rate = RATE(number of periods, payment, present value, future value, type, guess)

254

where: rate = i, the interest rate or discount rate number of periods = n, the number of years or periods payment = PMT, the annuity payment deposited or received at the end of each period future value = FV, the future value of the investment at the end of n periods or years present value = PV, the present value of the future sum of money type = when the payment is made, (0 if omitted) 0 = at end of period 1 = at beginning of period guess = a starting point when calculating the interest rate, if omitted, the calculations begin with a value of 0.1 or 10%

ANSWERS TO END-OF-CHAPTER QUESTIONS 5-1.

The concept of time value of money is recognition that a dollar received today is worth more than a dollar received a year from now or at any future date. It exists because there are investment opportunities on money, that is, we can place our dollar received today in a savings account and one year from now have more than a dollar.

5-2.

Compounding and discounting are inverse processes of each other. In compounding, money is moved forward in time, while in discounting money is moved back in time. This can be shown mathematically in the compounding equation: FVn

=

PV (1 + i)n

We can derive the discounting equation by multiplying each side of this equation by and we get: PV 5-3.

=

FVn

=

PV(1 + i)n

We know that FVn

Thus, an increase in i will increase FVn and a decrease in n will decrease FVn. 5-4.

Bank C which compounds daily pays the highest interest. This occurs because, while all banks pay the same interest, 5 percent, bank C compounds the 5 percent daily. Daily compounding allows interest to be earned more frequently than the other compounding periods.

255

5-5.

The values in the present value of an annuity table (Table 5-8) are actually derived from the values in the present value table (Table 5-4). This can be seen, by examining the values represented in each table. The present value table gives values of for various values of i and n, while the present value of an annuity table gives values of n

1

t =1

(1 +i) t

∑

for various values of i and n. Thus the value in the present value of annuity table for an n-year annuity for any discount rate i is merely the sum of the first n values in the 10

present value table. PVIFA

10%,10yrs

= 6.145.

∑

PVIF10%,n = 6.144 = 0.909 +

n =1

0.826 + 0.751 + 0.683 + 0.621 + 0.564 + 0.513 + 0.467 + 0.424 + 0.386 5-6.

An annuity is a series of equal dollar payments for a specified number of years. Examples of annuities include mortgage payments, interest payments on bonds, fixed lease payments, and any fixed contractual payment. A perpetuity is an annuity that continues forever, that is, every year from now on this investment pays the same dollar amount. The difference between an annuity and a perpetuity is that a perpetuity has no termination date whereas an annuity does.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 5-1A. (a)

(b)

FVn

=

PV (1 + i)n

FV10

=

$5,000(1 + 0.10)10

FV10

=

$5,000 (2.594)

FV10

=

$12,970

FVn

=

PV (1 + i)n

FV7

=

$8,000 (1 + 0.08)7

FV7

=

$8,000 (1.714)

FV7

=

$13,712

256

(c)

(d)

5-2A. (a)

(b)

(c)

(d)

5-3A. (a)

FV12

=

PV (1 + i)n

FV12

=

$775 (1 + 0.12)12

FV12

=

$775 (3.896)

FV12

=

$3,019.40

FVn

=

PV (1 + i)n

FV5

=

$21,000 (1 + 0.05)5

FV5

=

$21,000 (1.276)

FV5

=

$26,796.00

FVn

=

PV (1 + i)n

$1,039.50

=

$500 (1 + 0.05)n

2.079

=

FVIF 5%, n yr.

Thus n

=

15 years (because the value of 2.079 occurs in the 15 year row of the 5 percent column of Appendix B).

FVn

=

PV (1 + i)n

$53.87

=

$35 (1 + .09)n

1.539

=

FVIF 9%, n yr.

Thus, n

=

5 years

FVn

=

PV (1 + i)n

$298.60

=

$100 (1 + 0.2)n

2.986

=

FVIF 20%, n yr.

Thus, n

=

6 years

FVn

=

PV (1 + i)n

$78.76 1.486

= =

$53 (1 + 0.02)n FVIF 2%, n yr.

Thus, n

=

20 years

FVn

=

PV (1 + i)n

$1,948 3.896

= =

$500 (1 + i)12 FVIF i%, 12 yr.

Thus, i

=

12% (because the Appendix B value of 3.896 occurs in

257

the 12 year row in the 12 percent column)

258

(b)

(c)

(d)

5-4A. (a)

(b)

(c)

FVn

=

PV (1 + i)n

$422.10

=

$300 (1 + i)7

1.407

=

FVIFi%, 7 yr.

Thus, i

=

5%

FVn

=

PV (1 + i)n

$280.20

=

$50 (1 + i)20

5.604

=

FVIF i%, 20 yr.

Thus, i

=

9%

FVn

=

PV (1 + i)n

$497.60

=

$200 (1 + i)5

=

FVIFi%, 5 yr.

Thus, i

=

20%

PV

=

FVn

PV

=

$800

PV

=

$800 (0.386)

PV

=

$308.80

PV

=

FVn

PV

=

$300

PV

=

$300 (0.784)

PV

=

$235.20

PV

=

FVn

PV

=

$1,000

PV

=

$1,000 (0.789)

PV

=

$789

259

(d)

5-5A. (a)

(b)

(c)

(d)

PV

=

FVn

PV

=

$1,000

PV

=

$1,000 (0.233)

PV

=

$233

FVn

=

t PMT   ∑ (1 + i) 

FV10

=

$500  

FV10

=

$500 (12.578)

FV10

=

$6,289

FVn

=

t PMT   ∑ (1 + i) 

FV5

=

t $100   ∑ (1 + 0.1) 

FV5

=

$100 (6.105)

FV5

=

610.50

=

t PMT   ∑ (1 + i) 

FV7

=

7 −1 $35   ∑ (1 + 0.07) t =0

FV7

=

$35 (8.654)

FV7

=

$302.89

FVn

=

t PMT   ∑ (1 + i) 

FV3

=

t $25   ∑ (1 + 0.02) 

FV3

=

$25 (3.060)

FV3

=

$76.50

FVn

n −1



 t =0



10 −1

∑

 t =0

(1 + 0.05)

 n −1



 t =0



5 −1



 t =0



n −1



 t =0



n −1



 t =0



t

   

3 −1



t =0



260

t

   

5-6A. (a)

(b)

(c)

(d)

5-7A. (a)



n

  (1 + i)   1

PV

=

PMT  ∑

PV

=

$2,500  ∑

PV

=

$2,500 (7.024)

PV

=

$17,560

PV

=

PMT  ∑

PV

=

 3 1 $70   ∑ (1 + 0.03)  t =1

PV

=

$70 (2.829)

PV

=

$198.03

PV

=

 n PMT  ∑  t =1

PV

=

$280  ∑

PV

=

$280 (5.582)

PV

=

$1,562.96

PV

=

PMT  ∑

PV

=

$500  ∑

PV

=

$500 (6.145)

PV

=

$3,072.50

FVn

=

PV (1 + i)n

 t =1

t

 10

1 (1 + 0.07)

 t =1



n

 t =1





  (1 + i) t   1

n

 t =1

 10

 t =1

  (1 + i)   1 (1 + 0.06)

   

  (1 + i)   t

  (1 + 0.1) t   1

=

$10,000 (1 + 0.06)1

FV1

=

$10,000 (1.06)

FV1

=

$10,600

compounded for 5 years $10,000 (1 + 0.06)5 261

t

1

FV1

=

   

t

compounded for 1 year

FV5

t

1

7

 t =1

t

   

FV5

=

$10,000 (1.338)

FV5

=

$13,380

compounded for 15 years

(b)

FV15

=

$10,000 (1 + 0.06)15

FV15

=

$10,000 (2.397)

FV15

=

$23,970

FVn

=

PV (1 + i)n

compounded for 1 year at 8% FV1

=

$10,000 (1 + 0.08)1

FV1

=

$10,000 (1.080)

FV1

=

$10,800

compounded for 5 years at 8% FV5

=

$10,000 (1 + 0.08)5

FV5

=

$10,000 (1.469)

FV5

=

$14,690

compounded for 15 years at 8% FV15

=

$10,000 (1 + 0.08)15

FV15

=

$10,000 (3.172)

FV15

=

$31,720

compounded for 1 year at 10% FV1

=

$10,000 (1 + 0.1)1

FV1

=

$10,000 (1 + 1.100)

FV1

=

$11,000

compounded for 5 years at 10% FV5

=

$10,000 (1 + 0.1)5

FV5

=

$10,000 (1.611)

FV5

=

$16,110

compounded for 15 years at 10%

(c)

FV15

=

$10,000 (1 + 0.1)15

FV15

=

$10,000 (4.177)

FV15 = $41,770 There is a positive relationship between both the interest rate used to 262

compound a present sum and the number of years for which the compounding continues and the future value of that sum. 5-8A.

FVn

=

Account Theodore Logan III Vernell Coles Thomas Elliott Wayne Robinson Eugene Chung Kelly Cravens 5-9A. (a)

(b)

(c)

FVn

=

PV (1 + )mn PV $ 1,000 95,000 8,000 120,000 30,000 15,000

i 10% 12% 12% 8% 10% 12%

m 1 12 6 4 2 3

PV (1 + i)n

FV5

=

$5,000 (1 + 0.06)5

FV5

=

$5,000 (1.338)

FV5

=

$6,690

FVn

=

PV (1 + )mn

FV5

=

$5,000 (1 + )

FV5

=

$5,000 (1 + 0.03)10

FV5

=

$5,000 (1.344)

FV5

=

$6,720

FVn

=

PV (1 + )mn

FV5

=

5,000 (1 + )

FV5

=

$5,000 (1 + 0.01)

FV5

=

$5,000 (1.348)

FV5

=

$6,740

FVn

=

PV (1 + i)n

FV5

=

$5,000 (1 + 0.12)

FV5

=

$5,000 (1.762)

FV5

=

$8,810

FV5

=

PV

FV5

=

$5,000

2X5

6X5

mn 2X5

263

30

5

n 10 1 2 2 4 3

(1 + )mn 2.594 1.127 1.268 1.172 1.477 1.423

PV(1 + )mn $ 2,594 107,065 10,144 140,640 44,310 21,345

(d)

(e)

5-10A.

FV5

=

$5,000 (1 + 0.06)10

FV5

=

$5,000 (1.791)

FV5

=

$8,955

FV5

=

PV mn

FV5

=

$5,000 6X5

FV5

=

$5,000 (1 + 0.02)30

FV5

=

$5,000 (1.811)

FV5

=

$9,055

FVn

=

PV (1 + i)n

FV12

=

$5,000 (1 + 0.06)

FV12

=

5,000 (2.012)

FV12

=

$10,060

12

An increase in the stated interest rate will increase the future value of a given sum. Likewise, an increase in the length of the holding period will increase the future value of a given sum. Annuity A:

PV

=

 n PMT  ∑  t =1

PV

=

$8,500  ∑

PV

=

$8,500 (6.492)

PV

=

$55,182

 12

 t =1

  (1 + i)   1

t

1 (1 + 0.11)

t

   

Since the cost of this annuity is $50,000 and its present value is $55,182, given an 11 percent opportunity cost, this annuity has value and should be accepted.

264

Annuity B:

=

 n PMT  ∑  t =1

PV

=

 25 $7,000  ∑  t =1

PV

=

$7,000 (8.442)

PV

=

$59,094

PV

  (1 + i) t   1

1 (1 + 0.11)

t

   

Since the cost of this annuity is $60,000 and its present value is only $59,094, given an 11 percent opportunity cost, this annuity should not be accepted. Annuity C:



n

PMT  ∑

  (1 + i)  

PV

=

PV

=

PV

=

$8,000 (7.963)

PV

=

$63,704

 t =1  20 $8,000  ∑  t =1

1

t

1 (1 + 0.11)

t

   

Since the cost of this annuity is $70,000 and its present value is only $63,704, given an 11 percent opportunity cost, this annuity should not be accepted. 5-11A. Year 1:FVn

Year 2:FVn

Year 3:

=

PV (1 + i)n

FV1

=

15,000(1 + 0.2)1

FV1

=

15,000(1.200)

FV1

=

18,000 books

=

PV (1 + i)n

FV2

=

15,000(1 + 0.2)2

FV2

=

15,000(1.440)

FV2

=

21,600 books

FVn

=

PV (1 + i)n

FV3

=

15,000(1.20)3

FV3

=

15,000(1.728)

FV3

=

25,920 books

265

Book sales The sales trend graph is not linear because this is a compound growth trend. Just as compound interest occurs when interest paid on the investment during the first period is added to the principal of the second period, interest is earned on the new sum. Book sales growth was compounded; thus, the first year the growth was 20 percent of 15,000 books for a total of 18,000 books, the second year 20 percent of 18,000 books for a total of 21,600, and the third year 20 percent of 21,600 books for a total of 25,920. 5-12A.

25,000

FVn

=

PV (1 + i)n

FV1 FV1 FV1

= = =

FV2 FV2 FV2

= = =

41(1 + 0.10)1 41(1.10) 45.1 Home Runs in 1981 (in spite of the baseball strike). 41(1 + 0.10)2

FV3 FV3 FV3

= = =

FV4 FV4 FV4

= = =

FV5 FV5

= =

41(1.21) 49.61 Home Runs in 1982 41(1 + 0.10)3 41(1.331) 54.571 Home Runs in 1983. 41(1 + 0.10)4

20,000

41(1.464) 60.024 Home Runs in 1984. 41(1 + 0.10)5 41(1.611)

266

FV5 5-13A.

5-14A.

5-15A.

=

66.051 Home Runs in 1985 (for a new major league record). 

  (1 + i)  

n

1

PV

=

PMT  ∑

$60,000

=

PMT  ∑

$60,000 Thus, PMT

= =

PMT (9.823) $6,108.11 per year for 25 years.

=

n −1 PMT  ∑ t =0

 (1 + i) t   

$15,000

=

15 −1 PMT  ∑  t =0

(1 + 0.06)

$15,000

=

PMT (23.276)

Thus, PMT

=

$644.44

FVn

=

PV (1 + i)n

$1,079.50

=

$500 (FVIF i%, 10 yr.)

2.159

=

FVIF i%, 10 yr.

Thus, i

=

8%

FVn

t

 t =1



25

t =1

1 (1 + 0.09)

t

   

t

   

5-16A. The value of the home in 10 years FV10

=

PV (1 + .05)10

=

$100,000(1.629)

=

$162,900

How much must be invested annually to accumulate $162,900?

5-17A.

$162,900

=

10 −1 PMT  ∑  t =0

$162,900

=

PMT(15.937)

PMT

=

$10,221.50

FVn

=

PMT  ∑

$10,000,000

=

PMT  

$10,000,000

=

PMT(15.193)

Thus, PMT

=

$658,197.85

n −1 t =0

10 −1

∑

 t =0

267

 (1 + .10) t   

 (1 + i) t   

 (1 +.09) t   

5-18A.

One dollar at 12.0% compounded monthly for one year FVn

=

PV nm

FV1

=

$1(1 + .01)1

=

$1(1.127)

=

$1.127

One dollar at 13.0% compounded annually for one year FVn

=

PV (1 + i)n

FV1

=

$1(1 + .13)1

=

$1(1.13)

=

$1.13

The loan at 12% compounded monthly is more attractive. 5-19A. Investment A PV



  (1 + i)  

n

i

=

PMT  ∑

=

$10,000  ∑

=

$10,000(2.991)

=

$29,910

t

 t =1 

  (1 + .20)  

5

1

t

 t =1

Investment B First, discount the annuity back to the beginning of year 5, which is the end of year 4. Then, discount this equivalent sum to present. PV

= =

PV



n

PMT  ∑

 t =1  6 $10,000  ∑  t =1

  (1 + .20)   1

t

=

$10,000(3.326)

= = =

$33,260--then discount the equivalent sum back to present. FVn $33,260

=

$33,260(.482)

=

$16,031.32

=

FVn

Investment C PV

  (1 + i) t   1

268

=

$10,000 + $50,000 + $10,000

5-20A.

5-21A. (a)

(b)

(c)

(d)

5-22A.

5-23A.

=

$10,000(.833) + $50,000(.335) + $10,000(.162)

=

$8,330 + $16,750 + $1,620

=

$26,700

PV

=

FVn

PV

=

$1,000

PV

=

$1,000(.513)

PV

=

$513

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

$3,750

$8,333.33

$1,111.11

$1,900

PV(annuity due) =

PMT(PVIFAi,n)(l+i)

=

$1,000(6.145)(1+.10)

=

$6145(1.10)

=

$6759.50

FVn

=

. PV (1 + )m n

4

=

. 1(1 + )2 n

4

=

. (1 + 0.08)2 n

4

=

FVIF 8%, 2n yr.

A value of 3.996 occurs in the 8 percent column and 18-year row of the table in Appendix B. Therefore, 2n = 18 years and n = approximately 9 years.

269

5-24A. Investment A: PV

=

FVn (PVIFi,n)

PV

=

$2,000(PVIF10%, year 1) + $3,000(PVIF10%, year 2) + $4,000(PVIF10%, year 3) - $5,000(PVIF10%, year 4) + $5,000(PVIF10%, year 5)

= $2,000(.909) + $3,000(.826) + $4,000(.751) $5,000(.683) + $5,000(.621)

Investment B: PV PV

=

$1,818 + $2,478 + $3,004 - $3,415 + $3,105

=

$6,990.

=

FVn (PVIFi,n)

=

$2,000(PVIF10%, year 1) + $2,000(PVIF10%, year 2) + $2,000(PVIF10%, year 3) + $2,000(PVIF10%, year 4) + $5,000(PVIF10%, year 5)

=

$2,000(.909) + $2,000(.826) + $2,000(.751) + $2,000(.683) + $5,000(.621)

=

$1,818 + $1,652 + $1,502 + $1,366 + $3,105

=

$9,443.

270

Investment C: PV

=

FVn (PVIFi,n)

PV

=

$5,000(PVIF10%, year 1) + $5,000(PVIF10%, year 2) $5,000(PVIF10%, year 3) - $5,000(PVIF10%, year 4) + $15,000(PVIF10%, year 5)

= $5,000(.909) + $5,000(.826) - $5,000(.751) $5,000(.683) + $15,000(.621)

5-25A.

=

$4,545 + $4,130 - $3,755 - $3,415 + $9,315

=

$10,820.

The Present value of the $10,000 annuity over years 11-15. PV

=

  15 PMT   ∑   t =1

=

$10,000(9.712 - 7.360)

=

$10,000(2.352)

=

$23,520

1 (1 + .06) t

  10  −  ∑   t =1

1 (1 + .06) t

The present value of the $20,000 withdrawal at the end of year 15: PV

=

FV15

=

$20,000(.417)

=

$8,340

Thus, you would have to deposit $23,520 + $8,340 or $31,860 today. 5-26A.

5-27A.

5-28A.

PV

=

 10 PMT  ∑  t =1

$40,000

=

PMT (6.145)

PMT

=

$6,509

PV

=

 5 PMT  ∑  t =1

$30,000

=

$10,000 (PVIFAi%, 5 yr.)

3.0

=

PVIFAi%, 5 yr.

i

=

20%

PV

=

FVn

271

  (1 + .10) t   1

  (1 + i)   1

t

   

5-29A.

5-30A.

$10,000

=

$27,027 (PVIFi%, 5 yr.)

.370

=

PVIF22%, 5 yr.

Thus, i

=

22%

PV

=

PMT  ∑

$25,000

=

PMT  ∑

$25,000

=

PMT (3.605)

PMT

=

$6,934.81

 n

  t (1 + i) t = 1   1

 5

  t t = 1 (1 + .12)   1

The present value of $10,000 in 12 years at 11 percent is: 

1 n  (1 + i)

PV

=

FVn  

PV

=

$10,000  

PV

=

$10,000 (.286)

PV

=

$2,860

   



1  (1 +.11)

12

   

The present value of $25,000 in 25 years at 11 percent is: PV



1 (1 + .11) 

=

$25,000  

=

$25,000 (.074)

=

$1,850

   

25

Thus take the $10,000 in 12 years. 5-31A.

n −1



 t =0



=

t PMT   ∑ (1 + i) 

$20,000

=

 5 −1 PMT   ∑ (1 + .12) t =0

$20,000

=

PMT(6.353)

PMT

=

$3,148.12

FVn

272

t

   

5-32A. (a)

(b)

(c)

n −1



 t =0



FVn

=

t PMT   ∑ (1 + i) 

$50,000

=

PMT  

$50,000

=

PMT (FVIFA7%, 15 yr.)

$50,000

=

PMT(25.129)

PMT

=

$1,989.73. per year

PV

=

FVn

PV

=

$50,000 (PVIF7%, 15 yr.)

PV

=

$50,000(.362)

PV

=

$18,100 deposited today

15 −1

∑

 t =0

 (1 +.07) t   

The contribution of the $10,000 deposit toward the $50,000 goal is FVn

=

PV(1 + i)n

FVn

=

$10,000 (FVIF7%, 10 yr.)

FV10

=

$10,000(1.967)

=

$19,670

Thus only $30,330 need be accumulated by annual deposit.

5-33A. (a)

n −1



 t =0



FVn

=

t PMT   ∑ (1 + i) 

$30,330

=

PMT (FVIFA7%, 15 yr.)

$30,330

=

PMT [25.129]

PMT

=

$1,206.97 per year

This problem can be subdivided into (1) the compound value of the $100,000 in the savings account (2) the compound value of the $300,000 in stocks, (3) the additional savings due to depositing $10,000 per year in the savings account for 10 years, and (4) the additional savings due to depositing $10,000 per year in the savings account at the end of years 6-10. (Note the $20,000 deposited in years 6-10 is covered in parts (3) and (4).) (1)

Future value of $100,000 FV10

=

$100,000 (1 + .07)10

FV10

=

$100,000 (1.967)

FV10

=

$196,700

273

(2)

Future value of $300,000 FV10

=

$300,000 (1 + .12) 10

FV10

=

$300,000 (3.106)

10

=

$931,800

FV (3)

Compound annuity of $10,000, 10 years FV10

(4)

=

 n −1  PMT  ∑ (1 + i) t  t =0 

=

10 −1  $10,000  ∑ (1 + .07) t   t =0 

=

$10,000 (13.816)

=

$138,160

Compound annuity of $10,000 (years 6 - 10) FV5

 5 −1



t =0



=

t $10,000   ∑ (1 + .07) 

=

$10,000 (5.751)

=

$57,510

At the end of ten years you will have $196,700 + $931,800 + $138,160 + $57,510 = $1,324,170. (b)

5-34A.

5-35A.



20

  (1 + .10)   1

PV

=

PMT  ∑

$1,324,170

=

PMT (8.514)

PMT

=

$155,528

PV

=

PMT (PVIFAi%, n yr.)

$100,000

=

PMT (PVIFA15%, 20 yr.)

$100,000

=

PMT(6.259)

PMT

=

$15,977

PV

=

PMT (PVIFAi%, n yr.)

$150,000

=

PMT (PVIFA10%, 30 yr.)

$150,000

=

PMT(9.427)

PMT

=

$15,912

 t =1

274

t

5-36A.

At 10%: PV

=

$50,000 + $50,000 (PVIFA10%, 19 yr.)

PV

=

$50,000 + $50,000 (8.365)

PV

=

$50,000 + $418,250

PV

=

$468,250

PV

=

$50,000 + $50,000 (PVIFA20%, 19 yr.)

PV

=

$50,000 + $50,000 (4.843)

PV

=

$50,000 + $242,150

PV

=

$292,150

FVn(annuity due)

=

PMT(FVIFAi,n)(l+i)

=

$1000(FVIFA10%,10 years)(1+.10)

=

$1000(15.937)(1.1)

=

$17,530.70

=

PMT(FVIFAi,n)(l+i)

=

$1,000(FVIFA15%,10 years)(1+.15)

=

$1,000(20.304)(1.15)

=

$23,349.60

=

PMT(PVIFAi,n)(l+i)

=

$1,000(PVIFA10%,10 years)(1+.10)

=

$1,000(6.145)(1.10)

=

$6,759.50

=

PMT(PVIFAi,n)(l+i)

=

$1,000(PVIFA15%,10 years)(l+.15)

=

$1,000(5.019)(1.15)

=

$5,771.85

At 20%:

5-37A.

FVn(annuity due)

5-38A.

PV (annuity due)

PV (annuity due)

5-39A.

PV

=

PMT(PVIFAi,n)(PVIFi,n)

=

PMT(PVIFA10%,10 years)(PVIF10%,7 years)

=

$1,000(6.145)(.513)

=

$3,152.39

275

5-40A.

FVn

=

PV (FVIFi%, n yr.)

$6,500

=

.12(FVIFi%, 37 yr.)

solving using a financial calculator: i

=

34.2575%

5-41A. (a) 1/04

1/09

1/14

1/19

1/24

1/29

$50,000 $50,000 per year

$250,000

$100,000

There are a number of equivalent ways to discount these cash flows back to present, one of which is as follows (in equation form): PV

=

$50,000(PVIFA10%, 19 yr. - PVIFA10%, 4 yr.) + $250,000(PVIF10%, 20 yr.) + $50,000(PVIF10%, 23 yr. + PVIF10%, 24 yr.) + $100,000 (PVIF10%, 25 yr.)

=

$50,000 (8.365-3.170) + $250,000 (.149) + $50,000 (0.112 + .102) + $100,000 (.092)

(b) life.

=

$259,750 + $37,250 + $10,700 + $9,200

=

$316,900

If you live longer than expected you could end up with no money later on in

276

5-42A.

rate (i) number of periods (n) payment (PMT) present value (PV) type (0 = at end of period)

= = = = =

8% 7 $0 $900 0

Future value

=

$1,542.44

Excel formula: =FV(rate,number of periods,payment,present value,type) Notice that present value ($900) took on a negative value. 5-43A In 20 years you’d like to have $250,000 to buy a home, but you only have $30,000. At what rate must your $30,000 be compounded annually for it to grow to $250,000 in 20 years? number of periods (n) payment (PMT) present value (PV) future value (FV) type (0 = at end of period) guess i

= = = = = = =

20 $0 $30,000 $250,000 0 11.18%

Excel formula: =RATE(number of periods,payment,present value,future value,type,guess) Notice that present value ($30,000) took on a negative value. 5-44A. To buy a new house you take out a 25 year mortgage for $300,000. What will your monthly interest rate payments be if the interest rate on your mortgage is 8 percent? Two things to keep in mind when you're working this problem: first, you'll have to convert the annual rate of 8 percent into a monthly rate by dividing it by 12, and second, you'll have to convert the number of periods into months by multiplying 25 times 12 for a total of 300 months. Excel formula: =PMT(rate,number of periods,present value,future value,type) rate (i) number of periods (n) present value (PV) future value (FV) type (0 = at end of period)

= = = = =

monthly mortgage payment =

8%/12 300 $300,000 $0 0 ($2,315.45)

277

Notice that monthly payments take on a negative value because you pay them. You can also use Excel to calculate the interest and principal portion of any loan amortization payment. You can do this using the following Excel functions: Calculation:

Formula:

Interest portion of payment

=IPMT(rate,period,number of periods,present value,future value,type)

Principal portion of payment

=PPMT(rate,period,number of periods,present value,future value,type)

Where period refers to the number of an individual periodic payment. Thus, if you would like to determine how much of the 48th monthly payment went toward interest and principal you would solve as follows: Interest portion of payment 48:

($1,884.37)

The principal portion of payment 48: 5-45A.a.

b.

N

=

378

I/Y

=

6

PV

=

-24

PMT

=

0

CPT FV =

88.27 billion dollars

N

=

10

I/Y

=

10

CPT PV

c.

CPT I/Y

d.

($431.08)

=

-77.108 billion dollars

PMT

=

0

FV

=

200. billion

N

=

10

=

14.87%

PV

=

-50 billion

PMT

=

0

FV

=

200. billion

N

=

40

I/Y

=

7

PV

=

-100. billion

CPT PMT =

7.5 billion dollars

278

FV

=

0

279

5-46A. What will the car cost in the future? N

=

6

I/Y

=

3

PV

=

-15,000

PMT

=

0

CPT FV

=

17,910.78 dollars

How much must Bart put in an account today in order to have $17,910.78 in 6 years?

5-47A.

N

=

6

I/Y

=

7.5

CPT PV =

-11,605.50 dollars

PMT

=

0

FV

=

17,910.78

N

=

45

I/Y

=

8.75

PV

=

0

CPT PMT

= FV

-2,054.81 dollars

= 1,000,000

5-48A.First, we must calculate what Mr. Burns will need in 20 years, then we will know what he needs in 20 years and we can then calculate how much he needs to deposit each year in order to come up with that amount (note: once you calculate the present value, you must multiply your answer, in this case -$4.192 billion times (1 + i) because this is an annuity due): N

=

10

I/Y

=

20

CPT PV =

-4.1925 billion × 1.20 = -5.031 billion dollars

PMT

=

1 billion

FV

=

0

Next, we will determine how much Mr. Burns needs to deposit each year for 20 years to reach this goal of accumulating $5.031 billion at the end of the 20 years: N

=

20

I/Y

=

20

PV

=

0

CPT PMT= -26.9 million dollars

280

FV

=

5.031 billion

5-49A. What’s the $100,000 worth in 25 years (keep in mind that Homer invested the money 5 years ago and we want to know what it will be worth in 20 years)? N

=

25

I/Y

=

7.5

PV

=

-100,000

PMT

=

0

CPT FV =

609,833.96 dollars

Now we determine what the additional $1,500 per year will grow to (note that since Homer will be making these investments at the beginning of each year for 20 years we have an annuity due, thus, once you calculate the present value, you must multiply your answer, in this case $64,957.02 times (1 + i)): N

=

20

I/Y

=

7.5

PV

=

0

PMT

=

-1,500 64,957.02 × 1.075 = 69,828.80 dollars

CPT FV =

Finally, we must add the two values together: $609,833.96

+

$69,828.80

=

$679,662.76

5-50A. Since this problem involves monthly payments we must first, make P/Y = 12. Then, N becomes the number of months or compounding periods, N

=

60

I/Y

=

6.2

PV

=

-25,000

CPT PMT=

485.65 dollars

FV

0

=

5-51A. Since this problem involves monthly payments we must first, make P/Y = 12. Then, N becomes the number of months or compounding periods, N

=

36

CPT I/Y =

11.62%

PV

=

-999

PMT

=

33

FV

=

0

281

5-52A. First, what will be the monthly payments if Suzie goes for the 4.9 percent financing? Since this problem involves monthly payments we must first, make P/Y = 12. Then, N becomes the number of months or compounding periods, N

=

60

I/Y

=

4.9

PV

=

-25,000

CPT PMT=

470.64 dollars

FV

0

=

Now, calculate how much the monthly payments would be if Suzie took the $1,000 cash back and reduced the amount owed from $25,000 to $24,000. Again, since this problem involves monthly payments we must first, make P/Y = 12. N

=

60

I/Y

=

6.9

PV

=

-24,000

CPT PMT =

474.10 dollars

FV

0

=

5-53A. Since this problem involves quarterly compounding we must first, make P/Y = 4. Then, N becomes the number of quarters or compounding periods, N

=

16

I/Y

=

6.4%

PV

=

0

PMT

=

-1000

CPT FV = 18,071.11 dollars 5-54A. There are several ways you could solve this problem. One way would be to calculate the future value of an amount, say $100, deposited in each of these CDs would grow to at the end of a year. Let’s try this first. Since the first part of this problem involves daily compounding we must first, make P/Y = 365. Then, N becomes the number of days in a year, N

=

365

I/Y

=

4.95

PV

=

-100

PMT

=

0

CPT FV =

105.0742 or 5.0742%

282

Now, let’s look at monthly compounding we must first, and again, we’ll see what $100 will grow to at the end of a year. First, we make P/Y = 12. N

=

12

I/Y

=

5.0

PV

=

-100

PMT

=

0

CPT FV =

105.1162 or 5.1162%

An alternative approach would be to use the ICONV button on a Texas Instruments BA II-Plus calculator. That button calculates the APY, or annual percentage yield, also called the effective rate. 5-55A. Since this problem involves monthly payments we must first, make P/Y = 12. Then, N becomes the number of months or compounding periods, CPT N = 41.49 (rounded up to 42 months) I/Y =

12.9

PV =

-5000

PMT = 150 FV = 5-56A. a.

Since this problem begins using annual payments, make sure your calculator is set to P/Y=1. N

b.

0

=

12

CPT I/Y =

8.37%

PV

=

-160,000

PMT

=

0

FV

=

420,000

Again, since this problem begins using annual payments, make sure your calculator is set to P/Y=1 N

=

CPT I/Y

10

=

11.6123%

PV

=

-140,000

PMT

=

0

FV

=

420,000

283

c.

d.

Since this problem now involves monthly payments we must first, make P/Y = 12. Then, N becomes the number of months or compounding periods, N

=

120

I/Y

=

6

PV

=

-140,000

CPT PMT =

-1,008.57 dollars

FV

420,000

=

Since this problem now involves monthly payments we must first, make P/Y = 12. Then, N becomes the number of months or compounding periods. Also, since Professor ME will be depositing both the $140,000 (immediately) and $500 (monthly), they must have the same sign, N

=

120

CPT I/Y =

8.48%

PV

=

-140,000

PMT

=

-500

FV

=

420,000

SOLUTION TO INTEGRATIVE PROBLEM 1.

Discounting is the inverse of compounding. We really only have one formula to move a single cash flow through time. In some instances we are interested in bringing that cash flow back to the present (finding its present value) when we already know the future value. In other cases we are merely solving for the future value when we know the present value.

2.

The values in the present value of an annuity table (Table 5-8) are actually derived from the values in the present value table (Table 5-4). This can be seen, by examining the value, represented in each table. The present value table gives values of for various values of i and n, while the present value of an annuity table gives values of n 1 ∑ t =1 (1 + i) t

for various values of i and n. Thus the value in the present value of annuity table for an n-year annuity for any discount rate i is merely the sum of the first n values in the present value table. 3.

(a)

FVn

=

PV (1 + i)n

284

(b)

(c)

4.

5.

6.

FV10

=

$5,000(1 + 0.08)10

FV10

=

$5,000 (2.159)

FV10

=

$10,795

FVn

=

PV (1 + i)n

$1,671 =

$400 (1 + 0.10)n

4.1775 =

FVIF 10%, n yr.

Thus n=

15 years (because the value of 4.177 occurs in the 15 year row of the 10 percent column of Appendix B).

FVn

PV (1 + i)n

=

$4,046 =

$1,000 (1 + i)10

4.046 =

FVIF i%, 10 yr.

Thus, i =

15% (because the Appendix B value of 4.046 occurs in the 10 year row in the 15 percent column)

FVn

=

PV

=

$1,000

=

$1,000(1+.05)

=

$1,629

mn 2•5 10

An annuity due is an annuity in which the payments occur at the beginning of each period as opposed to occurring at the end of each period, which is when the payment occurs in an ordinary annuity. PV

PV(annuity due)

=

PMT(PVIFAi,n)

=

$1,000(PVIFA10%,7 years)

=

$1,000(4.868)

=

$4,868

=

PMT(PVIFAi,n)(l+i)

=

$1000(4.868)(l+.10)

=

$5,354.80

285

7.

FVn

FVn(annuity due)

8.

=

PMT(FVIFAi,n)

=

$1,000(9.487)

=

$9,487

=

PMT(FVIFAi,n)(l+i)

=

$1000(9.487)(l+.10)

=

$10,435.70

PV

=

PMT(PVIFAi,n)

$100,000

=

PMT(PVIFA10%, 25 years)

$100,000

=

PMT(9.077)

$11,016.86 = 9.

PV

PMT

= =

10.

11.

PV

PV

=

$12,500

=

PMT(PVIFAi,n)(PVIFi,n)

=

$1,000(PVIFA10%,10 years)(PVIF10%, 9 years)

=

$1,000(6.145)(.424)

=

$2,605.48

= =

(PVIF10%, 9 years)

= = 12.

APY

$4,240.00 m

=

4

=

-1

-1

=

4 [1 + .02] - 1

=

1.0824 - 1

=

.0824 or 8.24%

Solutions to Problem Set B 5-1B. (a)

FVn FV11

=

PV (1 + i)n =

$4,000(1 + 0.09)11

286

(b)

(c)

(d)

5-2B. (a)

(b)

(c)

(d)

FV11

=

$4,000 (2.580)

FV11

=

$10,320

FVn

=

PV (1 + i)n

FV10

=

$8,000 (1 + 0.08)10

FV10

=

$8,000 (2.159)

FV10

=

$17,272

FVn

=

PV (1 + i)n

FV12

=

$800 (1 + 0.12)12

FV12

=

$800 (3.896)

FV12

=

$3,117

FVn

=

PV (1 + i)n

FV6

=

$21,000 (1 + 0.05)6

FV6

=

$21,000 (1.340)

FV6

=

$28,140

FVn

=

PV (1 + i)n

$1,043.90

=

$550 (1 + 0.06)n

1.898

=

FVIF6%, n yr.

Thus n

=

11 years (because the value of 1.898 occurs in the 11 year row of the 6 percent column of Appendix B).

FVn

=

PV (1 + i)n

$88.44

=

$40 (1 + .12)n

2.211

=

FVIF12%, n yr.

Thus, n

=

7 years

FVn

=

PV (1 + i)n

$614.79

=

$110 (1 + 0.24)n

5.589

=

FVIF24%, n yr.

Thus, n

=

8 years

FVn

=

PV (1 + i)n

287

5-3B. (a)

(b)

(c)

(d)

5-4B. (a)

(b)

(c)

$78.30

=

$60 (1 + 0.03)n

1.305

=

FVIF3%, n yr.

Thus, n

=

9 years

FVn

=

PV (1 + i)n

$1,898.60

=

$550 (1 + i)13

3.452

=

FVIFi%, 13 yr.

Thus, i

=

10% (because the Appendix B value of 3.452 occurs in the 13 year row in the 10 percent column)

FVn

=

PV (1 + i)n

$406.18

=

$275 (1 + i)8

1.477

=

FVIFi%, 8 yr.

Thus, i

=

5%

FVn

=

PV (1 + i)n

$279.66

=

$60 ( 1 + i)20

4.661

=

FVIFi%, 20 yr.

Thus, i

=

8%

FVn

=

PV ( 1 + i)n

$486.00

=

$180 (1 + i)6

2.700

=

FVIFi%, 6 yr.

Thus, i

=

18%

PV

=

FVn

PV

=

$800

PV

=

$800 (0.386)

PV

=

$308.80

PV

=

FVn

PV

=

$400

PV

=

$400 (0.705)

PV

=

$282.00

PV

=

FVn

288

(d)

5-5B. (a)

(b)

PV

=

$1,000

PV

=

$1,000 (0.677)

PV

=

$677

PV

=

PV

=

$900

PV

=

$900 (0.194)

PV

=

$174.60

FVn

=

 n −1 PMT  ∑ t =0

FV10

=

10 −1 t  $500  ∑ (1 + 0.06)   t =0 

FV10

=

$500 (13.181)

FV10

=

$6,590.50

FVn

=

 n −1 PMT  ∑ t =0

FV5

=

 5 −1 $150  ∑ t =0

FV5

=

$150 (6.228)

FV5

=

$934.20

FVn

289

 (1 + i) t  

 (1 + i) t    (1 + 0.11) t  

(c)

(d)

5-6B. (a)

(b)

(c)

FVn

=

 n −1  PMT  ∑ (1 + i) t  t =0 

FV8

=

 8 −1 $35  ∑ t =0

FV8

=

$35 (10.260)

FV8

=

$359.10

FVn

=

 n −1  PMT  ∑ (1 + i) t  t =0 

FV3

=

 3 −1 t $25  ∑ (1 + 0.02)  t =0 

FV3

=

$25 (3.060)

FV3

=

$76.50

PV

=



 (1 + 0.07) t  

  (1 + i) t  

n

1

PMT  ∑

 t =1

 10

1

PV

=

$3,000  ∑

PV

=

$3,000 (6.710)

PV

=

$20,130

PV

=

PMT  ∑

  (1 + i) t  

PV

=

$50  ∑



1

PV

=

$50 (2.829)

PV

=

$141.45

PV

=

PMT  ∑

PV

=

$280  ∑

PV

=

$280 (5.971)

PV

=

$1,671.88



n

 t =1 3

 t =1



n

 t =1



8

 t =1

290

t

(1 + 0.08)

t =1

   

1

(1 + 0.03)

t

   

  (1 + i)   1

t

1 (1 + 0.07)

t

   

(d)

5-7B. (a)



n

PV

=

PMT  ∑

PV

=

$600  ∑

PV

=

$600 (6.145)

PV

=

$3,687.00

FVn

=

PV (1 + i)n

 t =1

  (1 + i) t   1

 10

 t =1

1 (1 + 0.1)

compounded for 1 year FV1

=

$20,000 (1 + 0.07)1

FV1

=

$20,000 (1.07)

FV1

=

$21,400

compounded for 5 years FV5

=

$20,000 (1 + 0.07)5

FV5

=

$20,000 (1.403)

FV5

=

$28,060

compounded for 15 years

(b)

FV15

=

$20,000 (1 + 0.07)15

FV15

=

$20,000 (2.759)

FV15

=

$55,180

FVn

=

PV (1 + i)n

compounded for 1 year at 9% FV1

=

$20,000 (1 + 0.09)1

FV1

=

$20,000 (1.090)

FV1

=

$21,800

compounded for 5 years at 9% FV5

=

$20,000 (1 + 0.09)5

FV5

=

$20,000 (1.539)

FV5

=

$30,780

compounded for 15 years at 9% FV5 FV5

=

$20,000 (1 + 0.09)15 = $20,000 (3.642)

291

t

   

FV5

=

$72,840

compounded for 1 year at 11% FV1

=

$20,000 (1 + 0.11)1

FV1

=

$20,000 (1.11)

FV1

=

$22,200

compounded for 5 years at 11% FV5

=

$20,000 (1 + 0.11)5

FV5

=

$20,000 (1.685)

FV5

=

$33,700

compounded for 15 years at 11%

(c)

5-8B.

FV5

=

$20,000 (1 + 0.11)15

FV5

=

$20,000 (4.785)

FV5 = $95,700 There is a positive relationship between both the interest rate used to compound a present sum and the number of years for which the compounding continues and the future value of that sum. FVn

=

Account Korey Stringer Erica Moss Ty Howard Rob Kelly Mary Christopher Juan Diaz 5-9B. (a)

(b)

FVn

=

PV (1 + )mn

PV 2,000 50,000 7,000 130,000 20,000 15,000

i 12% 12% 18% 12% 14% 15%

m 6 12 6 4 2 3

PV (1 + i)n

FV5

=

$6,000 (1 + 0.06)5

FV5

=

$6,000 (1.338)

FV5

=

$8,028

FVn

=

PV (1 + )mn

FV5

=

$6,000 (1 + )2 x 5

FV5

=

$6,000 (1 + 0.03)10

FV5

=

$6,000 (1.344)

FV5

=

$8,064

292

n 2 1 2 2 4 3

(1 + )mn 1.268 1.127 1.426 1.267 1.718 1.551

PV(1 + )mn $2,536 56,350 9,982 164,710 34,360 23,265

(c)

(d)

(e)

FVn

=

PV (1 + )mn

FV5

=

$6,000 (1 + )

FV5

=

$6,000 (1 + 0.01)30

FV5

=

$6,000 (1.348)

FV5

=

$8,088

FVn

=

PV (1 + i)n

FV5

=

$6,000 (1 + 0.12)5

FV5

=

$6,000 (1.762)

FV5

=

$10,572

FV5

=

PV

FV5

=

$6,000

FV5

=

$6,000 (1 + 0.06)10

FV5

=

6,000 (1.791)

FV5

=

$10,746

FV5

=

PV mn

FV5

=

$6,000

FV5

=

$6,000 (1 + 0.02)30

FV5

=

$6,000 (1.811)

FV5

=

$10,866

FVn

=

PV (1 + i)n

FV12

=

$6,000 (1 + 0.06)12

FV12

=

$6,000 (2.012)

FV12

=

$12,072

6X5

mn 2X5

6X5

An increase in the stated interest rate will increase the future value of a given sum. Likewise, an increase in the length of the holding period will increase the future value of a given sum.

5-10B. Annuity A:

PV

=



n

PMT  ∑

 t =1

293

  (1 + i)   1

t

 12

1

PV

=

$8,500  ∑

PV

=

$8,500 (6.194)

PV

=

$52,649

(1 + 0.12)

 t =1

t

   

Since the cost of this annuity is $50,000 and its present value is $52,649, given a 12 percent opportunity cost, this annuity has value and should be accepted. Annuity B:



  (1 + i) t   1

n

PV

=

PMT  ∑

PV

=

$7,000  ∑

PV

=

$7,000 (7.843)

PV

=$54,901

 t =1 

25

1 (1 + 0.12)

 t =1

t

   

Since the cost of this annuity is $60,000 and its present value is only $54,901 given a 12 percent opportunity cost, this annuity should not be accepted. Annuity C:



n

  (1 + i) t  

PV

=

PMT  ∑

PV

=

$8,000  ∑

PV

=

$8,000 (7.469)

 t =1 

1

20

 t =1

1 (1 + 0.12)

t

   

PV = $59,752 Since the cost of this annuity is $70,000 and its present value is only $59,752, given a 12 percent opportunity cost, this annuity should not be accepted. 5-11B. Year 1:

Year 2:

Year 3:

FVn

=

PV (1 + i)n

FV1

=

10,000(1 + 0.15)1

FV1

=

10,000(1.15)

FV1

=

11,500 books

FVn

=

PV (1 + i)n

FV2

=

10,000(1 + 0.15)2

FV2

=

10,000(1.322)

FV2

=

13,220 books

FVn

=

PV (1 + i)n

FV3

=

10,000(1 + 0.15)3

294

FV3

=

10,000(1.521)

FV3

=

15,210 books

Book sales 20,000

15,000

10,000

1

2

3

years

The sales trend graph is not linear because this is a compound growth trend. Just as compound interest occurs when interest paid on the investment during the first period is added to the principal of the second period, interest is earned on the new sum. Book sales growth was compounded; thus, the first year the growth was 15 percent of 10,000 books, the second year 15 percent of 11,500 books, and the third year 15 percent of 13,220 books. 5-12B.

FVn

=

PV (1 + i)n

FV1

=

41(1 + 0.12)1

FV1

=

41(1.12)

FV1

=

45.92 Home Runs in 1981 (in spite of the baseball strike).

FV2

=

41(1 + 0.12)2

FV2

=

41(1.254)

FV2

=

51.414 Home Runs in 1982

FV3

=

41(1 + 0.12)3

FV3

=

41(1.405)

FV3

=

57.605 Home Runs in 1983.

295

FV4

=

41(1 + 0.12)4

FV4

=

41(1.574)

FV4

=

64.534 Home Runs in 1984 (for a new major league record).

FV5

=

41(1 + 0.12)5

FV5

=

41(1.762)

FV5

=

72.242 Home Runs in 1985 (again for a new major league record).

Actually, Reggie never hit more than 41 home runs in a year. In 1982, he only hit 15, in1983 he hit 39, in 1984 he hit 14, in 1985 25 and 26 in 1986. He retired at the end of 1987 with 563 career home runs. 5-13B.

5-14B.

5-15B.

5-16B.



n

  (1 + i) t   1

PV

=

PMT  ∑

$120,000

=

PMT  ∑

$120,000

=

PMT(9.077)

Thus, PMT

=

$13,220.23 per year for 25 years

FVn

=

 n −1 PMT  ∑ t =0

$25,000

=

15 −1 t PMT  ∑ (1 + 0.07)   t =0 

$25,000

=

PMT(25.129)

Thus, PMT

=

$994.87

FVn

=

PV (1 + i)n

$2,376.50

=

$700 (FVIFi%, 10 yr.)

3.395

=

FVIFi%, 10 yr.

Thus, i

=

13%

 t =1



1

25

 t =1

(1 + 0.1)

t

   

 (1 + i) t  

The value of the home in 10 years FV10

=

PV (1 + .05)10

=

$125,000(1.629)

=

$203,625

How much must be invested annually to accumulate $203,625?

296

5-17B.

5-18B.

$203,625

=

10 −1 t PMT  ∑ (1 + .10)   t =0 

$203,625

=

PMT(15.937)

PMT

=

$12,776.87

FVn

=

 n −1 PMT  ∑ t =0

$15,000,000

=

10 −1 t PMT  ∑ (1 + .10)   t =0 

$15,000,000

=

PMT(15.937)

Thus, PMT

=

$941,206

 (1 + i) t  

One dollar at 24.0% compounded monthly for one year FVn

=

PV (1 + )nm

FV1

=

$1(1 + .02)1

=

$1(1.268)

=

$1.268

One dollar at 26.0% compounded annually for one year FVn

=

PV (1 + i)n

FV1

=

$1(1 + .26)1

=

$1(1.26)

=

$1.26

The loan at 26% compounded annually is more attractive. 5-19B. Investment A PV



  (1 + i)   i

n

=

PMT  ∑

=

$15,000  ∑

=

$15,000(2.991)

=

$44,865

t

 t =1 

5

 t =1

1 (1 + .20)

t

   

Investment B First, discount the annuity back to the beginning of year 5, which is the end of year 4. Then discount this equivalent sum to present.

297

PV

PV



  (1 + i) t  

n

1

=

PMT  ∑

=

$15,000  ∑

=

$15,000(3.326)

=

$49,890--then discount the equivalent sum back to present.

=

FVn

=

$49,890

=

$49,890(.482)

=

$24,046.98

=

FVn

=

$20,000 + $60,000

 t =1 

1

6

 t =1

(1 + .20)

t

   

Investment C PV

+ $20,000

5-20B.

5-21B. (a)

(b)

(c)

(d)

=

$20,000(.833) + $60,000(.335) + $20,000(.162)

=

$16,660 + $20,100 + $3,240

=

$40,000

PV

=

FVn

PV

=

$1,000

=

$1,000(.502)

=

$502

PV

=

PV

=

PV PV

= =

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

PV

=

$4,444

$11,538

$1,500

$1,667

298

5-22B. PV(annuity due)

5-23B.

=

PMT(PVIFAi,n)(l + i)

=

$1000(3.791)(1 + .10)

=

$3791(1.1)

=

$4,170.10

FVn

=

. PV (1 + )m n

7

=

1(1 + )2

7

=

(1 + 0.05)2

7

=

FVIF5%, 2n yr.

. n . n

A value of 7.040 occurs in the 5 percent column and 40-year row of the table in Appendix B. Therefore, 2n = 40 years and n = approximately 20 years. 5-24A. Investment A: PV

=

FVn (PVIFi,n)

PV

=

$5,000(PVIF10%, year 1) + $5,000(PVIF10%, year 2) + $5,000(PVIF10%, year 3) - $15,000(PVIF10%, year 4) + $15,000(PVIF10%, year 5)

= $5,000(.909) + $5,000(.826) + $5,000(.751) - $15,000(.683) + $15,000(.621) =

$4,545 + $4,130 + $3,755 - $10,245 + $9,315

=

$11,500.

299

Investment B: PV

=

FVn (PVIFi,n)

PV

=

$1,000(PVIF10%, year 1) + $3,000(PVIF10%, year 2) + $5,000(PVIF10%, year 3) + $10,000(PVIF10%, year 4) $10,000(PVIF10%, year 5)

= $1,000(.909) + $3,000(.826) + $5,000(.751) + $10,000(.683) - $10,000(.621) =

$909 + $2,478 + $3,755 + $6,830 - $6,210

=

$7,762.

PV

=

FVn (PVIFi,n)

PV

=

$10,000(PVIF10%, year 1) + $10,000(PVIF10%, year 2) +

Investment C:

$10,000(PVIF10%, year 3) + $10,000(PVIF10%, year 4) $40,000(PVIF10%, year 5)

= $10,000(.909) + $10,000(.826) + $10,000(.751) + $10,000(.683) - $40,000(.621) =

$9,090 + $8,260 + $7,510 + $6,830 - $24,840

=

$6,850.

5-25B. The Present value of the $10,000 annuity over years 11-15. PV

=

  15 PMT   ∑   t =1

=

$10,000(9.108 - 7.024)

=

$10,000(2.084)

=

$20,840

1 (1 + .07) t

  10  −  ∑   t =1

1 (1 + .07) t

The present value of the $15,000 withdrawal at the end of year 15: PV

=

FV15

=

$15,000(.362)

=

$5,430

Thus, you would have to deposit $20,840 + $5,430 or $26,270 today.

300

   

5-26B.

5-27B.

5-28B.

5-29B.

 10

   

1

PV

=

PMT  ∑

$45,000

=

PMT(6.418)

PMT

=

$7,012

PV

=

PMT  ∑

$45,000

=

$9,000 (PVIFAi%, 5 yr.)

5.0

=

PVIFAi%, 5 yr.

i

=

0%

PV

=

FVn

$15,000

=

$37,313 (PVIFi%, 5 yr.)

.402

=

PVIF20%, 5 yr.

Thus, i

=

20%

PV

=

PMT  ∑

$30,000

=

PMT  ∑

$30,000

=

PMT(2.974)

PMT

=

$10,087

 t =1



5

 t =1



n

 t =1



(1 + .09)

  (1 + i) t   1

  (1 + i) t   1

1

4

 t =1

t

(1 + .13)

t

   

5-30B. The present value of $10,000 in 12 years at 11 percent is: 

1 n  (1 + i)

PV

=

FVn  

PV

=

$10,000 ()

PV

=

$10,000 (.286)

PV

=

$2,860

   

The present value of $25,000 in 25 years at 11 percent is: PV = $25,000 () = $25,000 (.074) = $1,850 Thus take the $10,000 in 12 years. 5-31B.

FVn

=

 n −1 PMT  ∑ t =0

301

 (1 + i) t  

5-32B. (a)

(b)

(c)

$30,000

=

 5 −1 t PMT  ∑ (1 + .10)  t =0 

$30,000

=

PMT(6.105)

PMT

=$4,914

FVn

=

 n −1 PMT  ∑ t =0

$75,000

=

15 −1 t PMT  ∑ (1 + .08)   t =0 

$75,000

=

PMT (FVIFA8%, 15 yr.)

$75,000

=

PMT(27.152)

PMT

=

$2,762.23 per year

PV

=

FVn

PV

=

$75,000 (PVIF8%, 15 yr.)

PV

=

$75,000(.315)

PV

=

$23,625 deposited today

 (1 + i) t  

The contribution of the $20,000 deposit toward the $75,000 goal is FVn

=

PV (1 + i)n

FVn

=

$20,000 (FVIF8%, 10 yr.)

FV10

=

$20,000(2.159)

=

$43,180

Thus only $31,820 need be accumulated by annual deposit. FVn

=

 n −1 PMT  ∑ t =0

$31,820

=

PMT (FVIFA8%, 15 yr.)

$31,820

=

PMT [27.152]

PMT

=

$1,171.92 per year

302

 (1 + i) t  

5-33B.(a)

This problem can be subdivided into (1) the compound value of the $150,000 in the savings account, (2) the compound value of the $250,000 in stocks, (3) the additional savings due to depositing $8,000 per year in the savings account for 10 years, and (4) the additional savings due to depositing $2,000 per year in the savings account at the end of years 6-10. (Note the $10,000 deposited in years 6-10 is covered in parts (3) and (4).) (1)

(2)

(3)

Future value of $150,000 FV10 =

$150,000 (1 + .08)10

FV10 =

$150,000 (2.159)

FV10 =

$323,850

Future value of $250,000 FV10 =

$250,000 (1 + .12)10

FV10 =

$250,000 (3.106)

FV10 =

$776,500

Compound annuity of $8,000, 10 years FV10 =

(4)

 n −1 PMT  ∑ t =0

 (1 + i) t  

=

10 −1  $8,000  ∑ (1 + .08) t   t =0 

=

$8,000 (14.487)

=

$115,896

Compound annuity of $2,000 (years 6-10) FV5

=

 5 −1  $2,000  ∑ (1 + .08) t  t =0 

=

$2,000 (5.867)

=

$11,734

At the end of ten years you will have $323,850 + $776,500 + $115,896 + $11,734 = $1,227,980. 

1

20

PV

=

PMT  ∑

$1,227,980

=

PMT (7.963)

(b)

PMT =

 t =1

$154,210.72

303

(1 + .11)

t

   

5-34B.

PV

=

PMT (PVIFAi%, n yr.)

$200,000

=

PMT (PVIFA10%, 20 yr.)

$200,000

=

PMT(8.514)

PMT =

$23,491

PV

=

PMT (PVIFAi%, n yr.)

$250,000

=

PMT (PVIFA9%, 30 yr.)

$250,000

=

PMT(10.274)

5-35B.

PMT =

$24,333

5-36B. At 10%: PV

=

$40,000 + $40,000 (PVIFA10%, 24 yr.)

PV

=

$40,000 + $40,000 (8.985)

PV

=

$40,000 + $359,400

PV

=

$399,400

PV

=

$40,000 + $40,000 (PVIFA20%, 24 yr.)

PV

=

$40,000 + $40,000 (4.937)

PV

=

$40,000 + $197,480

PV

=

$237,480

5-37B FVn(annuity due)

=

PMT(FVIFAi,n)(l + i)

=

$1000(FVIFA5%, 5 years)(l + .05)

=

$1000(5.526)(1.05)

=

$5802.30

=

PMT(FVIFAi,n)(l + i)

=

$1,000(FVIFA8%, 5 years)(1 + .08)

=

$1,000(5.867)(1.08)

=

$6,336.36

=

PMT(PVIFAi,n)(l + i)

=

$1000 (PVIFA12%, 15 years)(1 + .12)

=

$1000(6.811)(1.12)

=

$7,628.32

At 20%:

FVn(annuity due)

5-38B. PV(annuity due)

304

PV(annuity due)

5-39B.

=

PMT(PVIFAi,n)(l + i)

=

$1000(PVIFA15%, 15 years)(l + .15)

=

$1000(5.847)(1.15)

=

$6,724.05

=

PMT(PVIFAi,n)(PVIFi,n)

=

$1000(PVIFA15%,10 years)(PVIF15%, 7 years)

=

$1000(5.019)(.376)

=

$1,887.14

FVn

=

PV (FVIFi%, n yr.)

$3,500

=

.12(FVIFi%, 38 yr.)

PV

5-40B.

solving using a financial calculator: i

=

31.0681%

5-41B. (a) 1/05

1/10

1/15

1/20

1/25

1/30

$60,000 $60,000 per year $300,000 $100,000 There are a number of equivalent ways to discount these cash flows back to present, one of which is as follows (in equation form): PV

=

$60,000 (PVIFA10%, 19 yr. - PVIFA10%, 4 yr.) + $300,000 (PVIF10%, 20 yr.) + $60,000 (PVIF10%, 23 yr. + PVIF10%, 24 yr.) + $100,000 (PVIF10%, 25 yr.)

= = = (b)

$60,000 (8.365-3.170) + $300,000 (.149) + $60,000 (0.112 + .102) + $100,000 (.092) $311,700 + $44,700 + $12,840 + $9,200 $378,440

If you live longer than expected you could end up with no money later on in life.

305

306

CHAPTER 7

Bonds Valuation CHAPTER ORIENTATION This chapter introduces the concepts that underlie asset valuation. We are specifically concerned with bonds. We also look at the concept of the bondholder's expected rate of return on an investment.

CHAPTER OUTLINE I.

Types of bonds A.

Debentures: unsecured long-term debt.

B.

Subordinated debentures: bonds that have a lower claim on assets in the event of liquidation than do other senior debtholders.

C.

Mortgage bonds: bonds secured by a lien on specific assets of the firm, such as real estate.

D.

Eurobonds: bonds issued in a country different from the one in whose currency the bond is denominated; for instance, a bond issued in Europe or Asia that pays interest and principal in U.S. dollars.

E.

Zero and low coupon bonds allow the issuing firm to issue bonds at a substantial discount from their $1,000 face value with a zero or very low coupon.

F.

1.

The disadvantages are, when the bond matures, the issuing firm will face an extremely large nondeductible cash outflow much greater than the cash inflow they experienced when the bonds were first issued.

2.

Zero and low coupon bonds are not callable and can be retired only at maturity.

3.

On the other hand, annual cash outflows associated with interest payments do not occur with zero coupon bonds.

Junk bonds: bonds rated BB or below.

307

II.

III.

Terminology and characteristics of bonds A.

A bond is a long-term promissory note that promises to pay the bondholder a predetermined, fixed amount of interest each year until maturity. At maturity, the principal will be paid to the bondholder.

B.

In the case of a firm's insolvency, a bondholder has a priority of claim to the firm's assets before the preferred and common stockholders. Also, bondholders must be paid interest due them before dividends can be distributed to the stockholders.

C.

A bond's par value is the amount that will be repaid by the firm when the bond matures, usually $1,000.

D.

The contractual agreement of the bond specifies a coupon interest rate that is expressed either as a percent of the par value or as a flat amount of interest which the borrowing firm promises to pay the bondholder each year. For example: A $1,000 par value bond specifying a coupon interest rate of 9 percent is equivalent to an annual interest payment of $90.

E.

The bond has a maturity date, at which time the borrowing firm is committed to repay the loan principal.

F.

An indenture (or trust deed) is the legal agreement between the firm issuing the bonds and the bond trustee who represents the bondholders. It provides the specific terms of the bond agreement such as the rights and responsibilities of both parties.

G.

The current yield on a bond refers to the ratio of annual interest payment to the bond’s market price.

H.

Bond ratings 1.

Three primary rating agencies exist—Moody’s, Standard & Poor’s, and Fitch Investor Services.

2.

Bond ratings are simply judgments about the future risk potential of the bond in question. Bond ratings are extremely important in that a firm’s bond rating tells much about the cost of funds and the firm’s access to the debt market.

3.

The different ratings and their implications are described.

Definitions of value A.

Book value is the value of an asset shown on a firm's balance sheet which is determined by its historical cost rather than its current worth.

B.

Liquidation value is the amount that could be realized if an asset is sold individually and not as part of a going concern.

C.

Market value is the observed value of an asset in the marketplace where buyers and sellers negotiate an acceptable price for the asset.

308

D.

IV.

Valuation: An Overview A.

B. V.

Intrinsic value is the value based upon the expected cash flows from the investment, the riskiness of the asset, and the investor's required rate of return. It is the value in the eyes of the investor and is the same as the present value of expected future cash flows to be received from the investment. The value of an asset is a function of three elements: 1.

The amount and timing of the asset's expected cash flows

2.

The riskiness of these cash flows

3.

The investors' required rate of return for undertaking the investment

Expected cash flows are used in measuring the returns from an investment.

Valuation: The Basic Process The value of an asset is found by computing the present value of all the future cash flows expected to be received from the asset. Expressed as a general present value equation, the value of an asset is found as follows: N

∑ (1

$C t

V

=

where Ct

=

the cash flow to be received at time t

V

=

the intrinsic value or present value of an asset producing expected future cash flows, Ct, in

t =1

+ k) t

years 1 through N

VI.

k

=

the investor's required rate of return

N

=

the number of periods

Bond Valuation A.

The value of a bond is simply the present value of the future interest payments and maturity value discounted at the bondholder's required rate of return. This may be expressed as: N

∑

$I t

$M

V b

=

where It

=

the dollar interest to be received in each payment

M

=

the par value of the bond at maturity

kb

=

the required rate of return for the bondholder

N

=

the number of periods to maturity

t =1

(1 + k b )

t

+

(1 + k b ) N

In other words, we are discounting the expected future cash flows to the present at the appropriate discount rate (required rate of return).

309

B.

If interest payments are received semiannually (as with most bonds), the valuation equation becomes: 2N

V

VII.

VIII.

b

=

∑ t =1

$I t 2 t kb   1 +  2  

+

$M k   1 + b  2  

2N

Bondholder's Expected Rate of Return (Yield to Maturity) A.

We compute the bondholder's expected rate of return by finding the discount rate that gets the present value of the future interest payments and principal payment just equal to the bond's current market price.

B.

The bondholder's expected rate of return is also the rate the investor will earn if the bond is held to maturity, provided, of course, that the company issuing the bond does not default on the payments.

Bond Value: Five Important Relationships A.

First relationship A decrease in interest rates (required rates of return) will cause the value of a bond to increase; an interest rate increase will cause a decrease in value. The change in value caused by changing interest rates is called interest rate risk.

B.

C.

Second relationship 1.

If the bondholder's required rate of return (current interest rate) equals the coupon interest rate, the bond will sell at par, or maturity value.

2.

If the bondholder's required rate of return exceeds the bond's coupon rate, the bond will sell below par value or at a "discount."

3.

If the bondholder's required rate of return is less than the bond's coupon rate, the bond will sell above par value or at a "premium."

Third relationship As the maturity date approaches, the market value of a bond approaches its par value.

D.

1.

The premium bond sells for less as maturity approaches.

2.

The discount bond sells for more as maturity approaches.

Fourth relationship A bondholder owning a long-term bond is exposed to greater interest rate risk than when owning a short-term bond.

310

E.

Fifth relationship The sensitivity of a bond's value to changing interest rates depends not only on the length of time to maturity, but also on the pattern of cash flows provided by the bond. 1.

The duration of a bond is simply a measure of the responsiveness of its price to a change in interest rates. The greater the relative percentage change in a bond price in response to a given percentage change in the interest rate, the longer the duration.

2.

Calculating duration n

P0

tC t (1 + k b ) t P0

duration

=

∑

where t

=

the year the cash flow is to be received

N

=

the number of years to maturity

Ct

=

the cash flow to be received in year t

kb =

= the bondholder's required rate of return the bond's present value

t =1

ANSWERS TO END-OF-CHAPTER QUESTIONS 7-1.

Book value is the asset's historical value and is represented on the balance sheet as cost minus accumulated depreciation. Liquidation value is the dollar sum that could be realized if the assets were sold individually and not as part of a going concern. Market value is the observed value for an asset in the marketplace where buyers and sellers negotiate a mutually acceptable price. Intrinsic value is the present value of the asset's expected future cash flows discounted at an appropriate discount rate.

7-2.

The value of a security is equal to the present value of cash flows to be received by the investor. Hence, the terms value and present value are synonymous.

7-3.

The first two factors affecting asset value (the asset characteristics) are the asset's expected cash flows and the riskiness of these cash flows. The third consideration is the investor's required rate of return. The required rate of return reflects the investor's risk-return preference.

7-4.

The relationship is inverse. As the required rate of return increases, the value of the security decreases, and a decrease in the required rate of return results in a price increase.

311

7-5.

(a)

The par value is the amount stated on the face of the bond. This value does not change and, therefore, is completely independent of the market value. However, the market value may change with changing economic conditions and changes within the firm. (b) The coupon interest rate is the rate of interest that is contractually specified in the bond indenture. As such, this rate is constant throughout the life of the bond. The coupon interest rate indicates to the investor the amount of interest to be received in each payment period. On the other hand, the investor's required rate of return is equivalent to the bond’s current yield to maturity, which changes with the changing bond's market price. This rate may be altered as economic conditions change and/or the investor's attitude toward the risk-return trade-off is altered.

7-6.

In the case of insolvency, claims of debt holders in general, including bonds, are honored before those of both common stock and preferred stock. However, different types of debt may also have a hierarchy among themselves as to the order of their claim on assets. Bonds also have a claim on income that comes ahead of common and preferred stock. If interest on bonds is not paid, the bond trustees can classify the firm insolvent and force it into bankruptcy. Thus, the bondholder's claim on income is more likely to be honored than that of common and preferred stockholders, whose dividends are paid at the discretion of the firm's management.

7-7.

Ratings involve a judgment about the future risk potential of the bond. Although they deal with expectations, several historical factors seem to play a significant role in their determination. Bond ratings are favorably affected by (1) a greater reliance on equity, and not debt, in financing the firm, (2) profitable operations, (3) a low variability in past earnings, (4) large firm size, and (5) little use of subordinated debt. In turn, the rating a bond receives affects the rate of return demanded on the bond by the investors. The poorer the bond rating, the higher the rate of return demanded in the capital markets. For the financial manager, bond ratings are extremely important. They provide an indicator of default risk that in turn affects the rate of return that must be paid on borrowed funds.

7-8.

The term debentures applies to any unsecured long-term debt. Because these bonds are unsecured, the earning ability of the issuing corporation is of great concern to the bondholder. They are also viewed as being more risky than secured bonds and as a result must provide investors with a higher yield than secured bonds provide. Often the issuing firm attempts to provide some protection to the holder through the prohibition of any additional encumbrance of assets. This prohibits the future issuance of secured long-term debt that would further tie up the firm's assets and leave the bondholders less protected. To the issuing firm, the major advantage of debentures is that no property has to be secured by them. This allows the firm to issue debt and still preserve some future borrowing power.

312

A mortgage bond is a bond secured by a lien on real property. Typically, the value of the real property is greater than that of the mortgage bonds issued. This provides the mortgage bondholders with a margin of safety in the event the market value of the secured property declines. In the case of foreclosure, the trustees have the power to sell the secured property and use the proceeds to pay the bondholders. In the event that the proceeds from this sale do not cover the bonds, the bondholders become general creditors, similar to debenture bondholders, for the unpaid portion of the debt. 7-9.

(a) Eurobonds are not so much a different type of security as they are securities, in this case bonds, issued in a country different from the one in whose currency the bond is denominated. For example, a bond that is issued in Europe or in Asia by an American company and that pays interest and principal to the lender in U.S. dollars would be considered a Eurobond. Thus, even if the bond is not issued in Europe, it merely needs to be sold in a country different from the one in whose currency it is denominated to be considered a Eurobond.

(b)

Zero and very low coupon bonds allow the issuing firm to issue bonds at a substantial discount from their $1,000 face value with a zero or very low coupon. The investor receives a large part (or all on the zero coupon bond) of the return from the appreciation of the bond at maturity.

(c)

Junk bonds refer to any bond with a rating of BB or below. The major participants in this market are new firms that do not have an established record of performance. Many junk bonds have been issued to finance corporate buyouts.

7-10. The expected rate of return is the rate of return that may be expected from purchasing a security at the prevailing market price. Thus, the expected rate of return is the rate that equates the present value of future cash flows with the actual selling price of the security in the market. 7-11. When the coupon interest rate does not equal the bondholder's required rate of return, the bond will be issued at either a premium or discount. If the investor's required rate of return is higher than the coupon interest rate, the bond will be issued at a discount to the investor. If the coupon rate is higher that the investor's required rate, the bond will be issued at a premium. 7-12. A premium bond is issued when the coupon rate is higher than the bondholder's required rate of return. The premium is the excess of the market value over the face value of the bond. A discount bond is issued when the bondholder's required rate of return is higher than the coupon rate. The discount is the excess of the face value of the bond over the market value. Over time, the premium or discount on a bond is amortized. This amortization allows the bondholder to realize an effective yield equal to their required rate of return.

313

7-13. A change in current interest rates (required rate of return) causes a change in the market value of a bond. However, the impact on value is greater for long-term bonds than it is for short-term bonds. The reason long-term bond prices fluctuate more than short-term bond prices in response to interest rate changes is simple. Assume an investor bought a 10-year bond yielding a 12 percent interest rate. If the current interest rate for bonds of similar risk increased to 15 percent, the investor would be locked into the lower rate for 10 years. If, on the other hand, a shorter-term bond had been purchased, say one maturing in 2 years, the investor would have to accept the lower return for only 2 years and not the full 10 years. At the end of year 2, the investor would receive the maturity value of $1,000 and could buy a bond offering the higher 15 percent rate for the remaining 8 years. Thus, interest rate risk is determined, at least in part, by the length of time an investor is required to commit to an investment. 7-14. The duration of a bond is simply a measure of the responsiveness of its price to a change in interest rates. The greater the relative percentage change in a bond price in response to a given percentage change in the interest rate, the longer the duration.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS 7-1A. Value (Vb)

=

12

∑

t =1

$80 (1 + .12)

t

+

$1,000 (1 + .12)

12 12 80 1000 CPT

→

ANSWER

314

-752.23

12

7-2A. If the interest is paid semiannually: Value (Vb) =

16

∑ t =1

$45 (1.04)

+

t

$1,000 (1.04)

16

16 4 45 1000 →

CPT

ANSWER

-1,058.26

If interest is paid annually: Value (Vb)

=

8

∑

t =1

$90 (1.08)

$1,000

+

t

(1.08)

8

8 8 90 1000 →

CPT

20

7-3A. $900 =

∑

t =1

$40 (1 + k b /2)

t

ANSWER +

-1,057.47

$1,000 (1 + k b /2) 20

20 900 40 1000 CPT

→

ANSWER

4.79%

semiannual rate

The rate is equivalent to 9.6 percent annual rate compounded semiannually, or 9.8 percent (1.0482 - 1) compounded annually.

315

20

7-4A. $945 =

∑

t =1

$90 (1 + k b )

$1,000

+

t

(1 + k b ) 20

20 945 90 1000 →

CPT

12

7-5A. $1,150 =

∑

t =1

$70 (1 + k b )

t

ANSWER

9.63%

$1,000

+

(1 + k b )12

12 1150 70 1000 →

CPT

15

7-6A. a.

$1,085 =

∑

t =1

ANSWER

$80 (1 + k b )

t

+

5.28%

$1,000 (1 + k b )15

15 1085 80 1000 CPT

→

ANSWER

316

7.06%

b.

Vb =

15

∑

t =1

$80 (1.10)

t

+

$1,000 (1.10)

15

15 10 80 1000 CPT

c.

7-7A. a.

b.

→

ANSWER

-847.88

Since the expected rate of return, 7.06 percent, is less than your required rate of return of 10 percent, the bond is not an acceptable investment. This fact is also evident because the market price, $1,085, exceeds the value of the security to the investor of $847.88. Value Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 100.00 0.12 15 $ 863.78

Value at Alternative Rates of Return Required Rate of Return Market Value

0.15 $ 707.63

Required Rate of Return Market Value

0.08 $1,171.19

c.

As required rates of return change, the price of the bond changes, which is the result of "interest-rate risk." Thus, the greater the investor's required rate of return, the greater will be his/her discount on the bond. Conversely, the less his/her required rate of return below that of the coupon rate, the greater the premium will be.

d.

Value at Alternative Maturity Dates Years to Maturity Required Rate of Return Market Value Required Rate of Return Market Value

e.

5 0.15 $ 832.39 0.08 $1,079.85

The longer the maturity of the bond, the greater the interest rate risk the investor is exposed to, resulting in greater premiums and discounts.

317

15

7-8A. $1,250

∑

=

t =1

$90 (1 + k b ) t

$1,000 (1 + k b )15

+

15 1250 90 1000 →

CPT

7-9A.(a)

Vb

20

$110 (1.09)

∑

=

ANSWER

t =1

$1,000 (1.09) 20

+

t

6.36%

20 9 110 1000 →

CPT

(b)

(i)

Vb

=

20

∑ t =1

ANSWER $110 (1.12)

t

+

-1,182.57 $1,000 (1.12) 20

20 12 110 1000 CPT

→

ANSWER

318

-925.31

(b)

(ii)

Vb

=

20

∑ t =1

$110 (1.06)

t

+

$1,000 (1.06) 20

20 6 110 1000 CPT

(c)

→

ANSWER

-1,573.50

We see that value is inversely related to the investor's required rate of return.

7-10A. Value Bond P Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 100.00 8% 5 $ 1,079.85

Value Bond Q Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 70.00 8% 5 $ 960.07

Value Bond R Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 120.00 8% 10 $ 1,268.40

Value Bond S Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 80.00 8% 10 $ 1,000.00

319

Value Bond T Par Value Coupon Required Rate of Return Years to Maturity Market Value

Bond

P

Q

$1,079.85 Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ct $100 100 100 100 1,100

R

$960.07

t*PV(Ct) Ct $93 171 238 294 3,743

$1,000.00 $ 65.00 8% 15 $ 871.61

$70 70 70 70 1,070

t*PV(Ct) $65 120 167 206 3,641

S

$1,268.40 Ct $120 120 120 120 120 120 120 120 120 1,120

$1,000.00

t*PV(Ct) Ct $111 206 286 353 408 454 490 519 540 5,188

T

$80 80 80 80 80 80 80 80 80 1,080

t*PV(Ct)

$871.61 Ct

t*PV(Ct)

$74 137 191 235 272 302 327 346 360 5,002

$65 $60 65 111 65 155 65 191 65 221 65 246 65 265 65 281 65 293 65 301 65 307 65 310 65 311 65 310 1,065 5,036

Sumof t * PV (Ct )

4,539

4,198

8,554

7,247

8,398

Duration

4.20

4.37

6.74

7.25

9.63

320

7

7-11A. a.$1,100 =

∑ t =1

$90 (1 + k b ) t

$1,000 (1 + k b ) 7

+

7 1100 90 1000 →

CPT

b.

Vb =

7

∑ t =1

$90 (1.07)

t

ANSWER

+

7.14%

$1,000 (1.07) 7

7 7 90 1000 →

CPT

c.

ANSWER

-1,107.79

Since the expected rate of return, 7.14 percent, is more than your required rate of return of 7 percent, the bond is an acceptable investment. This fact is also evident because the market price, $1,100, is less than the value of the security to the investor of $1,107.79. 12

7-12A. a.

$915

=

∑ t =1

$50 (1 + k b ) t

+

$1,000 (1 + k b )12

12 915 50 1000 CPT

→

ANSWER

6.01%

b. Since the required rate of return(9%) is greater than the expected rate of return(6%), you should not purchase the bond.

321

7-13A. Value Bond I Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 130.00 7% 7 $ 1,323.36

Value Bond II Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 90.00 7% 6 $1,095.33

Value Bond III Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 110.00 7% 12 $1,317.71

Value Bond IV Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 125.00 7% 5 $1,225.51

Value Bond V Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 80.00 7% 10 $1,070.24

322

Bond Bond Value Years 1 2 3 4 5 6 7 8 9 10

II

I

III

$1,323.36 $1,095.33 Ct tPV(Ct) Ct tPV(Ct) $130 $121 $90 $84 $130 $227 $90 $157 $130 $318 $90 $220 $130 $397 $90 $275 $130 $463 $90 $321 $130 $520 1,090 $4,358 1,130 $4,926

11 12 Sum of t*PV(Ct) Duration

$6,973 5.27

7-14A.(a)

Vb

15

∑

t=1

$9,622 7.30

$85 $ 1 ,0 0 0 + t ( 1 .0 9 ) ( 1 .0 91 5)

15 9 85 1000 →

CPT

(b)

(i)

Vb

=

15

∑ t =1

ANSWER $85 (1.11)

-959.70 +

t

$1,000 (1.11) 15

15 11 85 1000 →

CPT

(b)

(ii)

Vb

=

15

∑ t =1

V

$1,317.71 $1,225.51 $1,070.24 Ct tPV(Ct) Ct tPV(Ct) Ct tPV(Ct) $110 $103 $125 $117 $80 $75 $110 $192 $125 $218 $80 $140 $110 $269 $125 $306 $80 $196 $110 $336 $125 $381 $80 $244 $110 $392 $1,125 $4,011 $80 $285 $110 $440 $80 $320 $110 $480 $80 $349 $110 $512 $80 $372 $110 $538 $80 $392 $110 $559 $1,080 $5,490 1,11 0 $5,801

$5,415 4.94

=

IV

ANSWER

$85 (1.07)

t

15

323

+

-820.23

$1,000 (1.07) 15

$5,033 4.11

$7,863 7.35

7 85 1000 →

CPT

(c)

ANSWER

-1,136.62

As long as the required rate of return is less than the expected rate of return of 9%, you should purchase the bond Thus, if your required rate of return decreases to 7%, you should purchase the bond.

SOLUTION TO INTEGRATIVE PROBLEM 1.

Young Corp. Bond Value (Vb)

=

10

∑ t =1

$78 .00 (1 +.06 ) t

+

$1,000 (1 + .06 )10

+

$1,000 (1 + .09 )17

10 6 78 1000 CPT

→

ANSWER 17

-$1,132.48

∑ t =1

$75 .00 (1 +.09 ) t

ANSWER

-$871.85

Thomas Resorts Bond Value (Vb)

=

17 9 75.00 1000 CPT

→

324

4

∑

$79.75 (1 + .08)

ANSWER

-$999.17

Entertainment, Inc. Bond Value (Vb) =

t =1

t

+

$1,000 (1 + .08)

4 8 79.75 1000 CPT

→

10

2.

Young Corporation: $1,030 =

∑ t =1

$78 (1 + k b ) t

+

$1,000 (1 + k b )10

10 1,030 78 1000 CPT

→

ANSWER 17

Thomas Resorts:

$973

=

∑ t =1

7.37%

$75 (1 + k b ) t

+

17 973 75.00 1000 CPT

→

ANSWER

325

7.79%

$1,000 (1 + k b )17

4

4

Entertainment, Inc.:

$1,035 =

∑ t =1

$79.75 (1 + k b ) t

+

$1,000 (1 + k b ) 4

4 1,035 79.75 1000 →

CPT

3. 10

∑ t =1

i.

ANSWER

Young Corp. Bond Value (Vb)

$78 (1 + .09)

t

+

$1,000 (1 + .09)

6.94% =

10

10 9 78 1000 →

CPT

Thomas Resorts Bond Value

ANSWER

(Vb)

=

- $922.99

17

$75 .00 (1 +.12 ) t

∑ t =1

17 12 75.00 1000 →

CPT

ANSWER

- $679.62

Entertainment, Inc. Bond Value (Vb) = 4

$79 .75 + .11 ) t

∑ (1 t =1

+

$1,000 (1 + .11 ) 4

4 11 79.75 1000 →

CPT

3. 10

∑ t =1

ii

ANSWER

Young Corp. Bond Value (Vb)

$78 (1 + .03)

t

+

$1,000 (1 + .03)

10

10 3 78

326

- $906.15 =

+

$1,000 (1 + .12 )17

1000 →

CPT

Thomas Resorts Bond Value

ANSWER

(Vb) =

17

∑ t =1

- $1,409.45

$75.00 (1 + .06)

t

+

$1,000 (1 + .06)

17

17 6 75.00 1000 →

CPT

ANSWER

- $1,157.16

Entertainment, Inc. Bond Value (Vb) = 4

∑ t =1

$79.75 (1 +.05)

t

+

$1,000 (1 + .05)

4

4 5 79.75 1000 CPT

4.

→

ANSWER

- $1,105.49

As the interest rates rise and fall, we see the different effects on the bond prices depending on the length of time to maturity and whether the investor's required rate of return is above or below the coupon interest rate. If the investor’s required rate of return is above the coupon interest rate, the bond will sell at a discount (below par value), but if the investor’s required rate of return is below the coupon interest rate, the bond will sell at a price above its par value (premium).

327

5.

Duration of bonds Young Corp.

Entertainment, Inc.

Thomas Resorts Bond Value Required rate of return Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

$ 973.00

6%

9%

Ct t* PV(Ct) $ 78.00 $ 73.58 $ 78.00 138.84 78.00 196.47 78.00 247.13 78.00 291.43 78.00 329.92 78.00 363.12 78.00 391.51 78.00 415.51 1,078.00 6,019.50

Sum of t*PV(Ct) Duration

$1,030.00

$1,035.00 8%

Ct t* PV(Ct) Ct t* PV(Ct) 75.00 $ 68.81 $ 79.75 $ 73.84 75.00 126.25 79.75 136.75 75.00 173.74 79.75 189.92 75.00 212.53 1,079.75 3,174.59 75.00 243.72 75.00 268.32 75.00 287.19 75.00 301.12 75.00 310.79 75.00 316.81 75.00 319.71 75.00 319.98 75.00 318.02 75.00 314.21 75.00 308.86 75.00 302.24 1,075.00 4222.86

8,467.02

8,415.17

3,575.11

8.22

8.65

3.45

The value of the Entertainment, Inc. bonds will be less sensitive to interest rate changes than will Young Corporation and Thomas Resorts bonds. 6.

Although the Young Corporation bonds and the Thomas Resorts bonds have different terms to maturity, the duration of the two bonds is very similar. These two bonds will likely have similar sensitivity to changes in interest rates as evidenced by their duration values.

7.

The Entertainment, Inc. and Thomas Resorts bonds have lower expected rates of return than your required rate of return. Young Corporation’s expected rate of return is greater than your required rate of return. So we would buy Young Corporation and not Entertainment, Inc. or Thomas Resorts.

328

Solutions to Problem Set B 7-1B. Value (Vb)

=

10

∑ (1

t =1

$90 + .15)

+

t

$1,000 (1 + .15)

10 15 90 1000 →

CPT

ANSWER

-698.87

7-2B. If the interest is paid semiannually: Value (Vb)

=

22

∑

t =1

$50 t

(1.045)

+

$1,000 22

(1.045)

22 4.5 50 1000 →

CPT

ANSWER

-1068.92

If interest is paid annually: Value (Vb)

=

11

$100

∑ (1.09)

t =1

t

+

$1,000 (1.09)

11

11 9 100 1000 CPT

→

ANSWER

329

-1068.05

10

16

7-3B. $950 =

∑

t =1

$45 (1 + k b /2)

$1,000

+

t

(1 + k b /2) 16

16 950 45 1000 →

CPT

ANSWER

4.96%

The rate is equivalent to 9.92 percent annual rate, compounded semiannually or 10.17 percent (1.04962 - 1) compounded annually. 20

$100

t =1

(1 + k b ) t

7-4B. $975 =

∑

$1,000

+

(1 + k b ) 20

20 975 100 1000 →

CPT

15

7-5B. $1,175 =

∑ t =1

$80 (1 + k b ) t

ANSWER

+

10.30%

$1,000 (1 + k b )15

15 1175 80 1000 CPT

→

ANSWER

330

6.18%

14

7-6B. a.

$1,100 =

∑ t =1

$90 (1 + k b ) t

$1,000 (1 + k b )14

+

14 1100 90 1000 →

CPT

b.

Vb =

14

$90

∑ (1.10)

t =1

t

ANSWER

7.80%

$1,000

+

(1.10)

14

14 10 90 1000 CPT

→

ANSWER

-926.33

c.

Since the expected rate of return, 7.80 percent, is less than your required rate of return of 10 percent, the bond is not an acceptable investment. This fact is also evident because the market price, $1,100, exceeds the value of the security to the investor of $926.33.

a.

Value Par Value Coupon Required Rate of Return Years to Maturity Market Value

7-7B.

b.

$1,000.00 $ 80.00 7% 20 $ 1,105.94

Value at Alternative Rates of Return Required Rate of Return Market Value Required Rate of Return Market Value

10% $ 829.73 6% $1,229.40

c.

As required rates of return change, the price of the bond changes, which is the result of "interest-rate risk." Thus, the greater the investor's required rate of return, the greater will be his/her discount on the bond. Conversely, the less his/her required rate of return is below that of the coupon rate, the greater the premium will be.

d.

Value at Alternative Maturity Dates

331

Years to Maturity Required Rate of Return Market Value Required Rate of Return Market Value e.

10 10% $ 877.11 6% $1,147.20

The longer the maturity of the bond, the greater the interest-rate risk the investor is exposed to, resulting in greater premiums and discounts. 14

7-8B. $1,110

=

∑ t =1

$70 (1 + k b ) t

+

$1,000 (1 + k b )14

14 1110 70 1000 →

CPT

7-9B. (a)

Value (Vb)

=

ANSWER 17

∑ t =1

$70 (1 +.085)

5.83%

17

+

$1,000 (1 +.085 )17

17 8.5 70 1000 CPT

→

ANSWER

332

-867.62

(b)

(i)

Value (Vb)

17

∑

=

t =1

$70 $1,000 + 17 (1 +.11 )17 (1 +.11)

17 11 70 1000 →

CPT

(b)

(ii)

Value (Vb)

ANSWER 17

∑

=

t =1

-698.05

$70 $1,000 + 17 (1 +.06 )17 (1 +.06)

17 6 70 1000 CPT

(c)

→

ANSWER

-1,104.77

We see that value is inversely related to the investor's required rate of return.

7-10B. Value Bond A Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 90.00 7% 5 $ 1,082.00

Value Bond B Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 60.00 7% 5 $ 959.00

333

Value Bond C Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 120.00 7% 10 $ 1,351.18

Value Bond D Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 90.00 7% 15 $ 1,182.16

Value Bond E Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 75.00 7% 15 $ 1,045.54

Bond

Bond value Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A

$1,082.00

B

C

$959.00

$1,351.18

Ct t*PV(Ct) Ct t*PV(Ct) Ct t*PV(Ct) $90 $84 $60 $56 $120 $112 90 157 60 105 120 210 90 220 60 147 120 294 90 275 60 183 120 366 1,090 3,886 1,060 3,779 120 428 120 480 120 523 120 559 120 587 1,120 5,694

D

E

$1,182.16

$1,045.54

Ct t*PV(Ct) Ct t*PV(Ct) $90 $84 $75 $70 90 157 75 131 90 220 75 184 90 275 75 229 90 321 75 267 90 360 75 300 90 392 75 327 90 419 75 349 90 441 75 367 90 458 75 381 90 470 75 392 90 480 75 400 90 486 75 405 90 489 75 407 1,090 5,926 1,075 5,844

Sumof t * PV (Ct )

4,622

4,270

9,252

10,977

Duration

4.27

4.45

6.85

9.29

334

10,053 9.62

4

7-11B.

a.$1,350 =

∑ t =1

$120 (1 + k b ) t

+

$1,000 (1 + k b ) 4

4 1350 120 1000 →

CPT

b.

Vb =

4

∑ t =1

$120 (1.09)

t

ANSWER +

2.66%

$1,000 (1.09) 4

4 9 120 1000 → ANSWER -1,097.19 Since the expected rate of return, 2.66 percent is much less than your required rate of return of 9 percent, the bond is not an acceptable investment. This fact is also evident because the market price, $1,350, exceeds the value of the security to the investor of $1,097.19.

CPT

c.

25

7-12B. a.

$915

=

∑ t =1

$80 (1 + k b ) t

+

$1,000 (1 + k b ) 25

25 915 80 1000 CPT

b.

→

ANSWER

8.86%

Since the required rate of return(11%) is greater than the expected rate of return(8.86%), you should not purchase the bond.

335

7-13B. Value Bond J Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 95.00 10% 4 $984.15

Value Bond P Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $115 10% 12 $1,102.21

Value Bond Y Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 80 10% 16 $843.53

Value Bond Q Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 70.00 10% 20 $744.59

Value Bond Z Par Value Coupon Required Rate of Return Years to Maturity Market Value

$1,000.00 $ 130.00 10% 15 $1,228.18

336

Bond Bond Value

J

P

Y

Q

Z

$984.15

$1,102.21

$843.53

$744.59

$1,228.18

Ct tPV(Ct) Years 1 $95 $86 2 $95 $157 3 $95 $214 4 $1,095 $2,992 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Sum of t*PV(Ct) $3,449 Duration 3.50

7-14B.(a)

Vb

=

Ct tPV(Ct) $115 $105 $115 $190 $115 $259 $115 $314 $115 $357 $115 $389 $115 $413 $115 $429 $115 $439 $115 $443 $115 $443 1,115 $4,263

Ct $80 $80 $80 $80 $80 $80 $80 $80 $80 $80 $80 $80 $80 $80 $80 $1,080

$8,046 7.30 20

∑ t =1

$120 (1.08)

tPV(Ct)

$73 $132 $180 $219 $248 $271 $287 $299 $305 $308 $308 $306 $301 $295 $287 $3,761

Ct $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 $70 1,070

$7,581 8.99

t

+

$1,000 (1.08) 20

20 8 120 1000 CPT

→

ANSWER

337

-1,392.73

tPV(Ct)

$64 $116 $158 $191 $217 $237 $251 $261 $267 $270 $270 $268 $264 $258 $251 $244 $235 $227 $217 $3,181 $7,447 10.00

Ct $130 $130 $130 $130 $130 $130 $130 $130 $130 $130 $130 $130 $130 $130 $1,130

tPV(Ct)

$118 $215 $293 $355 $404 $440 $467 $485 $496 $501 $501 $497 $490 $479 $4,058

$9,799 7.98

(b)

(i)

Vb

=

20

∑ t =1

$120 (1.13)

t

+

$1,000 (1.13) 20

20 13 120 1000 →

CPT

(b)

(ii)

Vb

=

20

∑ t =1

ANSWER $120 (1.06)

t

-929.75 +

$1,000 (1.06) 20

20 6 120 1000 CPT

(c)

→

ANSWER

-1,688.20

As long as the required rate of return is less than the expected rate of return of 8%, you should purchase the bond Thus, if your required rate of return decreases to 6%, you should purchase the bond.

CHAPTER 8

338

Stock Valuation CHAPTER ORIENTATION This chapter continues the introduction of concepts underlying asset valuation began in Chapter 7. We are specifically concerned with valuing preferred stock and common stock. We also look at the concept of a stockholder’s expected rate of return on an investment.

CHAPTER OUTLINE I.

Preferred Stock A.

Features of preferred stock 1.

Owners of preferred stock receive dividends instead of interest.

2.

Most preferred stocks are perpetuities (non-maturing).

3.

Multiple classes, each having different characteristics, can be issued.

4.

Preferred stock has priority over common stock with regard to claims on assets in the case of bankruptcy.

5.

Most preferred stock carries a cumulative feature that requires all past unpaid preferred stock dividends to be paid before any common stock dividends are declared.

6.

Preferred stock may contain other protective provisions, such as granting voting rights in the event of non-payment of dividends.

7.

Preferred stock may contain provisions to convert to a predetermined number of shares of common stock.

8.

Some preferred stock contains provisions for an adjustable rate of return.

9.

If there is a participation feature, it allows preferred stockholders to participate in earnings beyond the payment of the stated dividend.

10.

Payment-in-kind (PIK) preferred stock, grants the investor additional preferred stock instead of dividends for a given period of time. Eventually cash dividends are paid.

339

11.

B.

Retirement features for preferred stock are frequently included. a.

Callable preferred refers to a feature which allows preferred stock to be called, or retired, like a bond.

b.

A sinking fund provision requires the firm periodically set aside an amount of money for the retirement of its preferred stock.

Valuation of preferred stock (Vps): The value of a preferred stock equals the present value of all future dividends. If the stock is nonmaturing, where dividends are expected in equal amount each year in perpetuity, the value may be calculated as follows: Vps = =

II.

Common Stock A.

B.

Features of Common Stock 1.

As owners of the corporation, common shareholders have the right to the residual income and assets after bondholders and preferred stockholders have been paid.

2.

Common stockholders are generally the only security holders with the right to elect the board of directors.

3.

Preemptive rights (if granted) entitle the common shareholder to maintain a proportionate share of ownership in the firm.

4.

Common stockholder’s liability as an owner of the corporation is limited to the amount invested in the stock.

5.

Common stock’s value is equal to the present value of all future cash flows expected to be received by the stockholder.

Valuing common stock 1.

Company growth occurs by: a.

the infusion of new capital, or

b.

the retention of earnings, which is called internal growth. The internal growth rate of a firm equals: Return on equity ×

2.

Although the bondholder and preferred stockholder are promised a specific amount each year, the dividend for common stock is based on the profitability of the firm and management's decision either to pay dividends or retain profits for reinvestment.

3.

The common dividend typically increases with the growth in corporate earnings.

4.

The earnings growth of a firm should be reflected in a higher price for the firm's stock.

340

5.

In finding the value of a common stock (Vcs), we should discount all future expected dividends (Dl, D2, D3, ..., D∞) to the present at the required rate of return for the stockholder (kcs). That is: Vcs =

6.

D1 D2 D∞ + +...+ 1 2 (1 + k cs ) (1 + k cs ) (1 + k cs ) ∞

If we assume that the amount of dividend is increasing by a constant growth rate each year, Dt

D0 (l + g)t

= where

g

= the growth rate

D0

= the most recent dividend payment

If the growth rate, g, is the same each year, t, and is less than the required rate of return, kcs, the valuation equation for common stock can be reduced to Vcs III.

=

=

Shareholder's Expected Rate of Return A.

The shareholder's expected rate of return is of great interest to financial managers because it tells about the investor’s expectations.

B.

Preferred stockholder's expected rate of return: If we know the market price of a preferred stock and the amount of the dividends to be received, the expected rate of return from the investment can be determined as follows: expected rate of return = or D

k ps = P 0 C.

Common stockholder's expected rate of return: 1.

The expected rate of return for common stock can be calculated from the valuation equations previously discussed.

341

2.

Assuming that dividends are increasing at a constant annual growth rate, g, we can show that the expected rate of return for common stock, kcs is k cs

=

+

=

+ g

Since dividend ÷ price is the "dividend yield," the Expected rate of return = + IV.

Appendix: The Relationship between Value and Earnings A.

Earnings and Value Relationship: The nongrowth firm 1.

2.

Nongrowth firms retain no profits for reinvestment purposes. a.

Investments are made to maintain status quo.

b.

Earnings and dividend growth stream is constant from year to year.

Value on nongrowth common stock, Vng: Vng =

B.

EPS k cs

1

=

D1 k cs

a.

Value of share changes in direct relationship with changes in earnings per share.

b.

Changes in the investor’s required rate of return will change share value.

Earnings and Value Relationship: The growth firm

1.

Growth firm reinvests profits back into the business.

2.

Value of stock equals the present value of the dividend stream plus the present value of the future growth resulting from reinvesting future earnings. Vcs =

EPS 1 + NVDG k cs

a.

NVDG is the net value of any dividend growth resulting from reinvestment of future earnings.

b.

Present value (PV1) from reinvesting part of the firms earnings in year 1 equals: PV 1 =

a.

r × EPS 1 × ROE k cs

− (r × EPS 1 )

Using the constant-growth model to value NVDG,

342

NVDG

b.

PV1 k cs − g

The value of a share of stock is therefore:

Vcs =

3.

=

EPS 1 PV1 + k cs k cs − g

Value of stock is influenced by a.

Size of the firm’s EPS,

b.

Percentage of profits retained,

c.

Spread between return generated on new investments and the investor’s required rate of return.

ANSWERS TO END-OF-CHAPTER QUESTIONS 8-1.

Preferred stock is often referred to as a hybrid security. This is because preferred stock has many characteristics of both common stock and bonds. It has characteristics of common stock, such as no fixed maturity date, nonpayment of dividends does not force bankruptcy, and the nondeductibility of dividends for tax purposes. But it is like bonds because the dividends are fixed in amount like interest payments. From the point of view of the preferred stockholder, this is not the most advantageous combination. On one hand, the dividends are limited as with bond interest, but the security of forced payment by the threat of bankruptcy is not there. Thus, from the point of view of the investor, the worst features of common stock and bonds are combined.

8-2.

To a certain extent, preferred stock dividends can be thought of as a liability. The major difference between preferred dividends in arrears and normal liabilities is that nonpayment of them cannot force the firm into bankruptcy. However, since the goal of the firm is common shareholder wealth maximization, which involves getting money to the common shareholders (dividends), preferred arrearages provide a barrier to achieving this goal.

8-3.

A cumulative feature requires all past unpaid preferred stock dividends be paid before any common stock dividends are declared. A stockholder would like preferred stock to have a cumulative dividend feature because without it there would be no reason why preferred stock dividends would not be omitted or passed when common stock dividends were passed. Since preferred stock does not have the dividend enforcement power of interest from bonds, the cumulative feature is necessary to protect the rights of preferred stockholders. Other frequent protective features serve to allow for voting rights in the event of nonpayment of dividends or to restrict the payment of common stock dividends if sinking-fund payments are not met or if the firm is in financial

343

difficulty. In effect, the protective features included with preferred stock are similar to the restrictive provisions included with long-term debt. 8-4.

Fixed rate preferred stock has dividends that do not vary from the fixed amount or from period to period. Adjustable rate preferred stock is preferred stock that has quarterly dividends that fluctuate with interest rates under a formula that ties the dividend payment at either a premium or discount to the highest of the three-month Treasury bill rate, the 10-year Treasury bond constant maturity rate, or the 20-year Treasury bond constant maturity rate. The rates have maximum and minimum levels called the dividend rate band. The purpose of allowing the dividend rate to fluctuate is to minimize the fluctuation in the value of the preferred stock. It is also very appealing in times of high and fluctuating interest rates.

8-5.

8-6.

With PIK (payment-in-kind) preferred stock, investors receive no dividends initially; they merely get more preferred stock, which in turn pays dividends in even more preferred stock. Usually after 5 or 6 years, if all goes well for the issuing company, cash dividends should replace the preferred stock dividends, generally ranging from 12 percent to 18 percent, to entice investors to purchase PIK preferred.

Convertibility allows a preferred stockholder to convert or exchange preferred stock for shares of common stock at a predetermined exchange rate. This option gives preferred stockholders more freedom in investment decisions by allowing them to convert into common stock at their discretion. It gives the preferred stockholder a higher cash return than the common stock but allows for sharing in some of the future appreciation of the common stock if they convert the stock. Preferred stock may be callable by the issuer so that in the event interest rates decline and cheaper funding becomes available, the stock may be called and new securities may be issued at a lower cost. To agree to the call feature, the investor requires a slightly higher rate of return. Call of a convertible preferred stock enables a company to turn the preferred stock into common equity; i.e., calling it without having to spend the cash.

8-7.

Both values are based on future cash flows to be received by stockholders. Preferred stock typically has a predetermined constant dividend. For common stock, the dividend is based on the profitability of the firm and on management’s decision to pay dividends or to retain the profits for reinvestment purposes. Thus, the growth of future dividends is a prime distinguishing feature of common stock.

8-8.

The expected rate of return is the rate of return that may be expected from purchasing a security at the prevailing market price. Thus, the expected rate of return is the rate that equates the present value of future cash flows with the actual selling price of the security in the market.

344

8-9.

The required rate of return is the discount rate that equates the present value of future cash flows with the intrinsic value of the security. As with the internal rate of return for a capital budgeting problem, we have to find the rate of return that sets the future cash flows equal to the cost of the security. This rate may have to be developed by trial and error.

8-10. The two types of return are dividend income and capital gains. The dividend income for common stockholders differs from preferred stockholders, in that no specified dividend amount is to be received. However, the common stockholders are permitted to participate in the growth of the company. As a result of this growth, their second source of return, price appreciation, is realized.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 8-1A.

Value (Vps)

8-2A.

Growth rate

8-3A.

Value (Vps)

8-4A.

=

$6 .12

=

$50.00

=

return on equity x retention rate

=

(16%) × (60%) = 9.6%

=

.14 × $100 .12

=

$14 .12

=

$116.67

Expected Rate of Return ps

8-5A. (a) (b)

=

Expected return =

Dividend Price

=

$1.95 $42 .16

Dividend Price

=

$3.40 $40

= .0463, or 4.63% = .085 = 8.5%

Given your 8 percent required rate of return, the stock is worth $42.50 to you. Value

=

Dividend Required Rate of Return

=

$3.40 .08

= $42.50

Since the expected rate of return (8.5%) is greater than your required rate of return (8%), or since the current market price ($40) is less than the value ($42.50), the stock is undervalued and you should buy.

345

8-6A.

Value (Vcs)

=

Dividend in Year 1 (1 + Required Rate)

$50

=

P1 $6 + (1 +.15 ) (1 +.15 )

+

Price in Year 1 (1 + Required Rate)

Rearranging and solving for P1: P1

=

$50 (1.15) - $6

P1

=

$51.50

The stock would have to increase $1.50 ($51.50 - $50) or 3 percent ($1.50/$50) to earn a 15% rate of return. 8-7A. (a)

Expected rate of return ( k cs )

cs cs

(b)

Vcs

=

=

Dividend in Year 1 growth + rate Market Price

=

$2.00 $22 .50

=

.1889, or 18.9%

$2.00 .17 − .10

+ .10

= $28.57

Yes, purchase the stock. The expected return is greater than your required rate of return. Also, the stock is selling for only $22.50, while it is worth $28.57 to you. 8-8A. Value (Vcs)

=

Vcs

=

Vcs

=

8-9A. Growth rate

Last Year Dividend (1 + Growth Rate) (Required Rate − Growth Rate)

$24.50

= return on equity x retention rate = (18%) × (40%) = 7.2%

8-10A. Expected Rate of Return ( k cs ) =

Last Year Dividend (1 + Growth Rate) Price

Rate k cs = + 0.095 k cs = 0.193, or 19.3%

346

+

Growth

8-11A.

Value (Vcs)

=

Dividend in Year 1 (1 + Required Rate)

Vcs

=

$1.85 $42 .50 + (1.11 ) (1.11 )

Vcs

=

+

Price in Year 1 (1 + Required Rate)

$39.95

8-12A. If the expected rate of return is represented by k cs : =

Dividend in Year 1 Price in Year 1 + (1 + k cs ) (1 + k cs )

k cs

=

Dividend in Year 1 + Price in Year 1 - 1 Current Price

k cs

=

$2.84 + $48 .00 $43 .00

k cs

=

0.1823, or 18.23%

k ps

=

Dividend Price

k ps

=

0.1091, or 10.91%

(b)

Value (Vps)

=

(c)

The investor's required rate of return (10 percent) is less than the expected rate of return for the investment (10.91 percent). Also, the value of the stock to the investor ($36) exceeds the existing market price ($33), so buy the stock.

Current Price

- 1

8-13A. (a)

8-14A.(a)

(b)

(c)

$3.60 $33 .00

Dividend Required Rate of Return

Expected Rate of Return

Investor's Value

=

=

= $3.60 = $36 0.10

Dividend in Year 1 Growth + Rate Market Price

=

$1.32 (1.08 ) + 0.08 $23 .50

=

0.1407, or 14.07%

=

Dividend in Year 1 Required Rate of Return - Growth Rate

=

$1.32 (1.08 ) 0.105 − 0.08

=

$57.02

Yes, the expected rate of return (14.07%) is greater than your required rate of return (10.5 percent). Also, your value of the stock ($57.02) is greater than the current market price ($23.50).

347

Dividend yield: Dividend ÷ stock price =

8-15A (a) (b)

$1.12 = 0.0229, or 2.29% $49

Using the nominal average returns of 12.2% for large-company stocks and the 3.8% nominal average return for U.S. Treasury Bills as shown in Table 6-1, the computation would be as follows:

(c)

risk − free  rate 

=

risk − free market + beta × return rate 

=

3.8% + 1.10 × (12.2% - 3.8%) = 13.04%

Expected rate of return

=

Dividend in Year 1 Growth + Rate Market Price

13.04%

=

$1.12 + g $49

Expected rate of return

-

.1304 = .0229 + g g = .1075, or 10.75% 8-16A Johnson & Johnson EPS (diluted) Dividend

2003 $2.40 $0.925

2002 $2.16 $0.795

Stock Price (6/24/04): $55.75 Growth rate: $2.40 = $1.39 (1 + i)4 i = .1463, or 14.63% k

cs

=

D1 +g P0

k

cs

=

$0.925 (1.1463) $55.75

k

cs

= .0190, or 1.90%

+ .1463

348

2001 $1.84 $0.70

2000 $1.61 $0.62

1999 $1.39 $0.55

8-17A. k ps

=

Dividend Price

k ps

=

0.18, or 18%

(b)

Value (Vps)

=

(c)

The investor's required rate of return (14 percent) is less than the expected rate of return for the investment (18 percent). Also, the value of the stock to the investor ($32.14) exceeds the existing market price ($25), so buy the stock.

(a)

Investor's Value

(a)

=

$4.50 $25

Dividend Required Rate of Return

= $4.50 = $32.14 0.14

8-18A.

(b)

(c)

8-19A. (a)

Expected Rate of Return

Dividend in Year 1 Required Rate of Return - Growth Rate

=

$2.30 (1.05 ) 0.15 −0.05

=

$24.15

=

Dividend in Year 1 Growth + Rate Market Price

=

$2.30 (1.05 ) + 0.05 $33

=

0.1232, or 12.32%

No, the expected rate of return (12.32%) is less than your required rate of return (15 percent). Also, your value of the stock ($24.15) is less than the current market price ($33). Growth rate = =

(b)

=

return on equity x retention rate (17%) × (30%) = 5.1%

(i) If retention rate is 40%: Growth rate = =

return on equity x retention rate (17%) × (40%) = 6.8%

(ii) If retention rate is 25%: Growth rate = =

return on equity x retention rate (17%) × (25%) = 4.25%

349

Expected rate

8-20A. (a)

of return ( k cs )

cs cs

(b)

Vcs

=

Dividend in Year 1 growth + rate Market Price

=

$1.75 (1 +0.04 ) + 0.04 $29 .50

=

.1017, or 10.17%

$1.75 (1 + 0.04 ) = $18.20 .14 − 0.04

=

No, do not purchase the stock. The expected return is less than your required rate of return. Also, the stock is selling for $29.50, while it is only worth $18.20 to you.

SOLUTION TO INTEGRATIVE PROBLEM 1.

Value (Vb) based upon your required rate of return: Bond: Vb

=

$140

12

∑

t =1

(1 + .12)

t

+

$1,000 (1 +.12 )12

12 12 140 1000 CPT

→

ANSWER

∞

$12

t =1

(1 +.14) t

-1123.89

Preferred Stock: Vps

=

∑

However, since the dividend is a constant amount each year with no maturity date (infinity), the equation can be reduced to Vps

=

Dividend Required Rate of Return

=

$12 .14

=

$85.71

Common Stock: Step 1:

Determine Growth Rate

350

10

$4.00 =

∑ t =1

$0.00 (1 + k b ) t

$8.00 (1 + k b )10

+

10 4 0 8 →

CPT

ANSWER

7.177%

Growth Rate (g) = 7.177% Step 2: Vcs

Solve for Value =

∞

∑ t =1

$3(1 + .07177) (1 + .20) t

t

If the growth rate (g) is assumed constant, the equation may be reduced to Vcs

=

Dividend at Year End Required Rate of Return − Growth Rate

=

D1 k cs − g

=

$3(1 +.07177 ) .20 −.07177

=

$25.08

2. Bond Preferred Stock Common Stock

Your Value $1,123.89 85.71 25.08

Selling Price $1,200.00 80.00 25.00

The bond should not be purchased because its market value is selling above its value to you. You can choose between the preferred stock and the common stock, because both have market values less than their values to you.

351

3.

Bond: Value (Vb)

=

12

∑ t =1

$140 (1 + .14)

t

+

$1,000 (1 + .14)

12

12 14 140 1000 →

CPT

ANSWER

-1000.00

You would not buy the bond; it is not worth $1,200.00. Preferred Stock: Vps

=

$12 .16

=

$75.00

Do not buy. Your value is less than what you would have to pay for the stock($80). Common Stock: Vcs

=

$3(1 +.07177 ) .18 −.07177

=

$29.71

Buy. Your value is greater than what you would have to pay for the stock($25). 4.

Assuming a growth rate of 12 percent: Vcs =

3(1 +.12 ) = $42 .00 .20 −.12

Buy the stock. Because of the expected increase in future dividends, the stock is now worth more to you ($42) than you would have to pay for it ($25) –assuming that the selling price did not increase also.

352

Solutions to Problem Set B 8-1B.

Value (Vps)

8-2B.

Growth rate

8-3B.

Value (Vps)

8-4B.

=

$7 .10

=

$70.00

=

return on equity x retention rate

=

(24%) × (70%) = 16.8%

=

.16 × $100 .12

=

$16 .12

=

$133.33

Expected Rate of Return

8-5B. (a) (b)

ps

=

Dividend Price

=

$2.35 $55 .16

= .0426, or 4.26%

Expected return

=

Dividend Price

=

$3.25 $38 .50

= .0844 , or 8.44%

Given your 8 percent required rate of return, the stock is worth $40.63 to you. Value

=

Dividend Required Rate of Return

=

$3.25 .08

= $40.63

Since the expected rate of return (8.44%) is greater than your required rate of return (8%), or since the current market price ($38.50) is less than the value ($40.63), the stock is undervalued and you should buy. 8-6B.

Value (Vcs)

=

Dividend in Year 1 (1 + Required Rate)

$52.75

=

P1 $6.50 + (1 +.16 ) (1 + .16 )

+

Price in Year 1 (1 + Required Rate)

Rearranging and solving for P1: P1

=

$52.75 (1.16) - $6.50

P1

=

$54.69

The stock would have to increase $1.94 ($54.69 - $52.75), or 3.68 percent, ($1.94/$52.75) to earn a 16% rate of return.

353

8-7B. (a)

(b)

Expected rate

Dividend in Year 1 + Market Price

=

of return ( k cs )

k cs

=

$2.50 $23 .00

k cs

=

0.2137, or 21.37%

Vcs

=

$2.50 .17 −.105

Growth Rate

+ .105

= $38.46

The expected rate of return exceeds your required rate of return, which means that the value of the security to you is greater than the current market price. Thus, you should buy the stock. 8-8B.

8-9B.

Value (Vcs)

=

Last Year Dividend (1 + Growth Rate) (Required Rate − Growth Rate)

Vcs

=

$3.75 (1 +.06 ) .20 −.06

Vcs

=

$28.39

Growth rate

=

return on equity x retention rate (24%) × (60%) = 14.4%

= 8-10B.

Expected Rate of Return ( k cs ) =

Last Year Dividend (1 + Growth Rate) Price

+ Growth

Rate =

k cs

$3.00 (1.085 ) $33 .84

+ 0.085 = 0.1812, or

18.12% 8-11B.

8-12B.

Value (Vcs)

Dividend in Year 1 (1 + Required Rate)

=

Vcs

=

Vcs

=

+

Price in Year 1 (1 + Required Rate)

$1.85 $40 .00 + (1.12 ) (1.12 )

$37.37

If the expected rate of return is represented by k cs : Current Price =

Dividend in Year 1 Price in Year 1 + (1 + k cs ) (1 + k cs )

k cs

=

Dividend in Year 1 + Price in Year 1 - 1 Current Price

k cs

=

$2.00 + $47 .00 $44 .00

k cs

=

0.1136, or 11.36%

354

- 1

8-13B. (a)

k ps

=

Dividend Price

$4.00 $35 .00

=

= 11.43%

Dividend Required Rate of Return

= $4.00 = $40

(b)

Value (Vps ) =

(c)

The investor's required rate of return (10 percent) is less than the expected rate of return for the investment (11.43 percent). Also, the value of the stock to the investor ($40) exceeds the existing market price ($35). The investor should buy the stock.

8-14B. (a)

(b)

(c)

8-15B (a) (b)

Expected Rate of Return

Investor's Value

Dividend in Year 1 + Market Pirce

=

$1.00 (1.08 ) + 0.08 $25 .00

=

0.1232, or 12.32%

=

Dividend in Year 1 Required Rate of Return − Growth Rate

=

$1.00 (1.08 ) 0.11 −0.08

= $36.00 Yes, the expected rate of return is greater than your required rate of return (12.32 percent versus 11 percent). Also, your value of the stock ($36.00) is higher than the current market price ($25.00). Dividend yield: Dividend ÷ stock price =

$1.20 $54

= 2.22%

Using the nominal average returns of 12.2% for large-company stocks and the 3.8% nominal average return for U.S. Treasury Bills as shown in Table 6-1, the computation would be as follows: Expected rate of return

(c)

=

0.10

Expected rate of return

11.36%

risk − free  rate 

=

risk − free market + beta × return rate 

=

3.8% + 0.90 × (12.2% - 3.8%) = 11.36%

=

Dividend in Year 1 Growth + Market Price Rate

=

$1.20 $54

.1136 = .0222 + g g = .0914, or 9.14%

355

+ g

-

8-16B Note to Instructor: Before the 10th edition of Financial Management was completed, we had not verified the earnings per share data for First Union Corporation. After the text went to production, we realized that First Union was merged into Wachovia Bank in 2001. We then planned to use the Wachovia earnings per share data, only to discover the significant volatility of the firm’s earnings over the past five years, which appears as follows: Earnings per share (diluted)

2003 $3.18

2002 $2.60

2001 $1.45

2000 $0.07

1999 $3.33

Since Wachovia’s earnings per share has actually decreased over the last five years, the growth rate in earnings per share is =1.146 percent (using 4 years to compute the growth rate). Clearly, the historical earnings per share do not provide a reasonable estimate of future earnings per share, which regrettably makes the problem difficult to use without having a meaningful growth estimate. Thus, the problem can only be used to show that relying on historical data does not always provide reasonable results. k ps

=

Dividend Price

k ps

=

0.1154, or 11.54%

(b)

Value (Vps)

=

(c)

The investor's required rate of return (10 percent) is less than the expected rate of return for the investment (11.54 percent). Also, the value of the stock to the investor, ($22.50) exceeds the existing market price ($19.50), so buy the stock.

(a)

Investor's Value

8-17B. (a)

$2.25 $19 .50

=

Dividend Required Rate of Return

= $2.25 = $22.50 0.10

8-18B.

(b)

(c)

8-19B. (a)

Expected Rate of Return

=

Dividend in Year 1 Required Rate of Return - Growth Rate

=

$1.95 (1.05 ) 0.12 −0.05

=

$29.25

=

Dividend in Year 1 Growth + Rate Market Price

=

$1.95 (1.05 ) + 0.05 $26

=

0.1288, or 12.88%

Yes, the expected rate of return (12.88%) is greater than your required rate of return (12 percent). Also, your value of the stock ($29.25) is greater than the current market price ($26). Growth rate

=

return on equity x retention rate

356

= (b)

(13%) × (20%) = 2.6%

(i) If retention rate is 35%: Growth rate

=

return on equity x retention rate

=

(13%) × (35%) = 4.55%

(ii) If retention rate is 13%: Growth rate

8-20B. (a)

=

return on equity x retention rate

=

(13%) × (13%) = 1.69%

Expected rate of return ( k cs )

cs cs

(b)

Vcs

=

growth rate

=

Dividend in Year 1 Market Price

=

$3.15 (1 + 0.07 ) + 0.07 $33 .75

=

.1699, or 16.99%

+

$3.15 (1 + 0.07 ) = $84.26 .11 − 0.07

Yes, purchase the stock. The expected return is significantly more than your required rate of return. Also, the stock is selling for $33.75, while it is worth $84.26 to you.

Solutions to Appendix 8A 8A-1. Using the NVDG model,

g

Vcs

=

EPS 1 k cs

where kcs

=

the investor's required rate of return

EPS1

=

the firm's earning per share in year 1

=

+

PV1 k cs − g

the growth rate, which is the firm's earnings retention rate times its return on equity.  r x EPS 1 x ROE  k cs 

  - (r x EPS1) 

PV1

=

r

=

the firm's earnings retention rate

ROE

=

the firm's return on equity investment

357

For our problem, PV1

= =

$4.0625 - $3.25

=

$0.8125

Vcs =

and

 (0.65 ) x ($ 5) x (0.20 )  - (0.65 x $5)   0.16  

$5 $0.8125 + .16 .16 −(0.65 )( 0.20 )

=

$31.25 + $27.08

=

$58.33

Using the more traditional dividend-growth model, we get: Vcs

=

D1 k cs − g

Since D1

=

EPS1(1 - the retention rate), and g

Vcs

=

=

the retention rate x return on equity

($ 5)(1 −.65 ) = $1.75 .16 − (. 65 )(. 20 ) .03

= $58.33

8A-2. Given the EPS1 is expected to be $7 and the investor's required rate of return is 18 percent, the value of the stock, assuming no growth opportunities would be: EPS 1 $7 Vcs = = $38.89 = k cs .18 where kcs

=

EPS1 =

the investor's required rate of return the firm's earning per share in year 1

To compute the present value of the growth opportunities, NVDG, for each scenario, we use the following equation: NVDG

=

PV1 k cs − g

 r x EPS 1 x ROE    - (r x EPS1) k cs   g = the growth rate, which is the firm's earnings retention rate times its return on equity.

where PV1 =

r ROE

= =

the firm's earnings retention rate the firm's return on equity investment

358

Given the different possible retention rates and ROEs, we may solve for the respective PV1s. The results are as follows: Possible

ROEs

Different Retention Rates

0%

30%

60%

16%

0.00

-0.23

-0.47

18%

0.00

0.00

0.00

24%

0.00

0.70

1.40

We next calculate the NVDG for each scenario by dividing the above PV1 values by kcs - g, which gives the following results: Possible ROEs 0%

30%

Different Retention Rates

60%

16%

0.00

-1.77

-5.56

18%

0.00

0.00

0.00

24%

0.00

6.48

38.89

Adding the $38.89 price, assuming no growth, to the above NVDGs, we get: Possible ROEs

0%

Different Retention Rates 30%

60%

16%

38.89

37.12

33.33

18%

38.89

38.89

38.89

24%

38.89

45.37

77.78

Thus, our results show that value is created only when management reinvests at above the investor's required rate of return. That is, growth may actually decrease the firm's value if the profitability of the new investments are not adequate enough to satisfy the investor's required returns.

359

CHAPTER 9

Capital Budgeting Decision Criteria CHAPTER ORIENTATION Capital budgeting involves the decision making process with respect to the investment in fixed assets; specifically, it involves measuring the incremental cash flows associated with investment proposals and evaluating the attractiveness of these cash flows relative to the project's costs. This chapter focuses on the various decision criteria.

CHAPTER OUTLINE I.

Methods for evaluating projects A.

The payback period method 1.

The payback period of an investment tells the number of years required to recover the initial investment. The payback period is calculated by adding the cash inflows up until they are equal to the initial fixed investment.

2.

Although this measure does, in fact, deal with cash flows and is easy to calculate and understand, it ignores any cash flows that occur after the payback period and does not consider the time value of money within the payback period.

3.

To deal with the criticism that the payback period ignores the time value of money, some firms use the discounted payback period method. The discounted payback period method is similar to the traditional payback period except that it uses discounted free cash flows rather than actual undiscounted free cash flows in calculating the payback period.

4.

The discounted payback period is defined as the number of years needed to recover the initial cash outlay from the discounted free cash 360

flows.

361

B.

Present-value methods 1.

The net present value of an investment project is the present value of its free cash flows less the investment’s initial outlay n

NPV

=

∑

t =1

FCF t (1 + k) t

- IO

where:

a.

FCFt =

the annual free cash flow in time period t (this can take on either positive or negative values)

k

=

the required rate of return or appropriate discount rate or cost of capital

IO

=

the initial cash outlay

n

=

the project's expected life

The acceptance criteria are accept if NPV ≥ 0 reject if NPV < 0

b.

2.

The advantage of this approach is that it takes the time value of money into consideration in addition to dealing with cash flows.

The profitability index is the ratio of the present value of the expected future free cash flows to the initial cash outlay, or n

∑

profitability index = a.

t =1

FCF t (1 + k) t IO

The acceptance criteria are accept if PI ≥ 1.0 reject if PI < 1.0

b.

The advantages of this method are the same as those for the net present value.

c.

Either of these present-value methods will give the same accept-reject decisions to a project.

362

C.

The internal rate of return is the discount rate that equates the present value of the project's future net cash flows with the project's initial outlay. Thus the internal rate of return is represented by IRR in the equation below: n

IO = 1.

∑

t =1

FCF t (1 + IRR)

t

The acceptance-rejection criteria are: accept if IRR ≥ required rate of return reject if IRR < required rate of return The required rate of return is often taken to be the firm's cost of capital.

2.

The advantages of this method are that it deals with cash flows and recognizes the time value of money; however, the procedure is rather complicated and time-consuming. The net present value profile allows you to graphically understand the relationship between the internal rate of return and NPV. A net present value profile is simply a graph showing how a project’s net present value changes as the discount rate changes. The IRR is the discount rate at which the NPV equals zero.

3.

The primary drawback of the internal rate of return deals with the reinvestment rate assumption it makes. The IRR implicitly assumes that the cash flows received over the life of the project can be reinvested at the IRR while the NPV assumes that the cash flows over the life of the project are reinvested at the required rate of return. Since the NPV makes the preferred reinvestment rate assumption it is the preferred decision technique. The modified internal rate of return (MIRR) allows the decision maker the intuitive appeal of the IRR coupled with the ability to directly specify the appropriate reinvestment rate. a.

To calculate the MIRR we take all the annual free tax cash inflows, ACIFt's, and find their future value at the end of the project's life compounded at the required rate of return - this is called the terminal value or TV. All cash outflows, ACOFt, are then discounted back to present at the required rate of return. The MIRR is the discount rate that equates the present value of the free cash outflows with the present value of the project's terminal value.

b.

If the MIRR is greater than or equal to the required rate of return, the project should be accepted.

363

ANSWERS TO END-OF-CHAPTER QUESTIONS 9-1.

9-2.

Capital budgeting decisions involve investments requiring rather large cash outlays at the beginning of the life of the project and commit the firm to a particular course of action over a relatively long time horizon. As such, they are costly and difficult to reverse, both because of: (1) their large cost and (2) the fact that they involve fixed assets, which cannot be liquidated easily.

The criticisms of using the payback period as a capital budgeting technique are: (1) (2) (3)

It ignores the timing of the free cash flows that occur during the payback period. It ignores all free cash flows occurring after the payback period. The selection of the maximum acceptable payback period is arbitrary.

The advantages associated with the payback period are: (1) (2) (3)

It deals with cash flows rather than accounting profits, and therefore focuses on the true timing of the project's benefits and costs. It is easy to calculate and understand. It can be used as a rough screening device, eliminating projects whose returns do not materialize until later years.

These final two advantages are the major reasons why it is used frequently. 9-3.

Yes. The payback period eliminates projects whose returns do not materialize until later years and thus emphasizes the earliest returns, which in a country experiencing frequent expropriations would certainly have the most amount of uncertainty surrounding the later returns. In this case, the payback period could be used as a rough screening device to filter out those riskier projects, which have long lives.

9-4.

The three, discounted cash flow capital budgeting criteria are the net present value, the profitability index, and the internal rate of return. The net present value method gives an absolute dollar value for a project by taking the present value of the benefits and subtracting out the present value of the costs. The profitability index compares these benefits and costs through division and comes up with a measure of the project's relative value—a benefit/cost ratio. On the other hand, the internal rate of return tells us the rate of return that the project earns. In the capital budgeting area, these methods generally give us the same accept-reject decision on projects but many times rank them differently. As such, they have the same general advantages and disadvantages, although the calculations associated with the internal rate of return method can become quite tedious and it assumes cash flows over the life of the life of the project are reinvested at the IRR. The advantages associated with these discounted cash flow methods are: (1) They deal with cash flows rather than accounting profits. (2) They recognize the time value of money. (3) They are consistent with the firm's goal of shareholder wealth maximization. 364

9-5

The advantage of using the MIRR, as opposed to the IRR technique is that the MIRR technique allows the decision maker to directly input the reinvestment rate assumption. With the IRR method it is implicitly assumed that the cash flows over the life of the project are reinvested at the IRR.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 9-1A. (a)

(b)

(c)

(d)

9-2A. (a)

(b)

IO

=

FCFt [PVIFIRR%,t yrs]

$10,000

=

$17,182 [PVIFIRR%,8 yrs]

0.582

=

PVIFIRR%,8 yrs

Thus, IRR

=

7%

$10,000

=

$48,077 [PVIFIRR%,10 yrs]

0.208

=

PVIFIRR%,10 yrs

Thus, IRR

=

17%

$10,000

=

$114,943 [PVIFIRR%,20 yrs]

0.087

=

PVIFIRR%,20 yrs

Thus, IRR

=

13%

$10,000

=

$13,680 [PVIFIRR%,3 yrs]

.731

=

PVIFIRR%,3 yrs

Thus, IRR

=

11%

I0

=

FCFt [PVIFAIRR%,t yrs]

$10,000

=

$1,993 [PVIFAIRR%,10 yrs]

5.018

=

PVIFAIRR%,10 yrs

Thus, IRR

=

15%

$10,000

=

$2,054 [PVIFAIRR%,20 yrs]

4.869

=

PVIFAIRR%,20 yrs

Thus, IRR

=

20%

365

(c)

(d)

9-3A. (a)

$10,000

=

$1,193 [PVIFAIRR%,12 yrs]

8.382

=

PVIFAIRR%,12 yrs

Thus, IRR

=

6%

$10,000

=

$2,843 [PVIFAIRR%,5 yrs]

3.517

=

PVIFAIRR%,5 yrs

Thus, IRR

=

13%

$10,000

=

$2,000 (1 + IRR)

1

+

$5,000 (1 + IRR)

2

+

$8,000 (1 + IRR)

3

Try 18%: $10,000

=

$2,000(0.847) + $5,000 (0.718) + $8,000 (0.609)

=

$1,694 + $3,590 + $4,872

=

$10,156

=

$2,000 (0.840) + $5,000 (0.706) + $8,000 (0.593)

=

$1,680 + $3,530 + $4,744

=

$9,954

Thus, IRR

=

approximately 19%

$10,000

=

Try 19% $10,000

(b)

$8,000 (1 + IRR)

1

+

$5,000 (1 + IRR)

2

+

$2,000 (1 + IRR)

3

Try 30% $10,000

=

$8,000 (0.769) + $5,000 (0.592) + $2,000 (0.455)

=

$6,152 + $2,960 + $910

=

$10,022

=

$8,000 (0.763) + $5,000 (0.583) + $2,000 (0.445)

=

$6,104 + $2,915 + $890

=

$9,909

=

approximately 30%

Try 31%: $10,000

Thus, IRR

366

(c)

$10,000

=

$2,000

5

∑

t =1

(1 + IRR)

t

+

$5,000 (1 + IRR ) 6

Try 11% $10,000

=

$2,000 (3.696) + $5,000 (0.535)

=

$7,392 + $2,675

=

$10,067

=

$2,000 (3.605) + $5,000 (0.507)

=

$7,210 + $2,535

=

$9,745

Thus, IRR

=

approximately 11%

NPV

=

Try 12% $10,000

9-4A. (a)

(b)

(c)

(d)

6

$450,000

t =1

(1 +.09)

∑

t

- $1,950,000

=

$450,000 (4.486) - $1,950,000

=

$2,018,700 - $1,950,000 = $68,700

=

$2,018 ,700 $1,950 ,000

=

1.0352

$1,950,000

=

$450,000 [PVIFAIRR%,6 yrs]

4.333

=

PVIFAIRR%,6 yrs

IRR

=

about 10% (10.1725%)

PI

Yes, the project should be accepted.

367

9-5A. (a)

Payback Period = $80,000/$20,000 = 4 years Discounted Payback Period Calculations:

Year

Undiscounted Cash Flows

PVIF10%,n

-$80,000 20,000 20,000 20,000 20,000 20,000 20,000

1.000 .909 .826 .751 .683 .621 .564

0 1 2 3 4 5 6

Discounted Cash Flows

Cumulative Discounted Cash Flows

-$80,000 18,180 16,520 15,020 13,660 12,420 11,280

Discounted Payback Period = 5.0 + 4,200/11,280 = 5.37 years. (b)

(c)

(d)

9-6A. (a)

NPV

=

6

$20,000

t =1

(1 +.10)

∑

t

- $80,000

=

$20,000 (4.355) - $80,000

=

$87,100 - $80,000 = $7,100

=

$87 ,100 $80 ,000

=

1.0888

$80,000

=

$20,000 [PVIFAIRR%,6 yrs]

4.000

=

PVIFAIRR%,6 yrs

IRR

=

about 13% (12.978%)

NPVA

=

PI

NPVB

6

$12,000

t =1

(1 +.12)

∑

t

- $50,000

=

$12,000 (4.111) - $50,000

=

$49,332 - $50,000 = -$668

=

6

$13,000

t =1

(1 +.12)

∑

t

- $70,000

=

$13,000 (4.111) - $70,000

=

$53,443 - $70,000 = -$16,557

368

-$80,000 -61,820 -45,300 -30,280 -16,620 -4,200 7,080

(b)

=

$49 ,332 $50 ,000

=

0.9866

=

$53 ,443 $70 ,000

=

0.7635

$50,000

=

$12,000 [PVIFAIRR%,6 yrs]

4.1667

=

PVIFAIRR%,6 yrs

IRRA

=

11.53%

$70,000

=

$13,000 [PVIFAIRR%,6 yrs]

5.3846

=

PVIFAIRR%,6 yrs

IRRB

=

3.18%

PIA

PIB

(c)

Neither project should be accepted. 9-7A. (a)

Project A: Payback Period = 2 years + $100/$200 = 2.5 years Project A: Discounted Payback Period Calculations:

Year 0 1 2 3 4 5

Undiscounted Cash Flows PVIF10%,n -$1,000 600 300 200 100 500

1.000 .909 .826 .751 .683 .621

369

Discounted Cash Flows -$1,000 545 248 150 68 311

Cumulative Discounted Cash Flows -$1,000 -455 -207 -57 11 322

Discounted Payback Period = 3.0 + 57/68 = 3.84 years. Project B: Payback Period = 2 years + $2,000/$3,000 = 2.67 years Project B: Discounted Payback Period Calculations:

Year

Undiscounted Cash Flows PVIF10%,n

0 1 2 3 4 5

-$10,000 5,000 3,000 3,000 3,000 3,000

Discounted Cash Flows

1.000 .909 .826 .751 .683 .621

Cumulative Discounted Cash Flows

-$10,000 4,545 2,478 2,253 2,049 1,863

-$10,000 -5,455 -2,977 -724 1,325 3,188

Discounted Payback Period = 3.0 + 724/2,049 = 3.35 years. Project C: Payback Period = 3 years + $1,000/$2,000 = 3.5 years Project C: Discounted Payback Period Calculations: Year 0 1 2 3 4 5

Undiscounted Cash Flows -$5,000 1,000 1,000 2,000 2,000 2,000

PVIF10%,n

Discounted Cash Flows

Cumulative Discounted Cash Flows

1.000 .909 .826 .751 .683 .621

-$5,000 909 826 1,502 1,366 1,242

-$5,000 -4,091 -3,265 -1,763 -397 845

370

Discounted Payback Period = 4.0 + 397/1,242 = 4.32 years.

9-8A. NPV9%

NPV11%

NPV13%

NPV15%

Project

Traditional Payback

Discounted Payback

A

Accept

Reject

B

Accept

Reject

C

Reject

Reject

=

8

∑

t =1

$1,000,000

- $5,000,000

(1 + .09) t

=

$1,000,000 (5.535) - $5,000,000

=

$5,535,000 - $5,000,000 = $535,000

=

8

∑

t =1

$1,000,000

- $5,000,000

(1 + .11) t

=

$1,000,000 (5.146) - $5,000,000

=

$5,146,000 - $5,000,000 = $146,000

=

$1,000,000 t =1 (1 + .13)t

=

$1,000,000 (4.799) - $5,000,000

=

$4,799,000 - $5,000,000 = -$201,000

=

8

∑

8

∑

t =1

- $5,000,000

$1,000,000

- $5,000,000

(1 + .15) t

=

$1,000,000 (4.487) - $5,000,000

=

$4,487,000 - $5,000,000 = -$513,000

9-9A. Project A: $50,000

=

$10,000 1

(1 + IRR A )

+

+

$15,000 (1 + IRR A )

$25,000 (1 + IRR A )

371

4

+

2

+

$20,000 (1 + IRR A )3

$30,000 (1 + IRR A )5

Try 23% $50,000

=

$10,000(.813) + $15,000(.661) + $20,000(.537) + $25,000(.437) + $30,000(.355)

=

$8,130 + $9,915 + $10,740 + $10,925 + $10,650

=

$50,360

=

$10,000(.806) + $15,000(.650) +$20,000(.524)

Try 24% $50,000

+ $25,000(.423) + $30,000(.341) =

$8,060 + $9,750 + $10,480 + $10,575 + $10,230

=

$49,095

=

just over 23%

$100,000

=

$25,000 [PVIFAIRR%,5 yrs]

4.00

=

PVIFAIRR%,5 yrs

Thus, IRR

=

8%

$450,000

=

$200,000 [PVIFAIRR%,3 yrs]

2.25

=

PVIFAIRR%,3 yrs

Thus, IRR

=

16%

Thus, IRR Project B:

Project C:

9-10A. (a)

(b)

NPV

NPV

=

$18,000

t =1

(1 +.10)

∑

t

- $100,000

=

$18,000(6.145) - $100,000

=

$110,610 - $100,000

=

$10,610

= = = =

(c)

10

10

$18,000

t =1

(1 +.15)

∑

t

- $100,000

$18,000(5.019) - $100,000 $90,342 - $100,000 -$9,658

If the required rate of return is 10% the project is acceptable as in part (a).

372

(d)

9-11A. (a)

(b)

(c)

$100,000

=

5.5556

=

$18,000 [PVIFAIRR%,10 yrs] PVIFAIRR%,10 yrs

IRR

=

Between 12% and 13% (12.41%)

n

ACOF

t =0

(1 + k)

∑

n

t t

=

∑

t =0

ACIF t (1 + k) n −t (1 + MIRR)

$10,000,000

=

$10,000,000

=

$10,000,000

=

MIRR

=

$10,000,000

=

$10,000,000

=

$10,000,000

=

MIRR

=

$10,000,000

=

$10,000,000

=

$10,000,000

=

MIRR

=

n

$3,000,000 (FVIFA 10%10years ) (1 + MIRR) 10 $3,000 ,000 (15 .937 ) (1 + MIRR )10 $47 ,811 ,000 (1 + MIRR )10

16.9375% $3,000,000 (FVIFA 12%10years ) (1 + MIRR) 10 $3,000 ,000 (17 .549 ) (1 + MIRR )10 $52 ,647 ,000 (1 + MIRR )10

18.0694% $3,000 ,000 ( FVIFA 14 %10 years ) (1 + MIRR )10 $3,000 ,000 (19 .337 ) (1 + MIRR )10 $58 ,011 ,000 (1 + MIRR )10

19.2207%

373

SOLUTION TO INTEGRATIVE PROBLEM 1.

Capital budgeting decisions involve investments requiring rather large cash outlays at the beginning of the life of the project and commit the firm to a particular course of action over a relatively long time horizon. As such, they are both costly and difficult to reverse, both because of: (1) their large cost; (2) the fact that they involve fixed assets which cannot be liquidated easily.

2.

Axiom 5: The Curse of Competitive Markets—Why It's Hard to Find Exceptionally Profitable Projects deals with the problems associated with finding profitable projects. When we introduced that axiom we stated that exceptionally successful investments involve the reduction of competition by creating barriers to entry either through product differentiation or cost advantages. In effect, without barriers to entry, whenever extremely profitable projects are found competition rushes in, driving prices and profits down unless there is some barrier to entry.

3.

Payback periodA

= 3 years +

Payback PeriodB

=

20 ,000 years 50 ,000

110 ,000 years 40 ,000

=

=

3.4 years

2.75 years

Project B should be accepted while project A should be rejected. 4.

The disadvantages of the payback period are: 1) ignores the time value of money, 2)ignores cash flows occurring after the payback period, 3)selection of the maximum acceptable payback period is arbitrary.

5.

Discounted Payback Period Calculations, Project A:

Year 0 1 2 3 4 5

Undiscounted Cash Flows -$110,000 20,000 30,000 40,000 50,000 70,000

PVIF12%,n 1.000 .893 .797 .712 .636 .567

Discounted Cash Flows -$110,000 17,860 23,910 28,480 31,800 39,690

Cumulative Discounted Cash Flows -$110,000 -92,140 -68,230 -39,750 -7,950 31,740

Discounted Payback Period = 4.0 + 7,950/39,690 = 4.20 years.

374

Discounted Payback Period Calculations, Project B:

Year

Undiscounted Cash Flows

0 1 2 3 4 5

PVIF12%,n

-$110,000 40,000 40,000 40,000 40,000 40,000

1.000 .893 .797 .712 .636 .567

Discounted Cash Flows -$110,000 35,720 31,880 28,480 25,440 22,680

Cumulative Discounted Cash Flows -$110,000 -74,280 -42,400 -13,920 11,520 34,200

Discounted Payback Period = 3.0 + 13,920/25,440 = 3.55 years. Using the discounted payback period method and a 3-year maximum acceptable project hurtle, neither project should be accepted. 6.

7.

NPVA

The major problem with the discounted payback period comes in setting the firm's maximum desired discounted payback period. This is an arbitrary decision that affects which projects are accepted and which ones are rejected. Thus, while the discounted payback period is superior to the traditional payback period, in that it accounts for the time value of money in its calculations, its use should be limited due to the problem encountered in setting the maximum desired payback period. In effect, neither method should be used. =

n

∑

t =1

=

=

FCF t (1 + k) t

- IO

$20,000(PVIF12%, 1 year) + $30,000 (PVIF12%, 2 years) +

$40,000(PVIF12%, 3 years) + $50,000 (PVIF12%, 4 years)

+

$70,000(PVIF12%, 5 years) - $110,000

$20,000(.893) + $30,000 (.797) + $40,000 (.712) + $50,000 (.636) + $70,000 (.567) - $110,000

NPVB

=

$17,860 + $23,910 + $28,480 + $31,800 + $39,690 - $110,000

=

$141,740-$110,000

=

$31,740

=

$40,000(PVIFA12%, 5 years) - $110,000

=

$40,000(3.605) - $110,000

=

$144,200-$110,000

=

$34,200 375

Both projects should be accepted 8.

9.

PIA

PIB

The net present value technique discounts all the benefits and costs in terms of cash flows back to the present and determines the difference. If the present value of the benefits outweighs the present value of the costs, the project is accepted, if not, it is rejected.

=

 n  ∑ FCF  t =1  t  (1 +k)   IO

=

$141 ,740 $110 ,000

=

1.2885

=

$144 ,200 $110 ,000

=

1.3109

t

      

Both projects should be accepted

12.

10.

The net present value and the profitability index always give the same accept reject decision. When the present value of the benefits outweighs the present value of the costs the profitability index is greater than one, and the net present value is positive. In that case, the project should be accepted. If the present value of the benefits is less than the present value of the costs, then the profitability index will be less than one, and the net present value will be negative, and the project will be rejected.

11.

For both projects A and B all of the costs are already in present dollars and, as such, will not be affected by any change in the required rate of return or discount rate. All the benefits for these projects are in the future and thus when there is a change in the required rate of return or discount rate their present value will change. If the required rate of return increased, the present value of the benefits would decline which would in turn result in a decrease in both the net present value and the profitability index for each project.

IRRA

=

20.9698%

IRRB

=

23.9193%

13.

14.

The required rate of return does not change the internal rate of return for a project, but it does affect whether a project is accepted or rejected. The required rate of return is the hurdle rate that the project's IRR must exceed in order to accept the project.

The net present value assumes that all cash flows over the life of the project are 376

reinvested at the required rate of return, while the internal rate of return implicitly assumes that all cash flows over the life of the project are reinvested over the remainder of the project's life at the IRR. The net present value method makes the most acceptable, and conservative assumption and thus is preferred. 15.

Project A: n

n

ACOF

t =0

(1 + k)

∑

$110,000

t t

=

∑ t =0

ACIF t (1 + k) n −t (1 + MIRR)

n

=

$20,000(FV IF12% , 4 years) + $30,000(FV IF12% , 3 years) + $40,000(FV IF12% , 2 years) + $50,000(FV IF12% , 1 year) + $70,000 (1 + MIRR A ) 5

$110,000

=

$20 ,000 (1.574 ) + $30 ,000 (1.405 ) + $40 ,000 (1.254 ) + $50 ,000 (1.120 ) + $70 ,000 (1 + MIRR A ) 5

$110,000 = $31 ,480 + $42 ,150 + $50 ,160 + $56 ,000 + $70 ,000 (1 + MIRR A ) 5 $249 ,790

$110,000

=

(1 + MIRR A )5

MIRRA

=

17.8247%

Project B:

$40,000(FVIFA12%,5years )

$110,000

=

$110,000

=

$110,000

=

(1 + MIRR B )5

MIRRB

=

18.2304%

(1 + MIRR B )5 $40,000(6. 353) (1 + MIRR

B)

5

$254,120

Both projects should be accepted because their MIRR exceeds the required rate of return. The modified internal rate of return is superior to the internal rate of return method because

377

MIRR assumes the reinvestment rate of cash flows is the required rate of return.

378

Solutions to Problem Set B 9-1B. (a)

(b)

(c)

(d)

9-2B. (a)

(b)

(c)

(d)

IO

=

FCFt [PVIFIRR%,t yrs]

$10,000

=

$19,926 [PVIFIRR%,8 yrs]

0.502

=

PVIFIRR%,8 yrs

Thus, IRR

=

9%

$10,000

=

$20,122 [PVIFIRR%,12 yrs]

0.497

=

PVIFIRR%,12 yrs

Thus, IRR =

6%

$10,000

=

$121,000 [PVIFIRR%,22 yrs]

0.083

=

PVIFIRR%,22 yrs

Thus, IRR

=

12%

$10,000

=

$19,254 [PVIFIRR%,5 yrs]

0.519

=

PVIFIRR%,5 yrs

Thus, IRR

=

14%

IO

=

FCFt [PVIFAIRR%,t yrs]

$10,000

=

$2,146 [PVIFAIRR%,10 yrs]

4.66

=

PVIFAIRR%,10 yrs

Thus, IRR

=

17%

$10,000

=

$1,960 [PVIFAIRR%,20 yrs]

5.102

=

PVIFAIRR%,20 yrs

Thus, IRR

=

19%

$10,000

=

$1,396 [PVIFAIRR%,12 yrs]

7.163

=

PVIFAIRR%,12 yrs]

Thus, IRR

=

9%

$10,000

=

$3,197 [PVIFAIRR%,5 yrs]

3.128

=

PVIFAIRR%,5 yrs

Thus, IRR

=

18%

379

9-3B. (a)

$10,000

=

$3,000 (1 + IRR)

+

1

$5,000 2

(1 + IRR)

+

$7,500 (1 + IRR)

3

Try 21%: $10,000

=

$3,000(0.826) + $5,000 (0.683) + $7,500 (0.564)

=

$2,478+ $3,415 + $4,230

=

$10,123

=

$3,000 (0.820) + $5,000 (0.672) + $7,500 (0.551)

=

$2,460 + $3,360 + $4,132.50

=

$9,952.50

Thus, IRR

=

approximately 22%

$12,000

=

Try 22% $10,000

(b)

$9,000 (1 + IRR)

1

+

$6,000 (1 + IRR)

2

+

$2,000 (1 + IRR)

3

Try 25% $12,000

=

$9,000 (0.800) + $6,000 (0.640) + $2,000 (0.512)

=

$7,200 + $3,840 + $1,024

=

$12,064

=

$9,000 (0.794) + $6,000 (0.630) + $2,000 (0.500)

=

$7,146 + $3,780 + $1,000

=

$11,926

Thus, IRR

=

nearest percent is 25%

$8,000

=

∑

Try 26%: $12,000

5

(c)

t =1

$2,000 (1 + IRR)

t

+

$5,000 (1 + IRR)

Try 18% $8,000

=

$2,000 (3.127) + $5,000 (0.370)

=

$6,254 + $1,850

=

$8,104

=

$2,000 (3.058) + $5,000 (0.352)

=

$6,116 + $1,760

=

$7,876

=

nearest percent is 18%

Try 19% $8,000

Thus, IRR

380

6

9-4B. (a)

(b)

(c)

(d) 9-5B. (a) (b)

(c)

(d)

9-6B. (a)

NPV

PI

6

$750,000

t =1

(1 +.11)

∑

t

- $2,500,000

=

$750,000 (4.231) - $2,500,000

=

$3,173,250 - $2,500,000

=

$673,250

=

$3,173 ,250 $2,500 ,000

=

1.2693

$2,500,000 =

$750,000 [PVIFAIRR%,6 yrs]

3.333

=

PVIFAIRR%,6 yrs

IRR

=

about 20% (19.90%)

Yes, the project should be accepted. Payback Period = $160,000/$40,000 = 4 years NPV

=

6

$40,000

t =1

(1 +.10)

∑

t

- $160,000

=

$40,000 (4.355) - $160,000

=

$174,200 - $160,000 = $14,200

=

$174 ,200 $160 ,000

=

1.0888

$160,000

=

$40,000 [PVIFAIRR%,6 yrs]

4.000

=

PVIFAIRR%,6 yrs

IRR

=

about 13% (12.978%)

NPVA

=

PI

NPVB

(b)

=

PIA

6

$12,000

t =1

(1 +.12)

∑

t

- $45,000

=

$12,000 (4.111) - $45,000

=

$49,332 - $45,000 = $4,332

=

6

$14,000

t =1

(1 +.12)

∑

t

- $70,000

=

$14,000 (4.111) - $70,000

=

$57,554 - $70,000 = -$12,446

=

$49 ,332 $45 ,000

381

=

1.0963

=

$57 ,554 $70 ,000

=

0.822

$45,000

=

$12,000 [PVIFAIRR%,6 yrs]

3.75

=

PVIFAIRR%,6 yrs

IRRA

=

15.34%

$70,000

=

$14,000 [PVIFAIRR%,6 yrs]

5.0000

=

PVIFAIRR%,6 yrs

IRRB

=

5.47%

PIB

(c)

Project A should be accepted. 9-7B. (a)

Project A: Payback Period

=

2 years

=

2 years + $1,000/$3,000 = 2.33 years

=

3 years + $1,000/$2,000 = 3.5 years

Project B: Payback Period Project C: Payback Period

9-8B. NPV9%

=

Project

Payback Period Method

A

Accept

B

Accept

C

Reject

8

∑

t =1

$2,500,000 (1 + .09) t

- $10,000,000

=

$2,500,000 (5.535) - $10,000,000

=

$13,837,500 - $10,000,000 = $3,837,500

NPV11% =

8

∑

t =1

$2,500,000 (1 + .11) t

- $10,000,000

=

$2,500,000 (5.146) - $10,000,000

=

$12,865,000 - $10,000,000 = $2,865,000

NPV13% =

8

∑

t =1

$2,500,000 (1 + .13) t

- $10,000,000

382

=

$2,500,000 (4.799) - $10,000,000

=

$11,997,500 - $10,000,000 = $1,997,500

NPV15% =

8

∑

$2,500,000

- $10,000,000

(1 + .15) t

t =1

=

$2,500,000 (4.487) - $10,000,000

=

$11,217,500 - $10,000,000 = $1,217,500

9-9B. Project A: $75,000

=

$10,000 (1 + IRR A )1

+

+

$10,000 (1 + IRR A )

$25,000 (1 + IRR A )

4

2

+

$30,000 (1 + IRR A )3

$30,000

+

(1 + IRR A )5

Try 10% $75,000

=

$10,000(.909) + $10,000(.826) + $30,000(.751) + $25,000(.683) + $30,000(.621)

=

$9,090 + $8,260 + $22,530 + $17,075 + $18,630

=

$75,585

=

$10,000(.901) + $10,000(.812) +$30,000(.731)

Try 11% $75,000

+ $25,000(.659) + $30,000(.593) =

$9,010 + $8,120 + $21,930+ $16,475 + $17,790

=

$73,325

Thus, IRR

=

just over 10%

$95,000

=

$25,000 [PVIFAIRR%,5 yrs]

3.80

=

PVIFAIRR%,5 yrs

Thus, IRR

=

just below 10%

=

$150,000 [PVIFAIRR%,3 yrs]

2.633

=

PVIFAIRR%,3 yrs

Thus, IRR

=

just below 7%

=

∑

Project B:

Project C: $395,000

10

9-10B. (a)

NPV

t =1

$25,000 (1 + .09)

t

383

- $150,000

(b)

NPV

=

$25,000(6.418) - $150,000

=

$160,450 - $150,000

=

$10,450

=

10

$25,000

t =1

(1 +.15)

∑

t

- $150,000

=

$25,000(5.019) - $150,000

=

$125,475 - $150,000

=

-$24,525

(c)

If the required rate of return is 9% the project is acceptable in part (a). It should be rejected in part (b) with a negative NPV.

(d)

$150,000 =

$25,000 [PVIFAIRR%,10 yrs]

6.000

=

PVIFAIRR%,10 yrs

IRR

=

Between 10% and 11% (10.558%)

9-11B. (a)

b)

c)

n

∑

t =0

ACOF

n

t

(1 + k) t

$8,000,000

=

$8,000,000

=

$8,000,000

=

MIRR

=

$8,000,000

=

$8,000,000

=

$8,000,000

=

MIRR

=

$8,000,000

=

=

n-t ∑ ACIF t (1 + k)

t =0

(1 + MIRR)

n

$2,000,000 (FVIFA10% ,8years ) (1 + MIRR) 8 $2,000,000 (11.436) (1 + MIRR)

8

$22,872000 (1 + MIRR)

8

14.0320% $2,000,000 (FVIFA12% ,8years ) (1 + MIRR) 8 $2,000,000 (12.300) (1 + MIRR)

8

$24,600,00 0 (1 + MIRR)

8

15.0749% $2,000,000 (FVIFA14% ,8years ) (1 + MIRR) 8

384

$8,000,000

=

$8,000,000

=

MIRR

=

$2,000,000 (13.233) (1 + MIRR)

8

$26,466,00 0 (1 + MIRR)

8

16.1312%

FORD'S PINTO (Ethics in Capital Budgeting) OBJECTIVE:

To force the students to recognize the role ethical behavior plays in all areas of Finance.

DEGREE OF DIFFICULTY:

Easy

Case Solution: With ethics cases there are no right or wrong answers - just opinions. Try to bring out as many opinions as possible without being judgmental.

CHAPTER 10

Cash Flows and Other Topics in Capital Budgeting CHAPTER ORIENTATION 385

Capital budgeting involves the decision-making process with respect to the investment in fixed assets; specifically, it involves measuring the free cash flows or incremental cash flows associated with investment proposals and evaluating the attractiveness of these cash flows relative to the project's costs. This chapter focuses on the estimation of those cash flows based on various decision criteria, and how to deal with capital rationing and mutually exclusive projects.

CHAPTER OUTLINE I.

What criteria should we use in the evaluation of alternative investment proposals? A.

Use free cash flows rather than accounting profits because free cash flows allow us to correctly analyze the time element of the flows.

B.

Examine free cash flows on an after-tax basis because they are the flows available to shareholders. C.

D.

Include only the incremental cash flows resulting from the investment decision. Ignore all other flows.

In deciding which free cash flows are relevant we want to: 1.

Use free cash flows rather than accounting profits as our measurement tool.

2.

Think incrementally, looking at the company with and without the new project. Only incremental after tax cash flows, or free cash flows, are relevant.

3.

Beware of cash flows diverted from existing products, again, looking at the firm as a whole with the new product versus without the new product.

386

II.

4.

Bring in working capital needs. Take account of the fact that a new project may involve the additional investment in working capital.

5.

Consider incremental expenses.

6.

Do not include stock costs as incremental cash flows.

7.

Account for opportunity costs.

8.

Decide if overhead costs are truly incremental cash flows.

9.

Ignore interest payments and financing flows.

Measuring free cash flows. We are interested in measuring the incremental after-tax cash flows, or free cash flows, resulting from the investment proposal. In general, there will be three major sources of cash flows: initial outlays, differential cash flows over the project's life, and terminal cash flows. A.

B.

Initial outlays include whatever cash flows are necessary to get the project in running order, for example: 1.

The installed cost of the asset

2.

In the case of a replacement proposal, the selling price of the old machine minus (or plus) any tax gain (or tax loss) offsetting the initial outlay

3.

Any expense items (for example, training) necessary for the operation of the proposal

4.

Any other non-expense cash outlays required, such as increased working-capital needs

Differential cash flows over the project's life include the incremental after-tax flows over the life of the project, for example: 1.

Added revenue (less added selling expenses) for the proposal

2.

Any labor and/or material savings incurred

3.

Increases in overhead incurred

4.

Changes in taxes.

5.

Change in net working capital.

6.

Change in capital spending.

7.

Make sure calculations reflect the fact that while depreciation is an expense, it does not involve any cash flows.

8.

A word of warning not to include financing charges (such as interest or preferred stock dividends), for they are implicitly taken care of in the discounting process.

387

C.

Terminal cash flows include any incremental cash flows that result at the termination of the project, for example: 1.

The project's salvage value plus (or minus) any taxable gains or losses associated with the project

2.

Any terminal cash flow needed, perhaps disposal of obsolete equipment

3. Recovery of any non-expense cash outlays associated with the project, such as recovery of increased working-capital needs associated with the proposal. III.

Measuring the cash flows using the pro forma method A.

A project’s free cash flows = project’s change in operating cash flows

B

-

change in net working capital

-

change in capital spending

If we rewrite this, inserting the calculations for the project’s change in operating cash flows (OCF), we get: A project’s free cash flows = Change in earnings before interest and taxes -

change in taxes

+

change in depreciation

-

change in net working capital

-

change in capital spending

C.

In addition to using the pro forma method for calculating operating cash flows, there are three other approaches that are also commonly used. A summary of all the different approaches follows,

D.

OCF Calculation: The Pro Forma Approach: Operating Cash Flows = Change in Earnings Before Interest and Taxes Change in Taxes + Change in Depreciation

E.

Alternative OCF Calculation 1: Add Back Approach Operating Cash Flows = Net income + Depreciation

E.

Alternative OCF Calculation 2: Definitional Approach Operating Cash Flows = Change in revenues - Change in cash expenses Change in Taxes

388

F.

Alternative OCF Calculation 3: Depreciation Tax Shield Approach Operating Cash Flows = (Revenues – cash expenses) X (1 – tax rate) + (change in depreciation X tax rate) You’ll notice that interest payments are no where to be found, that’s because we ignore them when we’re calculating operating cash flows. You’ll also notice that we end up with the same answer regardless of how we work the problem.

IV.

V.

Mutually exclusive projects: Although the IRR and the present-value methods will, in general, give consistent accept-reject decisions, they may not rank projects identically. This becomes important in the case of mutually exclusive projects. A.

A project is mutually exclusive if acceptance of it precludes the acceptance of one or more projects. Then, in this case, the project's relative ranking becomes important.

B.

Ranking conflicts come as a result of the different assumptions on the reinvestment rate on funds released from the proposals.

C.

Thus, when conflicting ranking of mutually exclusive projects results from the different reinvestment assumptions, the decision boils down to which assumption is best.

D.

In general, the net present value method is considered to be theoretically superior.

Capital rationing is the situation in which a budget ceiling or constraint is placed upon the amount of funds that can be invested during a time period. –

VI.

Theoretically, a firm should never reject a project that yields more than the required rate of return. Although there are circumstances that may create complicated situations in general, an investment policy limited by capital rationing is less than optimal.

Options in Capital Budgeting. Options in capital budgeting deal with the opportunity to modify the project. Three of the most common types of options that can add value to a capital budgeting project are: (1) the option to delay a project until the future cash flows are more favorable – this option is common when the firm has exclusive rights, perhaps a patent, to a product or technology, (2) the option to expand a project, perhaps in size or even to new products that would not have otherwise been feasible, and (3) the option to abandon a project if the future cash flows fall short of expectations.

389

ANSWERS TO END-OF-CHAPTER QUESTIONS 10-1. We focus on cash flows rather than accounting profits because these are the flows that the firm receives and can reinvest. Only by examining cash flows are we able to correctly analyze the timing of the benefit or cost. Also, we are only interested in these cash flows on an after tax basis as only those flows are available to the shareholder. In addition, it is only the incremental cash flows that interest us, because, looking at the project from the point of the company as a whole, the incremental cash flows are the marginal benefits from the project and, as such, are the increased value to the firm from accepting the project. 10-2. Although depreciation is not a cash flow item, it does affect the level of the differential cash flows over the project's life because of its effect on taxes. Depreciation is an expense item and, the more depreciation incurred, the larger are expenses. Thus, accounting profits become lower and, in turn, so do taxes, which are a cash flow item. 10-3. If a project requires an increased investment in working capital, the amount of this investment should be considered as part of the initial outlay associated with the project's acceptance. Since this investment in working capital is never "consumed," an offsetting inflow of the same size as the working capital's initial outlay will occur at the termination of the project corresponding to the recapture of this working capital. In effect, only the time value of money associated with the working capital investment is lost. 10-4. When evaluating a capital budgeting proposal, sunk costs are ignored. We are interested in only the incremental after-tax cash flows to the company as a whole. Regardless of the decision made on the investment at hand, the sunk costs will have already occurred, which means these are not incremental cash flows. Hence, they are irrelevant. 10-5. Mutually exclusive projects involve two or more projects where the acceptance of one project will necessarily mean the rejection of the other project. This usually occurs when the set of projects perform essentially the same task. Relating this to our discounted cash flow criteria, it means that not all projects with positive NPV's, profitability indexes greater than 1.0 and IRRs greater than the required rate of return will be accepted. Moreover, since our discounted cash flow criteria do not always yield the same ranking of projects, one criterion may indicate that the mutually exclusive project A should be accepted, while another criterion may indicate that the mutually exclusive project B should be accepted. 10-6. There are three principal reasons for imposing a capital rationing constraint. First, the management may feel that market conditions are temporarily adverse. In the early- and mid-seventies, this reason was fairly common, because interest rates were at an all-time high and stock prices were at a depressed level. The second reason is a manpower shortage, that is, a shortage of qualified managers to direct new projects. The final reason involves intangible considerations. For example, the management may simply fear debt, and so avoid interest payments at any cost. Or the common

390

stock issuance may be limited in order to allow the current owners to maintain strict voting control over the company or to maintain a stable dividend policy. Whether or not this is a rational move depends upon the extent of the rationing. If it is minor and noncontinuing, then the firm's share price will probably not suffer to any great extent. However, it should be emphasized that capital rationing and rejection of projects with positive net present values is contrary to the firm's goal of maximization of shareholders’ wealth. 10-7. When two mutually exclusive projects of unequal size are compared, the firm should select the project with the largest net present value, when there is no capital rationing. If there is capital rationing, then the firm should select the set of projects with the highest net present value. The firm needs to consider alternative uses of funds if the project with the lowest net present value is chosen. 10-8. The time disparity problem and the conflicting rankings that accompany it result from the differing reinvestment assumptions made by the net present value and internal rate of return decision criteria. The net present value criterion assumes that cash flows over the life of the project can be reinvested at the required rate of return; the internal rate of return implicitly assumes that the cash flows over the life of the project can be reinvested at the internal rate of return. 10.9.

The problem of incomparability of projects with different lives is not directly a result of the projects having different lives but of the fact that future profitable investment proposals are being affected by the decision currently being made. Again the key is: "Does the investment decision being made today affect future profitable investment proposals?" If so, the projects are not comparable. While the most theoretically proper approach is to make assumptions as to investment opportunities in the future, this method is probably too difficult to be of any value in most cases. Thus, the most common method used to deal with this problem is the creation of a replacement chain to equalize life spans. In effect, the reinvestment opportunities in the future are assumed to be similar to the current ones. Another approach is to calculate the equivalent annual annuity of each project.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 10-1A. (a)

Tax payments associated with the sale for $35,000 Recapture of depreciation = ($35,000-$15,000) (0.34) = $6,800

(b)

Tax payments associated with sale for $25,000 Recapture of depreciation

391

= ($25,000-$15,000) (0.34) = $3,400 (c)

No taxes, because the machine would have been sold for its book value.

(d)

Tax savings from sale below book value: Tax savings = ($15,000-$12,000) (0.34)

=

$1,020

10-2A. New Sales

$25,000,000

Less: Sales taken from existing product lines

- 5,000,000 $20,000,000

10-3A. Change in net working capital equals the increase in accounts receivable and inventory less the increase in accounts payable = $18,000 + $15,000 - $24,000 = $9,000. The change in taxes will be EBIT X marginal tax rate = $475,000 X .34 = $161,500. A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = + -

$475,000 $161,500 $100,000 $9,000 $0 = $404,500 10-4A. Change in net working capital equals the increase in accounts receivable and inventory less the increase in accounts payable = $8,000 + $15,000 - $16,000 = $7,000. The change in taxes will be EBIT X marginal tax rate = $900,000 X .34 = $306,000. A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = + -

$900,000 $306,000 $300,000 $7,000 $0

392

= $887,000

393

10-5A. Given this, the firm’s net profit after tax can be calculated as: Revenue - Cash expenses - Depreciation = EBIT - Taxes (34%) = Net income

$2,000,000 800,000 200,000 $1,000,000 340,000 $ 660,000

OCF Calculation: Pro Forma Approach Operating Cash Flows = Change in Earnings Before Interest and Taxes - Change in Taxes + Change in Depreciation = $1,000,000 - $340,000 + $200,000 = $860,000 Alternative OCF Calculation 1: Add Back Approach Operating Cash Flows = Net income + Depreciation = $660,000 + $200,000 = $860,000 Alternative OCF Calculation 2: Definitional Approach Operating Cash Flows = Change in revenues - Change in cash expenses – Change in Taxes = $2,000,000 - $800,000 -$340,000 = $860,000 Alternative OCF Calculation 3: Depreciation Tax Shield Approach Operating Cash Flows = (Revenues – cash expenses) X (1 – tax rate) + (change in depreciation X tax rate) = ($2,000,000 - $800,000) X (1-.34) + ($200,000 X.34) = $860,000 You’ll notice that interest payments are nowhere to be found, that’s because we ignore them when we’re calculating operating cash flows. You’ll also notice that we end up with the same answer regardless of how we work the problem. 10-6A. Given this, the firm’s net profit after tax can be calculated as: Revenue - Cash expenses - Depreciation = EBIT - Taxes (34%) = Net income

$3,000,000 900,000 400,000 $1,700,000 578,000 $1,122,000

394

As you can see, regardless of which method you use to calculate operating cash flows, you get the same answer: OCF Calculation: Pro Forma Approach Operating Cash Flows = Change in Earnings Before Interest and Taxes - Change in Taxes + Change in Depreciation = $1,700,000 - $578,000 + $400,000 = $1,522,000 Alternative OCF Calculation 1: Add Back Approach Operating Cash Flows = Net income + Depreciation = $1,122,000 + $400,000 = $1,522,000 Alternative OCF Calculation 2: Definitional Approach Operating Cash Flows = Change in revenues - Change in cash expenses – Change in Taxes = $3,000,000 - $900,000 -$578,000 = $1,522,000 Alternative OCF Calculation 3: Depreciation Tax Shield Approach Operating Cash Flows = (Revenues – cash expenses) X (1 – tax rate) + (change in depreciation X tax rate) = ($3,000,000 - $900,000)X(1-.34) + ($400,000 X.34) = $1,522,000 You’ll notice that interest payments are no where to be found, that’s because we ignore them when we’re calculating operating cash flows. You’ll also notice that we end up with the same answer regardless of how we work the problem. 10-7A. (a)

Initial Outlay Outflows: Purchase price Increased Inventory Net Initial Outlay

(b)

$1,000,000 50,000 $1,050,000

Differential annual cash flows (years 1-9) First, given this, the firm’s net profit after tax can be calculated as: Revenue - Cash expenses - Depreciation* = EBIT - Taxes (34%) = Net income

$1,000,000 560,000 100,000 $340,000 115,600 $224,400

395

A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $340,000 - $115,600 + $100,000* - $0 - $0 = $324,400 *Annual Depreciation on the new machine is calculated by taking the purchase price ($1,000,000) and adding in costs necessary to get the new machine in operating order (in this case $0) and dividing by the expected life. (c)

Terminal Cash flow (year 10) Inflows: Free Cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow

(d)

NPV

$324,400 50,000 $374,400

= $324,400 (PVIFA10%,9 yr.) + $374,400 (PVIF10%, 10 yr.) - $1,050,000 = $324,400 (5.759) + $374,400 (.386) - $1,050,000 = $1,868,220 + $144,518 - $1,050,000 = $962,738

10-8A. (a)

Initial Outlay Outflows: Purchase price Increased Inventory Net Initial Outlay

(b)

$5,000,000 1,000,000 $6,000,000

Differential annual cash flows (years 1-4) First, given this, the firm’s net profit after tax can be calculated as: Revenue - Cash expenses - Depreciation* = EBIT - Taxes (34%)

$5,000,000 3,500,000 1,000,000 $ 500,000 170,000

396

= Net income

$ 330,000

397

A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $500,000 - $170,000 + $1,000,000* - $0 - $0 = $1,330,000 *Annual Depreciation on the new machine is calculated by taking the purchase price ($5,000,000) and adding in costs necessary to get the new machine in operating order ($0) and dividing by the expected life. (c)

Terminal Cash flow (year 5) Inflows: Free Cash flow in year 5 Recapture of working capital (inventory) Total terminal cash flow

(d)

NPV

$1,330,000 1,000,000 $2,330,000

= $1,330,000 (PVIFA10%,4 yr.) + $2,330,000 (PVIF10%, 5 yr.) - $6,000,000 = $1,330,000 (3.170) + $2,330,000 (.621) - $6,000,000 = $4,216,100 + $1,446,930 - $6,000,000 = -$336,970

Since the NPV is negative, this project should be rejected. 10-9A. (a)

Initial Outlay Outflows: Purchase price Installation Fee Increased Working Capital Inventory Net Initial Outlay

398

$100,000 5,000 5,000 $110,000

(b)

Differential annual free cash flows (years 1-9) A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $35,000 - $11,900 + $10,500* - $0 - $0 = $33,600

* Annual Depreciation on the new machine is calculated by taking the purchase price ($100,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life. (c)

Terminal Free Cash flow (year 10) Inflows: Free Cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow

(d)

NPV

$33,600 5,000 $ 38,600

= $33,600 (PVIFA15%,9 yr.) + $38,600 (PVIF15%, 10 yr.) - $110,000 = $33,600 (4.772) + $38,600 (.247) - $110,000 = $160,339.20 + $9,534.20 - $110,000 = $59,873.40

Yes, the NPV > 0. 10-10A.(a)

Initial Outlay Outflows: Purchase price Installation Fee Training Session Fee Increased Inventory Net Initial Outlay

$ 500,000 5,000 25,000 30,000 $560,000

399

(b)

Differential annual free cash flows (years 1-9) A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $150,000 - $51,000 + $50,500* - $0 - $0 = $149,500

*Annual Depreciation on the new machine is calculated by taking the purchase price ($500,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life. (c)

Terminal Free Cash flow (year 10) Inflows: Free Cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow

(d)

NPV

$149,500 30,000 $ 179,500

= $149,500 (PVIFA15%,9 yr.) + $179,500 (PVIF15%, 10 yr.) - $560,000 = $149,500 (4.772) + $179,500 (.247) - $560,000 = $713,414 + $44,336.50 - $560,000 = $197,750.50

Yes, the NPV > 0. 10-11A.(a)

Initial Outlay Outflows: Purchase price Installation Fee Training Session Fee Increased Inventory Net Initial Outlay

$ 200,000 5,000 5,000 20,000 $230,000

400

(b)

Differential annual cash flows (years 1-9) A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $50,000 - $17,000 + $20,500* - $0 - $0 = $53,500

*Annual Depreciation on the new machine is calculated by taking the purchase price ($200,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life. (c)

Terminal Cash flow (year 10) Inflows: Free Cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow

(d)

NPV

$53,500 20,000 $ 73,500

= $53,500 (PVIFA10%,9 yr.) + $73,500 (PVIF10%, 10 yr.) - $230,000

= $53,500 (5.759) + $73,500 (.386) - $230,000 = $308,106.50 + $28,371 - $230,000 = $106,477.50 Yes, the NPV > 0.

401

10-12A Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 5 Units Sold 70,000 120,000 120,000 80,000 70,000 Sale Price $300 $300 $300 $300 $250 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%)

$21,000,000 9,800,000 $700,000 $10,500,000 $3,000,000 $7,500,000 $2,550,000

$36,000,000 16,800,000 $700,000 $18,500,000 $3,000,000 $15,500,000 $5,270,000

$36,000,000 16,800,000 $700,000 $18,500,000 $3,000,000 $15,500,000 $5,270,000

264

Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $7,500,000 $15,500,000 $15,500,000 Minus: Taxes $2,550,000 $5,270,000 $5,270,000 Plus: Depreciation $3,000,000 $3,000,000 $3,000,000 Equals: Operating Cash Flow $7,950,000 $13,230,000 $13,230,000

$24,000,000 11,200,000 $700,000 $12,100,000 $3,000,000 $9,100,000 $3,094,000

$17,500,000 9,800,000 $700,000 $7,000,000 $3,000,000 $4,000,000 $1,360,000

$9,100,000 $3,094,000 $3,000,000 $9,006,000

$4,000,000 $1,360,000 $3,000,000 $5,640,000

Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section IV) Change in Net Working Capital: Revenue: $21,000,000 $36,000,000 $36,000,000 $24,000,000 Initial Working Capital Requirement $200,000 Net Working Capital Needs: $2,100,000 $3,600,000 $3,600,000 $2,400,000 Liquidation of Working Capital Change in Working Capital: $200,000 $1,900,000 $1,500,000 $0 ($1,200,000) Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $7,950,000 $13,230,000 $13,230,000 $9,006,000 Minus: Change in Net Working Capital $200,000 $1,900,000 $1,500,000 $0 ($1,200,000) Minus: Change in Capital Spending $15,000,000 $0 $0 $0 $0 Free Cash Flow: ($15,200,000) $6,050,000 $11,730,000 $13,230,000 $10,206,000 NPV $17,461,989 PI 2.15

$17,500,000 $1,750,000 $1,750,000 ($2,400,000)

$5,640,000 ($2,400,000) $0 $8,040,000

IRR

45%

Should accept project

403

10-13A Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 5 Units Sold 80,000 100,000 120,000 70,000 70,000 Sale Price $250 $250 $250 $250 $250 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%)

$20,000,000 10,400,000 $300,000 $9,300,000 $1,400,000 $7,900,000 $2,686,000

$25,000,000 13,000,000 $300,000 $11,700,000 $1,400,000 $10,300,000 $3,502,000

$30,000,000 15,600,000 $300,000 $14,100,000 $1,400,000 $12,700,000 $4,318,000

265

Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $7,900,000 $10,300,000 $12,700,000 Minus: Taxes $2,686,000 $3,502,000 $4,318,000 Plus: Depreciation $1,400,000 $1,400,000 $1,400,000 Equals: Operating Cash Flow $6,614,000 $8,198,000 $9,782,000

$17,500,000 9,100,000 $300,000 $8,100,000 $1,400,000 $6,700,000 $2,278,000

$14,000,000 9,100,000 $300,000 $4,600,000 $1,400,000 $3,200,000 $1,088,000

$6,700,000 $2,278,000 $1,400,000 $5,822,000

$3,200,000 $1,088,000 $1,400,000 $3,512,000

Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section IV) Change in Net Working Capital: Revenue: $20,000,000 $25,000,000 $30,000,000 $17,500,000 Initial Working Capital Requirement $100,000 Net Working Capital Needs: $2,000,000 $2,500,000 $3,000,000 $1,750,000 Liquidation of Working Capital Change in Working Capital: $100,000 $1,900,000 $500,000 $500,000 ($1,250,000) Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $6,614,000 $8,198,000 $9,782,000 $5,822,000 Minus: Change in Net Working $100,000 $1,900,000 $500,000 $500,000 ($1,250,000) Capital Minus: Change in Capital Spending $7,000,000 $0 $0 $0 $0 Free Cash Flow: ($7,100,000) $4,714,000 $7,698,000 $9,282,000 $7,072,000 NPV $15,582,572.99

$14,000,000 $1,400,000 $1,400,000 ($1,750,000)

$3,512,000 ($1,750,000) $0 $5,262,000

PI IRR

3.19 85%

Should accept project.

405

10-14A.(a)

NPVA =

NPVB

(b)

(1 + 0.10 )1

- $500

=

$636.30 - $500

=

$136.30 $6,000

=

(1 + 0.10 )1

=

$5,454 - $5,000

=

$454

=

$636 .30 $500 .00

=

1.2726

=

$5,454 $5,000

=

1.0908

$500

=

$700 [PVIFIRR%,1 yr]

0.714

=

PVIFIRR%,1 yr

Thus, IRRA

=

40%

$5,000

=

$6,000 [PVIFIRR%,1 yr]

0.833

=

[PVIFIRR%,1 yr]

PIA

PIB

(c)

$700

- $5,000

Thus, IRRB= 20% (d)

10-15A.(a)

(b)

If there is no capital rationing, project B should be accepted because it has a larger net present value. If there is a capital constraint, the problem then focuses on what can be done with the additional $4,500 freed up if project A is chosen. If Dorner Farms can earn more on project A, plus the project financed with the additional $4,500, than it can on project B, then project A and the marginal project should be accepted. Payback A = 3.2 years Payback B = 4.5 years B assumes even cash flow throughout year 5. NPVA

=

5

$15,625

t =1

(1 + 0.10)

∑

t

- $50,000

=

$15,625 (3.791) - $50,000

=

$59,234 - $50,000

=

$9,234

406

=

$1,000 ,000 - $50,000 (1 + 0.10 ) 5

=

$100,000 (0.621) - $50,000

=

$62,100 - $50,000

=

$12,100

$50,000

=

$15,625 [PVIFAIRR %,5 yrs] A

3.2

=

PVIFAIRR%,5 yrs

Thus, IRRA

=

17%

$50,000

=

$100,000 [PVIFIRR %,5 yrs] B

NPVB

(c)

.50

= Thus, IRRB

PVIFIRR %,5 yrs B =

15%

(d)

The conflicting rankings are caused by the differing reinvestment assumptions made by the NPV and IRR decision criteria. The NPV criterion assumes that cash flows over the life of the project can be reinvested at the required rate of return or cost of capital, while the IRR criterion implicitly assumes that the cash flows over the life of the project can be reinvested at the internal rate of return.

(e)

Project B should be taken because it has the largest NPV. The NPV criterion is preferred because it makes the most acceptable assumption for the wealth maximizing firm.

10-16A. (a)

(b)

Payback A

=

1.589 years

Payback B

=

3.019 years

NPVA

=

3

$12,590

t =1

(1 + 0.15)

∑

- $20,000

=

$12,590 (2.283) - $20,000

=

$28,743 - $20,000

=

$8,743 9

NPVB

t

=

∑ t =1

$6,625 (1 + 0.15)

t

- $20,000

=

$6,625 (4.772) - $20,000

=

$31,615 - $20,000

=

$11,615

407

(c)

$20,000

=

Thus, IRRA

=

$20,000

=

Thus, IRRB

=

$12,590 [PVIFAIRR %,3 yrs] A 40% $6,625 [PVIFAIRR %,9 yrs] B 30%

(d)

These projects are not comparable because future profitable investment proposals are affected by the decision currently being made. If project A is taken, at its termination the firm could replace the machine and receive additional benefits while acceptance of project B would exclude this possibility.

(e)

Using 3 replacement chains, project A's cash flows would become: Year 0 1 2 3 4 5 6 7 8 9

NPVA

=

9

$12,590

t =1

(1 + 0.15)

∑

$20 ,000 (1 + 0.15 )

Cash flow -$20,000 12,590 12,590 - 7,410 12,590 12,590 - 7,410 12,590 12,590 12,590

3

−

t

- $20,000 -

$20 ,000 (1 + 0.15 )6

=

$12,590(4.772) - $20,000 - $20,000 (0.658) - $20,000 (0.432)

=

$60,079 - $20,000 - $13,160 - $8,640

=

$18,279

The replacement chain analysis indicated that project A should be selected as the replacement chain associated with it has a larger NPV than project B. Project A's EAA: Step 1: Calculate the project's NPV (from part b): NPVA = $8,743 Step 2: Calculate the EAA: EAAA = NPV / PVIFA15%, 3 yr. = =

$8,743 / 2.283 $3,830

Project B's EAA:

408

Step 1: Calculate the project's NPV (from part b): NPVB

=

$11,615

Step 2: Calculate the EAA: EAAB

=

NPV / PVIFA15%, 9 yr.

=

$11,615 / 4.772

=

$2,434

Project A should be selected because it has a higher EAA. 10-17A.(a)

Project A's EAA: Step1:

Calculate the project's NPV: NPVA

=

$20,000 (PVIFA10%, 7 yr.) - $50,000

=

$20,000 (4.868) - $50,000

=

$97,360 - $50,000

=

$47,360

Step 2: Calculate the EAA: EAAA =

NPV / PVIFA10%, 7 yr.

=

$47,360 / 4.868

=

$9,729

Project B's EAA: Step 1: Calculate the project's NPV: NPVB

=

$36,000 (PVIFA10%, 3 yr.) - $50,000

=

$36,000 (2.487) - $50,000

=

$89,532 - $50,000

=

$39,532

Step 2: Calculate the EAA: EAAB

=

NPV / PVIFA10%, 3 yr.

=

$39,532 / 2.487

=

$15,895

Project B should be selected because it has a higher EAA. (b)

NPV∞ ,A NPV∞ ,B

=

$9,729 / .10

=

$97,290

=

$15,895 / .10

409

=

$158,950

410

10-18A.(a) Project A B C D E F G

Cost $4,000,000 3,000,000 5,000,000 6,000,000 4,000,000 6,000,000 4,000,000

Profitability Index 1.18 1.08 1.33 1.31 1.19 1.20 1.18

Present Value of Future Cash Flows $4,720,000 3,240,000 6,650,000 7,860,000 4,760,000 7,200,000 4,720,000

NPV $ 720,000 240,000 1,650,000 1,860,000 760,000 1,200,000 720,000

COMBINATIONS WITH TOTAL COSTS BELOW $12,000,000 Projects A&B A&C A&D A&E A&F A&G B&C B&D B&E B&F B&G C&D C&E C&F C&G D&E D&F D&G E&F E&G F&G A&B&C A&B&G A&B&E A&E&G B&C&E B&C&G

Costs $ 7,000,000 9,000,000 10,000,000 8,000,000 10,000,000 8,000,000 8,000,000 9,000,000 7,000,000 9,000,000 7,000,000 11,000,000 9,000,000 11,000,000 9,000,000 10,000,000 12,000,000 10,000,000 10,000,000 8,000,000 10,000,000 12,000,000 11,000,000 11,000,000 12,000,000 12,000,000 12,000,000

NPV $ 960,000 2,370,000 2,580,000 1,480,000 1,920,000 1,440,000 1,890,000 2,100,000 1,000,000 1,440,000 960,000 3,510,000 2,410,000 2,850,000 2,370,000 2,620,000 3,060,000 2,580,000 1,960,000 1,480,000 1,920,000 2,610,000 1,680,000 1,720,000 2,200,000 2,650,000 2,610,000

Thus projects C&D should be selected under strict capital rationing as they provide the combination of projects with the highest net present value. (b)

Because capital rationing forces the rejection of profitable projects it is not an optimal strategy.

411

SOLUTION TO INTEGRATIVE PROBLEMS 1.

We focus on free cash flows rather than accounting profits because these are the flows that the firm receives and can reinvest. Only by examining cash flows are we able to correctly analyze the timing of the benefit or cost. Also, we are only interested in these cash flows on an after tax basis as only those flows are available to the shareholder. In addition, it is only the incremental cash flows that interest us, because, looking at the project from the point of the company as a whole, the incremental cash flows are the marginal benefits from the project and, as such, are the increased value to the firm from accepting the project.

2.

Although depreciation is not a cash flow item, it does affect the level of the differential cash flows over the project's life because of its effect on taxes. Depreciation is an expense item and, the more depreciation incurred, the larger are expenses. Thus, accounting profits become lower and in turn, so do taxes which are a cash flow item.

3.

When evaluating a capital budgeting proposal, sunk costs are ignored. We are interested in only the incremental after-tax cash flows, or free cash flows, to the company as a whole. Regardless of the decision made on the investment at hand, the sunk costs will have already occurred, which means these are not incremental cash flows. Hence, they are irrelevant.

412

Solution to Integrative Problem, parts 4, 5, & 6. Section I. Calculate the change in EBIT, Taxes, and Depreciation (this become an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 Units Sold 70,000 120,000 140,000 80,000 Sale Price $300 $300 $300 $300 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%)

$21,000,000 12,600,000 $200,000 $8,200,000 $1,600,000 $6,600,000 $2,244,000

$36,000,000 21,600,000 $200,000 $14,200,000 $1,600,000 $12,600,000 $4,284,000

5 60,000 $260

272

$42,000,000 25,200,000 $200,000 $16,600,000 $1,600,000 $15,000,000 $5,100,000

$24,000,000 14,400,000 $200,000 $9,400,000 $1,600,000 $7,800,000 $2,652,000

$15,600,000 10,800,000 $200,000 $4,600,000 $1,600,000 $3,000,000 $1,020,000

Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $6,600,000 $12,600,000 $15,000,000 Minus: Taxes $2,244,000 $4,284,000 $5,100,000 Plus: Depreciation $1,600,000 $1,600,000 $1,600,000 Equals: Operating Cash Flow $5,956,000 $9,916,000 $11,500,000

$7,800,000 $2,652,000 $1,600,000 $6,748,000

$3,000,000 $1,020,000 $1,600,000 $3,580,000

$24,000,000

$15,600,000

$2,400,000 ($1,800,000)

$1,560,000 $1,560,000 ($2,400,000)

Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $5,956,000 $9,916,000 $11,500,000 $6748,000 Minus: Change in Net Working Capital $100,000 $2,000,000 $1,500,000 $600,000 ($1,800,000) Minus: Change in Capital Spending $8,000,000 0 $0 0 0 Free Cash Flow: ($8,100,000) $3,956,000 $8,416,000 $10,900,000 $8,548,000

$3,580,000 ($2,400,000) 0 $5,980,000

Section III. Calculate the Net Working Capital (This becomes an input in the calculation of Free Cash Flows in Section IV). Change In Net Working Capital: Revenue: $21,000,000 $36,000,000 $42,000,000 Initial Working Capital Requirement $100,000 Net Working Capital Needs: $2,100,000 $3,600,000 $4,200,000 Liquidation of Working Capital Change in Working Capital: $100,000 $2,000,000 $1,500,000 $600,000

NPV =

$16,731,095.66

IRR =

77%

414

7.

Cash flow diagram $3,956,000

$8,416,000

$10,900,000

$8,548,000

$5,980,000

($8,100,000) 8.

NPV

= $16,731,095.66

9.

IRR

=

10.

Yes. This project should be accepted because the NPV ≥ 0. and the IRR ≥ required rate of return.

11.

a.

77%

NPVA

NPVB

b.

PIA

PIB

c.

=

$240 ,000 (1 + 0.10 )1

- $195,000

=

$218,182 - $195,000

=

$23,182

=

$1,650 ,000 (1 + 0.10 )1

- $1,200,000

=

$1,500,000 - $1,200,000

=

$300,000

=

$218 ,182 $195 ,000

=

1.1189

=

$1,500 ,000 $1,200 ,000

=

1.25

$195,000

= $240,000 [PVIFIRR %,1 yr] A

0.8125

= PVIFIRR %,1 yr A

Thus, IRRA = 23%

415

$1,200,000 = $1,650,000 [PVIFIRR %,1 yr] B 0.7273

= [PVIFIRR %,1 yr] B

Thus, IRRB = 37.5%

12.

d.

If there is no capital rationing, project B should be accepted because it has a larger net present value. If there is a capital constraint, the problem then focuses on what can be done with the additional $1,005,000 freed up if project A is chosen. If Caledonia can earn more on project A, plus the project financed with the additional $1,005,000, than it can on project B, then project A and the marginal project should be accepted.

a.

Payback A = 3.125 years Payback B = 4.5 years B assumes even cash flow throughout year 5.

b.

NPVA

=

5

$32,000

t =1

(1 + 0.11)

∑

t

- $100,000

= $32,000 (3.696) - $100,000 = $118,272 - $100,000 = $18,272 NPVB

=

$200 ,000 (1 + 0.11 )5

- $100,000

= $200,000 (0.593) - $100,000 = $118,600 - $100,000 = $18,600 c.

$100,000

= $32,000 [PVIFAIRR %,5 yrs] A

3.125

= PVIFAIRR %,5 yrs A

Thus, IRRA = 18.03% $100,000

= $200,000 [PVIFIRR %,5 yrs] B

.50

= PVIFIRR %,5 yrs B

Thus IRRB is just under 15% (14.87%).

416

13.

d.

The conflicting rankings are caused by the differing reinvestment assumptions made by the NPV and IRR decision criteria. The NPV criterion assume that cash flows over the life of the project can be reinvested at the required rate of return or cost of capital, while the IRR criterion implicitly assumes that the cash flows over the life of the project can be reinvested at the internal rate of return.

e.

Project B should be taken because it has the largest NPV. The NPV criterion is preferred because it makes the most acceptable assumption for the wealth maximizing firm.

a.

Payback A = 1.5385 years Payback B = 3.0769 years

b.

NPVA

=

3

$65,000

t =1

(1 + 0.14)

∑

t

- $100,000

= $65,000 (2.322) - $100,000 = $150,930 - $100,000 = $50,930 NPVB

=

9

$32,500

t =1

(1 + 0.14)

∑

t

- $100,000

= $32,500 (4.946) - $100,000 = $160,745 - $100,000 = $60,745 c.

$100,000

= $65,000 [PVIFAIRR %,3 yrs] A

Thus, IRRA = over 40% (42.57%) $100,000

= $32,500 [PVIFAIRR %,9 yrs] B

Thus, IRRB = 29% d.

These projects are not comparable because future profitable investment proposals are affected by the decision currently being made. If project A is taken, at its termination the firm could replace the machine and receive additional benefits while acceptance of project B would exclude this possibility.

417

e.

Using 3 replacement chains, project A's cash flows would become: Year 0 1 2 3 4 5 6 7 8 9 NPVA

Cash flow -$100,000 65,000 65,000 -35,000 65,000 65,000 - 35,000 65,000 65,000 65,000

=

9

$65,000

t =1

(1 + 0.14)

$100 ,000 (1 + 0.14 )

3

∑ −

t

- $100,000 -

$100 ,000 (1 + 0.14 ) 6

= $65,000(4.946) - $100,000 - $100,000 (0.675) - $100,000 (0.456) = $321,490 - $100,000 - $67,500 - $45,600 = $108,390 The replacement chain analysis indicated that project A should be selected as the replacement chain associated with it has a larger NPV than project B. Project A's EAA: Step 1: Calculate the project's NPV (from part b): NPVA

= $50,930

Step 2: Calculate the EAA: EAAA = NPV / PVIFA14%, 3 yr. = $50,930/ 2.322 = $21,934 Project B's EAA: Step 1: Calculate the project's NPV (from part b): NPVB

= $60,745

Step 2: Calculate the EAA: EAAB

= NPV / PVIFA14%, 9 yr. = $60,745 / 4.946

418

= $12,282 Project A should be selected because it has a higher EAA.

Solutions to Problem Set B 10-1B. (a)

Tax payments associated with the sale for $45,000: Recapture of depreciation = ($45,000-$20,000) (0.34) = $8,500

(b)

Tax payments associated with sale for $40,000: Recapture of depreciation = ($40,000-$20,000) (0.34) = $6,800

(c)

No taxes, because the machine would have been sold for its book value.

(d)

Tax savings from sale below book value: Tax savings = ($20,000-$17,000) (0.34) = $1,020

10-2B. New Sales Less: Sales taken from existing product lines

$100,000,000 - 40,000,000 $60,000,000

10-3B. Change in net working capital equals the increase in accounts receivable and inventory less the increase in accounts payable = $34,000 + $80,000 - $50,000 = $64,000. The change in taxes will be EBIT X marginal tax rate = $775,000 X .34 = $263,500. A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $775,000 - $263,500 + $200,000 - $64,000 - $0 = $647,500

419

10-4B. Change in net working capital equals the decrease in accounts receivable, the increase in inventory less the increase in accounts payable = -$10,000 + $15,000 - $36,000 = $31,000. The change in taxes will be EBIT X marginal tax rate = $300,000 X .34 = $102,000. A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $300,000 - $102,000 + $50,000 - ($31,000) - $0 = $279,000 10-5B. (a)

Initial Outlay

Outflows: Purchase price Installation Fee Increased Working Capital Inventory Net Initial Outlay (b)

$ 250,000 10,000 15,000 $275,000

Differential annual free cash flows (years 1-9) A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $70,000 - $23,800 + $26,000* - $0 - $0 = $72,200

*Annual Depreciation on the new machine is calculated by taking the purchase price ($250,000) and adding in costs necessary to get the new machine in operating order

420

(the installation fee of $10,000) and dividing by the expected life. (c)

Terminal Free Cash flow (year 10) Inflows: Differential free cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow

(d)

NPV

$72,200 15,000 $87,200

= $72,200 (PVIFA15%,9 yr.) + $87,200 (PVIF15%, 10 yr.) - $275,000 = $72,200 (4.772) + $87,200 (.247) - $275,000 = $344,538.40 + $21,538.40 - $275,000 = $91,076.80

Yes, the NPV > 0. 10-6B. (a)

Initial Outlay Outflows: Purchase price Installation Fee Training Session Fee Increased Inventory Net Initial Outlay

(b)

$ 1,000,000 50,000 100,000 150,000 $ 1,300,000

Differential annual free cash flows (years 1-9) A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $400,000 - $136,000 + $105,000* - $0 - $0 = $369,000 *Annual Depreciation on the new machine is calculated by taking the purchase price ($1,000,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $50,000) and dividing by the expected life.

421

(c)

Terminal Free Cash flow (year 10) Inflows: Differential flow in year 10 Recapture of working capital (inventory)

$369,000 150,000

Total terminal cash flow (d)

NPV

$519,000

= $369,000 (PVIFA12%,9 yr.) + $519,000 (PVIF12%, 10 yr.) - $1,300,000 = $369,000 (5.328) + $519,000 (.322) - $1,300,000 = $1,966,032 + $167,118 - $1,300,000 = $833,150

Yes, the NPV > 0. 10-7B. (a)

Initial Outlay

Outflows: Purchase price Installation Fee Training Session Fee Increased Inventory Net Initial Outlay (b)

$ 100,000 5,000 5,000 25,000 $ 135,000

Differential annual free cash flows (years 1-9) A project’s free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital change in capital spending = $25,000 - $8,500 + $10,500* - $0 - $0 = $27,000

*Annual Depreciation on the new machine is calculated by taking the purchase price ($100,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life.

422

(c)

Terminal Free Cash flow (year 10) Inflows: Differential flow in year 10 Recapture of working capital (inventory) Total terminal cash flow

(d)

NPV

$27,000 25,000 $52,000

= $27,000 (PVIFA12%,9 yr.) + $52,000 (PVIF12%, 10 yr.)

- $135,000 = $27,000 (5.328) + $52,000 (.322) - $135,000 = $143,856 + $16,744 - $135,000 = $25,600 Yes, the NPV > 0.

423

10-8B Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 5 Units Sold 1,000,000 1,800,000 1,800,000 1,200,000 700,000 Sale Price $800 $800 $800 $800 $600 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%)

$800,000,000 400,000,000 $10,000,000 $390,000,000 $40,000,000 $350,000,000 $119,000,000

$1,440,000,000 720,000,000 $10,000,000 $710,000,000 $40,000,000 $670,000,000 $227,800,000

$1,440,000,000 720,000,000 $10,000,000 $710,000,000 $40,000,000 $670,000,000 $227,800,000

282

Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $350,000,000 $670,000,000 $670,000,000 Minus: Taxes $119,000,000 $227,800,000 $227,800,000 Plus: Depreciation $40,000,000 $40,000,000 $40,000,000 Equals: Operating Cash Flow $271,000,000 $482,200,000 $482,200,000

$960,000,000 480,000,000 $10,000,000 $470,000,000 $40,000,000 $430,000,000 $146,200,000

$420,000,000 280,000,000 $10,000,000 $130,000,000 $40,000,000 $90,000,000 $30,600,000

$430,000,000 $146,200,000 $40,000,000 $323,800,000

$90,000,000 $30,600,000 $40,000,000 $99,400,000

Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section IV) Change in Net Working Capital: Revenue: $800,000,000 $1,440,000,000 $1,440,000,000 $960,000,000 Initial Working Capital Requirement $2,000,000 Net Working Capital Needs: $80,000,000 $144,000,000 $144,000,000 $96,000,000 Liquidation of Working Capital Change in Working Capital: $2,000,000 $78,000,000 $64,000,000 $0 ($48,000,000) Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $271,000,000 $482,200,000 $482,200,000 $323,800,000 Minus: Change in Net Working Capital $2,000,000 $78,000,000 $64,000,000 $0 ($48,000,000) Minus: Change in Capital Spending $200,000,000 $0 $0 $0 $0 Free Cash Flow: ($202,000,000) $193,000,000 $418,200,000 $482,200,000 $371,800,000 NPV $908,825,886.69 PI 5.5

$420,000,000 $42,000,000 $42,000,000 ($96,000,000)

$99,400,000 ($96,000,000) $0 $195,400,000

IRR

140%

Accept project

425

10-9B Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 Units Sold 70,000 100,000 140,000 70,000 Sale Price $280 $280 $280 $280 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%)

$19,600,000 9,800,000 $300,000 $9,500,000 $2,000,000 $7,500,000 $2,550,000

$28,000,000 14,000,000 $300,000 $13,700,000 $2,000,000 $111,700,000 $3,978,600

$39,200,000 19,600,000 $300,000 $19,300,000 $2,000,000 $17,300,000 $5,882,000

283

Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $7,500,000 $11,700,000 $17,300,000 Minus: Taxes $2,550,600 $3,978,600 $5,882,000 Plus: Depreciation $2,000,000 $2,000,000 $2,000,000 Equals: Operating Cash Flow $6,950,400 $9,722,400 $13,418,000

5 60,000 $180

$19,600,000 9,800,000 $300,000 $9,500,000 $2,000,000 $7,500,000 $2,550,000

$10,800,000 8,400,000 $300,000 $2,100,000 $2,000,000 $100,000 $34,000

$7,500,000 $3,107,600 $2,000,000 $6,950,000

$100,000 $34,000 $2,000,000 $2,066,000

Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section IV) Change in Net Working Capital: Revenue: $19,600,000 $28,000,000 $39,200,000 $19,600,000 Initial Working Capital Requirement $100,000 Net Working Capital Needs: $1,960,000 $2,800,000 $3,920,000 $1,960,000 Liquidation of Working Capital Change in Working Capital: $100,000 $1,860,000 $840,800 $1,120,000 ($1,960,000) Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $6,950,000 $9,722,400 $13,418,000 $6,950,400 Minus: Change in Net Working Capital $100,000 $1,860,000 $840,000 $1,120,000 ($1,960,000) Minus: Change in Capital Spending $10,000,000 $0 $0 $0 $0 Free Cash Flow: ($10,100,000) $5,090,400 $8,882,400 $12,298,400 $8,910,400 NPV $16,232,618 PI 2.6

$10,800,000 $1,080,000 $1,080,000 ($1,960,000)

$2,066,000 ($1,960,000) $0 $4,026,000

IRR

68.6%

Accept project

427

10-10B. (a)

NPVA

=

$800 (1 + 0.10 )1

- $650

= $727.20 - $650 = $77.20 NPVB

=

$5,500 (1 + 0.10 )1

- $4,000

= $5,000 - $4,000 = $1,000 (b)

PIA

=

$727 .20 $650 .00

= 1.1188 PIB

=

$5,000 $4,000

= 1.25 (c)

(d)

$650

= $800 [PVIFIRR %,1 yr] A

0.8125

=

Thus, IRRA

= 23%

$4,000

= $5,500 [PVIFIRR %,1 yr] B

0.7273

= [PVIFIRR %,1 yr] B

Thus, IRRB

= 37.5%

PVIFIRR %,1 yr A

If there is no capital rationing, project B should be accepted because it has a larger net present value. If there is a capital constraint, the problem then focuses on what can be done with the additional $3,350 freed up if project A is chosen. If Unk's Farms can earn more on project A, plus the project financed with the additional $3,350, than it can on project B, then project A and the marginal project should be accepted.

34

10-11B. (a)

Payback A = 3.125 years Payback B = 4.5 years B assumes even cash flow throughout year 5.

(b)

NPVA

=

5

$16,000

t =1

(1 + 0.11)

∑

t

- $50,000

= $16,000 (3.696) - $50,000 = $59,136 - $50,000 = $9,136 NPVB

=

$100 ,000 (1 + 0.11 )5

- $50,000

= $100,000 (0.593) - $50,000 = $59,300 - $50,000 = $9,300 (c)

$50,000

= $16,000 [PVIFAIRR %,5 yrs] A

3.125

= PVIFAIRR %,5 yrs A

Thus, IRRA = 18% $50,000

= $100,000 [PVIFIRR %,5 yrs] B

.50

= PVIFIRR %,5 yrs B

Thus IRRB is just under 15%. (d)

The conflicting rankings are caused by the differing reinvestment assumptions made by the NPV and IRR decision criteria. The NPV criterion assume that cash flows over the life of the project can be reinvested at the required rate of return or cost of capital, while the IRR criterion implicitly assumes that the cash flows over the life of the project can be reinvested at the internal rate of return.

(e)

Project B should be taken because it has the largest NPV. The NPV criterion is preferred because it makes the most acceptable assumption for the wealth maximizing firm.

35

10-12B. (a)

Payback A = 1.5385 years Payback B = 3.0769 years

(b)

NPVA

=

3

$13,000

t =1

(1 + 0.14)

∑

t

- $20,000

= $13,000 (2.322) - $20,000 = $30,186 - $20,000 = $10,186 NPVB

=

9

$6,500

t =1

(1 + 0.14)

∑

t

- $20,000

= $6,500 (4.946) - $20,000 = $32,149 - $20,000 = $12,149 (c)

$20,000

= $13,000 [PVIFAIRR %,3 yrs] A

Thus, IRRA = over 40% (42.57%) $20,000

= $6,500 [PVIFAIRR %,9 yrs] B

Thus, IRRB = 29.3% (d)

These projects are not comparable because future profitable investment proposals are affected by the decision currently being made. If project A is taken, at its termination the firm could replace the machine and receive additional benefits while acceptance of project B would exclude this possibility.

(e)

Using 3 replacement chains, project A's cash flows would become: Year 0 1 2 3 4 5 6 7 8 9

Cash flow -$20,000 13,000 13,000 - 7,000 13,000 13,000 - 7,000 13,000 13,000 13,000 36

NPVA $20 ,000 (1 + 0.14 )

3

9

$13,000

t =1

(1 + 0.14)

∑

= −

t

- $20,000 -

$20 ,000 (1 + 0.14 ) 6

= $13,000(4.946) - $20,000 - $20,000 (0.675) - $20,000 (0.456) = $64,298 - $20,000 - $13,500 - $9,120 = $21,678 The replacement chain analysis indicated that project A should be selected as the replacement chain associated with it has a larger NPV than project B. Project A's EAA: Step 1:

Calculate the project's NPV (from part b): NPVA

Step 2:

= $10,186

Calculate the EAA: EAAA = NPV / PVIFA14%, 3 yr. = $10,186 / 2.322 = $4,387

Project B's EAA: Step 1:

Calculate the project's NPV (from part b): NPVB

= $12,149

Step 2: Calculate the EAA: EAAB

= NPV / PVIFA14%, 9 yr. = $12,149 / 4.946 = $2,456

Project A should be selected because it has a higher EAA.

37

10-13B. (a)

Project A's EAA: Step 1: Calculate the project's NPV: NPVA = $20,000 (PVIFA10%, 7 yr.) - $40,000 = $20,000 (4.868) - $40,000 = $97,360 - $40,000 = $57,360 Step 2: Calculate the EAA: EAAA = NPV / PVIFA10%, 7 yr. = $57,360 / 4.868 = $11,783 Project B's EAA: Step 1: Calculate the project's NPV: NPVB

= $25,000 (PVIFA10%, 5 yr.) - $40,000 = $25,000 (3.791) - $40,000 = $94,775 - $40,000 = $54,775

Step 2: Calculate the EAA: EAAB

= NPV / PVIFA10%, 5 yr. = $54,775 / 3.791 = $14,449

Project B should be selected because it has a higher EAA. (b)

NPV∞ ,A

= $11,783 / .10 = $117,830

NPV∞ ,B

= $14,449 / .10 = $144,490

38

10-14B. (a) Project A B C D E F G

Cost $4,000,000 3,000,000 5,000,000 6,000,000 4,000,000 6,000,000 4,000,000

Profitability Index 1.18 1.08 1.33 1.31 1.19 1.20 1.18

Present Value of Future Cash Flows $4,720,000 3,240,000 6,650,000 7,860,000 4,760,000 7,200,000 4,720,000

NPV $ 720,000 240,000 1,650,000 1,860,000 760,000 1,200,000 720,000

COMBINATIONS WITH TOTAL COSTS BELOW $12,000,000 Projects A&B A&C A&D A&E A&F A&G B&C B&D B&E B&F B&G C&D C&E C&F C&G D&E D&F D&G E&F E&G F&G A&B&C A&B&E A&B&G A&E&G B&C&E B&C&G

Costs $ 7,000,000 9,000,000 10,000,000 8,000,000 10,000,000 8,000,000 8,000,000 9,000,000 7,000,000 9,000,000 7,000,000 11,000,000 9,000,000 11,000,000 9,000,000 10,000,000 12,000,000 10,000,000 10,000,000 8,000,000 10,000,000 12,000,000 11,000,000 11,000,000 12,000,000 12,000,000 12,000,000

NPV $ 960,000 2,370,000 2,580,000 1,480,000 1,920,000 1,440,000 1,890,000 2,100,000 1,000,000 1,440,000 960,000 3,510,000 2,410,000 2,850,000 2,370,000 2,620,000 3,060,000 2,580,000 1,960,000 1,480,000 1,920,000 2,610,000 1,720,000 1,680,000 2,200,000 2,650,000 2,610,000

Thus projects C&D should be selected under strict capital rationing as they provide the combination of projects with the highest net present value. (b)

Because capital rationing forces the rejection of profitable projects it is not an optimal strategy. 39

40

CHAPTER 11

Capital Budgeting

and Risk Analysis CHAPTER ORIENTATION The focus of this chapter will be on how to adjust for the riskiness of a given project or combination of projects.

CHAPTER OUTLINE I.

II.

Risk and the investment decision A.

Up to this point we have treated the expected cash flows resulting from an investment proposal as being known with perfect certainty. We will now introduce risk.

B.

The riskiness of an investment project is defined as the variability of its cash flows from the expected cash flow.

What measure of risk is relevant in capital budgeting? A.

In capital budgeting, a project can be looked at on three levels. 1.

First, there is the project standing alone risk, which is a project’s risk ignoring the fact that much of this risk will be diversified away as the project is combined with the firm’s other projects and assets.

2.

Second, we have the project’s contribution-to-firm risk, which is the amount of risk that the project contributes to the firm as a whole; this measure considers the fact that some of the project’s risk will be diversified away as the project is combined with the firm’s other projects and assets, but ignores the effects of diversification of the firm’s shareholders.

3.

Finally, there is systematic risk, which is the risk of the project from the viewpoint of a well-diversified shareholder; this measure considers the fact that some of a project’s risk will be diversified away as the project is combined with the firm’s other projects, and, in addition, some of the remaining risk will be diversified away by shareholders as they combine this stock with other stocks in their portfolio.

41

B.

III.

Because of bankruptcy costs and the practical difficulties involved in measuring a project’s level of systematic risk, we will give consideration to the project’s contribution-to-firm risk and the project’s systematic risk.

Methods for incorporating risk into capital budgeting A.

The certainty equivalent approach involves a direct attempt to allow the decision maker to incorporate his or her utility function into the analysis. 1.

In effect, a riskless set of cash flows is substituted for the original set of risky cash flows, between which the financial manager is indifferent.

2.

To simplify calculations, certainty equivalent coefficients (t's) are defined as the ratio of the certain outcome to the risky outcome between which the financial manager is indifferent.

3.

Mathematically, certainty equivalent coefficients can be defined as follows: αt

certain cash flow t risky cash flow t

=

4.

The appropriate certainty equivalent coefficient is multiplied by the original cash flow (which is the risky cash flow) with this product being equal to the equivalent certain cash flow.

5.

Once risk is taken out of the cash flows, those cash flows are discounted back to present at the risk-free rate of interest and the project's net present value or profitability index is determined.

6.

If the internal rate of return is calculated, it is then compared with the risk-free rate of interest rather than the firm's required rate of return.

7.

Mathematically, the certainty equivalent approach can be summarized as follows: n

NPV

=

t =1

where α

αt FCF t

∑ (1 + k

rf

)t

- IO

=

the certainty equivalent coefficient for time period t

FCFt =

the annual expected free cash flow in time period t

IO

=

the initial cash outlay

n

=

the project's expected life

krf

=

the risk-free interest rate

t

42

B.

The use of the risk-adjusted discount rate is based on the concept that investors demand higher returns for more risky projects. 1.

If the risk associated with the investment is greater than the risk involved in a typical endeavor, then the discount rate is adjusted upward to compensate for this risk.

2.

The expected cash flows are then discounted back to present at the risk-adjusted discount rate. Then the normal capital budgeting criteria are applied, except in the case of the internal rate of return, in which case the hurdle rate to which the project's internal rate of return is compared now becomes the risk-adjusted discount rate.

3.

Expressed mathematically, the net present value using the riskadjusted discount rate becomes n

IV.

FCF t

∑ (1 + k*)

NPV

=

where FCFt

=

the annual expected free cash flow in time period t

IO

=

the initial outlay

k*

=

the risk-adjusted discount rate

n

=

the project's expected life

t =1

t

- IO

Methods for measuring a project's systematic risk A.

Theoretically, we know that systematic risk is the "priced" risk, and thus, the risk that affects the stock's market price and thus the appropriate risk with which to be concerned. However, if there are bankruptcy costs (which are assumed away by the CAPM), if there are undiversified shareholders who are concerned with more than just systematic risk, if there are factors that affect a security's price beyond what the CAPM suggests, or if we are unable to confidently measure the project's systematic risk, then the project's individual risk carries relevance. Moreover, in general, a project's individual risk is highly correlated with the project's systematic risk, making it a reasonable proxy to use.

B.

In spite of problems in confidently measuring an individual firm's level of systematic risk, if the project appears to be a typical one for the firm, then using the CAPM to determine the appropriate risk return tradeoffs and then judging the project against them may be a warranted approach.

C.

If the project is not a typical project, we are without historical data and must either estimate the beta using accounting data or use the pure-play method for estimating beta. 1.

Using historical accounting data to substitute for historical price data in estimating systematic risk: To estimate a project's beta using accounting data we need only run a time series regression of the

43

division's return on assets on the market index. The regression coefficient from this equation would be the project's accounting beta and serves as an approximation for the project's true beta. 2.

V.

Additional approaches for dealing with risk in capital budgeting A.

B.

VI.

The pure play method for estimating a project's beta: The pure play method attempts to find a publicly traded firm in the same industry as the capital-budgeting project. Once the proxy or pure-play firm is identified, its systematic risk is determined and then used as a proxy for the project's systematic risk.

A simulation imitates the performance of the project being evaluated by randomly selecting observations from each of the distributions that affect the outcome of the project, combining those observations to determine the final output of the project, and continuing with this process until a representative record of the project's probable outcome is assembled. 1.

The firm's management then examines the resultant probability distribution, and if management considers enough of the distribution lies above the normal cutoff criterion, it will accept the project.

2.

The use of a simulation approach to analyze investment proposals offers two major advantages: a.

The financial managers are able to examine and base their decisions on the whole range of possible outcomes rather than just point estimates.

b.

They can undertake subsequent sensitivity analysis of the project.

A probability tree is a graphical exposition of the sequence of possible outcomes; it presents the decision maker with a schematic representation of the problem in which all possible outcomes are graphically displayed.

Other sources and measures of risk A.

Many times, especially with the introduction of a new product, the cash flows experienced in early years affect the size of the cash flows experienced in later years. This is called time dependence of cash flows, and it has the effect of increasing the riskiness of the project over time.

ANSWERS TO END-OF-CHAPTER QUESTIONS 11-1. The payback period method is frequently used as a rough risk screening device to eliminate projects whose returns do not materialize until later years. In this way, the earliest returns are emphasized, which in all likelihood have less uncertainty surrounding them.

44

11-2. The use of the risk-adjusted discount rate assumes that risk increases over time. When using the risk-adjusted discount rate method, we are adjusting downward the value of future cash flows that occur later in the future more severely than earlier ones. This assumption can be justified because flows that are expected further out in the future are more difficult to forecast and less certain than are flows that are expected in the near future. 11-3. The primary difference between the certainty equivalent approach and the riskadjusted discount rate approach is where the adjustment for risk is incorporated into the calculations. The certainty equivalent approach penalizes or adjusts downwards the value of the expected annual free cash flows, while the risk-adjusted discount rate leaves the cash flows at their expected value and adjusts the required rate of return, k, upwards to compensate for added risk. In either case the net present value of the project is being adjusted downwards to compensate for additional risk. An additional difference between these methods is that the risk-adjusted discount rate assumes that risk increases over time and that cash flows occurring later in the future should be more severely penalized. The certainty equivalent method, on the other hand, allows each cash flow to be treated individually. 11-4. A probability tree is a graphical exposition of the sequence of possible outcomes, presenting the decision maker with a schematic representation of the problem in which all possible outcomes are graphically displayed. Moreover, the computations and results of the computations are shown directly on the tree, so that the information can be easily understood. Thus the probability tree allows the manager to quickly visualize the possible future events, their probabilities, and outcomes. In addition, the calculation of the expected internal rate of return and enumeration of the distribution should aid the financial manager in his decision-making process. 11-5. The idea behind simulation is to imitate the performance of the project being evaluated. This is done by randomly selecting observations from each of the distributions that affect the outcome of the project, combining each of those observations and determining the final outcome of the project, and continuing with this process until a representative record of the project's probable outcome is assembled. In effect, the output from a simulation is a probability distribution of net present values or internal rates of return for the project. The decision maker then bases his decision on the full range of possible outcomes. 11-6. The time dependence of cash flows refers to the fact that, many times, cash flows in later periods are dependent upon the cash flows experienced in earlier periods. For example, if a new product is introduced and the initial public reaction is poor, resulting in low initial cash flows, then cash flows in future periods are likely to be low also. Examples include the introduction of any new products, for example, the Edsel on the negative side, and hopefully this book on the positive side.

45

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A n

11-1A. (a)

=

∑ i =1

A

Xi P(Xi)

= $4,000 (0.15) + $5,000 (0.70) + $6,000 (0.15) = $600 + $3,500 + $900 = $5,000

B

= $2,000 (0.15) + $6,000 (0.70) + $10,000 (0.15) = $300 + $4,200 + $1,500 = $6,000 n

(b)

NPV NPVA

=

∑ t =1

FCF t (1 + k*)

t

- I0

= $5,000 (3.605) - $10,000 = $18,025 - $10,000 = $8,025

NPVB

= $6,000 (3.352) - $10,000 = $20,112 - $10,000 = $10,112

(c)

One might also consider the potential diversification effect associated with these projects. If the project's cash flow patterns are cyclically divergent from those of the company, the overall risk of the company may be significantly reduced.

46

n

11-2A. (a)

=

∑ i =1

Xi P(Xi)

= $35,000 (0.10) + $40,000 (0.40) + $45,000 (0.40)

A

+ $50,000 (0.10) = $3,500 + $16,000 + $18,000 + $5,000 = $42,500 = $10,000 (0.10) + $30,000 (0.20) + $45,000 (0.40)

B

+ $60,000 (0.20) + $80,000 (0.10) = $1,000 + $6,000 + $18,000 + $12,000 + $8,000 = $45,000 n

(b)

∑

FCF t - IO (1 + k*) t

NPV

=

NPVA

= $42,500 (3.605) - $100,000

t =1

= $153,212.50 - $100,000 = $53,212.50 NPVB

= $45,000 (3.517) - $100,000 = $158,265 - $100,000

(c)

= $58,265 One might also consider the potential diversification effect associated with these projects. If the project's cash flow patterns are cyclically divergent from those of the company, the overall risk of the company may be significantly reduced.

11-3A. Project A: (A) Year 0 1 2 3 4

Expected Cash Flow -$1,000,000 500,000 700,000 600,000 500,000

(B) αt 1.00 .95 .90 .80 .70

(A x B) Present Value (Expected Factor at Present Cash Flow ) × (α t) 5% Value -$1,000,000 1.000 -$1,000,000 475,000 .952 452,200 630,000 .907 571,410 480,000 .864 414,720 350,000 .823 288,050 NPVA = $ 726,380

47

Project B: (A)

(B)

Expected Cash Flow -$1,000,000 500,000 600,000 700,000 800,000

Year 0 1 2 3 4

αt 1.00 .90 .70 .60 .50

(A x B) (Expected Cash Flow ) × (α t) -$1,000,000 450,000 420,000 420,000 400,000

Present Value Factor at Present 5% Value 1.000 -$1,000,000 .952 428,400 .907 380,940 .864 362,880 .823 329,200 NPVB = $ 501,420

Thus, project A should be selected, as it has a higher NPV. 11-4A. (A)

(B)

(A x B)

Present Value Year 0 1 2 3 4 5

Expected Cash Flow -$90,000 25,000 30,000 30,000 25,000 20,000

αt 1.00 0.95 0.90 0.83 0.75 0.65

(Expected Factor at Present Cash Flow ) × (α t) 7% Value -$90,000 1.000 -$90,000 23,750 .935 22,206 27,000 .873 23,571 24,900 .816 20,318 18,750 .763 14,306 13,000 .713 9,269 NPV = $ -330

Thus, this project should not be accepted because it has a negative NPV. 11-5A. NPVA

=

n

∑ t =1

FCF t (1 + k*)

t

- I0

= $30,000 (.893) + $40,000(.797) + $50,000(.712) + $90,000(.636) + $130,000(.567) - $250,000 = $26,790 + $31,880 + $35,600 + $57,240 + $73,710 - $250,000 = - $24,780 NPVB

=

n

∑ t =1

FCF (1 + k*)

t

- I0

= $135,000(3.127) - $400,000 = $422,145 - $400,000

48

= $22,145

49

11-6A. Project A: (A) Year 0 1 2 3 4

Expected Cash Flow -$ 50,000 15,000 15,000 15,000 45,000

(B) αt 1.00 .95 .85 .80 .70

(A x B) (Expected Cash Flow ) × (α t) -$ 50,000 14,250 12,750 12,000 31,500

Present Value Factor at Present 6% Value 1.000 -$ 50,000.00 .943 13,437.75 .890 11,347.50 .840 10,080.00 .792 24,948.00 NPVA = $ 9,813.25

Project B: (A) Year 0 1 2 3 4

Expected Cash Flow -$ 50,000 20,000 25,000 25,000 30,000

(B) αt 1.00 .90 .85 .80 .75

(A x B) (Expected Cash Flow ) × (α t) -$ 50,000 18,000 21,250 20,000 22,500

Present Value Factor at Present 6% Value 1.000 -$ 50,000.00 .943 16,974.00 .890 18,912.50 .840 16,800.00 .792 17,820.00 NPVB = $ 20,506.50

Thus project B should be selected, as it has a higher NPV

50

1 Year

2 Years

p = 0.6

0.18

-2.33%

$700,000

10.92%

0.36

3.93%

$1,100,000

29.25%

0.06

1.76%

$400,000

3.15%

0.06

0.19%

$700,000

19.60%

0.15

2.94%

p = 0.2

$1,000,000

33.33%

0.06

2.00%

p = 0.1

$1,300,000

45.36%

0.03

1.36%

$600,000

23.74%

0.01

0.24%

$900,000

37.77%

0.05

1.89%

$1,100,000

46.08%

0.04

1.84%

p = 0.6 P = 0.1

299

p = 0.5

- $1,200,000 $850,000 p = 0.1

p = 0.1 p = 0.5

$1,000,000

(A)(B)

-12.95%

p = 0.2

p = 0.3

Probability

$300,000

p = 0.3

$700,000

Joint each Branch

p = 0.4

1.00 Expected internal rate of return d.

The range of possible IRR’s from –12.95% to 46.08%

=

13.82%

11-7A. (a –c)

Internal Rate of Return for 0 Year

1 Year

3 Years $230,000

130.25%

0.09

11.72%

$180,000

124.68%

0.09

11.22%

$205,000

121.09%

0.15

18.16%

$155,000

114.96%

0.15

17.24%

$180,000

111.30%

0.06

6.68%

p = 0.5

$130,000

104.46%

0.06

6.27%]

p = 1.0

$10,000

-42.44%

0.24

-10.19%

p = 1.0

$0

-90.00%

0.16

-14.40%

2 Years p = 0.5 p = 0.5

Probability

(A)(B)

$200,000 p = 0.3

p = 0.5

p = 0.5 p = 0.5

300

$175,000 p = 0.6

$100,000 p = 0.2

p = 0.5

$-100,000 $150,000 p = 0.4

p = 0.6 $10,000 $10,000

d.

p = 0.4

$0

The range of possible IRR’s from –90.00% to 130.25%.

1.00 Expected internal rate of return

=

46.70%

11-8A. (a –c)

of Return for 0 Year

Internal Rate Joint each Branch

SOLUTIONS TO INTEGRATIVE PROBLEM 1.

First there is the project standing alone risk, which is a project's risk ignoring the fact that much of this risk will be diversified away as the project is combined with the firm's other projects and assets. Second, we have the project's contribution-tofirm risk, which is the amount of risk that the project contributes to the firm as a whole; this measure considers the fact that some of the project's risk will be diversified away as the project is combined with the firm's other projects and assets, but ignores the effects of diversification of the firm's shareholders. Finally, there is systematic risk, which is the risk of the project from the viewpoint of a well diversified shareholder; this measure considers the fact that some of a project's risk will be diversified away as the project is combined with the firm's other projects, and, in addition, some of the remaining risk will be diversified away by the shareholders as they combine this stock with other stocks in their portfolio.

2.

According to the CAPM, systematic risk is the only relevant risk for capital budgeting purposes; however, reality complicates this somewhat. In many instances a firm will have undiversified shareholders; for them the relevant measure of risk is the project's contribution to firm risk. The possibility of bankruptcy also affects our view of what measure of risk is relevant. Because the project's contribution to firm risk can affect the possibility of bankruptcy, this may be an appropriate measure of risk since there are costs associated with bankruptcy.

3.

The primary difference between the certainty equivalent approach and the riskadjusted discount rate approach is where the adjustment for risk is incorporated into the calculations. The certainty equivalent approach penalizes or adjusts downwards the value of the expected annual free cash flows, while the risk-adjusted discount rate leaves the cash flows at their expected value and adjusts the required rate of return, k, upwards to compensate for added risk. In either case the net present value of the project is being adjusted downwards to compensate for additional risk. An additional difference between these methods is that the risk-adjusted discount rate assumes that risk increases over time and that cash flows occurring later in the future should be more severely penalized. The certainty equivalent method, on the other hand, allows each cash flow to be treated individually.

4.

A probability tree is a graphical exposition of the sequence of possible outcomes, presenting the decision maker with a schematic representation of the problem in which all possible outcomes are graphically displayed. Moreover, the computations and results of the computations are shown directly on the tree, so that the information can be easily understood. Thus the probability tree allows the manager to quickly visualize the possible future events, their probabilities, and outcomes. In addition, the calculation of the expected internal rate of return and enumeration of the distribution should aid the financial manager in his decision-making process.

5.

The idea behind simulation is to imitate the performance of the project being evaluated. This is done by randomly selecting observations from each of the distributions that affect the outcome of the project, combining each of those

40

observations and determining the final outcome of the project, and continuing with this process until a representative record of the project's probable outcome is assembled. In effect, the output from a simulation is a probability distribution of net present values or internal rates of return for the project. The decision maker then bases his decision on the full range of possible outcomes. 6.

Sensitivity analysis involves determining how the distribution of possible net present values or internal rates of return for a particular project is affected by a change in one particular input variable. This is done by changing the value of one input variable while holding all other input variables constant. 7.

8.

The time dependence of cash flows refers to the fact that, many times, cash flows in later periods are dependent upon the cash flows experienced in earlier periods. For example, if a new product is introduced and the initial public reaction is poor, resulting in low initial cash flows, then cash flows in future periods are likely to be low also. Examples include the introduction of any new products, for example, the Edsel on the negative side, and hopefully this book on the positive side.

Project A:

(A)

(B) Expected Cash Flow

Year 0 1 2 3 4

-$150,000 40,000 40,000 40,000 100,000

(A x B) αt

Present Value (Expected Factor at Cash Flow ) × (α t) 7%

1.00 .90 .85 .80 .70

-$150,000 36,000 34,000 32,000 70,000

(B)

(A x B)

Present Value

1.000 -$150,000 .935 33,660 .873 29,682 .816 26,112 .763 53,410 NPVA = - $ 7,136

Project B: (A)

0 1 2 3 4

Expected YearCash Flow -$200,000 50,000 60,000 60,000 50,000

αt 1.00 .95 .85 .80 .75

Present Value (Expected Factor at Present Cash Flow ) × (α t) 7% Value -$200,000 1.000 -$200,000 47,500 .935 44,413 51,000 .873 44,523 48,000 .816 39,168 37,500 .763 28,613 NPVB = - $ 43,283

41

Thus, neither project should be selected, as they both have negative NPVs.

42

1 Year

Joint each Branch

2 Years p = 0.3 p = 0.7

$300,000 p = 0.4

Probability

(A)(B)

$200,000

-12.08%

0.12

-1.45%

$300,000

0.00%

0.28

0.00%

$250,000

0.00%

0.08

0.00%

$450,000

20.55%

0.20

4.11%

$650,000

37.26%

0.12

4.47%

$300,000

17.54%

0.04

0.70%

$500,000

36.19%

0.10

3.62%

$700,000

51.84%

0.04

2.07%

$1,000,000

71.94%

0.02

1.44%

p = 0.2 p = 0.5

298

p = 0.4 -$600,000 $350,000

p = 0.3

p = 0.2

p = 0.2

p =0.5

$450,000

p = 0.2 p = 0.1

1.00 Expected internal rate of return The range of possible IRR’s from -12.08% to 71.94%.

=

14.96%

Part 9

Internal Rate of Return for 0 Year

Solutions to Problem Set B n

11-1B. (a)

=

X

∑

Xi P(Xi)

i =1

X

X

A =

$5,000 (0.20) + $6,000 (0.60) + $7,000 (0.20)

=

$1,000 + $3,600 + $1,400

=

$6,000

B =

$3,000 (0.20) + $7,000 (0.60) + $11,000 (0.20)

=

$600 + $4,200 + $2,200

=

$7,000 FCF t

n

(b)

NPV

=

NPVA =

t =1

(1 + k*)

t

- I0

$6,000 (3.517) - $10,000

=

$21,102 - $10,000

=

$11,102

NPVB =

(c)

∑

$7,000 (3.127) - $10,000

=

$21,889 - $10,000

=

$11,889

One might also consider the potential diversification effect associated with these projects. If the project's cash flow patterns are cyclically divergent from those of the company, the overall risk of the company may be significantly reduced.

44

n

11-2B. (a)

=

X

∑ i =1

X

A =

Xi P(Xi)

$40,000 (0.10) + $45,000 (0.40) + $50,000 (0.40) + $55,000 (0.10)

X

=

$4,000 + $18,000 + $20,000 + $5,500

=

$47,500

B =

$20,000 (0.10) + $40,000 (0.20) + $55,000 (0.40) + $70,000 (0.20) + $90,000 (0.10)

=

$2,000 + $8,000 + $22,000 + $14,000 + $9,000

=

$55,000 FCF t

n

(b)

NPV

=

NPVA =

t =1

(1 + k*)

t

- I0

$47,500 (3.696) - $125,000

=

$175,560 - $125,000

=

$50,560

NPVB =

(c)

∑

$55,000 (3.517) - $125,000

=

$193,435 - $125,000

=

$68,435

One might also consider the potential diversification effect associated with these projects. If the project's cash flow patterns are cyclically divergent from those of the company, the overall risk of the company may be significantly reduced.

45

11-3B. Project A:

(A)

(B)

(A x B)

Present Value Expected Cash Flow -$100,000 600,000 750,000 600,000 550,000

Year 0 1 2 3 4

αt 1.00 .90 .90 .75 .65

(Expected Factor at Present Cash Flow ) × (α t) 5% Value -$100,000 1.000 -$100,000 540,000 .952 514,080 675,000 .907 612,225 450,000 .864 388,800 357,500 .823 294,222.50 NPVA = $ 1,709,327.50

Project B:

(A) Year 0 1 2 3 4

(B) Expected Cash Flow -$100,000 600,000 650,000 700,000 750,000

(A x B) αt 1.00 .95 .75 .60 .60

(Expected Cash Flow ) × (α t) -$100,000 570,000 487,500 420,000 450,000

Present Value Factor at Present 5% Value 1.000 -$100,000 .952 542,640 .907 442,162.50 .864 362,880 .823 370,350 NPVB = $1,618,032.50

Thus, project A should be selected, as it has a higher NPV. 11-4B.

(A) (B)

Year 0 1 2 3 4 5

(A x B) Expected Cash Flow -$100,000 30,000 25,000 30,000 20,000 25,000

αt 1.00 0.95 0.90 0.83 0.75 0.65

Present Value (Expected Factor at Present Cash Flow ) × .( α t) 8% Value -$100,000 1.000 -$100,000 28,500 .926 26,391 22,500 .857 19,283 24,900 .794 19,771 15,000 .735 11,025 16,250 .681 11,066 NPV = -$ 12,464

46

Thus, this project should not be accepted because it has a negative NPV.

47

11-5B. NPVA

FCF t

n

∑

=

t =1

=

(1 + k*)

t

- IO

$30,000 (.885) + $40,000(.783) + $50,000(.693) + $80,000(.613) + $120,000(.543) - $300,000

=

$26,550 + $31,320 + $34,650 + $49,040 + $65,160 - $300,000

NPVB

=

- $93,280

=

∑

n

t =1

FCF (1 + k*)

t

- IO

=

$130,000(3.127) - $450,000

=

$406,510 - $450,000

=

-$43,490

11-6B. Project A:

(A)

(B)(A x B) Expected Cash Flow -$ 75,000 20,000 20,000 15,000 50,000

Year 0 1 2 3 4

αt 1.00 .95 .85 .80 .70

(Expected Cash Flow ) x (α t) -$ 75,000 19,000 17,000 12,000 35,000

Present Value Factor at Present 7% Value 1.000 -$ 75,000.00 .935 17,765.00 .873 14,841.00 .816 9,792.00 .763 26,705.00 NPVA = ($ 5,897.00)

Project B:

(A) Year 0 1 2 3 4

(B) Expected Cash Flow -$ 75,000 25,000 30,000 30,000 25,000

(A x B) αt

(Expected Cash Flow ) x (α t)

1.00 .95 .85 .80 .75

-$ 75,000 23,750 25,500 24,000 18,750 48

Factor at 7% 1.000 .935 .873 .816 .763

Present Value Present Value -$ 75,000.00 22,206.25 22,261.50 19,584.00 14,306.25

NPVB = $ 3,358.00 Thus project B should be selected, as it has a higher NPV.

49

1 Year

Internal Rate Joint each Branch

2 Years

Probability

(A)(B)

$300,000

-15.12%

0.06

-0.9072%

$700,000

7.69%

0.30

2.3070%

$1,100,000

25.25%

0.24

6.0600%

$400,000

0.00%

0.06

0.0000%

$700,000

15.75%

0.15

2.3625%

$900,000

24.73%

0.06

1.4838%]

$1,300,000

40.44%

0.03

1.2132%

$600,000

46.82%

0.03

1.4046%

$900,000

58.94%

0.06

3.5364%

$1,100,000

66.27%

0.01 1.00 Expected internal rate of return

0.6627%

p = 0.1 p = 0.5 $750,000

p = 0.4

p = 0.6 p = 0.2

303

-$1,300,000

p = 0.5

p = 0.3

p = 0.2 $900,000 p = 0.1 p = 0.1

p = 0.3 p = 0.6 $1,500,000

(d)

p = 0.1

The range of possible IRR’s from -15.12% to 66.27

=

18.1230%

11-7B. (a –c)

of Return for 0 Year

1 Year

2 Years

Internal Rate Joint each Branch

Probability

(A)(B)

$255,000

115.83%

.105

12.16227%

$205,000

110.76%

.105

11.6298%

$210,000

101.15%

.175

17.7013%

$160,000

95.18%

.175

16.6565%

$170,000

86.57%

.070

6.0599%

$120,000

79.42%

.070

5.5594%

$10,000

-46.70%

.180

-8.4060%

$0

-91.67%

.120

-11.0004%

3 Years

p = 0.5 p = 0.5 $225,000 p = 0.3

p = 0.5

p = 0.5

$180,000 p = 0.5 p = 0.2

p = 0.7

304

$100,000

p = 0.5

-$120,000

p = 0.5 $140,000 p = 0.3

p = 1.0

p = 0.6 $10,000 $10,000

p = 0.4

p = 1.0 $0

1.00 Expected internal rate of return

(d)

The range of possible IRR’s from –91.67% to 115.83%

=

50.3627%

11-8B. (a –c)

of Return for 0 Year

MADE IN THE U. S. A., DUMPED IN BRAZIL, AFRICA, . . . (Ethics in Capital Budgeting) OBJECTIVE:

To force the student to recognize the role ethical behavior plays in all areas of Finance.

DEGREE OF DIFFICULTY:

Easy

Case Solution: With ethics cases there are no right or wrong answers - just opinions. Try to bring out as many opinions as possible without being judgmental. In this case the question centers around what to do when a product is no longer salable.

136

CHAPTER 12

Cost of Capital CHAPTER ORIENTATION In Chapters 7 and 8 we considered the valuation of debt and equity instruments. The concepts advanced there serve as a foundation for determining the required rate of return for the firm and for specific investment projects. The objective in this chapter is to determine the required rate of return to be used in evaluating investment projects.

CHAPTER OUTLINE I.

The concept of the cost of capital A.

B.

C.

II.

Defining the cost of capital: 1.

The rate that must be earned in order to satisfy the required rate of return

2.

The rate of return on investments at which the price of a firm's common stock will remain unchanged.

Investor’s required rate of return is not the same as the firm’s cost of capital due to 1.

Taxes: Interest payments on debt are tax deductible to the firm.

2.

Flotation costs: Firms incur expenses when issuing securities that reduce the proceeds to the firm.

Financial Policy 1.

Each type of capital used by the firm (debt, preferred stock, and common stock) should be incorporated into the cost of capital, with the relative importance of a particular source being based on the percentage of the financing provided by each source of capital.

2.

Using the cost of a single source of capital as the hurdle rate is tempting to management, particularly when an investment is financed entirely by debt. However, doing so is a mistake in logic and can cause problems.

Computing the weighted cost of capital. A firm's weighted cost of capital is a function of (l) the individual costs of capital, (2) the capital structure mix, and (3) the level of financing necessary to make the investment. A.

Determining individual costs of capital.

137

1.

The before-tax cost of debt is found by trial-and-error by solving for kd in NPd where

n

$I t

t =1

(1 + k d ) t

∑

=

$M

+

(1 + k d ) n

NPd

=

the market price of the debt, less flotation costs,

$It

=

the dollar interest paid to the investor each period,

$M

=

the maturity value of the debt

kd

=

before-tax cost of the debt (before-tax required rate of return on debt)

n

=

the number of periods to maturity.

The after-tax cost of debt equals:

kd (1 - T)

where T = corporate tax rate 2.

Cost of preferred stock (required rate of return on preferred stock), kps, equals the dividend yield based upon the net price (market price less flotation costs), or kps =

3.

4.

dividend net price

=

D NP ps

Cost of Common Stock. There are two measurement techniques to obtain the required rate of return on common stock. a.

dividend-growth model

b.

capital asset pricing model

Dividend growth model a.

Cost of internally generated common equity, kcs kcs =

dividend in year1 market price

kcs =

D1 + g Pcs

138

annual growth  in dividends

+ 

   

b.

Cost of new common stock, kncs kncs =

D1 + g NPcs

where NPcs = the market price of the common stock less flotation costs incurred in issuing new shares. 5.

Capital asset pricing model =

krf + β (km - krf)

=

the cost of common stock

krf

=

the risk-free rate

β

=

beta, measure of the stock's systematic risk

km

=

the expected rate of return on the market

kc where kc

6.

B.

It is important to notice that the major difference between the equations presented here and the equations from Chapters 7 and 8 is that the firm must recognize the flotation costs incurred in issuing the security.

Selection of weights. The individual costs of capital will be different for each source of capital in the firm's capital structure. To use the cost of capital in investment analyses, we must compute a weighted, or overall, cost of capital. 1.

It will be assumed that the company's current financial mix resulting from the financing of previous investments is relatively stable and that these weights will closely approximate future financing patterns. 2. In computing weights, we could use either the current market values of the firm's securities or the book values as shown in the balance sheet. Since we will be issuing new securities at their current market value, and not at book (historical) values, we should use the market value of the securities in calculating our weights.

III.

PepsiCo approach to weighted average cost of capital A.

PepsiCo calculates the divisional cost of capital for its snack, beverage and restaurant organizations by first finding peer-group firms for each division and using their average betas, after adjusting for differences in financial leverage, to compute the division's cost of equity. They also use accounting betas in estimating the cost of equity. They then compute the cost of debt for each division. Finally, they calculate a weighted cost of capital for each division.

139

B.

PepsiCo's WACC basic computation E   D  kwacc = kcs   + kd[1-T]   D +E  D +E 

where:

C.

kwacc =

the weighted average cost of capital

kcs

=

the cost of equity capital

kd

=

the before-tax cost of debt capital

T

=

the marginal tax rate

E/(D+E)=

percentage of financing from equity

D/(D+E)=

percentage of financing from debt

Calculating the Cost of Equity Based on capital asset pricing model: kcs

=

krf + β (km - krf)

kcs

=

the cost of common stock

krf

=

the risk-free rate

β

=

beta, measure of the stock's systematic risk

km

=

the expected rate of return on the market

where:

Betas for each division are estimated by calculating an average unlevered beta from a group of divisional peers. The average beta for each division's peer group is unlevered and then relevered using that division's target debt-to-equity ratio. D.

Calculating the Cost of Debt The after-tax cost of debt is equal to: kd (1 - T) where: kd

=

before-tax cost of debt

T

=

marginal tax rate

140

IV.

Required rate of return for individual projects A.

Using the weighted cost of capital. Investments with an internal rate of return exceeding the weighted cost of capital should be accepted. Doing so, we must assume that the project has similar business risk as existing assets. Otherwise, the weighted cost of capital does not apply.

B.

The weighted cost of capital, kwacc does not allow for varying levels of project risk. We need to specify the appropriate required rates of return for investments having different amounts of risk.

C.

Risk also results from the decisions made within the company. This risk is generally divided into two classes: 1.

Business risk is the variability in returns on assets and is affected by the company’s investment decisions.

2.

Financial risk is the increased variability in returns to the common stockholder as a result of using debt and preferred stock.

ANSWERS TO END-OF-CHAPTER QUESTIONS 12-1. The cost of capital is the rate that must be earned on investments in order to satisfy the required rate of return of the firm's investors. This rate is a function of the investors' required rate of return, the corporation's tax rate, and the flotation costs incurred in issuing new securities. Therefore, the cost of capital determines the rate of return that must be achieved on the company's investments, so as to earn the target return of the firm's investors. Stated differently, the cost of capital is the rate of return that will leave the price of the common stock unchanged. 12-2. Two objectives may be given for determining a company's weighted average cost of capital: (1)

The weighted average cost of capital is used as the minimum acceptable rate of return for capital investments. The value of the firm should be maximized by accepting all projects where the net present value is positive when discounted at the firm's weighted average cost of capital.

(2)

The weighted average cost of capital is also used in evaluating a firm’s historical performance. That is, to create shareholder value a firm must not only earn a profit in the traditional accounting sense, but it must earn a return on its invested capital that is acceptable to the investors who provide the firm’s financing. This “acceptable return” is the firm’s weighted average cost of capital.

12-3. All types of capital, including debt, preferred stock, and common stock, should be incorporated into the cost of capital computation, with the relative importance of a particular source being based upon the percentage of financing to be provided.

141

12-4. The effect of taxes on the firm's cost of capital is observed in computing the cost of debt. Since interest is a tax deductible expense, the use of debt indirectly decreases the firm's taxes. Therefore, since we have computed the internal rate of return on an after-tax basis, we also compute the cost of debt on an after-tax basis. In completing a security offering, investment bankers and other involved individuals receive a commission for their services. As a result, the amount of capital net of these flotation costs is less than the funds invested by the individual purchasing the security. Consequently, the firm must earn more than the investors' required rate of return to compensate for this leakage of capital. 12-5. a.

Equity capital can be raised by either retaining profits within the firm or by issuing new common stock. Either route represents funds invested by the common stockholder. The first avenue simply indicates that the common stockholder permits management to retain capital that could be remitted to these investors.

b.

Even though a new stock issue does not result from retaining internal common equity, these funds should not be reinvested unless management can reasonably expect to satisfy the investors' required rate of return. In essence, even though no explicit out-of-pocket cost results from retaining the capital, the cost in measuring a firm's cost of capital is actually the opportunity cost associated with these funds for the investor.

c.

The two popular methods for computing the cost of equity capital include (1) the dividend-growth model, and (2) the capital asset pricing model. The first approach finds the rate of return that equates the present value of future dividends, assuming a constant growth rate, with the current market price of the security. The CAPM finds the appropriate required rate of return, given the firm's systematic risk.

12-6 In general, the relative costs of various sources of capital reflect the riskness of the source to the investor. For example, for a given firm, we would expect debt securities to be less risky than preferred stock which is less risky than common stock. Consequently, debt would demand a lower required return than the firm’s preferred stock, which is lower than the required rate of return for common stock.

142

SOLUTIONS TO END-OF-CHAPTER PROBLEMS The following notations are used in this group of problems: kps

=

the cost of preferred stock.

kcs

=

the cost of internally generated common funds

kncs

=

the cost of new common stock.

g

=

the growth rate.

kd

=

the before-tax cost of debt.

T

=

the marginal tax rate.

Dt

=

dollar dividend per share, where Do is the most recently paid dividend and D1 is the forthcoming dividend.

P

=

the value (present value) of a security.

NP

=

the value of a security less any flotation costs incurred in issuing the security

a.

Net price after flotation costs

12-1A.

10

$1068.75

=

∑ t =1

kd

b.

c.

kncs

kcs

=

=

$1,125 (1 - .05)

=

$1068.75

$1,000 $110 + t (1 + k d )10 (1 + k d )

9.89% =

kd(1-T)

=

6.53%

=

D1 + g NPcs

=

$1.80 (1 +.07 ) + .07 $27 .50 (1 −.05 )

=

.1437 = 14.37%

=

D1 + g Pcs

143

d.

e.

kps

=

$3.50 + .07 $43

=

.1514 = 15.14%

=

D NP ps

=

$13 .50 $154

=

.0877 = 8.77%

After tax cost of debt

=

.09 x$150 $175 (1 −.12 )

= kd (1 - T) = 12% (1 - .34) = 7.92%

12-2A. a.

b.

c.

After tax cost of debt

=

kd(1 - T)

=

8%(1 - 0.34)

=

5.28%

kncs

=

D1 + g NP cs

kncs

=

$1.05 (1 +0.05 ) + 0.05= $25 (1 −0.09 )

$1,150(.90)

=

$1,035 20

$1,035

=

∑ t =1

Rate

=

net price after flotation costs

$1,000 $120 + t (1 + k d ) 20 (1 + kd)

Value

144

9.85%

Value

For:

11%

$1,079.56

kd%

1,035.00

$1,079.56

12%

1,000.00 $ 44.56

kd

d.

e.

12-3A.

=

$

$44 .56  0.11 +    × 0.01

=

 $79 .56 

After tax cost of debt

=

kd (1 - T)

After tax cost of debt

=

11.56% (1 - 0.34)

kps

=

D NP ps

kps

=

$7 $85

kcs

=

D1 + g Pcs

kcs

=

$3 + 0.04 $38

kncs

=

D1 + g NPcs

kncs

=

$1.45 (1 +0.06 ) + 0.06 $27 (1 −0.06 )

=

79.56 .1156

=

= 11.56%

7.63%

8.24%

=

145

11.90%

=

.1206

= 12.06%

12-4A.

$958 (1 - 0.11) costs).

=

$852.62

=

$70

15

∑

(1 + k d )

t =1

t

+

$1,000 (1 + k d )15

Rate

Value

Value

8%

$914.20

$914.13

kd%

852.62

9%

______

839.27

$61.58

$74.86

For:

kd

$852.62 = the net price (value less flotation

=

 $61 .58   × 0.01=  $74 .86 

0.08 +  =

12-5A.

kps

=

D NP ps

12-6A.

NPd

=

∑

$945

=

$2.50 $32 .50

=

$I t

t =1

(1 + k d )

15

$120

t =1

= 8.82%

8.82% (1 - 0.18) = 7.23%

n

∑

.0882

t

+

t

+

(1 + k d )

=

7.69%

$M (1 + k d ) n $1,000 (1 + k d )15

Since the net price on the bonds, $945, is less than the $1,000 par value, the beforetax cost of the debt must be greater than the 12 percent coupon interest rate ($120 ÷ $1,000).

kd

Rate

Value

Value

12%

$1,000.00

$1,000.00

kd%

945.00

13%

_______

935.44

$ 55.00

$ 64.56

=

After tax cost of debt

 $55 .00   × .01 = .1285 = 12.85%  $64 .56 

.12 +  =

kd(1 - T) = 12.85%(1 - .34) = 8.48%

146

12-7A.

Cost of preferred stock (kps)

12-8A.

kcs

D

kps =

Dividend Net Price

=

14% x $100 $98

=

14.29%

=

D1 + g Pcs

=

$0.70 (1 + 0.15 ) + 0.15 $21 .50

=

.1874 = 18.74%

= NP ps =

$14 $98

12-9A.If the firm pays out 50 percent of its earnings in dividends, its recent earnings must have been $8 ($4 dividend divided by .5). Thus, earnings increased from $5 to $8 in five years. Using Appendix C and looking for a table value of .625 ($5/$8), the annual growth rate is approximately ten percent. a.

Cost of internal common stock (kcs): kcs

b.

=

 D1    + g P  cs 

=

$4(1 +.10 ) $4.40 + .10 = + .10 $58 $58

=

.1759 = 17.59%

Cost of external common (new common) stock, kncs kncs

=

 D1    + g  NPcs 

=

$4.40 + .10 $58 (1 −0.08 )

=

$4.40 $53 .36

=

.1825 = 18.25%

+ .10

12-10A.

147

a.

b.

Price (Pd)

=

NPd

∑

t =1

(1 +0.09 )10

=

$1,320.52

=

$1,320.52(1 - 0.105)

=

$1,181.87

d.

Cost of debt: =

=

10

∑

t =1

Rate

kd

(1 + 0.09)

$1,000

+

$140(6.418) + $1000(.422)

Number of Bonds

For

t

=

c.

$1,181.87

$140

10

$500 ,000 $1,181 .87

$140 (1 + k d )

+

t

= 423.06 ≈ 424 Bonds

$1,000 (1 + k d )10

Value

Value

10%

$1,246.30

kd%

1,181.87

11%

________

1,176.46

$

$ 69.84

=

$1,246.30

64.43

$64 .43  0.10 +    ×(0.01 ) = .1092 = 10.92%  $69 .84 

After tax cost of debt = 10.92%(1 - 0.34) = 7.21% 12-11A. a.

1.

Price (Pd)

=

$100

10

∑

t =1

(1 + 0.09)

t

+

$1,000 (1 + 0.09 )10

=

$100 (6.418) + $1,000 (.422)

=

$1,063.80

148

2.

3.

4.

NPd

$1,063.80 (1 - 0.105)

=

$952.10

Number of Bonds

=

$500 ,000 $952 .10

=

525.15 ≈ 526 Bonds

Cost of debt: $952.10

For:

kd

=

$100

10

∑

t =1

(1 + k d )

Rate

Value

10% kd% 11%

$1,000.00 952.10 ________ $ 47.90

=

After tax cost of debt = b.

=

t

+

$1,000 (1 + k d )10

Value $1,000.00 940.90 $ 59.10

$47 .90  0.10 +    × (0.01 ) = .1081 = 10.81%  $59 .10 

10.81%(1 - 0.34) = 7.13%

There is a very slight decrease in the cost of debt because the flotation costs associated with the higher coupon bond are higher ($138.65 in flotation costs for the 14 percent coupon bond versus $111.70 for the 10 percent coupon bond).

12-12A. Source Common Stock Preferred Stock Debt

Capital Structure 40% 10% 50%

After-tax cost of capital 18% 10% 8% x (1-.35) kwacc =

149

Weighted cost 7.2% 1.0% 2.6% 10.8%

12-13A. Net price after flotation costs

=

$975 - $15

=

$960.00

Cost of debt: 15

$960.00

∑

=

t =1

For:

kd

$1,000 $60 + t (1 + k d )15 (1 + k d )

Rate

Value

6% kd% 7%

$1,000.00 960.00 ________ $ 40.00

=

After tax cost of debt =

Value $1,000.00 908.48 $ 91.52

 $40 .00   × (0.01 ) = .064 = 6.4%  $91 .52 

0.06 + 

6.4%(1 - 0.30) = 4.48%

Cost of common stock, kncs kncs

=

= = Source

 D1    + g  NPcs  $2.25 + .05 $30 (1 −0.05 )

.129 = 12.9% Capital Structure

After-tax cost of capital

Weighted cost

Debt

60%

4.48%

2.69%

Common Stock

40%

12.9%

5.16% kwacc =

150

7.85%

12-14A. Net price after flotation costs

=

$1,050 (1-.04)

=

$1,008.00

Cost of debt: 10

$1,008.00

$1,000 $70 t + (1 + k d )10 (1 + k d )

∑

=

t =1

For:

Rate

Value

6% kd% 7%

$1,096.84 1,008.00 ________ $ 88.84

kd

After tax cost of debt

=

=

Value $1,096.84 1,000.00 $ 96.84

 $88 .84   × (0.01 ) = .069 = 6.9%  $96 .84 

0.06 + 

6.9 %(1 - 0.30) = 4.8%

Cost of preferred stock (kps) D

kps =

Dividend Net Price

=

$2.00 $2 = $25 −$3 $22

=

.091 = 9.1%

= NP ps

Cost of common stock, kncs kncs

=

= =

 D1    + g  NPcs  $3(1 +.10 ) + .10 $55 −$5

.166 = 16.6%

Source

Market Value

Weight

After-tax cost of capital

Bonds

$4,000,000

.33

4.8%

1.6%

Preferred Stock

2,000,000

.17

9.1%

1.5%

Common Stock

6,000,000

.50

16.6%

8.3%

12,000,000

1.00

kwacc =

11.4%

151

Weighted Cost

SOLUTION TO INTEGRATIVE PROBLEM Nealon, Inc. - Weighted Cost of Capital Cost of Debt: $1,035 (1 - .15)

=

$879.75

=

$879.75

For:

$80

16

∑

(1 + k d )

t =1

Rate

= NPd

9% kd% 10%

=

After tax cost of debt

+

$1,000 (1 + k d )16

Value

Value

$917.04 879.75

$917.04 843.92 $ 73.12

$ 37.29 kd

t

0.09 +  

$37 .29   x (0.01) =  $73 .12 

=

.0951 = 9.51%

9.51%(1 - .34) = 6.28%

Cost of Preferred Stock: kps

=

D NP ps

$1.50 ($ 19 −$2.01 )

=

=

8.83%

Cost of Internal Common Equity: kcs

=

D1 + g Pcs

=

$2.50 (1 +0.06 ) + 0.06 $35

=

.1357 = 13.57%

Weighted Cost of Capital (kwacc) is calculated as follows: Bonds Preferred Stock Common Stock

Weights .38 .15 .47 1.00

Costs 6.28% 8.83% 13.57%

152

Weighted Costs 2.39% 1.32% 6.38% kwacc = 10.09%

Solutions for Problem Set B The following notations are used in this group of problems: kps

=

the cost of preferred stock.

kcs

=

the cost of internally generated common funds

kncs

=

the cost of new common stock.

g

=

the growth rate.

kd

=

the before-tax cost of debt.

T

=

the marginal tax rate.

Dt

=

dollar dividend per share, where Do is the most recently paid dividend and D1 is the forthcoming dividend.

P

=

the value (present value) of a security.

NP

=

the value of a security less any flotation costs incurred in issuing the security

a.

Net price after flotation costs

12-1B.

$1,057.50

=

=

$1,057.50

∑

(1 + k d )

t =1

t

Value

11% kd% 12%

$1,058.68 1,057.50 $

kd

$1,125 (1 - .06)

$120

10

Rate For:

=

=

1.18

+

$1,000 (1 + k d )10

Value $1,058.68 1,000.00 $ 58.68

$1.18  .11 +    × .01 = .1102 = 11.02%  $58 .68 

After tax cost of debt =

kd(1 - T)

After tax cost of debt =

11.02%(1 - .34) = 7.27%

153

b.

c.

d.

e.

kncs

kcs

kps

=

D1 + g NPcs

=

$1.75 (1 +.08 ) + .08 $28 .00 (1 −.05 )

=

.1511 = 15.11%

=

D1 + g Pcs

=

$3.25 + .07 $43 .50

=

.1447 = 14.47%

=

D .10 ($125 ) = NP ps $150 (1 −.12 )

=

$12 .5 $132

=

.0947 = 9.47%

After tax cost of debt =

kd (1 - T)

=

13% (1 - .34)

=

8.58%

12-2B. a.

After tax cost of debt =

kd(1 - T)

After tax cost of debt =

9%(1 - 0.34)

After tax cost of debt =

5.94%

154

b.

c.

kncs

=

D1 + g NPcs

kncs

=

$1.25 (1 +0.06 ) + 0.06 = 10.85% $30 (1 −0.09 )

$1,125(.90)

=

$1,012.50 = net price after flotation costs

$1,012.50

=

∑

20

t =1

Rate 12% kd% 13%

For:

$1,000 $130 20 + (1 + k d ) (1 + k d ) t

Value $1,074.97 1,012.50

Value $1,074.97 1,000.00 74.97

$ 62.47

d.

e.

 $62 .47   0.01  $74 .97 

=

0.12 + 

After tax cost of debt

=

kd (1 - T)

After tax cost of debt

=

12.83% (1 - 0.34)

kd

$

kps

=

D NP ps

kps

=

$8.75 $90

kcs

=

D1 + g Pcs

kcs

=

+ 0.05 = 15.52%

= 9.72%

155

=

=

8.47%

.1283 = 12.83%

12-3B.

12-4B.

kncs

=

D1 NPcs

kncs

=

$1.30 (1 +0.07 ) + 0.07 = .1229 = 12.29% $28 (1 −0.06 )

$950 (1 - 0.11) costs). $845.50

+ g

=

$845.50 = the net price (value less flotation

$80

15

∑

=

(1 + k d )

t =1

Rate 10% kd% 11%

For:

Value $847.48 845.50

t

(1 + k d )15

Value $847.48 784.28 $63.20

$1.98 kd

$1,000

+

$1.98  0.10 +    × 0.01 = .1004 = 10.04%

=

 $63 .20 

After tax cost of debt

=

12-5B.

kps

=

D NP ps

12-6B.

NPd

=

∑

$950

=

10.04% (1 - 0.19) = 8.13% =

$I t

n

t =1

(1 + k d )

t =1

+

t

$130

15

∑

$2.75 $32 .50

(1 + k d )

t

+

= 8.46% $M (1 + k d ) n $1,000 (1 + k d )15

Since the net price on the bonds, $950, is less than the $1,000 par value, the beforetax cost of the debt must be greater than the 13 percent coupon interest rate ($130 ÷ $1,000). Rate 13% kd% 14%

Value $1,000.00 950.00 $

kd

=

After tax cost of debt

50.00

Value $1,000.00 938.46 $ 61.54

.13 +  

$50 .00   × .01 = .1381 = 13.81%  $61 .54 

=

kd(1 - T) = 13.81%(1 - .34) = 9.11%

156

12-7B.

Cost of preferred stock (kps)

12-8B.

kcs

D

=

Dividend Net Price

=

13 % x$100 $13 = $97 $97

=

13.40%

=

D1 + g Pcs

=

= NP ps

$0.80 (1 + 0.16 ) + 0.16 $22 .50

= .2012 = 20.12% 12-9B. If the firm pays out 50 percent of its earnings in dividends, its recent earnings must have been $9 ($4.50 dividend divided by .5). Thus, earnings increased from $5 to $9 in five years. Using Appendix C and looking for a table value of .556 ($5/$9), the annual growth rate is approximately twelve percent. a.

Cost of internal common stock (kcs): kcs

b.

=

 D1    + g  Pcs 

=

$4.50 (1 +.12 ) + .12 $60

=

$5.04 + .12 $60

=

.204 = 20.4%

Cost of external common (new common) stock, kncs kncs

=

 D1    + g  NPcs 

=

$5.04 + .12 $60 (1 −0.09 )

=

$5.04 + .12 $54 .60

=

.2123 = 21.23%

12-10B.

157

a.

b.

c.

d.

Price (Pd)

NPd

$150

10

∑

=

t =1

(1 + 0.10)

t

$1,000

+

(1 +0.10 )10

=

$150(6.145) + $1000(.386)

=

$1,307.75

=

$1,307.75(1 - 0.115)

=

$1,157.36

Number of Bonds

=

$600 ,000 $1,157 .36

=

518.4 ≈ 519 bonds

Cost of debt: $1,157.36

10 $150 $1,000 ∑ + t t =1 (1 + k d ) (1 + k d )10

=

Rate For

Value

12%

$1,169.50

kd%

1,157.36

Value $1,169.50

13%

1,108.90 $ 12.14

kd

=

After tax cost of debt

$ 60.60

$12 .14  0.12 +    × (0.01 ) = 12.20%  $60 .60 

=

12.20%(1 - 0.34) = 8.05%

12-11B.

10

a.

1.

2.

Price (Pd)

NPd

=

∑t =

1

$1 0 0 (1 + 0.1 0)t

+

$1,000 (1 + 0.10 )10

=

$100 (6.145) + $1,000 (.386)

=

$1,000.00

=

$1,000.00 (1 - 0.115)

=

$885.00

158

3.

4.

Number of Bonds

=

$600 ,000 $885 .00

=

678 Bonds

Cost of debt: $885.00

For:

=

$100

10

∑

t =1

(1 + k d )

Value $887.00 885.00

12% kd% 13%

=

After tax cost of debt b,

+

$1,000 (1 + k d )10

Value $887.00 837.60 $49.40

$2.00

kd

t

$2.00  0.12 +    × (0.01 ) = .1204 = 12.04%  $49 .40 

=

12.04%(1 - 0.34) = 7.95%

There is a very slight decrease in the cost of debt because the flotation costs associated with the higher coupon bond are higher (flotation costs are $150.39 for the 15 percent coupon bond versus $115 for the 10 percent coupon bond)

12-12B. Bias Corporation - Weighted Cost of Capital

Bonds Preferred Stock Common Stock

Capital Structure $1,100 250 3,700 $5,050

Weights 0.2178 0.0495 0.7327 1.0000

Individual Costs 6.0% 13.5% 19.0%

Weighted Costs 1.31% 0.67% 13.92% 15.90%

12-13B. Source Common Stock Preferred Stock Debt

Capital Structure 50% 15% 35% 100%

159

After-tax cost of capital 20% 12% 10% (1-.34) kwacc =

Weighted cost 10.0% 1.8% 2.3% 14.1%

12-14B. Net price after flotation costs

=

$1,100- $20

=

$1,080.00

Cost of debt: 40

$1,080.00

∑

=

t =1

Semi-annual Rate For:

$1,000 $40 + t (1 + k d ) 40 (1 + k d )

Value

Value

3%

$1,231.60

$1,231.60

kd%

1,080.00

4%

________

1,000.00

$ 151.60

$ 231.60

 $151 .6   × (0.01 ) = .0365 = 3.65%  $231 .60 

semi-annual kd

=

0.03 + 

annual kd

=

3.65% x 2 = 7.3%

=

7.3%(1 - 0.34) = 4.8%

After tax cost of debt Cost of common stock, kncs kncs

=

 D1    + g  NPcs 

=

$2.00 + .08 $80 (1 −0.10 )

=

.108 = 10.8%

Source

Capital

After-tax cost of capital

Weighted cost

St r u ct u re Common Stock

60%

10.8%

6.48%

Debt

40%

4.8%

1.92% kwacc =

160

8.4%

12-15B. Net price after flotation costs

=

$950 (1-.06)

=

$893.00

Cost of debt: 20

$893.00

∑

=

t =1

Rate 9% kd% 10%

For:

kd

=

$1,000 $80 t + (1 + k d ) 20 (1 + k d )

Value $908.32 893.00 ________ $ 15.32

Value $908.32 830.12 $ 78.20

$15 .32  0.09 +    × (0.01 ) = .092 = 9.2%  $78 .20 

After tax cost of debt = 10.4 % x (1 - 0.34) = 6.07% Cost of preferred stock (kps) D

Dividend Net Price

kps =

= NP ps

=

$2.50 $2.50 = $35 −$5 $30

=

.083 = 8.3%

Cost of common stock, kncs kncs

= = =

 D1    + g  NPcs  $2(1 +.08 ) + .08 $50 (1 −.10 )

.128 = 12.8%

Source

Market Value

Weight

Bonds

$500,000

.50

6.07%

3.04%

Preferred Stock

100,000

.10

8.3%

.83%

Common Stock

400,000

.40

12.8%

5.12%

$1,000,000

1.00

kwacc =

8.99%

161

After-tax cost of capital Weighted Cost

CHAPTER 13

Managing for Shareholder Value CHAPTER ORIENTATION This chapter identifies methods to measure firm value and techniques that can be employed to assure management and the firm’s board of directors make decisions that increase the value of the firm. Increases in firm value lead to increases in stock value, which aligns with the firm’s goal of maximizing shareholder wealth. Measures such as free-cash flow valuation, market value added, and economic value added can be used to evaluate the firm’s performance. Management of the firm can be provided compensation incentives that guide their decisions toward increasing the value of the firm.

CHAPTER OUTLINE I.

Top Creators of Shareholder Wealth A.

Market Value Added (MVA) measures wealth created by the firm 1. 2. 3.

B.

Value creation results from two activities: 1. 2.

II.

MVA = Firm value – invested capital Firm value = market value of firm’s outstanding debt and equity securities Invested capital = total funds invested in the firm Identifying performance measures linked to value creation that are under management’s control Designing incentives to encourage employees to base decisions on these performance metrics.

Business Valuation A.

Accounting model 1. 2.

Focuses on firm’s earnings Assumes increases (decreases) in earnings will lead directly to increases (decreases) in stock price based on the price-earnings relationship

3.

Decreases in current earnings may result in increases in future cash flows, which may increase firm value and stock price.

162

B.

Free cash flow model 1.

Firm Value

=

Focuses on firm’s projected cash flows for all future years a.

Future years cash flows consist of the cash flows during a planning period of a finite number of years and a terminal value of all years beyond the planning period

b.

Firm value is calculated as

Free Cash Flow 3 Free Cash Flow 1 Free Cash Flow 2 Free Cash Flow 4 Terminal Value + + + + 1 2 3 4 4 (1 + k ) (1 + k ) (1 + k ) (1 + k ) (1 + k ) wacc wacc wacc wacc wacc

Terminal value is calculated as Free Cash Flow 5 k wacc

Terminal Value 4 =

2.

Components of free cash flow values a. b. c. d.

3. III.

IV.

Estimated revenues Estimated net operating profits Investment in net working capital Capital expenditures

Firm value equals market value of its debt and equity

Value Drivers A.

Managers can increase firm value by managing value drivers.

B.

Using value drivers to increase firm value may increase equity value.

Economic Value Added (EVA®) A.

EVA is the change in firm value during a specific time interval, usually 1 year

B.

EVA is calculated as

[

]

  N etO perating  W eightedA verage Invested  E V At =  ProfitA fter  −  C ostof × C apital   T ax(N O PA T)   C apital(k ) t -1  t  w acc  

 

C.

 

EVA can also be calculated as

on Invested − Weighted Average  × Invested EVA t =  Return  Capital (IC) Capital (ROIC) Cost of Capital (k ) t t −1 wacc  

163

V.

Paying for Performance A.

Agency problems arise when firm ownership and management are separate.

B.

Linking EVA measures to employee compensation encourages employees to act on behalf of owners

C.

Compensation Policy 1.

Three components of compensation are base pay, bonus, and longterm compensation

2.

The mix of base pay and performance-based pay is important in attracting quality employees and achieving target performance measures.

3.

Percentage of total compensation that is ‘at-risk’ typically increases with employee rank.

4.

Incentive pay should be linked to achieving target performance measures. a.

Incentive pay can be calculated as

   Actual Performanc e  Incentive =  Base   Fraction    of Pay  Pay   Pay   at Risk   Target Performanc e   

5.

b.

Bounded incentive pay rewards employees only when a minimum threshold of performance is achieved and caps the bonus payout at a maximum level of performance.

c.

Unbounded incentive pay has no upper or lower bonus limits.

Incentive pay can be paid in cash, stock, or a combination of cash and stock. a.

Stock rewards employees for current and future performance.

b.

Stock compensation may be the majority of CEO and Board of Directors’ pay.

ANSWERS TO END-OF-CHAPTER QUESTIONS 13-1. The accounting model of equity evaluation focuses on reported earnings in conjunction with the market’s valuation of those earnings as reflected in the priceearnings ratio. For example, if the price-earnings ratio is 20 then a dollar increase in earnings per share should create $20 in additional equity value per share. Similarly, a one-dollar loss in earnings per share may lead to a drop of $20 in share value.

164

The accounting model has its limitations, however. For example, this method relies on historical earnings and ignores other factors that may influence the share value in the market. 13-2. The free cash flow valuation model provides a method for analyzing firm value as the present value of the firm's projected free cash flows. 13-3. A.

B.

C.

D.

Sales growth—annual growth of revenues. Steps a firm’s management can take to manage its sales growth: •

Implement a new promotional campaign to promote existing or new products.

•

Form a distributional alliance to enter a new market.

•

Invest in R&D to create new products.

•

Acquire a competitor’s firm.

Operating profit margin—net operating income as a percent of a firm’s revenue. Steps that can be taken to manage the operating profit margin: •

Initiate cost control programs to reduce operating and administrative expenses.

•

Invest in a promotional campaign aimed at improving the brand image of the firm’s products or services in an effort to support premium-pricing policies.

Net working capital to sales ratio—the percent of new investments in current assets (excluding the part financed by non-interest bearing liabilities) relative to firm sales. Steps to manage the net working capital to sales ratio: •

Initiate inventory control policies designed to reduce the time that inventory is held before sale.

•

Implement a program of credit analysis and control designed to either decrease the time customers take to pay for their purchases or to incorporate penalties for late payment.

•

Negotiate more lenient credit terms from the firm’s suppliers.

Property, plant, and equipment to sales ratio—the percent of firm sales that is invested in property, plant, and equipment. Steps to manage the property, plant, and equipment to sales ratio: •

Consider outsourcing of production to strategic partners who might be more efficient in their operations so as to reduce the firm’s need for plant and equipment.

•

Implement stringent controls over the acquisition of new plant and equipment to assure that all purchases are economically viable.

165

•

Improve maintenance of existing plant and equipment to improve operating time, which reduces the need for additional plant and equipment.

166

13-4. Economic Value Added (EVA) measures the change in firm value over a specific period of time. Managers of a firm use EVA to evaluate the performance of the firm over specific intervals of time, usually one year. EVA for a particular year (e.g., year t) is defined as follows:

 N etO p e rating E V At =  P ro fitA fte r  −  T a x(N O P A Tt )  

  W e ig h teAd v e rag e   ×  In v e ste d C o st o f   C ap itat l− 1  )   C a p ital(k w a cc  

An alternative definition of EVA is:

Return Invested − Weighted Average  ×  Invested  EVA t =  Capital (ROIC)t Cost of Capital(k wacc )  Capital (IC)t −1   EVA is related to MVA in the following way: MVA is the present value of all future EVAs over the life of the firm. Thus, managing the firm in ways that increase EVA will generally lead to a higher MVA. 13-5. Fundamental components of a firm’s compensation program: A. Base pay is the fixed salary component of compensation. B. Bonus payment. This is generally a quarterly, semi-annual, or annual cash payment that is dependent upon firm performance compared to targets set at the beginning of the period. EVA provides one such performance measure that can be used in this regard. C. Long-term compensation. This consists of stock options and grants that are also made periodically to employees. This type of compensation is the most direct method available to the firm to align the interests of the firm’s employees with those of its shareholders. Note that both bonus and long-term compensation are at-risk in that they are both dependent upon performance of the individual and the firm. We often use the term incentive or performance-based compensation to describe this at-risk component of managerial compensation. 13-6. The four basic issues that every firm’s compensation program must address are: A. How much to pay for a particular job B. The portion of the total compensation package should be in base salary and the portion should be incentive based C. How to link incentive pay to performance D. The portion of the incentive pay to be paid as a cash bonus and the portion to be paid in long-term (equity) compensation Issue #1: How much to pay? How much to pay for a particular job is dictated by market forces. This means that a firm must be constantly comparing its pay scales with the labor market because the firm will

167

only be able to hire good employees where it offers a competitive level of total compensation. The size of the total compensation package may determine where employees go to work, but the mix of base pay and performance based pay will determine how hard they will work. Issue #2: Base pay versus at-risk or incentive compensation Usually a firm's highest-ranking employees generally have a larger fraction of their total compensation “at-risk” and the fraction declines with the employee's rank in the firm. Most firms base the at-risk fraction of an employee’s compensation on either salary level or responsibilities. This often mirrors the responsibilities of the firm’s top managers and their ability to control firm performance. Issue #3: Linking incentive compensation to performance The third issue in designing a compensation program relates to choosing a functional relationship between performance and pay for the incentive portion of the compensation package. The basic formula for specifying this relationship is: Incentive Pay

 Base =   Pay 

 Fraction     of Pay   at - Risk 

   Actual Performanc e        Target Performanc e  

There are two types of incentive compensation plans based on the above formula. The first type is called unbounded incentive compensation plan. This means in the above equation there are no limits specified as to the maximum or minimum levels of incentive pay that can be earned. The other type is called bounded incentive compensation plan. This system provides for a minimum or threshold level of performance (in relation to the target level) before the incentive plan kicks in, and a maximum level of performance (again in relation to the target) above which no incentive pay is rewarded. Consequently, incentive compensation is only paid for performance levels that fall within the minimum and maximum levels. Issue #4: Paying with a cash bonus versus equity A firm can pay its compensation plan in cash, stock or some mixture of the two. If the firm chooses stock then the employees are rewarded for current performance and are also provided with a long-term incentive to improve performance. Equity-based compensation is an important and valuable tool in a firm’s compensation package.

Solutions to Problem Set A 13-1A. Given: Earnings for 2001 per share Closing stock price for 2001 Estimated earnings per share for 2002

$ 1.90 $25.50 $ 1.06

168

Price-earnings ratio:

Closing stock price/earnings per share

13.42

Estimated stock price for 2002:

Price-earnings ratio × estimated earnings per share for 2002

$14.23

13-2A. Given: Sales growth for years 1-3

10.0%

Operating profit margin

16.0%

Net working capital to sales ratio

13.0%

Property, plant, and equipment to sales ratio

18.0%

Beginning sales

$ 27,272.73

Cash tax rate

30.0%

Total liabilities

$

Cost of capital

4,000.00 12.0%

Number of shares

2,000.00

FREE CASH FLOWS: Years Sales Operating income (Earnings Before Interest and Taxes) Less cash tax payments

1

2

3

4

$30,000.00 4,800.00

$33,000.00 5,280.00

$36,300.00 5,808.00

$36,300.00 5,808.00

(1,440.00)

Net operating profits after taxes (NOPAT)

$ 3,360.00

(1,584.00) $ 3,696.00

(1,742.40) $ 4,065.60

(1,742.40) $ 4,065.60

Less investments: Investment in Net Working Capital

(354.55)

(390.00)

(429.00)

-

Capital expenditures (CAPEX)

(490.91)

(540.00)

(594.00)

-

Total investments Free cash flow PV of FCF Present value of free cash flows: Planning horizon cash flows Terminal value in year 4: 33,880.00 PV of terminal value a) Firm value Invested capital (year 0) b) Market Value Added Debt Shareholder value ($30,730.94 – 4,000) No. of shares c) Value per share

$ (845.46)

$ (930.00) $ (1,023.00)

$

$ 2,514.54

$ 2,766.00

$ 3,042.60

$ 4,065.60

2,245.13

2,205.04

2,165.66

$24,115.11

$ 6,615.83 $ 24,115.11 $ 30,730.94 $ 9,818.18 $ 20,912.76 $ 4,000.00 $ 26,730.94 2,000.00 $ 13.37

169

-

13-3A. Sales growth for years 1-3 Operating profit margin Net working capital to sales ratio Current assets to sales ratio Property, plant, and equipment to sales ratio Beginning sales Cash tax rate Total liabilities Cost of capital Number of shares

10.0% 16.0% 13.0% 18.0% 18.0% $27,272.73 30.0% $ 4,000.00 12.0% 2,000.00 Years 0

Change in current assets Current assets Capital expenditures Property, plant and equipment Total Capital = Total Assets - Non-interest liabilities

$ 4,909.09 4,909.09 $ 9,818.18

1 $ 354.55 $ 5,263.64 $ 490.91 $ 5,400.00 $10,663.64

2 $ 390.00 $ 5,653.64 $ 540.00 $ 5,940.00 $11,593.64

3 $ 429.00 $ 6,082.64 $ 594.00 $ 6,534.00 $12,616.64

4 $ $ 6,082.64 $ $ 6,534.00 $12,616.64

1 $30,000.00 4,800.00 (1,440.00) $3,360.00 $(1,178.18)

2 $33,000.00 5,280.00 (1,584.00) $ 3,696.00 $(1,279.64)

3 4 and beyond $36,300.00 $ 36,300.00 5,808.00 $ 5,808.00 (1,742.40) (1,742.40) $ 4,065.60 $ 4,065.60 $ (1,391.24) $ (1,514.00)

$2,181.82 $ 10,663.64

$2,416.36 $11,593.64

$ 2,674.36 $12,616.64

a) Calculation of EVA: Years 0 Sales Operating income Less cash tax payments Net operating profits after taxes (NOPAT) Less capital charge (Invested Capital x Kwacc) Economic Value Added Invested Capital b) Return on Invested Capital (NOPATt ÷ ICt-1) c) Market Value Added = PV(EVAs) Plus Invested Capital (year 0) Firm Value

$ 9,818.18

34.22%

34.66%

$ 2,551.60 $12,616.64

35.07%

$20,640.89 9,818.18 $31,459.07

a. The EVAs are positive each year, indicating Bergman is creating value for its shareholders. b. The ROIC is greater than the cost of capital, so the firm is creating value for its shareholders. When the ROIC is greater than the cost of capital, we should see positive EVAs. c. The present value of the EVAs exceeds the market value added in Problem 13-2A.

170

32.22%

13-4A. Given: Base pay Incentive % Target EVA Performance

$

100,000.00 20.00% $ 20,000,000.00

a. Unbounded incentive plan Actual EVA Performance

Scenario A $ 15,000,000

Plant Manager Compensation Base pay Incentive pay Total compensation

$ 100,000.00 15,000.00 $ 115,000.00

b. Bounded incentive plan (80/120) Scenario A Actual EVA Performance $15,000,000 Plant Manager Compensation Base pay Incentive pay Total compensation

$ $

100,000.00 100,000.00

Scenario B $ 20,000,000

Scenario C $ 30,000,000

$ 100,000.00 20,000.00 $ 120,000.00

$ 100,000.00 30,000.00 $ 130,000.00

Scenario B $20,000,000

$ 100,000.00 20,000.00 $ 120,000.00

Scenario C $30,000,000

$ $

100,000.00 24,000.00 124,000.00

This plan encourages employees to meet targets only within range of performance where payout varies with performance (between floor and cap). Employees have no incentive to improve performance if below floor or above cap.

SOLUTION TO INTEGRATIVE PROBLEM A.

From the financial statements of RealNetworks over the 1996-98 period we can tell that it did not earn profit. Indeed, it suffered increasing losses in every year, and in 1998, the firm lost over $20 million.

B.

The invested capital for RealNetworks at the end of 1998 should be the sum of the current figure of total assets less noninterest-bearing liabilities in its balance sheet and part of the marketing and R&D expenditure it paid but will generate value in future years. Charging the full marketing and R&D expenditures against revenues in the year in which the expenditures are made will distort total assets as an indication of the firm’s invested capital. The investment in marketing and R&D does not create value only for the year it is made. Actually, it will bring benefits for the company in several future years. Therefore, putting the whole amount in the income statement for one year cannot properly reveal the company’s performance for that year because the revenue the company created only related to a part of the total investment in marketing and R&D.

171

C.

The EVA for year t is defined as following:

 Net Operating   Weighted Average  ×  Invested  EVA t =  Profit After  −  Cost of Tax (NOPAT)t   Capital (k wacc )  Capitalt −1      Using the GAAP financial reports of 1998, assuming that the invested capital equals total assets – accounts payable – accrued expenses – other current liabilities – deferred revenue, and weighted average cost of capital is 20%, we get the following result: EVA1998 = (-20840) – (20% x 78,865) = -36,613 However, as we discussed in part B, NOPAT is understated since we put the entire marketing and R&D expenditure for 1998 in the GAAP accounting earnings sheet for that year. Invested capital is also understated for the same reason. If we amortize the marketing and R&D expenditures over several years, during which it will generate value, our EVA result will be positive.

Solutions to Problem Set B 13-1B. Given: Earnings for 2001 per share Closing stock price for 2001 Estimated earnings per share for 2002 Price-earnings ratio: Estimated stock price for 2002:

$ 0.87 $ 16.06 $ 1.09 Closing stock price/ earnings per share Price-earnings ratio × estimated earnings per share for 2000

172

18.46 $ 20.12

13-2B. Given: Sales growth for years 1-3

10.0%

Operating profit margin

17.0%

Net working capital to sales ratio

13.0%

Property, plant and equipment to sales ratio

18.0%

Beginning sales

$ 31,363.64

Cash tax rate

28%

Total liabilities

$ 6,000.00

Cost of capital

15.0%

No. of shares

4,000.00

FREE CASH FLOWS:

Years 1

Sales Operating income (Earnings Before Int. & Taxes) Less cash tax payments

2

$ 34,500.00 $ 37,950.00 5,865.00 6,451.50

3 $ 41,745.00 7,096.65

4 $ 41,745.00 7,096.65

(1,642.20)

(1,806.42)

(1,987.06)

$ 4,222.80

$ 4,645.08

$ 5,109.59

$ 5,109.59

Investment in Net Working Capital

(407.73)

(448.50)

(493.35)

-

Capital expenditures (CAPEX)

(564.55)

(621.00)

(683.10)

-

Net operating profits after taxes (NOPAT)

(1,987.06)

Less investments:

Total investments Free cash flow PV of FCF

$ (972.28) $ (1,069.50) $ (1,176.45) $ $ 3,250.52 2,826.54

Present value of free cash flows: Planning horizon Terminal value In year 10: PV of terminal value a) Firm value Invested capital in year (0) b) Market Value Added c) Calculation of equity value Firm Value Less: Debt Equals: Shareholder value Number of shares Value per share

$ 3,575.58 $

3,933.14

$ 5,109.59

2,703.65

2,586.10

$ 22,397.59

$ 8,116.29 34,063.93 $ 22,397.59 $ 30,513.88 11,290.91 $ 19,222.97 $ 30,513.88 $ 6,000.00 $ 24,513.88 4,000.00 $ 6.13

173

-

13-3B. Given: Sales growth for years 1-3 Operating profit margin Net working capital to sales ratio Current assets to sales ratio Property, plant and equipment to sales ratio Beginning sales Cash tax rate Total liabilities Cost of capital Number of shares

10.0% 17.0% 13.0% 18.0% 18.00% $ 31,363.64 28.00% $ 6,000.00 15.00% 4,000.00 Years 0

Change in current assets Current assets Capital expenditures Property, plant and equipment Total Capital = Total Assets - Non-interest liabilities (Invested Capital) a) Calculation of EVA:

1 $ 407.73 $ 5,645.45 $ 6,053.18 $ 564.55 5,645.45 $ 6,210.00 $ 11,290.90 $12,263.18

Years 0 Sales Operating income Less cash tax payments Net operating profits after taxes (NOPAT) Less capital charge (Invested Capital x Kwacc) Economic Value Added b) Return on Invested Capital (NOPATt ÷ ICt-1) c) MVA and the present value of future EVAs Market Value Added = PV(EVAs) Plus Invested Capital (year 0) Firm Value

2 3 $ 448.50 $ 493.35 $ 6,501.68 $ 6,995.03 $ 621.00 $ 683.10 $ 6,831.00 $ 7,514.10 $13,332.68 $14,509.13

4 $ $ 6,995.03 $ $ 7,514.10 $14,509.13

1 $34,500.00 5,865.00 (1,642.20) $ 4,222.80 $(1,693.64) $ 2,529.16

2 $37,950.00 6,451.50 (1,806.42) $ 4,645.08 $(1,839.48) $ 2,805.60

3 $41,745.00 7,096.65 (1,987.06) $ 5,109.59 $ (1,999.90) $ 3,109.69

4 & beyond $ 41,745.00 7,096.65 (1,987.06) $ 5,109.59 $(2,176.37) $ 2,933.22

37.40%

37.88%

38.32%

35.22%

$ 19,996.52 11,290.90 $31,287.42

a. The EVAs are positive each year, indicating the Bergman is creating value for its shareholders. b. The ROIC is greater than the cost of capital, so the firm is creating value for its shareholders. When the ROIC is greater than the cost of capital, the EVAs are positive. c. The present value of the EVAs exceeds the market value added in Problem 13-2B.

174

13-4B. Given: Base pay Incentive % Target EVA Performance

$

150,000 30.00% $30,000,000

a. Unbounded incentive plan Scenario A $20,000,000

Actual EVA Performance Division Manager Compensation Base pay $ 150,000.00 Incentive pay 30,000.00 Total compensation $ 180,000.00 b. Bounded incentive plan (80/120) Scenario A Actual EVA Performance $20,000,000 Division Manager Compensation Base pay $ 150,000.00 Incentive pay Total compensation $ 150,000.00

Scenario B $30,000,000

Scenario C $40,000,000

$ 150,000.00 45,000.00 $ 195,000.00

$ 150,000.00 60,000.00 $ 210,00.00

Scenario B $30,000,000

Scenario C $40,000,000

$ 150,000.00 30,000.00 $ 180,000.00

$ 150,000.00 54,000.00 $ 204,000.00

This plan encourages employees to meet targets within range of performance where payout varies with performance (between floor and cap). Employees have no incentive to improve performance if below floor or above cap.

175

CHAPTER 14

Raising Capital in the Financial Markets CHAPTER ORIENTATION This chapter considers the market environment in which long-term capital is raised. The underlying rationale for the existence of security markets is presented, investment banking services and procedures are detailed, private placements are discussed, and security market regulation is reviewed.

CHAPTER OUTLINE I.

II.

The mix of corporate securities sold in the capital market. A.

When corporations raise cash in the capital market, what type of financing vehicle is most favored? The answer to this question is corporate bonds. The corporate debt markets clearly dominate the corporate equity markets when new (external) funds are being raised.

B.

From our discussion on the cost of capital, we understand that the U.S. tax system inherently favors debt as a means of raising capital. During the 19992001 period, bonds and notes accounted for about 76.9 percent of new corporate securities sold for cash.

Why financial markets exist A.

Financial markets consist of institutions and procedures that facilitate transactions in all types of financial claims.

B.

Some economic units spend more than they earn during a given period of time. Some economic units spend less than they earn. Accordingly, a mechanism is needed to facilitate the transfer of savings from those economic units that have a savings surplus to those that have a savings deficit. Financial markets provide such a mechanism.

C.

The function of financial markets then is to allocate savings in an economy to the ultimate demander (user) of the savings.

D.

If there were no financial markets, the wealth of an economy would be lessened. Savings could not be transferred to economic units, such as business firms, which are most in need of those funds.

176

III.

Financing business: The movement of funds through the economy. A.

B.

IV.

In a normal year the household sector is the largest net supplier of funds to the financial markets. We call the household sector then a savings-surplus sector. 1.

The household sector can also be a savings-deficit sector.

2.

From 1995 – 1999, the household sector was a net user of financial capital as a result of taking advantage of low interest rate mortgages.

In contrast, the nonfinancial business sector is typically a savings-deficit sector. 1.

The nonfinancial business sector can also be a savings-surplus sector.

2.

Economic conditions and corporate profitability influence the ability of this sector to provide funds to the financial market.

C.

In recent years, the foreign sector has become a major savings-surplus sector.

D.

Within the domestic economy, the nonfinancial business sector is dependent on the household sector to finance its investment needs.

E.

The movement of savings through the economy occurs in three distinct ways: 1.

The direct transfer of funds

2.

Indirect transfer using the investment banker

3.

Indirect transfer using the financial intermediary

Components of the U.S. financial market system A.

Public offerings can be distinguished from private placements. 1.

2.

The public (financial) market is an impersonal market in which both individual and institutional investors have the opportunity to acquire securities. a.

A public offering takes place in the public market.

b.

The security-issuing firm does not meet (face-to-face) the actual investors in the securities.

In a private placement of securities, only a limited number of investors have the opportunity to purchase a portion of the issue. a.

The market for private placements is more personal than its public counterpart.

b.

The specific details of the issue may actually be developed on a face-to-face basis among the potential investors and the issuer.

177

c.

Venture capital (1)

B.

C.

Start-up firms often turn to venture capitalists to raise funds. (a)

Broader public markets find these firms too risky.

(b)

Venture capitalists are willing to accept the risks because of an expectation of higher returns.

(1)

Venture capital firms that acquire equity in a start-up firm manage risk by sitting on the firm’s board of directors or actively monitoring management’s activities.

(2)

Venture capital is often provided by established nonventure-capitalist firms that take a minority investment position in an emerging firm or create a separate venture capital subsidiary. (a)

The investment approach allows the established firm to gain access to new technology and to create strategic alliances.

(b)

The subsidiary approach allows the established firm to retain human and intellectual capital.

Primary markets can be distinguished from secondary markets. 1.

Securities are first offered for sale in a primary market. For example, the sale of a new bond issue, preferred stock issue, or common stock issue takes place in the primary market. These transactions increase the total stock of financial assets in existence in the economy.

2.

Trading in currently existing securities takes place in the secondary market. The total stock of financial assets is unaffected by such transactions.

The money market can be distinguished from the capital market. 1.

The money market consists of the institutions and procedures that provide for transactions in short-term debt instruments which are generally issued by borrowers who have very high credit ratings. a.

"Short-term" means that the securities traded in the money market have maturity periods of not more than 1 year.

b.

Equity instruments are not traded in the money market.

c.

Typical examples of money market instruments are (l) U.S. Treasury bills, (2) federal agency securities, (3) bankers' acceptances, (4) negotiable certificates of deposit, and (5) commercial paper.

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2.

D.

The capital market consists of the institutions and procedures that provide for transactions in long-term financial instruments. This market encompasses those securities that have maturity periods extending beyond 1 year.

Organized security exchanges can be distinguished from over-the-counter markets. 1.

2.

Organized security exchanges are tangible entities whose activities are governed by a set of bylaws. Security exchanges physically occupy space and financial instruments are traded on such premises. a.

Major stock exchanges must comply with a strict set of reporting requirements established by the Securities and Exchange Commission (SEC). These exchanges are said to be registered.

b.

Organized security exchanges provide several benefits to both corporations and investors. They (l) provide a continuous market, (2) establish and publicize fair security prices, and (3) help businesses raise new financial capital.

c.

A corporation must take steps to have its securities listed on an exchange in order to directly receive the benefits noted above. Listing criteria differ from exchange to exchange.

Over-the-counter markets include all security markets except the organized exchanges. The money market is a prominent example. Most corporate bonds are traded over-the-counter. a.

NASDAQ, a telecommunication system providing an information link among brokers and dealers in the OTC markets, accounted for 43% of the national exchange equity market trading in the U.S., measured in dollar volume for the year 1998. Nasdaq Stock Market, Inc. trades securities of over 3,600 public companies as of 2002.

V.

The Investment Banker A.

The investment banker is a financial specialist who acts as an intermediary in the selling of securities. The investment banker works for an investment banking house (firm).

B.

Three basic functions are provided by the investment banker: 1.

The investment banker assumes the risk of selling a new security issue at a satisfactory (profitable) price. This is called underwriting. Typically, the investment banking house, along with the underwriting syndicate, actually buys the new issue from the corporation that is raising funds. The syndicate (group of investment banking firms) then sells the issue to the investing public at a higher (hopefully) price than it paid for it.

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C.

VI.

2.

The investment banker provides for the distribution of the securities to the investing public.

3.

The investment banker advises firms on the details of selling securities.

Several distribution methods are available for placing new securities into the hands of final investors. The investment banker's role is different in each case. 1.

In a negotiated purchase, the firm in need of funds contacts an investment banker and begins the sequence of steps leading to the final distribution of the securities that will be offered. The price that the investment banker pays for the securities is "negotiated" with the issuing firm.

2.

In a competitive-bid purchase, the investment banker and underwriting syndicate are selected by an auction process. The syndicate willing to pay the greatest dollar amount per new security to the issuing firm wins the competitive bid. This means that it will underwrite and distribute the issue. In this situation, the price paid to the issuer is not negotiated; instead, it is determined by a sealed-bid process much on the order of construction bids.

3.

In a commission (or best-efforts), offering the investment banker does not act as an underwriter but rather attempts to sell the issue in return for a fixed commission on each security that is actually sold. Unsold securities are simply returned to the firm hoping to raise funds.

4.

In a privileged subscription, the new issue is not offered to the investing public. It is sold to a definite and limited group of investors. Current stockholders are often the privileged group.

5.

In a direct sale, the issuing firm sells the securities to the investing public without involving an investment banker in the process. This is not a typical procedure.

More on Private placements: The Debt Side A.

Each year billions of dollars of new securities are privately (directly) placed with final investors. In a private placement, a small number of investors purchase the entire security offering. Most private placements involve debt instruments.

B.

Large financial institutions are the major investors in private placements. These include (l) life insurance firms, (2) state and local retirement funds, and (3) private pension funds.

C.

The advantages and disadvantages of private placements as opposed to public offerings must be carefully evaluated by management. 1.

The advantages include (a) greater speed than a public offering in actually obtaining the needed funds, (b) lower flotation costs than are

180

associated with a public issue, and (c) increased flexibility in the financing contract. 2.

VII.

Flotation costs A.

B.

VIII.

The disadvantages include (a) higher interest costs than are ordinarily associated with a comparable public issue, (b) the imposition of restrictive covenants in the financing contract, and (c) the possibility that the security may have to be registered some time in the future at the lender's option.

The firm raising long-term capital typically incurs two types of flotation costs: (l) the underwriter's spread and (2) issuing costs. The former is typically the larger. 1.

The underwriter's spread is the difference between the gross and net proceeds from a specific security issue. This absolute dollar difference is usually expressed as a percent of the gross proceeds.

2.

Many components comprise issue costs. The two most significant are (l) printing and engraving and (2) legal fees. For comparison purposes, these are usually expressed as a percent of the issue's gross proceeds.

SEC data reveal two relationships about flotation costs. 1.

Issue costs (as a percent of gross proceeds) for common stock exceed those of preferred stock, which exceed those of bonds.

2.

Total flotation costs per dollar raised decrease as the dollar size of the security issue increases.

Regulation A.

The primary market is governed by the Securities Act of 1933. 1.

The intent of this federal regulation is to provide potential investors with accurate and truthful disclosure about the firm and the new securities being sold.

2.

Unless exempted, the corporation selling securities to the public must register the securities with the SEC.

3.

Exemptions allow follow for a variety of conditions. For example, if the size of the offering is small enough (less than $1.5 million), the offering does not have to be registered. If the issue is already regulated or controlled by some other federal agency, registration with the SEC is not required. Railroad issues and public utility issues are examples.

4.

If not exempted, a registration statement is filed with the SEC containing particulars about the security-issuing firm and the new security.

5.

A copy of the prospectus, a summary registration statement, is also filed. It will not yet have the selling price of the security printed on it;

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it is referred to as a red herring and called that until approved by the SEC.

B.

C.

D.

6.

If the information in the registration statement and prospectus is satisfactory to the SEC, the firm can proceed to sell the new issue. If the information is not satisfactory, a stop order is issued which prevents the immediate sale of the issue. Deficiencies have to be corrected to the satisfaction of the SEC before the firm can sell the securities.

7.

The SEC does not evaluate the investment quality of any issue. It is concerned instead with the presentation of complete and accurate information upon which the potential investor can act.

The secondary market is regulated by the Securities Exchange Act of 1934. This federal act created the SEC. It has many aspects. 1.

Major security exchanges must register with the SEC.

2.

Insider trading must be reported to the SEC.

3.

Manipulative trading that affects security prices is prohibited.

4.

Proxy procedures are controlled by the SEC.

5.

The Federal Reserve Board has the responsibility of setting margin requirements. This affects the proportion of a security purchase that can be made via credit.

The Securities Acts Amendments of 1975 touched on three important issues. 1.

Congress mandated the creation of a national market system (NMS). Implementation details of the NMS were left to the SEC. Agreement on the final form of the NMS is yet to come.

2.

Fixed commissions (also called fixed brokerage rates) on public transactions in securities were eliminated.

3.

Financial institutions, like commercial banks and insurance firms, were prohibited from acquiring membership on stock exchanges where their purpose in so doing might be to reduce or save commissions on their own trades.

In March 1982, the SEC adopted "Rule 415." This process is now known as a shelf registration or a shelf offering. 1.

This allows the firm to avoid the lengthy, full registration process each time a public offering of securities is desired.

2.

In effect, a master registration statement that covers the financing plans of the firm over the coming two years is filed with the SEC. After approval, the securities are sold to the investing public in a piecemeal fashion or "off the shelf."

3.

Prior to each specific offering, a short statement about the issue is filed with the SEC.

182

E.

IX.

Congress passed in July 2002 the Public Company Accounting Reform and Investor Protection Act. The short name for the act became the SarbanesOxley Act of 2002. 1.

The Sarbanes-Oxley Act was passed as the result of a large series of corporate indiscretions.

2.

The act contains 11 “titles” which tightened significantly the latitudes given to corporate advisors (like accountants, lawyers, company officers, and boards of directors) who have access to or influence company decisions.

3.

The initial title of the act created the Public Company Accounting Oversight Board. This board’s purpose is to regulate the accounting industry relative to public companies that they audit. Members are appointed by the SEC.

4.

As recently June of 2003, the oversight board itself published a set of ethics rules to police its own set of activities.

The Multinational Firm: Efficient Financial Markets and Intercountry Risk A.

The United States’ highly developed, complex and competitive financial markets facilitate the transfer of savings from the saving-surplus sector to the saving-deficit sector.

B.

Multinational firms are reluctant to invest in countries with ineffective financial systems. 1.

Financial and political systems lacking integrity will often be rejected for direct investment by multinational firms.

2.

Countries that experience significant devaluation of its currency may also be considered too risky for investment.

ANSWERS TO END-OF-CHAPTER QUESTIONS 14-1. Financial markets are institutions and procedures that facilitate transactions in all types of financial claims. Financial markets perform the function of allocating savings in the economy to the ultimate demander(s) of the savings. Without these financial markets, the total wealth of the economy would be lessened. Financial markets aid the rate of capital formation in the economy. 14-2. A financial intermediary issues its own type of security which is called an indirect security. It does this to attract funds. Once the funds are attracted, the intermediary purchases the financial claims of other economic units in order to generate a return on the invested funds. A life insurance company, for example, issues life insurance policies (its indirect security) and buys corporate bonds in large quantities.

183

14-3. The money market consists of all institutions and procedures that accomplish transactions in short-term debt instruments issued by borrowers with (typically) high credit ratings. Examples of securities traded in the money market include U.S. Treasury Bills, bankers’ acceptances, and commercial paper. Notice that all of these are debt instruments. Equity securities are not traded in the money market. It is entirely an over-the-counter market. On the other hand, the capital market provides for transactions in long-term financial claims (those claims with maturity periods extending beyond one year). Trades in the capital market can take place on organized security exchanges or over-the-counter markets. 14-4. Organized stock exchanges provide for: (1)

A continuous market. This means a series of continuous security prices is generated. Price changes between trades are dampened, reducing price volatility, and enhancing the liquidity of securities.

(2)

Establishing and publicizing fair security prices. Prices on an organized exchange are determined in the manner of an auction. Moreover, the prices are published in widely available media like newspapers.

(3)

An aftermarket to aid businesses in the flotation of new security issues. The continuous pricing mechanism provided by the exchanges facilitates the determination of offering prices in new flotations. The initial buyer of the new issue has a ready market in which he can sell the security should he need liquidity rather than a financial asset.

14-5. The criteria for listing can be labeled as follows: (1) profitability; (2) size; (3) market value; (4) public ownership. 14-6. Most bonds are traded among very large financial institutions. Life insurance companies and pension funds are typical examples. These institutions deal in large quantities (blocks) of securities. An over-the-counter bond dealer can easily bring together a few buyers and sellers of these large quantities of bonds. By comparison, common stocks are owned by millions of investors. The organized exchanges are necessary to accomplish the "fragmented" trading in equities. 14-7. The investment banker is a middleman involved in the channeling of savings into long-term investment. He performs the functions of: (1) underwriting; (2) distributing; (3) advising. By assuming underwriting risk, the investment banker and his syndicate purchase the securities from the issuer and hope to sell them at a higher price. Distributing the securities means getting those financial claims into the hands of the ultimate investor. This is accomplished through the syndicate's selling group. Finally, the investment banker can provide the corporate client with sound advice on which type of security to issue, when to issue it, and how to price it. 14-8. In a negotiated purchase, the corporate security issuer and the managing investment banker negotiate the price that the investment banker will pay the issuer for the new offering of securities. In a competitive-bid situation, the price paid to the corporate security issuer is determined by competitive (sealed) bids, which are submitted by several investment banking syndicates hoping to win the right to underwrite the offering.

184

14-9. Investment banking syndicates are established for three key reasons: (1) the investment banker who originates the business probably cannot afford to purchase the entire new issue himself; (2) to spread the risk of loss among several underwriters; (3) to widen the distribution network. 14-10. Several positive benefits are associated with private placements. The first is speed. Funds can be obtained quickly, primarily due to the absence of a required registration with the SEC. Second, flotation costs are lower as compared to public offerings of the same dollar size. Third, greater financing flexibility is associated with the private placement. All of the funds, for example, need not be borrowed at once. They can be taken over a period of time. Elements of the debt contract can also be renegotiated during the life of the loan. 14-11. As a percent of gross proceeds, flotation costs are inversely related to the dollar size of the new issue. Additionally, common stock is more expensive to issue than preferred stock, which is more expensive to issue than debt. 14-12. The answer on this is clear. The corporate debt markets dominate the corporate equity markets when new funds are raised. The tax system of the U.S. economy favors debt financing by making interest expense deductible from income when computing the firm's federal tax liability. Consider all corporate securities offered for cash over the period 1999-2001. The percentage of the total represented by bonds and notes was 76.9 percent compared to 23.1 percent equity. 14-13. The household sector is the largest net supplier of savings to the financial markets. Foreign financial investors have recently been net suppliers of savings to the financial markets. On the other hand, the nonfinancial corporate business sector is most often a savings-deficit sector. The U.S. Government sector too is a deficit sector in most years. 14-14. First, there may be a direct transfer of savings from the investor to the borrower. Second, there may be an indirect transfer that used the services provided by an investment banker. Third, there may be an indirect transfer that uses the services of a financial intermediary. Private pension funds and life insurance companies are prominent examples of the latter case.

185

CHAPTER 15

Analysis and Impact of Leverage CHAPTER ORIENTATION This chapter focuses on useful aids for the financial manager in determining the firm's proper financial structure. It includes the definitions of the different kinds of risk, a review of breakeven analysis, the concepts of operating leverage, financial leverage, the combination of both leverages, and their effect on EPS (earnings per share).

CHAPTER OUTLINE I.

Business risk and financial risk A.

Risk is defined as the likely variability associated with expected revenue streams. 1.

B.

C.

The variations in the income stream can be attributed to a.

The firm's exposure to business risk

b.

The firm's decision to incur financial risk

Business risk is defined as the variability of the firm's expected earnings before interest and taxes. 1.

Business risk is measured by the firm's corresponding expected coefficient of variation.

2.

Dispersion in operating income does not cause business risk. It is the result of several influences, such as the company’s cost structure, product demand characteristics, and intra-industry competition.

Financial risk is a direct result of the firm's financing decision. It refers to the additional variability in earnings available to the firm’s common stockholders and the additional chance of insolvency borne by the common shareholder when financial leverage is used. 1.

Financial leverage is the financing of a portion of the firm's assets with securities bearing a fixed rate of return in hopes of increasing the return to the common shareholders.

186

2.

II.

Financial risk is passed on to the common shareholders who must bear most of the inconsistencies of returns to the firm after the deduction of fixed payments.

Break-even Analysis A.

The objective of break-even analysis is to determine the break-even quantity of output by studying the relationships among the firm’s cost structure, volume of output, and operating profit. 1.

B.

C.

D.

The break-even quantity of output results in an EBIT level equal to zero.

Use of the model enables the financial officer to 1.

Determine the quantity of output that must be sold to cover all operating costs.

2.

Calculate the EBIT achieved at various output levels.

Some potential applications include 1.

Capital expenditure analysis as a complementary technique to discounted cash flow evaluation models

2.

Pricing policy

3.

Labor contract negotiations

4.

Evaluation of cost structure

5.

Financial decision making

Essential elements of the break-even model 1.

2.

Production costs must be separated into fixed costs and variable costs. Fixed costs do not vary as the sales volume or the quantity of output changes. Examples include a.

Administrative salaries

b.

Depreciation

c.

Insurance premiums

d

Property taxes

e.

Rent

Variable costs vary in total as output changes. Variable costs are fixed per unit of output. Examples include a.

Direct materials

b.

Direct labor

c.

Energy cost associated with production

d.

Packaging

e.

Freight-out

187

f. 3.

4.

E.

Sales commissions

In order to implement the break-even model, it is necessary for the financial manager to a.

Identify the most relevant output range for planning purposes.

b.

Approximate all costs in the semifixed and semivariable range and allocate them to the fixed and variable cost categories.

Total revenue and volume of output a.

Total revenue (sales dollars) is equal to the selling price per unit multiplied by the quantity sold.

b.

Volume of output refers to the firm’s level of operations and is expressed as a unit quantity or sales dollars.

Finding the break-even point 1.

The break-even model is just an adaptation of the firm's income statement expressed as sales - (total variable costs + total fixed costs) = profit

2.

Three ways to find the break-even point are explained. a.

b.

c.

Trial and error (1)

Select an arbitrary output level.

(2)

Calculate the corresponding EBIT amount.

(3)

When EBIT equals zero, the break-even point has been found.

Contribution margin analysis (1)

Unit selling price - unit variable cost = contribution margin

(2)

Fixed cost divided by the contribution margin per unit equals the break-even quantity in units.

Algebraic analysis (l)

(2)

QB

= the break-even level of units sold,

P

= the unit sales price,

F

= the total fixed cost for the period,

V

= unit variable cost.

Then, QB =

F P −V

188

F.

G.

III.

The break-even point in sales dollars 1.

It is convenient to calculate the break-even point in terms of sales dollars if the firm deals with more than one product. It can be computed by using data from the firm's annual report.

2.

Since variable cost and selling price per unit are assumed constant, the ratio of total variable costs to total sales is a constant for any level of sales.

Limitations of break-even analysis 1.

Assumes linear cost-volume-profit relationship.

2.

The total revenue curve is presumed to increase linearly with the volume of output.

3.

Assumes constant production and sales mix.

4.

This is a static form of analysis.

Operating Leverage A.

Operating leverage is the responsiveness of a firm's EBIT to fluctuations in sales. Operating leverage results when fixed operating costs are present in the firm's cost structure.

B.

This responsiveness can be measured as follows: degree of operating % change in EBIT leverage from the = DOLs = % change in sales base sales level

C.

If unit costs are available, the DOL can be measured by Q(P −V)

DOLs = Q(P −V) −F D.

If an analytical income statement is the only information available, the following formula is used: DOLs =

revenue before fixed costs EBIT

=

S − VC S − VC − F

Note: All three formulas provide the same results. E.

Implications of operating leverage 1.

At each point above the break-even level, the degree of operating leverage decreases.

2.

At the break-even level of sales, the degree of operating leverage is undefined.

3.

Operating leverage is present when the percentage change in EBIT divided by the percentage change in sales is greater than one.

4.

The degree of operating leverage is attributed to the business risk that a firm faces. 189

IV.

Financial Leverage A.

To see if financial leverage has been used to benefit the common shareholder, the focus will be on the responsiveness of the company's earnings per share (EPS) to changes in its EBIT.

B.

The firm is using financial leverage and is exposing its owners to financial risk when % change in EPS % change in EBIT

C.

is greater than 1.00

A measure of the firm's use of financial leverage is as follows: degree of financial % change in EPS leverage from the = DFLEBIT = % change in EBIT base EBIT level

D.

1.

The degree of financial leverage concept can be either in the positive or negative direction.

2.

The greater the degree of financial leverage, the greater the fluctuations in EPS.

An easier way to measure financial leverage is DFLEBIT =

EBIT EBIT − I

where I is the sum of all fixed financing costs V.

Combining operating and financial leverage A.

Changes in sales revenues cause greater changes in EBIT. If the firm chooses to use financial leverage, changes in EBIT turn into larger variations in both EPS and EAC. Combining operating and financial leverage causes rather large variations in EPS.

B.

One way to measure the combined leverage can be expressed as degree of combined % change in EPS leverage from the = DCLs = % change in sales base sales level

If the DCL is equal to 5.0 times, then a 1% change in sales will result in a 5% change in EPS. C.

The degree of combined leverage is the product of the two independent leverage measures. Thus: DCLS = (DOLS ) x (DFLEBIT)

190

D.

Another way to compute DCLs is with the following equation: Q(P −V)

DCLs = Q(P − V) − F −I E.

Implications of combining operating and financial leverage 1.

Total risk can be managed by combining operating and financial leverage in different degrees.

2.

Knowledge of the various leverage measures helps to determine the proper level of overall risk that should be accepted.

ANSWERS TO END-OF-CHAPTER QUESTIONS 15-1. Business risk is the uncertainty that envelops the firm's stream of earnings before interest and taxes (EBIT). One possible measure of business risk is the coefficient of variation in the firm's expected level of EBIT. Business risk is the residual effect of the: (1) company's cost structure, (2) product demand characteristics, (3) intraindustry competitive position. The firm's asset structure is the primary determinant of its business risk. Financial risk can be identified by its two key attributes: (1) the added risk of insolvency assumed by the common stockholder when the firm chooses to use financial leverage; (2) the increased variability in the stream of earnings available to the firm's common stockholders. 15-2. Financial leverage is financing a portion of the firm's assets with securities bearing a fixed (limited) rate of return. Anytime the firm uses preferred stock to finance assets, financial leverage is employed. 15-3. Operating leverage is the use of fixed operating costs in the firm's cost structure. When operating leverage is present, any percentage fluctuation in sales will result in a greater percentage fluctuation in EBIT. 15-4. Break-even analysis, as it is typically presented, categorizes all operating costs as being either fixed or variable. Based upon this division of costs, the break-even point is computed. The computation procedure for the cash break-even point omits any noncash expenses that the firm might incur. Typical examples of noncash expenses include depreciation and prepaid expenses. The ordinary break-even point will always exceed the cash break-even point, provided some noncash charges are present. 15-5. The most important shortcomings of break-even analysis are: (1)

The cost-volume-profit relationship is assumed to be linear over the entire range of output.

(2)

All of the firm's production is assumed to be salable at the fixed selling price.

(3)

The sales mix and production mix is assumed constant.

191

(4)

The level of total fixed costs and the variable cost to sales ratio is held constant over all output and sales ranges.

15-6. Total risk exposure is the result of the firm's use of both operating leverage and financial leverage. Business risk and financial risk produce this total risk. A company that is normally exposed to a high degree of business risk may manage its financial structure in such a way as to minimize financial risk. A firm that enjoys a stable pattern in its earnings before interest and taxes might reasonably elect to use a high degree of financial leverage. This would increase both its earnings per share and its rate of return on the common equity investment. 15-7. By taking the degree of combined leverage times the sales change of a negative 15 percent, the earnings available to the firm's common shareholders will decline by 45 percent. 15-8. As the sales of a firm increase, two things occur that bias the cost and revenue functions toward a curvilinear shape. First, sales will increase at a decreasing rate. As the market approaches saturation, the firm must cut its price to generate sales revenue. Second, as production approaches capacity, inefficiencies occur that result in higher labor and material costs. Furthermore, the firm's operating system may have to bear higher administrative and fixed costs. The result is higher per unit costs as production output increases.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions To Problem Set A 15-1A. Product Line Piano Violin Cello Flute

Sales 61,250 37,500 98,750 52,500

V.C. 41,650 22,500 61,225 25,725

C.M. 19,600 15,000 37,525 26,775

C.M. Ratio 32% 40% 38% 51%

Total

250,000

151,100

98,900

40%

Break-even Point S* = F/(1-VC/S) = 50,000/(1-VC/S) = 50,000/.4 = 125,000 50,000 F 50,000 S* = 1 − VC  = 1 − $151,100  =   .4 $250,000  S   

192

= 125,000

15-2A. Break-even Quantity =

QB

QB

=

F (P −V)

QB

=

$360,000 $30 - (.70)($30)

QB

=

40,000 bottles

15-3A. Degree of Operating Leverage = DOLS DOLS =

Q(P −V) [Q(P −V) −F]

V

70% x $30

=

=$21

DOLS =

50 ,000 ($ 30 −$21 ) [50 ,000 ($ 30 −$21 ) −$360 ,000 ]

DOLS =

5 times

15-4A. (a) Sales Variable Costs Revenue before fixed costs Fixed costs EBIT

Jake's Lawn Chairs $600,640.00 $326,222.60

Sarasota Sky Lights $2,450,000 $1,120,000

Jefferson Wholesale $1,075,470 $957,000

$274,417.40 $120,350.00 $ 154,067.40

$1,330,000 $850,000 $ 480,000

$118,470 $89,500 $ 28,970

(b) Jake's Lawn Chairs: QB =

Sarasota Skylights: QB

$120 ,350 F = $ 32 −$17 .38 P −V

=

$120 ,350 $14 .62

=

$850 ,000 $875 − $400

= $850 ,000

= 1,789

$89 ,500 $97 .77 −$87

= $89 ,500

= 8,310

Jefferson Wholesale: QB =

= 8,232 $475

$10 .77

(c)

Revenue Before Fixed Costs = EBIT =

Jake's Lawn Chairs

Sarasota Skylights

Jefferson Wholesale

$274 ,417 .40 $154 ,067 .40

$1,330,000 $480,000

$118 ,470 $28 ,970

1.78 times

2.77 times

4.09 times

193

(d)

Jefferson Wholesale, since its degree of operating leverage exceeds that of the other two companies.

15-5A. (a)

Revenue Before Fixed Costs EBIT

(b)

EBIT = EBIT − I

=

$22 ,950 ,000 $13 ,750 ,000

$13 ,750 ,000 $13 ,750 ,000 −$1,350 ,000

$13 ,750 ,000 $12 ,400 ,000

(c) (d)

1.67 times

= = 1.11 times

DCL45,750,000 S*

=

= (1.67) (1.11) = 1.85 times

=

F VC 1− S

=

$9,200 ,000 .502

=

$9,200 ,000 $22 ,800 ,000 1− $45 ,750 ,000

=

(e)

(25%) × (1.85) = 46.25%

(a)

QB =

(b)

F S* = 1 − VC S

$9,200 ,000 1 −.498

=

$18,326,693.23

15-6A. $170 ,000 $170 ,000 F = = = 6,296 pairs of shoes $85 −$58 $27 P −V

$170 ,000 = 1 − $58 $85

=

$170 ,000 1 −.682

=

$170 ,000 .318

= $534,591.20

(c) Sales Variable Costs Revenue before fixed costs Fixed costs EBIT

7,000 Pairs of Shoes $595,000 406,000 $189,000 170,000 $ 19,000

194

9,000 Pairs of Shoes $765,000 522,000

15,000 Pairs of Shoes $1,275,000 870,000

$243,000 170,000 $ 73,000

$405,000 170,000 $ 235,000

(d) 7,000 Pairs of Shoes

9,000 Pairs of Shoes

$189 ,000 $19 ,000

=

15,000 Pairs of Shoes

$243 ,000 $73 ,000

9.95 times

$405 ,000 $235 ,000

3.33 times

1.72 times

Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point. 15-7A. (a)

QB

=

$630 ,000 F = $180 − $110 P −V

(b)

S*

=

9000 units × $180 = $1,620,000

=

$630 ,000 $70

= 9000 Units

Alternatively, S*

= =

Note:

F $630 ,000 VC = $110 1− 1− S $180 $630 ,000 1 − 0.6111

Sales Variable Costs Revenue before fixed costs Fixed costs EBIT

=

$630 ,000 .3889

= $1,619,954

$1,619,954 differs from $1,620,000 due to rounding.

(c)

(d)

=

12,000 units $2,160,000 1,320,000

15,000 units $2,700,000 1,650,000

20,000 units $3,600,000 2,200,000

840,000 630,000 $ 210,000

1,050,000 630,000 $ 420,000

1,400,000 630,000 $ 770,000

12,000 units

15,000 units

20,000 units

$840 ,000 $210 ,000

$1,050 ,000 $420 ,000

$1,400 ,000 $770 ,000

4 times

=

2.5 times

=

1.82 times

Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point. 15-8A. (a) Blacksburg 195

Lexington

Williamsburg

Sales Variable costs Revenue before fixed costs Fixed costs EBIT

Furniture $1,125,000 926,250

Cabinets $1,600,000 880,000

Colonials $520,000 188,500

$198,750 35,000 $163,750

$720,000 100,000 $620,000

$331,500 70,000 $261,500

(b) Blacksburg Furniture :

QB

=

$35 ,000 $35 ,000 F = = = 13,208 $2.65 P − V $15 .00 −$12 .35

QB

=

$100 ,000 $400 −$220

Williamsbu rg Colonials : QB

=

$70 ,000 $40 .00 −$14 .50

units Lexington Cabinets :

=

$100 ,000 $180

=

= 556 units

$70 ,000 $25 .50

= 2745 units

(c) Blacksburg Furniture

Lexington Cabinets

Revenue Before $198 ,750 Fixed Costs $163 ,750 EBIT

$720 ,000 $620 ,000

$331 ,500 $261 ,500

1.16 times

1.27 times

= (d)

1.21 times

Williamsburg Colonials

Williamsburg Colonials, since its degree of operating leverage exceeds that of the other two companies.

15-9A. (a)

{S- (VC + F)} (1-T) = $50,000  S − 

  VC   S + F     (1 − T ) = $50,000   S  

[S – VC - } (1 – T) = $50,000 {$375,000 - $206,250 – F} (0.6) = $50,000 ($168,750 - F) (0.6) = $50,000 F = $85,416.67 (b)

QB =

F P −V

F S* = 1 − VC S

$85 ,416 .67 $27 .00 −$14 .85

=

=

$85 ,416 .67 1 −.55

196

= $85 ,416 .67 $12 .15

= $189,815

= 7,030 units

15-10A.(a)

Find the EBIT level at the forecast sales volume: EBIT = .26 S

Therefore, EBIT = (0.26) ($3,250,000) = $845,000 Next, find total variable costs: VC = 0.5, S

so,

VC = (0.5) $3,250,000 = $1,625,000

Now, solve for total fixed costs: S - (VC + F) = $845,000 $3,250,000 - ($1,625,000 + F) = $845,000 F = $780,000 (b)

S* =

$780 ,000 1 − 0 .5

= $1,560,000

15-11A. $16 ,500 ,000 $8,500 ,000

(a)

Revenue before Fixed costs EBIT

(b)

EBIT EBIT − I

(c)

DCL$30,000,000= (1.94) × (1.13) = 2.19 times

(d)

F S* = 1 − VC S

$8,500 ,000

= $7,500 ,000

=

= 1.94 times

= 1.13 times

$8,000 ,000 = 1 − $13 .5m $30 .0m

=

$8,000 ,000 1 −0.45

=

$8,000 ,000 0.55

$14,545,455 (e)

(25%) × (2.19) = 54.75%

15-12A.Given the data for this problem, several approaches are possible for finding the break-even point in units. The approach below seems to work well with students. Step (1)

Compute the operating profit margin: Operating Profit Margin x Operating Asset Turnover = Return on operating assets (M) x (5) = 0.25 M = .05

197

=

Step (2)

Compute the sales level associated with the given output level: Sales = 5 $20,000,00 0

Sales = $100,000,000 Step (3)

Compute EBIT: (.05) ($100,000,000) = $5,000,000

Step (4)

Compute revenue before fixed costs. Since the degree of operating leverage is 4 times, revenue before fixed costs (RBF) is 4 times EBIT as follows: RBF = (4) × ($5,000,000) = $20,000,000

Step (5)

Compute total variable costs: (Sales) - (Total variable costs) = $20,000,000 $100,000,000 - (Total variable costs) = $20,000,000 Total variable costs = $80,000,000

Step (6)

Compute total fixed costs: RBF - Fixed costs = $5,000,000 $20,000,000 - fixed costs = $5,000,000 Fixed costs = $15,000,000

Step (7)

Find the selling price per unit, and the variable cost per unit: P =

$100 ,000 ,000 = $10.00 10 ,000 ,000 $80 ,000 ,000

V = 10 ,000 ,000 = $8.00 Step (8)

Compute the break-even point: QB =

F = $15 ,000 ,000 = $15 ,000 ,000 = ($ 10 ) −($ 8) $2 P −V

7,500,000 units

198

15-13A. (a)

(b)

QB

=

F = $540 ,000 = $540 ,000 = 10,000 units $180 − $126 $54 P −V

S*

=

F VC 1− S

$540 ,000 $126 1− $180

=

=

$540 ,000 1 −0.7

=

$540 ,000 .3

= $1,800,000 (c) Sales Variable costs Revenue before fixed costs Fixed costs

12,000 Units $2,160,000 1,512,000 $ 648,000 540,000

15,000 Units $2,700,000 1,890,000 $ 810,000 540,000

20,000 Units $3,600,000 2,520,000 $1,080,000 540,000

EBIT

$ 108,000

$ 270,000

$ 540,000

(d)

12,000 units

15,000 units

$648 ,000 = 6 times $108 ,000

20,000 units

$810 ,000 = 3 times $270 ,000

$1,080 ,000 = 2 times $540 ,000

Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point. 15-14A. (a) Sales Variable costs Revenue before fixed costs Fixed costs EBIT (b)

Oviedo Seeds: QB

Oviedo Seeds $1,400,000 1,120,000 $280,000 25,000

Gainesville Sod $2,000,000 1,300,000 $ 700,000 100,000

Athens Peaches $1,200,000 840,000 $ 360,000 35,000

$ 255,000

$ 600,000

$ 325,000

=

$25 ,000 F = = $25 ,000 $14 .00 −$11 .20 $2.80 P −V

=

8,929 units

Gainesville Sod: QB = = Athens Peaches: QB = =

$100 ,000 $200 −$130

=

$100 ,000 $70

1,429 units $35 ,000 $25 .00 −$17 .50

4,667 units

199

= $35 ,000 $7.50

(c) Oviedo Seeds

Gainesville Sod

$280 ,000 = 1.098 times $255 ,000

$700 ,000 = 1.167 times $600 ,000

Athens Peaches $360 ,000 = 1.108 times $325 ,000

(d)

Gainesville Sod, since its degree of operating leverage exceeds that of the other two companies.

15-15A. (a)

{S - [VC + F]} (1 - T) = $40,000  S − 

  VC   S  S  + F (1 − T ) = $40,000    

{($400,000) - ($160,000) - F} (0.6) = $40,000 ($240,000 - F) (0.6) = $40,000 F = $173,333.33 (b)

Q

B

S*

=

F = $173 ,333 .33 = 14,444 units $12 P −V

=

F VC 1− S

=

$173 ,333 .33 1 −0.40

= $288,888.88

15-16A. (a)

{S - [VC + F] } (1-T) = $80,000  S − 

  VC   S  S  + F (1 − T ) = $80,000    

{($2,000,000) - (1,400,000) - F} (.6) = $80,000 ($600,000 - F) (.6) = $80,000 $360,000 - .6F = $80,000 F = $466,666.67 (b)

QB

=

F = $466 ,666 .67 $24 P −V

200

= 19,444 units

S*

=

F VC 1− S

=

$1,555,555.57

=

$466 ,666 .67 1 −.7

=

$466 ,666 .67 .3

15-17A. (a)

S (1 - 0.75) - $300,000 = $240,000 0.25S = $540,000 S = $2,160,000 = (P × Q) Now, solve the above relationship for P:

(b)

200,000 (P)

=

$2,160,000

P

=

$10.80

Sales Less: Total variable costs Revenue before fixed costs Less: Total fixed costs EBIT

$2,160,000 1,620,000 $540,000 300,000 $ 240,000

15-18A. (a)

S (1 - .6) - $300,000 = $250,000 .4S = $550,000 S = $1,375,000 = (P × Q) Solve the above relationship for P.

(b)

200,000 (P)

=

$1,375,000

P

=

$6.875

Sales Less: Total variable costs Revenue before fixed costs Less: Total fixed costs EBIT

$1,375,000 825,000 $550,000 300,000 $ 250,000

201

15-19A. (a)

First, find the EBIT level at the forecast sales volume: = 0.28 So:

EBIT = (0.28) $3,750,000 = $1,050,000 Next, find total variable costs: = 0.5

So:

VC = (0.50) $3,750,000 = $1,875,000 Then, solve for total fixed costs: S - (VC + F) = $1,050,000 $3,750,000 - ($1,875,000 + F) = $1,050,000 F = $825,000

(b)

S*

$825 ,000 1 −0.5

=

= $1,650,000

15-20A. (a)

QB

=

$180 ,000 F = $150 P −V

=

F VC 1− S

$180 ,000 1 −0.70

(b)

S*

(c)

DOL$2,500,000 = 5,000 ($ 500 −$350 ) −$180 ,000

= $600,000

5,000 ($ 500 −$350 )

$750 ,000 $570 ,000

(d)

=

= 1,200 units

= 1.316 times

(20%) x (1.316) = 26.32% Increase

202

15-21A. (a)

QB =

F = $50 ,000 = $50 ,000 $25 −$15 $10 P −V

F

(b)

$50 ,000

S* = 1 − VC S

= 1 − $15

=

$25

(c) Sales Variable costs Revenue before fixed costs Fixed costs EBIT

(d)

4000 units $40 ,000 −$10 ,000

(e)

15-22A.

= -4X

= 5,000 units

$50 ,000 1 −0.6

=

$50 ,000 .4

= $125,000

4000 units $100,000 60,000 $ 40,000 50,000

6000 units $150,000 90,000 $ 60,000 50,000

8000 units $200,000 120,000 $ 80,000 50,000

$-10,000

$ 10,000

$ 30,000

6000 units $60 ,000 $10 ,000

= 6X

8000 units $80 ,000 $30 ,000

= 2.67X

The degree of operating leverage decreases as the firm's sales level rises above the break-even point. Compute the present level of break-even output: Q

B

=

F = $120 ,000 $12 −$7 P −V

= 24,000 units

Compute the new level of fixed costs at the break-even output: S–V–F=0 ($12) (24,000) - ($5) (24,000) - F = 0 $288,000 - $120,000 - F = 0 $168,000 = F Compute the addition to fixed costs: $168,000 - $120,000 = $48,000 addition

203

15-23A.

DOL$360,000

=

30 ,000 ($ 12 −$7) 30 ,000 ($ 12 −$7) −$120 ,000

=

$150 ,000 = 5 times $30 ,000

Any percentage change in sales will magnify EBIT by a factor of 5. 15-24A. (a)

DOL$480,000

=

40 ,000 ($ 12 −$7) 40 ,000 ($ 12 −$7) −120 ,000

=

$200 ,000 $80 ,000

= 2.5 times

(b)

DFL$80,000

=

$80 ,000 $80 ,000 −$30 ,000

(c)

DCL$480,000

=

40 ,000 ($ 12 −$7) 40 ,000 ($ 12 −$7) −$120 ,000 −$30 ,000

=

$200 ,000 = 4 times $50 ,000

= 1.6 times

Alternatively: (DOLS) x (DFLEBIT) = DCLS (2.5) x (1.6) = 4 times 15-25A.

The task is to find the break-even point in units for the firm. Several approaches are possible, but the one presented below makes intuitive sense to students. Step (1)

Compute the operating profit margin: (Operating Profit Margin) x (Operating Asset Turnover) = Return on Operating Assets (M) x (5) = 0.15 M = 0.03

Step (2)

Compute the sales level associated with the given output level: Sales $3,000,000

= 5

Sales = $15,000,000 Step (3)

Compute EBIT: (0.03) ($15,000,000) = EBIT = $450,000

204

Step (4)

Compute revenue before fixed costs. Since the degree of operating leverage is 8 times, revenue before fixed costs (RBF) is 8 times EBIT as follows: RBF = (8) × ($450,000) = $3,600,000

Step (5)

Compute total variable costs: Sales - Total variable costs = $3,600,000 $15,000,000 - Total variable costs = $3,600,000 Total variable costs = $11,400,000

Step (6)

Compute total fixed costs: RBF - Fixed costs = $450,000 $3,600,000 - Fixed costs = $450,000 Fixed costs = $3,150,000

Step (7)

Find the selling price per unit, and the variable cost per unit:

Step (8)

P =

$15 ,000 ,000 1,600 ,000

= $9.375

V =

$11 ,400 ,000 1,600 ,000

= $7.125

Compute the break-even point: QB =

$3,150 ,000 F = ($ 9.375 ) −($ 7.125 ) = P −V

$3,150 ,000 $2.25

15-26A.

= 1,400,000 units

Compute the present level of break-even output: QB =

F = $300 ,000 = 50,000 units $20 −$14 P −V

Compute the new level of fixed costs at the break-even output. S–V–F=0 ($20) (50,000) - ($12) (50,000) – F = 0 $400,000 = F Compute the addition to fixed costs: $400,000 - $300,000 = $100,000 addition 15-27A. (a)

Revenue before fixed costs EBIT

$3,000 ,000

= $1,000 ,000 205

= 3 times

(b)

$1,000 ,000 EBIT = $800 ,000 EBIT − I

(c)

DCL$12,000,000 = (3) × (1.25) = 3.75 times

(d)

F S* = 1 − VC S $2,000 ,000 1 −0.75

= 1.25 times

$2,000,000 = 1 − $9m = $12m

=

$2,000 ,000 0.25

= $8,000,000

15-28A. (a)

Revenue before fixed costs EBIT

(b)

$4,000 ,000 EBIT = $2,500 ,000 = 1.6 times EBIT − I

(c)

DCL$16,000,000 = (2) (1.6) = 3.2 times

(d)

(20%) (3.2) = 64% Increase

(e)

F S* = 1 − VC S $4,000 ,000 1 −0.5

$8,000 ,000

= $4,000 ,000

$4,000,000 = 1 − $8m = $16m

= $8,000,000

206

= 2 times

15-29A.a. A Sales $40,000 Variable costs* 24,000 Contribution margin $16,000 Contribution margin ratio 40%

B $50,000 34,000 $16,000 32%

C $20,000 16,000 $ 4,000 20%

D $10,000 4,000 $ 6,000 60%

Total $120,000 78,000 $ 42,000 35%

*Variable costs = (Sales) (1 - contribution margin ratio) b.

35%

c..

Break-even point in sales dollars: F S* = 1 − VC S

=

$29 ,400 1 −0.65

15-30A. A Sales $30,000 Variable costs* 18,000 Contribution margin $12,000 Contribution margin ratio 40%

=

B $44,000 29,920 $14,080 32%

$29 ,400 0.35

C $40,000 32,000 $ 8,000 20%

= $84,000 D $6,000 2,400 $ 3,600 60%

Total $120,000 82,320 $ 37,680 31.4%

*Variable costs = (sales) (1- contribution margin ratio). b.

31.4%

c..

Break-even point in sales dollars: F

S* = 1 − VC S

=

$29 ,400 0.314

= $93,631

Toledo's management would prefer the sales mix identified in problem 15-29A. That sales mix provides a higher EBIT ($12,600 vs. $8,280) and a lower break-even point ($84,000 vs. $93,631).

SOLUTION TO INTEGRATIVE PROBLEM: In solving for the break-even point in units, the following step-by-step approach seems to be the most logical to students and the easiest for them to understand. COMPUTE BREAK-EVEN POINT: STEP 1:

Compute the operating profit margin: Operating Profit Margin [M] x Operating Asset Turnover = Return on operating assets M x 7 = 35% M = 5%

207

STEP 2:

Compute the sales level associated with the given output level: Operating Assets x Operating Asset Turnover = Sales $2,000,000 x 7 = Sales Sales = $14,000,000

STEP 3:

Compute EBIT: Sales [STEP 2] x Operating Profit Margin [STEP 1] = EBIT $14,000,000 x 5% = EBIT EBIT = $700,000

STEP 4:

Compute revenue before fixed costs: EBIT [STEP 3] x Degree of Operating Leverage = Revenue before Fixed Costs $700,000 x 5 = Revenue before Fixed Costs Revenue before Fixed Costs = $3,500,000

STEP 5:

Compute total variable costs: Sales [STEP 2] - Revenue before Fixed Costs [STEP 4] = Total Variable Costs $14,000,000 - $3,500,000 = Total Variable Costs Total Variable Costs = $10,500,000

STEP 6:

Compute total fixed costs: Revenue before Fixed Costs [STEP 4] - EBIT [STEP 3] = Fixed Costs $3,500,000 - $700,000 = Fixed Costs Fixed Costs = $2,800,000

STEP 7:

Find selling price per unit (P) and variable cost per unit (V): P = Sales [STEP 2] / Output in Units P = $14,000,000 / 50,000 units P = $280.00 V = Total Variable Costs [STEP 5] / Output in Units V = $10,500,000 / 50,000 units V = $210.00

208

STEP 8:

Compute break-even point (in units): QB = F [STEP 6] / (P - V) [STEP 7] QB = $2,800,000 / ($280.00 - $210.00)

QB = 40,000 units After determining the break-even point using the approach described above, the students have the information necessary to prepare an analytical income statement as follows: Sales [STEP 2] Variable Costs [STEP 5] Revenue before Fixed Costs Fixed Costs [STEP 6] EBIT Interest Expense Earnings Before Taxes Taxes (35%) Net Income

$14,000,000 10,500,000 $3,500,000 2,800,000 $700,000 400,000 $300,000 105,000 $195,000

Thereafter, the students have the data they need to answer questions (a) - (e) as follows: (a)

Degree of financial leverage: DFLEBIT = EBIT / (EBIT - Interest) DFLEBIT = $700,000 / ($700,000 - $400,000) DFLEBIT = 2.33

(b)

Degree of Combined Leverage: DCLS = DOLS x DFLEBIT DCLS = 5 x 2.33 DCLS = 11.65

(c)

Break-even point in sales dollars:

F S* = 1 − VC

S

$2,800,000 S* = 1 - $10,500,00 0 $14,000,00 0 S* = $11,200,000 (d)

“If sales increase 30%, by what percent would EBT increase?” % increase in EBT = % increase in Sales x DCLS

209

% increase in EBT = 30% x 11.65 % increase in EBT = 350% (e)

Analytical Income Statement to verify effect of 30% increase in sales: Sales]

$18,200,000

Variable Costs

13,650,000

Revenue Before Fixed Costs

$4,550,000

Fixed Costs [STEP 6]

2,800,000

EBIT

$1,750,000

Interest Expense

400,000

Earnings Before Taxes

$1,350,000

Taxes (35%)

472,500

Net Income

$877,500

It may be useful to develop the following “proof” to assist in explaining the interrelationships of the various values: % change in EBT = (EBTafter - EBTbefore) / EBTbefore % change in EBT = ($1,350,000 - $300,000) / $300,000 % change in EBT = 350% which agrees with the following: % change in EBT = % change in Sales x DCLS % change in EBT = 30% x 11.65 % change in EBT = 350%

Solutions To Problem Set B 15-1B. Break-even Quantity =

QB

QB

=

F (P −V)

P

=

$20,000,00 0 40,000,000 units

=

$.50 per unit

V

=

$16,000,00 0 40,000,000 units

=

$.40 per unit

QB

=

$2,400 ,000 ($ 0.50 −$0.40 )

QB

=

24,000,000 units

thus,

210

211

15-2B. Degree of Combined Leverage = Degree of Operating Leverage Degree of Financial Leverage

DCLS = DOLS = DFLEBIT

DOLS

=

Q(P −V) [Q(P −V) −F]

P

=

$20,000,00 0 40,000,000 units

=

$.50 per unit

V

=

$16,000,00 0 40,000,000 units

=

$.40 per unit

DOLS

=

40 ,000 ,000 ($ 0.50 − $0.40 ) [40 ,000 ,000 ($ 0.50 −$0.40 ) −$2,400 ,000 ]

DOLS

=

2.50 times

DFLEBIT

=

EBIT (EBIT −1)

DFLEBIT

=

$1,600 ,000 ($ 1,600 ,000 −$800 ,000 )

DFLEBIT

=

2.00 times

DCLS

=

Q(P −V) [Q(P −V) −F −I]

DCLS

=

DCLS

=

$4,000 ,000 $800 ,000

DCLs

=

5.00 times

thus,

and

40 ,000 ,000 ($ 0.50 − $0.40 ) [ 40 ,000 ,000 ($ 0.50 − $0.40 ) − $2,400 ,000 − $800 ,000 ]

15-3B. (a)

QB

=

$650 ,000 F = $175 − $115 P −V

212

=

$650 ,000 $60

= 10,833 Units

(b)

S*

=

(10,833 units) × ($175) = $1,895,775

Alternatively, S*

Note:

=

F VC 1− S

=

$650 ,000 1 − 0.6571

$650 ,000 = 1 − $115 $175 $650 ,000 .3429

=

$1,895,596 differs from $1,895,775 due to rounding.

(c)

10,000 units $1,750,000 1,150,000 600,000 650,000 -$50,000

Sales Variable costs Revenue before fixed costs Fixed costs EBIT (d)

= $1,895,596

10,000 units

16,000 units $2,800,000 1,840,000 960,000 650,000 $ 310,000

16,000 units

$600 ,000 = -12 times −$50 ,000

$960,000 $310,000

20,000 units $3,500,000 2,300,000 1,200,000 650,000 $ 550,000 20,000 units

$1,200 ,000 $550 ,000

= 3.1 times

= 2.2

times Notice that the degree of operating leverage decreases as the firm's sales level rises above the break-even point. 15-4B. (a) Sales Variable costs Revenue before fixed costs Fixed costs EBIT (b)

QB 6,400 units

Durham Furniture $1,600,000 1,100,000

Raleigh Cabinets $1,957,500 1,080,000

$500,000 40,000 $460,000

$877,500 150,000 $727,500

=

F P −V

=

$288,750 60,000 $228,750

$40 ,000 $20 .00 −$13 .75

QB =

$150 ,000 $435 −$240

QB =

$60 ,000 $35 .00 −$15 .75

213

Charlotte Colonials $525,000 236,250

=

$150 ,000 $195

=

$40 ,000 $6.25

= 769 units

= $60 ,000 $19 .25

= 3,117 units

=

(c) Durham Furniture =

Raleigh Furniture

$500 ,000 $460 ,000

=

= 1.09 times

$877 ,500 $727 ,500

Charlotte Colonials =

1.21 times

$288 ,750 $228 ,750

1.26 times

(d)

Charlotte Colonials, since its degree of operating leverage exceeds that of the other two companies.

(a)

{S - [VC + F]} (1 - T) = $55,000

15-5B.  S − 

  VC   S  S  + F (1 − T ) = $55,000    

{$400,008 - [257,148 + F ]} (0.55) = $55,000 ($142,860 - F) (0.55) = $55,000 F = $42,860 (b)

QB

S* 15-6B. (a)

=

$42 ,860 F = = $42 ,860 $28 .00 −$18 .00 $10 .00 P −V

=

F VC 1− S

=

$42 ,860 1 − 0.643

= $120,056

Find the EBIT level at the forecast sales volume: EBIT S

= .28

Therefore, EBIT = (0.28) ($3,750,000) = $1,050,000 Next, find total variable costs: VC S

so:

= 0.55,

VC = (0.55) $3,750,000 = $2,062,500 Now, solve for total fixed costs: S - (VC + F) = $1,050,000 $3,750,000 - ($1,687,500 + F) = $1,050,000 F = $637,500

214

= 4,286 units

=

$637 ,500 1 −0.55

(b)

S*

= $1,416,667

(a)

= $14 ,000 ,000 = 1.71 times

(b)

EBIT EBIT − I

(c)

DCL$40,000,000= (1.71) × (1.09) = 1.86 times

15-7B.

(d)

(e) 15-8B.

$24 ,000 ,000

S*

$14 ,000 ,000

= $12 ,850 ,000

= 1.09 times

=

F $10,000,00 0 VC = $16m 1− 1− S $40m

=

$10 ,000 ,000 1 −0.4

=

$10 ,000 ,000 0.6

= $16,666,667

(20%) × (1.86) = 37.2%

Given the data for this problem, several approaches are possible for finding the break-even point in units. The approach below seems to work well with students. Step (1)

Compute the operating profit margin: (Operating Profit Margin) x (Operating Asset Turnover) = Return on Operating Assets (M) x (5) = 0.25 M = .05

Step (2)

Compute the sales level relative to the given output level: Sales = 5 $18,000,00 0

Sales = $90,000,000 Step (3)

Compute EBIT: (.05) ($90,000,000) = $4,500,000

Step (4)

Compute revenue before fixed costs. Since the degree of operating leverage is 6 times, revenue before fixed costs (RBF) is 6 times EBIT as follows: RBF = (6) × ($4,500,000) = $27,000,000

215

Step (5)

Compute total variable costs: (Sales) - (Total variable costs) = $27,000,000 $90,000,000 - (Total variable costs) = $27,000,000 Total variable costs = $63,000,000

Step (6)

Compute total fixed costs: RBF - Fixed costs = $4,500,000 $27,000,000 - fixed costs = $4,500,000 Fixed costs = $22,500,000

Step (7)

Find the selling price per unit, and the variable cost per unit:

Step (8)

P =

$90 ,000 ,000 = $12.86 7,000 ,000

V =

$63 ,000 ,000 = $9.00 7,000 ,000

Compute the break-even point: QB

$22 ,500 ,000 ($ 12 .86 ) −($ 9)

=

F P −V

=

$22 ,500 ,000 $3.86

=

F P −V

=

= 5,829,016 units

15-9B. (a)

QB

units (b)

S*

=

F VC 1− S

=

$550 ,000 1 − 0 .8

$550 ,000 $175 − $140

= $550 ,000 $35

= 15,714

$550 ,000 = 1 − $140 $175

(c) Sales Variable costs Revenue before fixed costs Fixed costs EBIT

=

=

$550 ,000 .2

= $2,750,000

12,000 Units $2,100,000 1,680,000 $ 420,000 550,000

15,000 Units $2,625,000 2,100,000 $ 525,000 550,000

20,000 Units $3,500,000 2,800,000 $700,000 550,000

-$130,000

-$25,000

$ 150,000

216

(d)

12,000 units

$420 ,000 −$130 ,000

15,000 units $525 ,000 −$25 ,000

= -3.2 times

20,000 units

= -21 times

$700 ,000 $150 ,000

= 4.67

times 15-10B. (a)

(b)

Sales Variable costs Revenue before fixed costs Fixed costs

Farm City Seeds $1,800,000 1,410,000 $390,000 30,000

Empire Sod $1,710,000 1,305,000 $ 405,000 110,000

Golden Peaches $1,400,000 950,000 $ 450,000 33,000

EBIT

$ 360,000

$ 295,000

$ 417,000

Farm City: QB

=

units

$30 ,000 F = = $30 ,000 $ 15 . 00 − $ 11 . 75 $3.25 P −V

Empire Sod: QB

=

$110 ,000 $190 − $145

Golden Peaches: QB

=

$33 ,000 $28 .00 −$19

(c)

15-11B. (a)

=

$110 ,000 $45

= 2,444 units

$33 ,000 $9

= 3,667 units

Farm City

Empire

Golden

Seeds

Sod

Peaches

$390 ,000 = 1.083 times $360 ,000

(d)

=

= 9,231

$405 ,000 = 1.373 times $295 ,000

$450 ,000 = 1.079 times $417 ,000

Empire Sod, since its degree of operating leverage exceeds that of the other two companies. {S – [VC + F]} (1-T) = $38,000  S − 

  VC   S  S  + F (1 − T ) = $38,000    

[($420,002) - ($222,354) - F] (0.65) = $38,000 ($197,648 - F) (0.65) = $38,000 F = $139,186.46

217

(b)

QB

S* 15-12B. (a)

=

F = $139 ,186 .46 $8 P −V

=

F VC 1− S

=

= 17,398 units

$139 ,186 .46 1 −0.5294

= $295,764

{S – [VC + f]} (1 – T) = $70,000  S − 

  VC   S + F     (1 − T ) = $70,000   S  

[ ($2,500,050) - (1,933,372) - F ] (.55) = $70,000 ($566,678 - F) (.55) = $70,000 ($311,672.9 - .55F) = $70,000 F = $439,405.27 (b)

QB

S*

15-13B. (a)

=

F = $439 ,405 .27 = 25,847 units $17 P −V

=

F $439,405.2 7 $439,405.2 7 VC = = 1− 1 − .7733 .2267 S

=

$1,938,268

=

$439 ,405 .27 .2267

S (1 - 0.8) - $335,000 = $270,000 0.2S = $605,000 S = $3,025,000 = (P × Q) Now, solve the above relationship for P:

(b)

175,000 (P)

=

$3,025,000

P

=

$17.29

Sales Less: Total variable costs Revenue before fixed costs Less: Total fixed costs

$3,025,750 2,420,600 $605,150 335,000

EBIT

$ 270,150

218

15-14B. (a)

(b)

15-15B. (a)

S (1-.75) - $300,000 = $250,000 .25S = $550,000 S = $2,200,000 = (P × Q) Solve the above relationship for P: 190,000 (P) = $2,200,000 P = $11.58 Sales Less: Total variable costs Revenue before fixed costs Less: Total fixed costs

$2,200,000 1,650,000 $550,000 300,000

EBIT

$ 250,000

First, find the EBIT level at the forecast sales volume: EBIT = 0.25 S

So:

EBIT = (0.25) $4,250,000 = $1,062,500 Next, find total variable costs: = 0.4

So:

VC = (0.40) $4,250,000 = $1,700,000 Then, solve for total fixed costs: S - (VC + F) = $1,062,500 $4,250,000 - ($1,700,000 + F) = $1,062,500 F = $1,487,500

(b)

15-16B. (a)

(b)

S* = $1,487 ,500 1 − .4

QB =

F P −V

F S* = 1 − VC S

= $2,479,167

=

$200 ,000 = 1,600 units $125

=

$200,000 = $759,878 1 − 0.7368

219

(c)

(d) 15-17B. (a)

(b)

DOL$2,850,000

=

6,000 ($ 475 −$350 ) 6,000 ($ 475 −$350 ) −$200 ,000

$750 ,000 $550 ,000

=

1.364 times

(13%) x (1.364) =

QB

S*

17.73% Increase

=

F = $55 ,000 = $55 ,000 $28 −$17 $11 P −V

=

F VC 1− S

$55 ,000 = 1 − $17 $28

= 5,000 units

$55 ,000 1 − 0.607

=

=

$55 ,000 .393

=

$139,949 (c) Sales Variable costs Revenue before fixed costs Fixed costs

4,000 units $112,000 68,000 $ 44,000 55,000

6,000 units $168,000 102,000 $ 66,000 55,000

EBIT

-$11,000

$ 11,000

(d)

4000 units $44 ,000 −$11 ,000

(e)

15-18B.

= -4X

6000 units $66 ,000 $11 ,000

= 6X

8,000 units $224,000 136,000 $ 88,000 55,000 $ 33,000

8000 units $88 ,000 $33 ,000

= 2.67X

The degree of operating leverage decreases as the firm's sales level rises above the break-even point. Compute the present level of break-even output: QB =

F = $135 ,000 $13 −$6 P −V

= 19,286 units

Compute the new level of fixed costs at the break-even output: S–V–F=0 ($13) (19,286) - ($5) (19,286) - F = 0 $250,718 - $96,430 - F = 0 $154,288 = F Compute the addition to fixed costs: $154,288 - $135,000 = $19,288 addition

220

15-19B.

DOL$520,000

=

40 ,000 ($ 13 −$6) 40 ,000 ($ 13 −$6) −$135 ,000

=

$280 ,000 145 ,000

= 1.93 times

Any percentage change in sales will magnify EBIT by a factor of 1.93. 15-20B. (a)

DOL$650,000

=

50 ,000 ($ 13 −$6) 50 ,000 ($ 13 −$6) −135 ,000

=

$350 ,000 = 1.63 times $215 ,000

(b)

DFL$215,000 =

$215 ,000 = 1.39 times $215 ,000 −$60 ,000

(c)

DCL$650,000 =

50 ,000 ($ 13 −$6) 50 ,000 ($ 13 −$6) −$135 ,000 −$60 ,000

=

$350 ,000 $155 ,000

= 2.26 times

Alternatively: DOLS x DFLEBIT = DCLS 1.63 x 1.39 = 2.26 times 15-21B.

The task is to find the break-even point in units for the firm. Several approaches are possible, but the one presented below makes intuitive sense to students.

Step (1)

Compute the operating profit margin: (Operating Profit Margin) x (Operating Asset Turnover) = Return on Operating Assets (M) x (6) = 0.16 M = 0.0267

Step (2)

Compute the sales level associated with the given output level: Sales $3,250,000

= 6

Sales = $19,500,000 Step (3)

Compute EBIT: (0.0267) ($19,500,000) = EBIT = $520,000

221

Step (4)

Compute revenue before fixed costs. Since the degree of operating leverage is 9 times, revenue before fixed costs (RBF) is 9 times EBIT as follows: RBF = (9) ($520,000) = $4,680,000

Step (5)

Compute total variable costs: Sales - Total variable costs = $4,680,000 $19,500,000 - Total variable costs = $4,680,000 Total variable costs = $14,820,000

Step (6)

Compute total fixed costs: RBF - Fixed costs = $520,000 $4,680,000 - Fixed costs = $520,000 Fixed costs = $4,160,000

Step (7)

Find the selling price per unit, and the variable cost per unit:

Step (8)

P =

$19 ,500 ,000 1,700 ,000

= $11.471

V =

$14 ,820 ,000 1,700 ,000

= $8.718

Compute the break-even point: QB =

$4,160 ,000 $4,160 ,000 F = ($ 11 .471 ) −($ 8.718 ) = $2.753 P −V

1,511,079 units 15-22B.

Compute the present level of break-even output:

QB =

F = $375 ,000 = 31,250 units $25 −$13 P −V

Compute the new level of fixed costs at the break-even output. S–V–F=0 ($25) (31,250) - ($11) (31,250) - F = 0 $437,500 = F Compute the addition to fixed costs: $437,500 - $375,000 = $62,500 addition 15-23B. (a)

$4,250 ,000 Revenue before fixed costs = $1,250 ,000 EBIT

(b)

EBIT = EBIT − I

(c)

DCL$13,750,000 = (3.4) × (1.25) = 4.25 times

$1,250 ,000 $1,000 ,000

= 1.25 times

222

= 3.4 times

=

(d)

S*

=

F 3,000,000 VC = $9.5m 1− 1− S $13.75m

=

$3,000,000 $3,000,000 = = $9,705,597 1 − 0.6909 0.3091

15-24B. $11 ,000 ,000 = 2.2 times $5,000 ,000

(a)

Revenue before fixed costs EBIT

(b)

EBIT = EBIT − I

(c)

DCL$18,000,000 = (2.2) × (1.54) = 3.39 times

(d)

(15%) × (3.39) = 50.9%

(e)

S*

=

$5,000 ,000 = 1.54 times $3,250 ,000

=

F VC 1− S

$6,000,000 = 1 − $7m $18m

=

$6,000 ,000 1 −0.389

15-25B.a. Sales Variable costs* Contribution margin Contribution margin ratio

= $9,819,967

A $38,505 23,103 $15,402 40%

B $61,995 42,157 $19,838 32%

C $29,505 23,604 $ 5,901 20%

*Variable costs = (Sales) (1 - contribution margin ratio) b.

35.43%

c.

Break-even point in sales dollars: F S* = 1 − VC S

$96 ,862

= 1 − $150 ,000

223

= $98,800

D Total $19,995 $150,000 7,998 96,862 $ 11,997 $ 53,138 60% 35.43%

15-26B.a. Sales Variable costs* Contribution margin Contribution margin ratio

A $49,995 29,997 $19,998 40%

B $62,505 42,503 $20,002 32%

C $25,005 20,004 $ 5,001 20%

D Total 12,495 $150,000 4,998 97,502 $ 7,497 $ 52,498 60% 35%

*Variable costs = (sales) (1- contribution margin ratio). b.

35%

c.

Break-even point in sales dollars: F S* = 1 − VC S

=

$35 ,000 0.35

= $100,000

Wayne's management would prefer the sales mix identified in problem 15-25B. That first sales mix provides a higher EBIT ($18,138 vs. $17,498) and a lower break-even point ($98,800 vs. $100,000).

224

CHAPTER 16 Planning the

Firm's Financing Mix CHAPTER ORIENTATION This chapter concentrates on the way the firm arranges its sources of funds. The cost of capital – capital structure argument is highlighted. A moderate view on the effect of financial leverage use on the composite cost of capital is adopted. Later, techniques useful to the financial officer faced with the determination of an appropriate financing mix are described.

CHAPTER OUTLINE I.

Introduction A.

B.

II.

A distinction between financial structure and capital structure 1.

Financial structure is the mix of items on the right-hand side of the firm's balance sheet.

2.

Capital structure is the mix of long-term sources of funds.

3.

The main focus will be capital structure management and not the appropriate maturity composition of the sources of funds.

The objective of capital structure management is to mix the permanent sources of funds in a manner that will maximize the company's common stock price. This proper mix of fund sources is referred to as the optimal capital structure.

A glance at capital structure theory A.

The cost of capital – capital structure argument may be characterized by this question: Can the firm affect its overall cost of funds by varying the mixture of financing sources used?

B.

If the firm's cost of capital can be affected by the degree to which it uses financial leverage, then capital structure management is important.

225

C.

III.

IV.

V.

The analytical discussion revolves around a simplified version of the basic dividend valuation model. 1.

It assumes (a) cash dividends paid will not change over the infinite holding period, and (b) the firm retains none of its current earnings.

2.

The analytical setting for the discussion of capital structure theory assumes (a) corporate income is not subject to any taxation, (b) capital structures consist of only stocks and bonds, (c) the expected values of all investors' forecasts of the future levels of net operating income for each firm are identical, and (d) securities are traded in perfect or efficient financial markets.

Extreme position 1: The Independence Hypothesis (NOI Theory) A.

When business income is not subject to taxation, the firm's composite cost of capital and common stock price are both independent of the degree to which the firm chooses to use financial leverage.

B.

Total market value of the firm's outstanding securities is unaffected by the arrangement of the right-hand side of the balance sheet.

C.

The independence hypothesis rests upon what is called the net operating income (NOI) approach to valuation.

D.

The use of a greater degree of financial leverage may result in greater earnings and dividends, but the firm's cost of common equity will rise at precisely the same rate as the earnings and dividends.

Extreme position 2: The Dependence Hypothesis (NI Theory) A.

The dependence hypothesis suggests that both the weighted cost of capital and the firm's common stock price are affected by the firm's use of financial leverage.

B.

Regardless of the firm's use of debt financing, both its cost of debt and equity capital will not be affected by capital structure adjustments.

C.

The cost of debt is less than the cost of common equity, implying greater financial leverage use will lower the weighted cost of capital indefinitely

D.

The dependence hypothesis rests upon what is called the net income (NI) approach to valuation.

A moderate position: Corporate Income is Taxed and Firms May Fail A.

Admits to the following facts: (1) interest expense is tax deductible, and (2) the probability of suffering bankruptcy costs is directly related to the use of financial leverage.

226

B.

When interest expense is tax deductible, the sum of the cash flows that the firm could pay to all contributors of corporate capital is affected by its financing mix. This is not the case when an environment of no corporate taxation is presumed. 1.

2.

The amount of the tax shield on interest may be calculated as =

r (M) (t)

where

r

= the interest rate paid on outstanding debt

M

= the principal amount of the debt

t

= the firm's tax rate

This position presents the view that the tax shield must have value in the marketplace. 3.

VI.

Tax shield

Therefore, financial leverage affects firm value, and it must also affect the cost of corporate capital.

C.

There is some point at which the expected cost of default is large enough to outweigh the tax shield advantage of debt financing. At that point, the firm will turn to common equity financing.

D.

The determination of the firm's financing mix is centrally important to both the financial manager and the firm's owners.

Firm Value, Agency Costs, the Static Trade-off Theory, and the Pecking Order Theory A.

B.

C.

To ensure that agent-managers act in the stockholders' best interest requires 1.

Proper incentives to do so through compensation plans and perquisites

2.

Decisions that are monitored through bonding, auditing financial statements, limiting decisions, and reviewing the perquisites

Agency problems stem from conflicts of interest between firm management and owners; capital structure management encompasses a natural conflict between stockholders and bondholders. 1.

To reduce the conflict of interest, creditors and stockholders may agree to include several protective covenants in the bond contract.

2.

Monitoring costs should differ in direct proportion to low or high levels of leverage.

Static trade-off theory distinguished from pecking order theory 1.

Static trade-off theory provides for the identification of a precise optimum financing mix. This financing mix should logically determine the firm's targeted leverage ratio.

2.

Static trade-off theory "prices" both expected financial distress costs and agency costs.

227

VII.

VIII.

3.

Pecking order theory suggests that firm's finance projects within a well-defined hierarchy that begins with internally generated funds and ends with new common equity (the least desired funds source).

4.

Thus, pecking order theory provides no precisely defined target leverage ratio since typical leverage metrics just reflect the firm's cumulative external financing needs over time.

Agency costs, free cash flow, and capital structure A.

Free cash flow, as defined by Professor Michael C. Jensen, is the "cash flow in excess of that required to fund all projects that have positive net present values when discounted at the relevant cost of capital."

B.

Like the pecking order theory, the free cash flow theory of capital structure does not give a precise solution that determines the firm's optimal financing mix.

C.

The free cash flow theory does provide a framework and rationale for justifying why shareholders and their boards of directors might use more debt (financial leverage) to control management behavior and decisions.

D.

The upshot of all of these theories and perspectives is that the determination of the firm's financing mix is centrally important to the financial manager. The firm's stockholders are indeed affected by capital structure decisions; these decisions affect the firm's stock price.

Basic tools of capital structure management A.

The use of financial leverage has two effects on the earnings stream flowing to common stockholders: (l) the added variability in the earnings per share (EPS) stream that accompanies the use of fixed-charge securities and (2) the level of EPS at a given earnings before interest and taxes level (EBIT) associated with a specific capital structure.

B.

The objective of EBIT-EPS analysis is to find the EBIT level that will equate EPS regardless of the financing plan chosen 1.

A graphic or algebraic analysis can be used.

2.

By allowing for sinking fund payments, the analysis can focus upon uncommitted earnings per share.

3.

EBIT-EPS analysis considers only the level of the earnings stream and ignores the variability in it.

C.

Comparative leverage ratios involve the computation of various balance sheet leverage ratios and coverage ratios.

D.

The use of industry norms in conjunction with comparative leverage ratios can aid in arriving at an appropriate financing mix.

228

E.

IX.

X.

Cash flow analysis (company-wide cash flows) is the study of projected impact of capital structure decisions on corporate cash flows. According to this tool, the appropriate level of financial leverage is reached when the chance of running out of cash is exactly equal to that which management will assume. An underlying assumption is that management's risk-bearing preferences are conditioned by the investing marketplace.

The Multinational Firm: Beware of Currency Risk A.

Currency risk exists for firms that have sales in non-U.S. markets.

B.

Earnings must be converted from foreign currencies into dollars and reported in the firm’s financial statements.

C.

Variations in exchange rates impact firm’s overall earnings. 1.

This can impact stock price, negatively if foreign currency depreciated in value against the dollar or positively if the currency appreciated in value.

2.

Firms with high exposure to currency risk may choose to minimize other financial risk.

How financial managers use this material A.

The opinions and practices of financial executives reinforce the major topics covered in this chapter.

B.

Target debt ratios are widely used by financial officers.

C.

Executives operationalize debt capacity in different ways. The most popular approach is to define the firm's debt capacity as a target percent of total capitalization.

D.

Changes in the aggregate business environment, known as business cycles, affect capital structure decisions. Some phases of the cycle favor debt financing over equity financing; in other phases equity financing is preferred.

E.

The single most important factor that should affect the firm's financing mix is the underlying nature of the business in which it operates. A firm's business risk must be carefully assessed.

ANSWERS TO END-OF-CHAPTER QUESTIONS 16-1. (a)

Financial structure: the mix of all items that appear on the right-hand side of the company's balance sheet.

(b)

Capital structure: the mix of long-term funds used by the firm.

(c)

Optimal capital structure: the mix of long-term funds that will minimize the composite cost of capital for raising a given amount of funds.

229

(d)

Debt capacity: the maximum proportion of debt that the firm can include in its capital structure and still maintain its lowest composite cost of capital.

16-2. The decision to use financial leverage by the firm affects both the level and variability of the EPS flowing to the common stockholders. EBIT-EPS analysis deals only with the level (amount) of EPS available under a given financing plan. The variability in the earnings stream associated with the plan is ignored. EBIT-EPS analysis then disregards the riskiness inherent to a particular financing alternative. 16-3. The objective of capital structure management is to mix the permanent sources of funds used by the firm in a manner that will maximize the company's common stock price. 16-4. Balance sheet leverage ratios compare the firm's use of funds supplied by creditors to those supplied by owners. The inputs to these metrics come from the company's balance sheet. Coverage ratios relate the earnings or cash flow amounts that are available for servicing financing contracts to the associated financing costs. The inputs to computing coverage ratios generally come from the company's income statement. At times, footnotes to the financial statements might have to be consulted to complete some coverage ratios. Table 16-7 in the text identifies the calculation methods for several popular leverage ratios. 16-5. If revenues from sales are highly volatile, then other things being equal, cash flows will be volatile. This would make it difficult to meet, on a timely basis, a large amount of fixed financing costs. Because of this, a high degree of financial risk will be avoided by firms that operate in industries which experience large sales fluctuations. 16-6. If the firm's overall cost of capital is not affected by varying the mixture of financing sources used, then capital structure management would be a meaningless activity. Likewise, this infers that if the value of the firm is independent of the firm's financing mix, then capital structure management is a sterile process. 16-7. Within the realm of capital structure theory, the independence hypothesis offers that both common stock price and the composite cost of capital are not affected by the firm's use of financial leverage. This presumes that interest expense is not tax deductible. 16-8. Professors Modigliani and Miller are leading proponents of this theory. 16-9. This means that the shape of the firm's composite cost of capital curve is saucershaped, or U-shaped, with respect to the use of financial leverage. Over moderate degrees of leverage use, the overall cost of capital decreases. Throughout the optimal range of leverage use, the cost of capital curve is relatively flat. At excessive degrees of leverage use, the overall cost of capital rises. The result is a saucer shaped cost of capital curve. 16-10. The EBIT-EPS indifference point is the level of EBIT that will equate EPS regardless of the financing plan ultimately chosen from a set of two alternatives. 16-11. UEPS is the earnings available to the common shareholders minus sinking fund payments that have been honored.

230

16-12. Industry norms for the various balance sheet leverage ratios and coverage ratios only provide rough guidelines for the design of the firm's financing mix. Norms are usually averages or some other measure of central tendency. Few firms in reality will have the same operating characteristics as a hypothetical "normal" firm. Thus, norms are best used on an "exception" basis. That is, if the firm's capital structure ratios differ widely from the norms, then a defensible explanation for that condition should be available. 16-13. Free cash flow is the cash flow in excess of that required to fund all projects that have positive net present values when discounted at the relevant cost of capital. 16-14. The free cash flow theory of capital structure suggests that management works "best" under the threat of financial failure. By increasing the use of leverage-inducing instruments in the firm's capital structure, then shareholders will enjoy increased control over management. This, in turn, reduces the agency costs of free cash flow. 16-15. During the 1980s several studies suggest that financial leverage use increased substantially compared to the 1970s. This trend began reversing in the early 1990s as the market for common equities improved. 16-16. It makes sense for financial managers to be familiar with the business cycle because financial market and product market conditions can change abruptly during the cycle. This means that company policies and decisions may differ over different phases (say expansion or contraction) of the cycle. 16-17. Financial managers clearly favor the use of internally generated equity in the financing of capital budgets.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 16-1A. a.

FC

=

Interest + Sinking Fund

FC

=

($15 Million) (.18) +

FC

=

$2,700,000 + $500,000 = $3,200,000

b.

$15 million 30 years

CBr

=

Cb0 + NCFr – FC

Where: CB0

=

$2,000,000

=

$3,200,000

FC and

NCFr =

$4,950,000 - $4,000,000 = $950,000

so,

CBr

=

$2,000,000 + $950,000 - $3,200,000

CBr

=

-$250,000

231

c.

We see that the company has a preference for a $2 million cash balance. The combination of the recessionary period and the proposed issue of bonds would put the firm’s recessionary cash balance (CBr) at -$250,000. The combination of the negative number and the statement that the firm likes a cash balance of $2 million suggest strongly that the proposed bond issue be postponed.

16-2A. The following formula can be used to solve for the amount of cash collections on sales, CS, required to provide the desired end of year cash balance: CBr

=

C0 + (CS + OR) - (Pa + RM + En) - FC

Solving for the required minimum cash receipts from sales: CS

=

CBr - {C0 + OR - (Pa + RM + En) - FC}

then, simplifying: CS

=

CBr - C0 - OR + Pa + RM + En + FC

where CBr C0 OR Pa RM En FC

= = = = = = =

desired cash balance at end of recessionary period = cash balance at beginning of period = other cash receipts (as percent of sales receipts) = payroll expenditures (as percent of sales receipts) = raw material payments (as percent of sales receipts) = total nondiscretionary expenditures = fixed financial charges =

$200,000 $200,000 5% 30% 25% $500,000 $140,000

thus CS

= {CBr - C0 + En + FC} / {1 - (-OR% + Pa% + RM%)}

CS

=

{$200 ,000 − $200 ,000 + $500 ,000 + $140 ,000 } {1 − (−5% + 30 % + 25%)}

=

$1,280,000

PROOF: CBr

= C0 + (CS + OR) - (Pa + RM + En) - FC

CBr

= $200,000 + ($1,280,000 + .05 x $1,280,000) - (.30 x $1,280,000 + .25 x $1,280,000 + $500,000) - $140,000

CBr CBr =

= $200,000 + $1,280,000 + $64,000 - $384,000 - $320,000 - $500,000 - $140,000 $200,000

232

16-3A. At the EBIT indifference level: EPS (All Debt Plan)

=

EPS (Debt and Equity Plan)

=

[(EBIT − I)(1 − t) − P −SF] SDebtEquity

that is, [(EBIT − I)(1 − t) − P − SF] SAllDebt [(EBIT − $90,000)(1 − .35) − $50,000] 100,000 [(EBIT − $32,000)(1 −.35) − $20,000] (100,000 + 30,000)

.65EBIT − $108,500 10

=

=

.65EBIT − $40,800 13

=

$514,103

(EBIT − I)(1 − t) − P Ss

=

(EBIT − I)(1 − t) − P Sb

(EBIT − $0)(1 − 0.5) − 0 1,000,000

=

(EBIT − $600,000)( 1 − 0.5) − 0 700,000

=

0.5EBIT − $300,000 7

EBIT 16-4A. (a)

0.5EBIT 10

EBIT (b)

$2,000,000

Plan A $2,000,000 0 $2,000,000 1,000,000 $1,000,000 0 $1,000,000 $ 1.00

EBIT Interest EBT Taxes NI P EAC EPS

(c)

=

See following analysis chart.

233

Plan B $2,000,000 600,000 $1,400,000 700,000 $ 700,000 0 $ 700,000 $ 1.00

(d)

Since $2,400,000 exceeds $2,000,000, the levered plan (Plan B) will provide for higher EPS.

$2

1.5

Plan A

Plan B

1.0

$1.0 Indif. level

0.5 $600,000 0 $ 1 Mi l .

$ 2 Mi l .

16-5A. (a)

($30) (900,000 shares) = $27,000,000

(b)

Kc =

Dt Et $6 = = = 20% $30 Po Po

In the all equity firm Kc = Ko, Thus, Ko = 20% (c)

Kc = (1)

$6.21 = 20.7% $30 .0

EBIT - Interest EAC ÷ = Dt

$5,400,000 120,000 $5,280,000 850,000 $6.21

shares*

*$1,500,000 ÷ $30 = 50,000 shares retired. (2)

$6.21 −$6.00 = 0.035 or 3.5% $6.00

234

$ 3 Mi l .

$ 4 Mi l .

16-6A. (a)

(3)

20.7% − 20.0% = 0.035 or 3.5% 20.0%

(4)

25 .5 1.5 ( 20 .7%) + (8.0%) = 20.0% 27 27

(EBIT − 0)(1 − 0.4) 80,000 shares

0.6EBIT 80

EBIT

=

(EBIT − $120,000)( 1 − 0.4) 40,000 shares

=

0.6EBIT − $72,000 40

=

$240,000

(b)

Plan A $240,000 0 $240,000 96,000 $144,000 80,000 $1.80

EBIT Interest EBT Taxes (40%) EAC ÷ No. of common shares EPS 16-7A. (a)

(EBIT − 0)(1 − 0.34) 100,000 shares

0.66EBIT 10

EBIT (b)

=

Plan B $240,000 120,000 $120,000 48,000 $72,000 40,000 $1.80

(EBIT − $110,000)( 1 − 0.34) 50,000 shares

=

0.66EBIT − $72,600 5

=

$220,000

Since $300,000 exceeds the indifference level of $220,000 from part (a), the levered alternative (Plan B) will generate the higher EPS.

235

(c)

Here we compute EPS for each financing plan, apply the relevant price/earnings ratios, and, thereby, forecast a common stock price for each plan. Thus, we have: EBIT Interest EBT Taxes (34%) NI

Plan A $300,000 0 $300,000 102,000 $198,000

Plan B $300,000 110,000 $190,000 64,600 $125,400

P EAC ÷ No. of common shares EPS x P-E ratio = Projected Stock Price

0 $198,000 100,000 $1.98 19 $37.62

0 $125,400 50,000 $2.508 15 $37.62

The added riskiness of Plan B, owing to the use of financial leverage, is reflected in the lower P-E ratio associated with Plan B (i.e., 15x versus 19x for Plan A). The rational investor will prefer Plan A (unlevered) as the same projected stock price ($37.62) can be obtained with a lower level of risk exposure. 16-8A. (a) (EBIT − 0)(1 − 0.34) 75,000 shares

.66EBIT 75

EBIT

=

(EBIT − $150,000)( 1 − 0.34) 50,000 shares

=

.66EBIT − $99,000 50

=

$450,000

(b)

Plan A $450,000 0 $450,000 153,000 $297,000 75,000 $3.96

EBIT Interest EBT Taxes (34%) EAC ÷ No. of common shares EPS

236

Plan B $450,000 150,000 $300,000 102,000 $198,000 50,000 $3.96

16-9A. (a)

(EBIT − $0)(1 − 0.5) 100,000 shares 0.5EBIT 10

EBIT

= = =

(b)

(EBIT − $320,000)( 1 − 0.5) 50,000 shares 0.5EBIT − $160,000 5

$640,000 Plan A $640,000 0 $640,000 320,000 $320,000 0 $320,000 100,000 $ 3.20

EBIT Interest EBT Taxes (50%) NI P EAC ÷ No. of Common Shares EPS

Plan B $640,000 320,000 $320,000 160,000 $160,000 0 $160,000 50,000 $ 3.20

(c)

Since $800,000 exceeds the calculated indifference level of $640,000, the levered plan (Plan B) will generate the higher EPS.

(d)

To solve this part of problem 10-6A, compute EPS under each financial alternative. Then apply the relevant price-earnings ratio for each plan. An associated common stock price for each plan can then be forecast. This follows. Plan A $800,000 0 $800,000 400,000 $400,000 0 $400,000 100,000 $ 4.00 12 $48.00

EBIT Interest EBT Taxes (50%) NI P EAC ÷ No. of Common Shares EPS X P-E Ratio = Projected Stock Price

Plan B $800,000 320,000 $480,000 240,000 $240,000 0 $240,000 50,000 $ 4.80 10 $48.00

The riskiness is reflected in a lower P-E ratio for Plan B of 10 versus that of 12 for Plan A (the all common equity plan). The decision now can logically shift to Plan A (unlevered). The investors obtain the same stock price of $48.00 under both plans. The risk of Plan A is lower, so it would be preferable.

237

16-10A. (a)

(b)

FC

=

Interest + Sinking Fund

FC

=

($10 million) (.15) +

FC

=

$1,500,000 + $500,000 = $2,000,000

CBr

=

CB0 + NCFr - FC

CB0

=

$1,000,000

FC

=

$2,000,000

($10millio 20yr.

n)

where:

and, NCFr =

$4,300,000 - $3,400,000 = $900,000

so, CBr (c)

16-11A. (a)

=

$1,000,000 + $900,000 - $2,000,000

CBr = - $100,000 We see that the company has a preference for a $1 million cash balance. The combination of the recessionary period and the proposed issue of bonds would put the firm's recessionary cash balance (CBr ) at -$100,000. The combination of this negative number and the statement that the firm likes a cash balance of $1 million suggests strongly that the proposed bond issue be postponed. (EBIT − $0)(1 − 0.4) 60,000 0.6EBIT 6

EBIT

= = =

(b)

(EBIT − $100,000)( 1 − 0.4) 40,000 0.6EBIT − $60,000 4

$300,000 Plan A $300,000 0 $300,000 120,000 $180,000 0 $180,000 $ 3.00

EBIT Interest EBT Taxes (40%) NI P EAC EPS

238

Plan B $300,000 100,000 $200,000 80,000 $120,000 0 $120,000 $ 3.00

16-12A. (a)

(EBIT − I)(1 − t) − P Ss

=

(EBIT − I)(1 − t) − P Sb

(EBIT − $0)(1 − 0.5) − 0 1,400,000

=

(EBIT − $320,000)( 1 − 0.5) − 0 1,000,000

=

0.5EBIT − $160,000 10

=

$1,120,000

0.5EBIT 14

EBIT (b)

Plan A $1,120,000 0 $1,120,000 560,000 $ 560,000 0 $ 560,000 $ 0.40

EBIT Interest EBT Taxes NI P EAC EPS

Plan B $1,120,000 320,000 $ 800,000 400,000 $ 400,000 0 $ 400,000 $ 0.40

(c)

Analysis chart is on the following page.

(d)

Since $1,800,000 exceeds $1,120,000, the levered plan (Plan B) will provide for higher EPS.

16-13A.

(a)

At EBIT of $1,800,000 the respective EPS amounts are: Plan A = $0.64 (rounded from $0.6429) Plan B = $0.74 The stock prices then are: Plan A: ($0.64) (12) = $7.68 Plan B: ($0.74) (10) = $7.40 So Plan A offers the higher stock price.

(b)

($0.74) (PE) PE

(c)

=

$7.68

=

= 10.378 times

The penalized price/earnings ratio resulting from use of financial leverage may well favor the unlevered financing plan when the ultimate effect on the firm's stock price is considered.

239

$0.60

Plan B

Plan A

0.50

$0.40 Indif. level

EPS

0.40

0.30

0.20

0.10

$1,120,000

$320,000

0

$0..5 Mil.

$1.0 Mil.

$1.5 Mil.

$2.0 Mil.

EBIT 16-14A. (a) (b)

FC

= Interest + Sinking Fund

FC

= $400,000 + $250,000 = $650,000

CBr

= CBo + NCFr - FC

where: CBo FC

= =

$500,000 $650,000

=

$3,200,000 - $2,900,000 = $300,000

= =

$ 500,000 + $300,000 - $650,000 $150,000

and, NCFr so, CBr CBr

240

(c)

16-15A. (a)

(b) (c) 16-16A. (a) (b)

The firm ordinarily carries a $500,000 cash balance. This analysis shows that during a tight economic period the firm's cash balance (CBr) could fall to as low as $150,000. Management might well decide not to issue the proposed bonds. Firm C appears to be excessively levered. Both its debt ratio and burden coverage ratio are unfavorable relative to the industry norm. The firm's price/earnings ratio is significantly lower (6 versus 10) than the industry norm. Firm B. The investing market place seems to place more weight on coverage ratios than balance sheet leverage measures. Thus, Firm B's price/earnings ratio exceeds that of Firm A. Firm Y seems to be most appropriately levered. Its price/earnings ratio exceeds that of both Firms X and Z. The first financial leverage effect refers to the added variability in the earnings-per-share stream caused by the firm's use of leverage-inducing financial instruments. The second financial leverage effect concerns the level of earnings per share at a specific EBIT associated with a specific capital structure. Beyond some critical EBIT level, earnings per share will be higher if more (rather than less) leverage is used. Based on the tabular data in this problem the market seems to be weighing the second leverage effect more heavily. Thus, Firm Z seems to be underlevered.

16-17A. (a)

($20) (1,000,000 shares) = $20,000,000

(b)

Kc =

Dt Et $5 = = = 25% $20 Po Po

In the all equity firm Kc = Ko, thus, Ko = 25% (c)

Kc = (1)

(2)

$5.179 $20 .0

= 25.895%

EBIT - Interest EAC ÷ = Dt $5.179 − $5.000 5.000

$5,000,000 80,000 $4,920,000 950,000 $5.179 = 0.0358 or 3.58%

(3)

25.895% − 25.000% = 0.0358 or 3.58% 25.000%

(4)

19 1 (25 .895 ) + (8.00 ) = 25.0% 20 20

241

16-18A. (a)

($40) (600,000 shares) = $24,000,000

(b)

Kc =

Dt Et $7 = = = 17.5% $40 Po Po

In the all equity firm Kc = Ko, thus, Ko = 17.5% (c)

Kc =

$7.13 $40 .000

= 17.825%

(1) EBIT - Interest EAC ÷ = Dt

$4,200,000 100,000 $4,100,000 575,000 $7.13

shares*

*$1,000,000 ÷ $40 = 25,000 shares retired

16-19A. (a)

(2)

$7.13 −$7.00 $7.00

(3)

17.825% − 17.500% = 1.86% 17.500%

(4)

23 1 (17 .825 %) + (10 .00 %) = 17.5% 24 24

= 1.86%

Plan B will always dominate Plan C, the preferred stock alternative, by 0.5 ($1,800)/8,000 shares or $0.1125 a share. Thus, only alternative A versus B and A versus C need be evaluated. Those calculations appear below. Plan A versus Plan B (EBIT − $0)(1 − 0.5) − 0 = 10,000

(EBIT − $1,800)(1 − 0.5) 8,000

EBIT = $9,000

Plan A versus Plan C (EBIT − $0)(1 − 0.5) − 0 (EBIT − 0)(1 − 0.5) − $1,800 = 10,000 8,000

EBIT = $18,000 (b)

Since long-term EBIT is forecast to be $22,000, the data favor use of financing alternative B, the bond plan. This is well above the A versus B indifference level of $9,000.

242

SOLUTION TO INTEGRATIVE PROBLEM PART I 1.

EBIT-EPS ANALYSIS At the EBIT indifference level: EPS (LLP)

=

EPS (HLP)

[(EBIT − I)(1 − t) − P] SLLP

=

[(EBIT − I)(1 − t) − P] SHLP

[(EBIT − $220,000)( 1 −.35) − 0] 400,000

=

[(EBIT − $840,000)( 1 −.35) − 0] 200,000

=

.65EBIT − $546,000 20

=

$1,460,000

.65EBIT − $143,000 40

EBIT

See graph on following page. 2. The analytical income statement demonstrating that EPS (LLP) = EPS (HLP) is as follows: EBIT Interest EBT Taxes (35%) NI P EAC ÷ # of common shares EPS 3. 4.

LLP $1,460,000 220,000 $1,240,000 434,000 $806,000

HLP $1,460,000 840,000 $620,000 217,000 $403,000

0 $806,000 400,000 $2.015

0 $403,000 200,000 $2.015

The expected long-term EBIT of $1,300,000 does not exceed the EBIT indifference level. Consequently, the low leveraged plan, LLP, will produce the higher EPS. To determine the financing plan that should be recommended, it is necessary to compute the expected stock price under each plan. To do so, EPS is computed first, then the projected stock price is computed, as follows:

243

EBIT-EPS INDIFFERENCE CHART

EPS in DOLLARS

$4.000

$3.500 HLP $3.000

$2.500 LLP

$2.015 $2.000

411 $1.500 EBIT Indifference Level $1.000

$1,460,000

$0.500

$0.000 $0

$200,000

$400,000

$600,000

$800,000

$1,000,000

$1,200,000

EBIT in Dollars

$1,400,000

$1,600,000 $1,800,000 $2,000,000

245

LLP $1,300,000 220,000 $1,080,000 378,000 $702,000 0 $702,000 400,000 $1.755 18 $31.590

EBIT Interest EBT Taxes (35%) NI P EAC ÷ Number of common shares EPS x P/E ratio = Projected stock price

HLP $1,300,000 840,000 $460,000 161,000 $299,000 0 $299,000 200,000 $1.495 14 $20.930

The preferred plan is the one with the higher projected stock price, namely LLP. It also can be noted that the greater riskiness of HLP results in the market applying a lower price/earnings multiple to the expected EPS. 5.

To find the P/E ratio that equates the stock prices for both plans at the given EBIT level, it is only necessary to solve the formula, EARNINGS x P/E RATIO = PRICE, as follows: Price [under LLP] ÷ Earnings [under HLP] = P/E Ratio

PART 2 6.

$31.59 1.495 21.130

RECESSIONARY CASH FLOW ANALYSIS

Total fixed financial charges, FC, the firm would have to pay next year are computed using the following formula: FC = interest expense + sinking fund/year where Proposed dollar amount of new bonds x Interest rate = Interest expense

LLP $2,000,000 x 11% $220,000

HLP $6,000,000 x 14% $840,000

Proposed dollar amount of new bonds x Sinking fund requirement/year = Sinking fund/year

$2,000,000 x 10% $200,000

$6,000,000 x 10% $600,000

$420,000

$1,440,000

thus, FC =

65

7.

The cash balance at the end of the recessionary year, CBr, is computed using the following formula: CBr = C0 + (CS + OR) - (Pa + RM + Te + En) - FC where C0 = Cash balance at beginning of period CS = Cash collections from sales OR = Miscellaneous cash receipts Pa = Payroll expenditures RM = Raw material payments Te = Estimated tax payments En = All other nondiscretionary cash outlays FC (as computed) thus, CBr =

8.

= = = = = = = =

LLP $500,000 $4,000,000 $200,000 $1,500,000 $1,000,000 $265,000 $700,000 $420,000 $815,000

HLP $500,000 $4,000,000 $200,000 $1,500,000 $1,000,000 $54,000 $700,000 $1,440,000 $6,000

The firm prefers to maintain a cash balance of $500,000. Yet, the combined effect of a recession and the costs associated with the proposed new debt would result in recessionary cash balances of $815,000 and $6,000 for LLP and HLP, respectively. Consequently, the lower leverage plan, LLP, is recommended over the higher leverage plan, HLP.

Solutions to Problem Set B 16-1B. The following formula can be used to solve for the amount of cash collections on sales, CS, required to provide the desired end of year cash balance: CBr

=

C0 + (CS + OR) - (Pa + RM + En) - FC

Solving for the required minimum cash receipts from sales: CS

=

CBr - {C0 + OR - (Pa + RM + En) - FC}

then, simplifying: CS

=

CBr - C0 - OR + Pa + RM + En + FC

66

where CBr C0 OR Pa RM En FC

= = = = = = =

desired cash balance at end of recessionary period = cash balance at beginning of period = other cash receipts (as percent of sales receipts) = payroll expenditures (as percent of sales receipts) = raw material payments (as percent of sales receipts) = total nondiscretionary expenditures = fixed financial charges =

$400,000 $400,000 5% 40% 20% $500,000 $300,000

thus CS = {CBr - C0 + En + FC} / {1 - (-OR% + Pa% + RM%)} CS =

{$40,000 − $400 ,000 + $5000 ,000 + $300 ,000} {1 − (−5% + 40% + 20%)}

=

$1,777,778

PROOF: CBr

=

C0 + (CS + OR) - (Pa + RM + En) - FC

CBr

=

$400,000 + ($1,777,778 + .05 x $1,777,778) - (.40 x $1,777,778 + .20 x $1,777,778 + $500,000) - $300,000

CBr

=

$400,000 + $1,777,778 + $88,889 - $711,111 - $355,556 $500,000 - $300,000

CBr

=

$400,000

16-2B. At the EBIT indifference level: EPS (All Debt Plan)

=

EPS (Debt and Equity Plan)

=

[(EBIT −I)(1 − t) − P −SF] SDebt & Equity

that is, [(EBIT − I)(1 − t) − P − SF] SAllDebt [(EBIT − $200,000)( 1 −.35) − $100,000] 100,000

.65EBIT − $230,000 10

EBIT

=

[(EBIT − $48,000)(1 −.35) − $30,000] (100,000 + 70,000)

=

.65EBIT − $61,200 17

=

$724,835

67

16-3B. (a)

(EBIT − 0)(1 − 0.34) 150,000 shares

0.66EBIT 15

EBIT (b) (c)

=

(EBIT − $220,000)( 1 − 0.34) 50,000 shares

=

0.66EBIT − $145,200 5

=

$330,000

Since $450,000 exceeds the indifference level of $330,000 from part (a), the levered alternative (Plan B) will generate the higher EPS. Here we compute EPS for each financing plan, apply the relevant price/earnings ratios, and, thereby, forecast a common stock price for each plan. Thus, we have: Plan A $450,000 0 $450,000 153,000 $297,000 _______0 $297,000 150,000 $ 1.98 19 $37.62

EBIT Interest EBT Taxes (34%) NI P EAC ÷ No. of common shares EPS x P-E ratio = Projected Stock Price

Plan B $450,000 220,000 $230,000 78,200 $151,800 _______0 $151,800 50,000 $ 3.036 12.39 $37.62

The added riskiness of Plan B, owing to the use of financial leverage, is reflected in the lower P-E ratio associated with Plan B (i.e., 12.39x versus 19x for Plan A). The rational investor will prefer Plan A (unlevered) as the same projected stock price ($37.62) can be obtained with a lower level of risk exposure. 16-4B. (a)

(EBIT − 0)(1 − 0.34) 80,000 shares

=

(EBIT − $320,000)( 1 − 0.34) 50,000 shares

.66EBIT 80

=

.66EBIT − $211,200 50

=

$853,333

EBIT (b)

Plan A $853,333 0 $853,333 290,133 $563,200 80,000 $7.04

EBIT Interest EBT Taxes (34%) EAC ÷ No. of common shares EPS

68

Plan B $853,333 320,000 $533,333 181,333 $352,000 50,000 $7.04

16-5B. (a)

(EBIT − $0)(1 − 0.5) 75,000 shares

0.5EBIT 75

EBIT

=

(EBIT − $140,000)( 1 − 0.5) 50,000 shares

=

0.5EBIT − $70,000 50

=

$420,000

(b)

Plan A $420,000 0 $420,000 210,000 $210,000 0 $210,000 75,000 $ 2.80

EBIT Interest EBT Taxes (50%) NI P EAC ÷ No. of Common Shares EPS (c) (d)

Plan B $420,000 140,000 $280,000 140,000 $140,000 0 $140,000 50,000 $ 2.80

Since $750,000 exceeds the calculated indifference level of $420,000, the levered plan (Plan B) will generate the higher EPS. To solve this part of the problem, compute EPS under each financial alternative. Then apply the relevant price-earnings ratio for each plan. An associated common stock price for each plan can then be forecast. This follows. Plan A Plan B EBIT $750,000 $750,000 Interest 0 140,000 EBT $750,000 $610,000 Taxes (50%) 375,000 305,000 NI $375,000 $305,000 P 0 0 EAC $375,000 $305,000 ÷ No. of Common Shares 75,000 50,000 EPS $ 5.00 $ 6.10 × P-E Ratio 12 9.836 = Projected Stock Price $60.00 $60.00 Riskiness is reflected in a lower P-E ratio for Plan B of 9.836 versus that of 12 for Plan A (the all common equity plan). The decision now can logically shift to Plan A (unlevered). The investors obtain the same stock price of $60.00 under both plans. There is less risk in Plan A, so it would be preferable.

69

16-6B. (a)

(b)

FC

=

16-7B.(a)

n)

= ($11 million) (.16) +

FC

= $1,760,000 + $550,000 = $2,310,000

CBr = CB0 + NCFr - FC CB0

=

$500,000

FC

=

$2,310,000

and,

NCFr

=

$3,800,000 - $3,600,000 = $200,000

so,

CBr

=

$500,000 + $200,000 - $2,310,000

CBr

=

- $1,610,000

We see that the company has a preference for a $500,000 cash balance. The combination of the recessionary period and the proposed issue of bonds would put the firm's recessionary cash balance (CBr) at -$1,610,000. The combination of this negative number and the statement that the firm likes a cash balance of $500,000 suggests strongly that the proposed bond issue be postponed. (EBIT − $0)(1 − 0.4) 75,000

0.6EBIT 75

EBIT

=

(EBIT − $240,000)( 1 − 0.4) 55,000

=

0.6EBIT − $144,000 55

=

$900,000

(b)

Plan A $900,000 0 $900,000 360,000 $540,000 0 $540,000 $ 7.20

EBIT Interest EBT Taxes (40%) NI P EAC EPS 16-8B. (a)

($11millio 20yr.

FC

where:

(c)

Interest + Sinking Fund

(EBIT − I)(1 − t) − P Ss (EBIT − $0)(1 − 0.5) − 0 1,200,000

0.5EBIT 120

EBIT

Plan B $900,000 240,000 $660,000 264,000 $396,000 0 $396,000 $ 7.20

=

(EBIT − I)(1 − t) − P Sb

=

(EBIT − $315,000)( 1 − 0.5) − 0 850,000

=

0.5EBIT − $157,500 85

=

(b)

70

$1,080,000 Plan A

Plan B

EBIT Interest EBT Taxes (50%) NI P EAC EPS

$1,080,000 0 $1,080,000 540,000 $ 540,000 0 $ 540,000 $ 0.45

$1,080,000 315,000 $ 765,000 382,500 $ 382,500 0 $ 382,500 $ 0.45

(c)

Analysis chart follows.

(d)

Since $1,500,000 exceeds $1,080,000, the levered plan (Plan B) will provide for higher EPS.

$0.65

Plan B

Plan A

0.55

$0.45 Indif. level

EPS

0.45

0.35

0.25

0.15 $315,000

0

$0.5 Mil.

$1,080,000

$1.0 Mil. $1.5 Mil. EBIT

71

$2.0 Mil.

16-9B. (a)

At EBIT of $1,500,000 the respective EPS amounts are: Plan A = $0.63 Plan B = $0.70 The stock prices then are: Plan A: ($0.63) (13) = $8.19 Plan B: ($0.70) (11) = $7.70 Plan A offers the higher stock price.

(b)

(c)

($0.70) (P/E)

=

$8.19

P/E

=

$8.19 $0.70

= 11.7 times

The penalized price/earnings ratio resulting from use of financial leverage may well favor the unlevered financing plan when the ultimate effect on the firm's stock price is considered.

16-10B. (a)

FC = Interest + Sinking Fund FC = $600,000 + $300,000 = $900,000

(b) where: and, so,

(c)

16-11B. (a)

(b) (c)

CBr

=

Co + NCFr - FC

Co

=

$750,000

FC

=

$900,000

NCFr =

$3,700,000 - $3,200,000 = $500,000

CBr

=

$ 750,000 + $500,000 - $900,000

CBr

=

$350,000

The firm ordinarily carries a $750,000 cash balance. This analysis shows that during a tight economic period the firm's cash balance (CBr) could fall to as low as $350,000. Management might well decide not to issue the proposed bonds. Firm C appears to be excessively levered. Both its debt ratio and burden coverage ratio are unfavorable relative to the industry norm. The firm's price/earnings ratio is significantly lower (5 versus 10) than the industry norm. Firm B. The investing market place seems to place more weight on coverage ratios than balance sheet financial leverage measures. Thus, Firm B's price/earnings ratio exceeds that of Firm A.

72

16-12B. (a) (b)

Firm Y seems to be most appropriately levered. Its price/earnings ratio exceeds that of both Firms X and Z. The first financial leverage effect refers to the added variability in the earnings-per-share stream caused by the firm's use of leverage-inducing financial instruments. The second financial leverage effect concerns the level of earnings per share at a specific EBIT associated with a specific capital structure. Beyond some critical EBIT level, earnings per share will be higher if more (rather than less) leverage is used. Based on the tabular data in this problem, the market seems to be weighing the second leverage effect more heavily. Thus, Firm Z seems to be underlevered.

16-13B. (a)

($22) (1,000,000 shares) = $22,000,000

(b)

Kc =

Dt Et $4.75 = = = 21.59% $22 Po Po

In the all equity firm Kc = Ko, thus, Ko = 21.59% (c)

Kc = (1)

$4.882 $22 .0

= 22.19%

EBIT - Interest EAC ÷ = Dt

$4,750,000 90,000 $4,660,000 954,545* $4.882

*$1,000,000 ÷ $22 = 45,455 shares retired

16-14B. (a) (b)

(2)

$4.882 −$4.750 4.750

(3)

22.19% − 21.59% = 0.0278 or 2.78% 21.59%

(4)

954 ,545 45 ,455 ( 22 .19 ) + (9.00 ) = 21.59% 1,000 ,000 1,000 ,000

= 0.0278 or 2.78%

($38) (575,000 shares) = $21,850,000 Kc =

Dt Et $7.826 = = $38 Po Po

= 20.595%

In the all equity firm Kc = Ko, thus, Ko = 20.595%

73

(c)

Kc = (1)

$8.095 = 21.3% $38 .00

EBIT - Interest EAC ÷ Dt

$4,500,000 165,000 $4,335,000 535,526 $8.095

shares*

*$1,500,000 ÷ $38 = 39,474 shares retired

16-15B. (a)

(2)

$8.095 −$7.826 $7.826

(3)

21.3% − 20.595% = 3.423% 20.595%

(4)

535 ,526 39 ,474 (21 .3%) + (11 .0%) = 20.59% 575 ,000 575 ,000

= 3.437%

Plan B will always dominate Plan C, the preferred stock alternative, by 0.5 ($5,000)/10,000 shares or $0.25 a share. Thus, only alternatives A versus B and A versus C need be evaluated. Those calculations appear below. Plan A versus Plan B (EBIT − $0)(1 − 0.5) − 0 15,000

EBIT

=

(EBIT − $5,000)(1 − 0.5) 10,000

=

$15,000

=

(EBIT − 0)(1 − 0.5) − $5,000 10,000

=

$30,000

Plan A versus Plan C (EBIT − $0)(1 − 0.5) − 0 15,000

EBIT (b)

Since long-term EBIT is forecast to be $36,000, the data favor use of financing alternative B, the bond plan. This is well above the A versus B indifference level of $15,000. Earnings per share

Plan A $1.20

Plan B $1.55

Earnings per share is highest under Plan B.

74

Plan B $1.55

CHAPTER 17

Dividend Policy and Internal Financing CHAPTER ORIENTATION In determining the firm's dividend policy, two issues are important: the dividend payout ratio and the stability of the dividend payment over time. In this regard, the financial manager should consider the investment opportunities available to the firm and any preference that the company's investors have for dividend income or capital gains. Also, stock dividends, stock splits, or stock repurchases can be used to supplement or replace cash dividends.

CHAPTER OUTLINE I.

The trade-offs in setting a firm's dividend policy A.

B.

II.

If a company pays a large dividend, it will therefore: 1.

Have a low retention of profits within the firm.

2.

Need to rely heavily on a new common stock issue for equity financing.

If a company pays a small dividend, it will therefore: 1.

Have a high retention of profits within the firm.

2.

Will not need to rely heavily on a new common stock issue for equity financing. The profits retained for reinvestment will provide the needed equity financing.

Impact of Dividend Policy on Stock Price A.

The importance of a firm's dividend policy depends on the impact of the dividend decision on the firm's stock price. That is, given a firm's capital budgeting and borrowing decisions, what is the impact of the firm's dividend policies on the stock price?

75

B.

Three views about the importance of a firm's dividend policy. 1.

View 1: a.

Assumes that the dividend decision does not change the firm's capital budgeting and financing decisions.

b.

Assumes perfect capitals markets, which means:

c.

2.

Dividends do not matter

(1)

There are no brokerage commissions when investors buy and sell stocks.

(2)

New securities can be issued without incurring any flotation costs.

(3)

There are no personal or corporate income taxes.

(4)

Complete information about the firm is free and equally readily available to all investors.

(5)

There are no conflicts of interest between management and stockholders.

(6)

Financial distress nonexistent.

bankruptcy

costs

are

Under the foregoing assumptions, it may be shown that the market price of a corporation's common stock is unchanged under different dividend policies. If the firm increases the dividend to its stockholders, it has to offset this increase by issuing new common stock in order to finance the available investment opportunities. If on the other hand, the firm reduces its dividend payment, it has more funds available internally to finance future investment projects. In either policy, the present value of the resulting cash flows to be accrued to the current investors is independent of the dividend policy. By varying the dividend policy, only the type of return is affected (capital gains versus dividend income), not the total return.

View 2: a.

and

High dividends increase stock value

Dividends are more predictable than capital gains because management can control dividends, while they cannot dictate the price of the stock. Thus, investors are less certain of receiving income from capital gains than from dividend income. The incremental risk associated with capital gains relative to dividend income should therefore cause us to use a higher required rate in discounting a dollar of capital gains than the rate used for discounting a dollar of dividends. In so doing, we would give a higher value to the dividend income than we would the capital gains.

76

b.

3.

Criticisms of view 2. (1)

Since the dividend policy has no impact on the volatility of the company's overall cash flows, it has no impact on the riskiness of the firm.

(2)

Increasing a firm's dividend does not reduce the basic riskiness of the stock; rather, if dividend payment requires management to issue new stock, it only transfers risk and ownership from the current owners to the new owners.

View 3:

Low dividends increase value

Stocks that allow us to defer taxes (low dividends-high capital gains) will possibly sell at a premium relative to stocks that require us to pay taxes currently (high dividends-low capital gains). Only then will the two stocks provide comparable after-tax returns, which suggests that a policy to pay low dividends, will result in a higher stock price. That is, high dividends hurt investors, while low dividends-high retention help the firm's investors. But wait, then came 2003 and Congress again felt the need to change the tax code as it pertained to both dividend income and capital gains income. On May 28 President Bush signed into law the “Jobs and Growth Tax Relief Reconciliation Act of 2003.” Recall that part of the impetus for this Act was the recession 2001. In a nutshell this 2003 Act lowered the top tax rate on dividend income to 15 percent from a previous top rate of 38.6 percent, and also lowered the top rate paid on realized longterm capital gains to the same 15 percent from a previous 20 percent. Thus, you can see that the so-called investment playing field was (mostly) leveled for dividend income relative to qualifying capital gains. This rather dramatic change in the tax code will immediately remind you of Principle 8: Taxes Bias Business Decisions. In effect, a major portion of the previous bias against paying cash dividends to investors was mitigated. But, not all of it. C.

Additional thoughts about the importance of a firm's dividend policy. 1.

Residual dividend theory: Because of flotation costs incurred in issuing new stock, firms must issue a larger amount of securities in order to receive the amount of capital required for investments. As a result, new equity capital will be more expensive than capital raised

77

through retained earnings. Therefore, financing investments internally (and decreasing dividends) instead of issuing new stock may be favored. This is embodied in the residual dividend theory, where a dividend would be paid only when any internally generated funds remain after financing the equity portion of the firm's investments. 2.

The clientele effect: If investors do in fact have a preference between dividends and capital gains, we could expect them to seek out firms that have a dividend policy consistent with these preferences. They would in essence "sort themselves out" by buying stocks which satisfy their preferences for dividends and/or capital gains. In other words, there would be a "clientele effect," where firms draw a given clientele based on their stated dividend policy. However, unless there is a greater aggregate demand for a particular policy than is being satisfied in the market, dividend policy is still unimportant, in that one policy is as good as the other. The clientele effect only tells us to avoid making capricious changes in a company's dividend policy.

3.

Information effect.

4.

a.

We know from experience that a large, unexpected change in dividends can have significant impact on the stock price. Despite such "evidence," it is not unreasonable to hypothesize that dividend policy only appears to be important, because we are not looking at the real cause and effect. It may be that investors use a change in dividend policy as a signal about the firm's "true" financial condition, especially its earning power.

b.

Some would argue that management frequently has inside information about the firm that it cannot make available to the investors. This difference in accessibility to information between management and investors, called information asymmetry, may result in a lower stock price than would be realized if we had conditions of certainty. Dividends become a means in a risky marketplace to minimize any "drag" on the stock price that might come from differences in the level of information available to managers and investors.

Agency costs: Conflicts between management and stockholders may exist, and the stock price of a company owned by investors who are separate from management may be less than the stock value of a closely-held firm. The difference in price is the cost of the conflict to the owners, which has come to be called agency costs. A firm's dividend policy may be perceived by owners as a tool to minimize agency costs. Assuming the payment of a dividend requires management to issue stock to finance new investments, then new investors will be attracted to the company only if management

78

provides convincing information that the capital will be used profitably. Thus, the payment of dividends indirectly results in a closer monitoring of management's investment activities. In this case, dividends may provide a meaningful contribution to the value of the firm. 5.

D.

Expectations theory: As the time approaches for management to announce the amount of the next dividend, investors form expectations as to how much the dividend will be. When the actual dividend decision is announced, the investor compares the actual decision with the expected decision. If the amount of the dividend is as expected, even if it represents an increase from prior years, the market price of the stock will remain unchanged. However, if the dividend is higher or lower than expected, the investors will reassess their perceptions about the firm and the value of the stock.

The empirical evidence about the importance of dividend policy 1.

Statistical tests. To test the relationship between dividend payments and security prices, we could compare a firm's dividend yield (dividend/stock price) and the stock's total return, the question being, "Do stocks that pay high dividends provide higher or lower returns to the investors?" Such tests have been conducted using a variety of the most sophisticated statistical techniques available. Despite the use of these extremely powerful analytical tools involving intricate and complicated procedures, the results have been mixed. However, over long periods of time, the results have given a slight advantage to the low-dividend stocks; that is, stocks that pay lower dividends appear to have higher prices. The findings are far from conclusive, however, owing to the relatively large standard errors of the estimates.

2.

Reasons for inconclusive results from the statistical tests.

3.

a.

To be accurate, we would need to know the amount of dividends investors expect to receive. Since these expectations cannot be observed, we can only use historical data, which may or may not relate to expectations.

b.

Most empirical studies have assumed a linear relationship between dividend payments and stock prices. The actual relationship may be nonlinear, possibly even with discontinuities in the relationship.

Since our statistical prowess does not provide us with any conclusive evidence, researchers have surveyed financial managers about their perceptions of the relevance of dividend policy. In such surveys, the evidence favors the relevance of dividend policy, but not just overwhelming so. For the most part, managers are divided between believing that dividends are important and having no opinion in the matter.

79

E.

III.

Conclusions about the importance of dividend policy 1.

As a firm's investment opportunities increase, the dividend payout ratio should decrease.

2.

The firm's dividend policy appears to be important; however, appearances may be deceptive. The real issue may be the firm's expected earnings power and the riskiness of these earnings.

3.

If dividends influence stock price, it probably comes from the investor's desire to minimize and/or defer taxes and from the role of dividends in minimizing agency costs.

4.

If the expectations theory has merit, which we believe it does, it behooves management to avoid surprising the investors when it comes to the firm's dividend decision.

Dividend policy decisions A.

Other practical considerations 1.

Legal restrictions a.

b.

A corporation may not pay a dividend (l)

if the firm's liabilities exceed its assets

(2)

if the amount of the dividend exceeds the accumulated profits (retained earnings)

(3)

if the dividend is being paid from capital invested in the firm

Debtholders and preferred stockholders may impose restrictive provisions on management, such as common dividends not being paid from earnings prior to the payment of interest or preferred dividends.

2.

Liquidity position: The amount of a firm's retained earnings and its cash position are seldom the same. Thus, the company must have adequate cash available as well as retained earnings to pay dividends.

3.

Absence or lack of other sources of financing: All firms do not have equal access to the capital markets. Consequently, companies with limited financial resources may rely more heavily on internally generated funds.

4.

Earnings predictability: A firm that has a stable earnings trend will generally pay a larger portion of its earnings in dividends. If earnings fluctuate significantly, a larger amount of the profits may be retained to ensure that enough money is available for investment projects when needed.

5.

Ownership control: For many small firms, and certain large ones, maintaining the controlling vote of common stock is very important.

80

These owners would prefer the use of debt and retained profits to finance new investments rather than to issue new stock. 6.

B.

C.

D.

IV.

Inflation: Because of inflation, the cost of replacing equipment has increased substantially Depreciation funds tend to become insufficient. Hence, greater profit retention may be required.

Alternative dividend policies 1.

Constant dividend payout ratio: The percentage of earnings paid out in dividends is held constant. Therefore, the dollar amount of the dividend fluctuates from year to year.

2.

Stable dollar dividend per share: Relatively stable dollar dividend is maintained. The dividend per share is increased or decreased only after careful investigation by the management.

3.

Small, regular dividend plus a year-end extra: Extra dividend is paid out in prosperous years. Management's objective is to avoid the connotation of a permanent dividend increase.

Basis for stable dividends 1.

Stable dividend policy is most common of the three options.

2.

Managers were found to be reluctant to change the amount of the dividend, especially when it came to decreasing the amount.

3.

Increasing-stream hypothesis of dividend policy states that dividend stability is a smoothing of the dividend stream to minimize the effect of other types of company reversals. a.

Corporate managers attempt to have a gradually increasing dividend over the long-term.

b.

If dividend reduction is necessary, it should be large enough to reduce the probability of future cuts.

Dividend policy and corporate strategy: Things will change—even dividend policy. 1.

The recessions of 1990 to 1991 and 2001 induced a large number of American corporations to revisit their broadest corporate strategies, including adjusting dividend policies.

2.

One firm that altered its dividend policy in response to new strategies was the W.R. Grace & Co., headquartered in Columbia, Maryland.

3.

Table 17-5 in the text reviews W.R. Grace’s actual dividend policies over the 1992 to 1996 time frame. The firm’s payout ratio and the absolute amount of the cash dividend paid per share declined in a significant fashion over this period.

Dividend payment procedures A.

Dividends are generally paid quarterly.

81

V.

B.

The declaration date is the date on which the firm's board of directors announces the forthcoming dividends.

C.

The date of record designates when the stock transfer books are to be closed. Investors who own stock on this date are entitled to the dividend.

D

Brokerage firms terminate the right of ownership to the dividend two working days prior to the date of record. This date is called the ex-dividend date.

E.

Dividend checks are mailed on the payment date.

Stock dividends and stock splits A.

Both a stock dividend and a stock split involve issuing new shares of stock to current stockholders.

B.

The investor’s percentage ownership in the firm remains unchanged. The investor is neither better nor worse off than before the stock split/dividend.

C.

On an economic basis there is no difference between a stock dividend and a stock split.

D.

For accounting purposes, the stock split has been defined as a stock dividend exceeding 25 percent of the number of shares currently outstanding.

E.

Accounting treatment

F.

VI.

1.

For a stock dividend, the dollar amount of the dividend is transferred from retained earnings to the capital accounts (par and paid-in capital).

2.

In the case of a split, the dollar amounts of the capital accounts do not change. Only the number of shares is increased while the par value of each share is decreased proportionately.

Rationale for a stock dividend or split 1.

Shareholders benefit because the price of stock may not fall precisely in proportion to the share increase; thus, the stockholders' value is increased.

2.

If a company is encountering cash problems, it can substitute a stock dividend for a cash dividend. Investors will probably look beyond the stock dividend to determine the underlying reasons for conserving cash.

Stock repurchases A.

B.

A number of benefits exist justifying stock repurchases instead of dividend payments. Included in these are: 1.

to provide an internal investment opportunity

2.

to modify the firm's capital structure

3.

to impact earnings per share, thus increasing stock price

Share repurchase as a dividend decision 82

1.

A firm may decide to repurchase its shares, increasing the earnings per share, which should be reflected in a higher stock price.

83

2.

C.

D.

VII.

The investor's choice a.

For tax purposes, the investor may prefer the firm to repurchase stock in lieu of a dividend. Dividends formerly were taxed as ordinary income, whereas any price appreciation resulting from the stock repurchase would be taxed as a capital gain, and can be deferred until the gain is realized.

b.

The investor may prefer dividend payment because (l)

Dividends are viewed as being more dependable than stock repurchases.

(2)

The price the firm must pay for its stock may be too high.

(3)

Riskiness of the firm's capital structure may increase, lowering the P/E ratio and thus the stock price.

Financing or investment decision 1.

A stock repurchase effectively increases the debt-equity ratio towards higher debt, thus repurchase is viewed as a financing decision.

2.

When buying its own stock at depressed prices, a firm may consider the repurchase as an investment decision. However, this action is not a true investment opportunity; buying its own stock does not provide the expected returns as other investments do.

The repurchase procedure 1.

A public announcement should be made detailing the amount, purpose and procedure for the stock repurchase.

2.

Open market purchase – stock is bought at the current market price.

3.

Tender offer - more formal offer where offer for stock is at a specified price, usually above current market price.

4.

Negotiated basis - repurchasing from specific, major shareholders at a negotiated price.

The Multinational firm: The Case of Low Dividend Payments A.

During economic prosperity, multinational firms look to international markets for high net present value projects. 1.

This provides diversification of country-related economic risks.

2.

Firm can achieve cost advantages over its competitors.

B.

U.S. multinational firms favor the UK and Canada for direct investments.

C.

U.S. multinational firms concentrate investments in manufacturing industries when investing internationally. 1.

Firms can achieve lower labor costs by employing workers in a foreign country. 84

2. VIII.

Lower labor costs improve a firm’s competitive position.

How Financial Managers Use This Material A.

In the text, actual examples of dividend policy in action are presented that deal with Coca-Cola and the Walt Disney Company.

B.

And we are reminded that the differential tax treatment of cash dividends as opposed to capital gains can give investors a preferential tax advantage when shares are repurchased, as the capital gains can be deferred. This is not possible with the receipt of cash dividends. The income tax has to be paid in the year that the dividends are actually received by the investor.

ANSWERS TO END-OF-CHAPTER QUESTIONS 17-1. The dividend payout ratio indicates the amount of dividends paid relative to the earnings available to common stockholders, or dividend-per-share divided by earnings-per-share. 17-2. A firm's net profits are used to pay dividends and/or to finance new investments. As larger dividends are paid, the retained earnings available for reinvestment are reduced. Conversely, as a larger amount of profits is reinvested, the capital available for common stockholders' dividends is reduced. 17-3. (a)

In a perfect market, there are no brokerage commissions, no flotation costs, no taxes, no information content assigned to a particular dividend policy, complete information about a firm is available to every investor, no conflicts of interest between management and stockholders and financial distress and bankruptcy costs are nonexistent..

(b) A firm's dividend policy is irrelevant in a perfect market. Management may choose between retaining profits and paying dividends without affecting the value of the firm's security. Therefore, the only wealth-creating activities in a perfect market are management's investment and financing decisions. 17-4. The existence of flotation costs eliminates the indifference between financing by internal capital and new stock. Financing investments through retained earnings will be preferred to avoid flotation costs and capital leakage. If no other perfect market

85

assumptions have been relaxed, new stock would be issued only after internally generated funds have been exhausted. 17-5. (a)

According to the residual dividend theory, dividends are paid only if retained earnings are available after financing all acceptable investments.

(b) This theory may not be feasible in the short term because the year-toyear variability in dividend payments is undesirable. The theory can be used in the long term if management projects financing needs for several years. A target dividend payout ratio for this planning horizon can be established that will distribute the residual capital smoothly over the period.

86

17-6. Taxes on dividend income are paid when the dividend is received, while taxes on capital gains are deferred until the stock is actually sold. 17-7. Statutory restrictions prevent a corporation from paying dividends if its liabilities exceed its assets, the amount of the dividend exceeds retained earnings, or the dividend is being paid from capital invested in the firm. The restrictions in debt and preferred stock contracts may also limit dividends. These contract provisions may stipulate that dividends are not to be paid from earnings prior to the debt payment. Also, a certain amount of working capital may be required. Finally, if any preferred dividends have gone unpaid, a provision may restrict payment of common dividends. 17-8. Dividends are paid with cash. If there is little or no cash available, the firm will be unable to pay dividends. 17-9. For many smaller companies, maintaining voting control of the common stock is very important. Issuing new stock is unattractive to these firms if it results in a dilution of the control of the current stockholders. Financing by debt and through profits will be preferred. Thus, the firm's growth is limited to the amount of debt capital available and the company's ability to generate profits. 17-10. (a)

Corporate managers are reluctant to change dividends without being confident that the change is reflective of the company's long-term earnings prospects. This is why most managers avoid a change in dividends in response to temporary fluctuations in earnings and are especially reluctant to make a dividend cut. They would prefer instead to develop a gradually increasing dividend series over time. This smoothing of the dividend stream is done in an effort to minimize the effect of other types of company reversals.

(b) Investors also prefer a stable dividend policy because they perceive a change in the dividend payment to reflect management's view of the firm's long-term earnings prospects. Also, many investors rely upon dividends for current income, and this need is best satisfied by the stable dividend. Another reason for the popularity of the stable dividend is the requirement of many states that financial institutions invest only in companies with a regular dividend payment. 17-11. The declaration date is the date that the dividend is formally authorized by the board of directors. Investors shown to own the stock on the date of record receive the dividends. The ex-dividend date is two days prior to the record date. This date was set by stock brokerage companies as the date when the right of ownership to the dividend is terminated. 17-12. The stockholder is benefited only if the price of the stock does not fall in direct proportion to the number of new shares issued. An advantage to the corporation is the conservation of cash for investment opportunities. 17-13. A stock repurchase might be used by a firm to provide an alternative to cash dividends, to provide an "internal" investment opportunity, to alter the firm's capital structure, or any of a variety of other reasons stemming from a reduction of the number of shares outstanding. 87

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 17-1A. Dividend Policies a. Constant payout ratio of 40%

b.

Year

$ Dividend

Profits × payout/shares

1 2 3 4 5

0.40 0.80 0.64 0.36 1.20

1,000,000 × 0.4 / 1,000,000 2,000,000 × 0.4 / 1,000,000 1,600,000 × 0.4 / 1,000,000 900,000 × 0.4 / 1,000,000 3,000,000 × 0.4 / 1,000,000

Stable target payout of 40% 8,500,000 × 0.4 Target dividend = 1,000,000 5

c.

= 0.68

Small regular dividend of $0.50 plus year-end extra

Base profits: 1,500,000 % of extra profits: 50% Year 1 2 3 4 5

$ Dividend 0.50 0.75 0.55 0.50 1.25

Payout Calculation 0.50 0.5 + [(2,000,000 – 1,500 000 * 0.5 / 1,000,000] 0.5 + [(1,600,000 -,1,500,000) * 0.5 / 1,000,000] 0.50 0.5 + [(3,000,000 – 1,500,000) * 0.5 / 1,000,000]

17-2A. Number of shares to be issued: $10 ,000 ,000 $120 −$15

= 95,238 shares

Dollar size of the issue: 95,238 shares x $120 = $11,428,560

88

17-3A.

Flotation Costs and Issue Size Flotation costs Stock price Net to firm

0.18 $85.00 $5,800,000

Dollar issue size

= $ 7,073,171

=

$5,800,000/(1-.18)

Number of shares

= $ 7,073,171 ÷ $85/share 83,214 shares

17-4A. Terra Cotta - Residual Dividend Theory Total financing needed Retained earnings Debt ratio Equity ratio Equity financing needed Dividends

$640,000 $400,000 0.4 0.6 $384,000 = $ 16,000 =

$640,000(.6) $400,000 - $384,000

17-5A. RCB - Stock Dividend Before dividend Shares outstanding Net income Price/Earnings Stock dividend Investor's share

$

Current price

$

Value before dividend

$

After dividend Shares outstanding New price

2,000,000 550,000 10 20% 100 550,000

2.75= P/E x EPS = 10 × 2,000 ,000 275.00 = $2.75 x 100 shares 2,400,000

= 2,000,000 x (1 + 0.2) $2.29 = P/E x EPS=10 x

$550,000 2,400 ,000

Investor's shares Value after dividend

120 $ 275.00

= =

100 x 1.2 120 x $2.29

Change

$

=

$275 (before) - $275 (after)

0.00

The value of the investors' holdings does not change because the price of the stock reacted fully to the increase in the shares outstanding.

89

17-6A.

Harris, Inc. - Dividends in Perfect Markets

Dividend Plans Year 1996 1997 1998

Plan A $ 2.50 $ 2.50 $45.75

Required rate of return

a. b.

Plan B $ 4.25 $ 4.75 $40.66

0.18

Value stock A

$31.76

Value stock B

$31.76

$2.50 $2.50 $45.75 + + 2 (1 +.18) (1 +.18) (1 +.18) 3 $4.25 $4.75 $40.66 + + = 2 (1 + .18) (1 + .18) (1 + .18) 3

=

There is no effect on the value of the common stock. An investor's preference for current income, tax consequences, informational content, and transaction costs may change your answer.

17-7A. Stetson Manufacturing, Inc. - Long Term Dividend Policy Debt ratio Equity ratio Shares outstanding

Year 1 2 3 4 5 a.

0.35 0.65 100,000 (A)

(B)

Investment $ 350,000 475,000 200,000 980,000 600,000

Funds Available Internally $ 250,000 450,000 600,000 650,000 390,000 $2,340,000

(C) Equity Contribution (A x .65) $ 227,500 308,750 130,000 637,000 390,000 $1,693,250

Residual Dividend Year 1 2 3 4 5

Dividend =

Funds Available − Equity Contributi on 100,000 Shares

$0.225 $1.41 $4.70 $0.13 $0.00

90

($2,340,00 0 − $1,693,250 )/5 100,000 Shares

b.

Target Dividend = $1.29 =

c.

The target dividend allows for consistency of income to the stockholder and income in all years whereas the year-toyear dividend would not pay a dividend in year five.

17-8A. Trexco Corporation - Stock Split Market price Split multiple Shares outstanding a.

b.

$

You own Investor's shares Position before split

98.00 2 25,000

0.05 1,250 $122,500

x

Price after split Your shares after split Position after split Net gain

$

= $98 ÷ 2 = 1,250 x 2 = 2,500 shares x $49 per share

Price fall Price after split Position after split Net gain

0.4 $ 58.80 $147,000 $ 24,500

=

49.00 2,500 $122,500 $ 0

25,000

= 1,250 Shares x $98 per share

= $98.00 (1 - .4) = 2,500 Shares x $58.80 per share = $147,000 - $122,500

17-9A. Crystal Cargo, Inc. - Dividend Policies Year 1 2 3 4 5 Total Profits After Taxes Shares Outstanding a.

Profits After Taxes $1,400,000 2,000,000 1,860,000 900,000 2,800,000 $8,960,000 1,000,000

Constant Payout Ratio of 50% Year 1 2 3 4 5

Dividend $0.70 $1.00 $0.93 $0.45 $1.40

= Profits x Payout Ratio ÷ Shares = $1,400,000 (.5) ÷ 1,000,000 = $2,000,000 (.5) ÷ 1,000,000 = $1,860,000 (.5) ÷ 1,000,000 = $ 900,000 (.5) ÷ 1,000,000 = $2,800,000 (.5) ÷ 1,000,000

91

b.

Stable target payout of 50% $8,960,000 (.5)/5 1,000,000

Target dividend = $0.90 = c.

Small regular dividend of $0.50 plus year-end extra Base profits % of extra profits Year 1 2 3 4 5

17-10A.

$1,500,000 50%

Dividend 0.50 0.75 = 0.68 = 0.50 1.15 =

.50+[($2,000,000-$1,500,000)(.5)/1,000,000] .50+[($1,860,000-$1,500,000)(.5)/1,000,000] .50+[($2,800,000-$1,500,000)(.5)/1,000,000]

Dunn Corporation - Repurchase of Stock Proposed dividend Shares outstanding Earnings per share Ex-dividend price Proposed dividend/share

$ 500,000 250,000 $ 5.00 $ 50.00 $2.00

a.

Repurchase price

$

b.

Number of shares repurchased

c.

The capital gains to be received by the stockholder would not be equal to the intended dividend, thus resulting in a dollar benefit or loss to the stockholders.

d.

Unless you have a need for current income, you would probably prefer the stock repurchase plan.

17-11A.

52.00

= $50 + $2

9,615

= $500,000 ÷ ($50 + $2)

Number of shares to be issued $14 ,000 ,000 $95 −$9.50

= 163,743 share

Dollar size of the issue 163,743 shares x $95 = $15,555,585

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17-12A.

Martinez, Inc. - Residual Dividend Theory Total financing needed Retained earnings Debt ratio Equity ratio Equity financing needed **Dividends**

$1,200,000 $450,000 0.70 0.30 $360,000 $ 90,000

= $1,200,000 (0.30) = $450,000 - $360,000

Thus, the firm would pay $90,000 dividends. 17-13A.

Rainy Corporation - Stock Split Market price Split multiple Shares outstanding

a.

b.

You own Position before split

$

86.00 2 80,000

16,000 shares $1,376,000

Price after split Your shares after split Position after split Net gain

$

43.00 32,000 $1,376,000 $ 0

Price fall Price after split Position after split Net gain

0.45 $ 47.30 $1,513,600 $ 137,600

= .20 x 80,000 = 16,000 Shares x $86 per share = = =

$86 ÷ 2 16,000 x 2 32,000 shares x $43 per share

= = =

$86.00 (1 - .45) 32,000 Shares x $47.30 per share $1,513,600 - $1,376,000

SOLUTION TO INTEGRATIVE PROBLEM Burns’ main argument is that dividends are more important in some periods and less important in others. His discussion certainly gives us the impression that “dividend policy matters.” He also sounds like he believes the “bird in the hand is worth two in the bush” theory. However, he fails to prove that a shareholder’s value is greater whether a dividend is paid or whether it is not paid. Obviously, he is correct in saying that in some years more of an investor’s returns come in the form of dividends, and in other years more is in the form of capital gains. But that does not prove that a dividend payment is inherently good or bad. It is simply a tradeoff between one form of return and another. Also of great importance, he fails to acknowledge the fact that dividends (or any form of distribution to shareholders) should be paid when the firm cannot earn its cost of capital and retained when it can earn more than the cost of capital. Retaining profits and investing them in negative NPV projects destroys shareholder value – period. Thus, the more important question is what can be done with the money within the firm versus what the shareholder can do with the money apart

93

from the company, and not how much dividends contribute to a shareholder’s total returns in a given year. Solutions to Problem Set B 17-1B. Number of shares to be issued: $12 ,000 ,000 $115 −$17

= 122,449 shares

Dollar size of the issue: 122,449 shares x $115 = $14,081,635 17-2B.

Flotation Costs and Issue Size Flotation costs Stock price Net to firm

17-3B.

0.14 $76.00 $6,100,000

Dollar issue size

=

$7,093,023

Number of shares

=

93,329

=

$6,100,000/(1-.14)

shares ($7,093,023 ÷ $76/share)

Steven Miller - Residual Dividend Theory Total financing needed $650,000 Retained earnings $375,000 Debt ratio 0.35 Equity ratio 0.65 Equity financing needed $422,500 Dividends ($47,500)

= $650,000(.65) = $375,000 - $422,500

Thus, the firm would pay no dividends and would also have to issue $47,500 in stock. 17-4B.

DCA - Stock Dividend Before dividend Shares outstanding Net income Price/Earnings Stock dividend Investor's shares

2,500,000 $ 600,000 10 18% 120 $600,000

Current price

$

2.40 = P/E x EPS=10 x $2,500,000 288.00 = $2.40 x 120 shares

Value before dividend After dividend Shares outstanding

$

New price

$

2.03

Investor's shares Value after dividend

$

141.6 288.00

Change

$

0.00

2,950,000

94

= 2,500,000 x (1+.18) $600,000

= P/E x EPS = 10 x $2,950,000 = 120 (1.18) = 141.6 x $2.03 = $288(before) - $288 (after)

The value of the investors' holdings does not change because the price of the stock reacted fully to the increase in the shares outstanding. Montford, Inc. - Dividends in Perfect Markets

17-5B.

Dividend Plans Year 1997 1998 1999

Plan A $ 2.55 $ 2.55 $45.60

Plan B $ 4.35 $ 4.70 $40.62

Required rate of return

0.17

Value stock A

$32.51 =

$2.55 $2.55 + (1 + .17) (1 +.17)

Value stock B

$32.51 =

$4.35 $4.70 + (1 + .17) (1 +.17)

2

+

$45.60 (1 +.17)

2

+

$40.62 (1 +.17)

3

3

a.

There is no effect on the value of the common stock.

b.

An investor's preference for current income, tax consequences, informational content, and transaction costs might change our conclusion.

17-6B. Wells Manufacturing, Inc. - Long Term Dividend Policy Debt ratio Equity ratio Shares outstanding

Year 1 2 3 4 5 a.

0.40 0.60 125,000 (A)

(B)

Investment $ 360,000 450,000 230,000 890,000 600,000

Funds Available Internally $225,000 440,000 600,000 650,000 400,000 $2,315,000

(C) Equity Contribution (A x .60) $ 216,000 270,000 138,000 534,000 360,000 $1,518,000

Residual Dividend Year 1 2 3 4 5

Dividend =

Funds Available − Equity Contributi on 125,000 Shares

$0.07 $1.36 $3.70 $0.93 $0.32

95

($2,315,00 0 − $1,518,000 )/5 125,000Sha res

b.

Target Dividend = $1.28 =

c.

The target dividend allows for consistency of income to the stockholder and income in all years whereas the year-to-year dividend would result in wide year-to-year variations.

17-7B. Standlee Corporation - Stock Split

a.

b.

17-8B.

Market price Split multiple Shares outstanding

$

98.00 2 30,000

You own Investor's shares Position before split

0.08 x 30,000 = 2,400 $235,200 = 2,400 Shares x $98 per share

Price after split Your shares after split Position after split Net gain

$

Price fall Price after split Position after split

0.45 $ 53.90 $258,720

= $98.00 (1 - .45) = 4,800 Shares x $53.90 per share

Net gain

$ 23,520

= $258,720 - $235,200

49.00 4,800 $235,200 $ 0

= $98 ÷ 2 = 2,400 x 2 = 4,800 shares x $49 per share

Carlson Cargo, Inc. - Dividend Policies Year 1 2 3 4 5 Total Profits After Taxes

Profits After Taxes $1,500,000 2,000,000 1,750,000 950,000 2,500,000 $8,700,000

Shares Outstanding a.

Constant Payout Ratio of 40% Year 1 2 3 4 5

b.

1,000,000

Dividend $0.60 $0.80 $0.70 $0.38 $1.00

Stable target payout of 40%

96

= = = = = =

Profits x Payout Ratio ÷ Shares $1,500,000 (.4) ÷ 1,000,000 $2,000,000 (.4) ÷ 1,000,000 $1,750,000 (.4) ÷ 1,000,000 $ 950,000 (.4) ÷ 1,000,000 $2,500,000 (.4) ÷ 1,000,000

Target dividend = $0.70 = c.

$8,700 ,000 (. 4) / 5 1,000 ,000

Small regular dividend of $0.50 plus year-end extra Base profits % of extra profits Year 1 2 3 4 5

1,500,000 50%

Dividend 0.50 0.75 = .50+[($2,000,000-$1,500,000)(.5)/1,000,000] 0.63 = .50+[($1,750,000-$1,500,000)(.5)/1,000,000] 0.50 1.00 = .50+[($2,500,000-$1,500,000)(.5)/1,000,000]

17-9B. B. Phillips Corporation - Repurchase of Stock Proposed dividend Shares outstanding Earnings per share Ex-dividend price Proposed dividend/share

$ 550,000 275,000 $ 6.00 $ 45.00 $2.00

a.

Repurchase price

$

b.

Number of shares repurchased

c.

The capital gains to be received by the stockholder would not be equal to the intended dividend, thus resulting in a dollar benefit or loss to the stockholders. Unless you have a need for current income, you would probably prefer the stock repurchase plan.

d. 17-10B.

47.00 11,702

= $45 + $2 = $550,000 ÷ ($45 + $2)

Number of shares to be issued $16 ,000 ,000 $100 −$12

= 181,819 share

Dollar size of the issue 181,818 shares x $100 = $18,181,800 17-11B.

Maness, Inc. - Residual Dividend Theory Total financing needed Retained earnings Debt ratio Equity ratio Equity financing needed Dividends

$ 1,500,000 $ 525,000 0.65 0.35 $ 525,000 $0

= $1,500,000 (0.35) = $525,000 - $525,000

Thus, the firm would pay no dividend, but it would also not have to issue any stock.

97

17-12B.

Star Corporation - Stock Split Market price Split multiple Shares outstanding

a.

You own Position before split

$

90 2 90,000 22,500 shares $2,025,000

Price after split

$

Your shares after split

b.

= 22,500 shares x $90 per share

45.00

= $90 ÷ 2

45,000

= 22,500 x 2

Position after split

$2,025,000

Net gain

$

= 45,000 shares x $45 per share

0

Price fall Price after split

= 0.25 x 90,000

0.45 $

49.50

= $90 (1 - .45)

Position after split

$2,227,500

= 45,000 Shares x $49.50 per share

Net gain

$ 202,500

= $2,227,500 - $2,025,000

98

CHAPTER 18 Working-Capital Management and Short-Term Financing

CHAPTER ORIENTATION In this chapter we introduce working-capital management in terms of managing the firm's liquidity. Specifically, net working capital is defined as the difference in current assets and current liabilities. The hedging principle is offered as one approach to addressing the firm's liquidity problems. In addition, this chapter deals with the sources of short-term financing that must be repaid within 1 year.

CHAPTER OUTLINE I.

II.

Managing current assets A.

Like fixed assets, the firm's investment in current assets is determined by the marginal benefits derived from investing in them compared with their acquisition cost.

B.

However, the mix of current and fixed assets of the firm's investment in total assets is an important determinant of the firm's liquidity. That is, the greater the firm's investment in current assets, other things remaining the same, the greater the firm's liquidity. This is generally true since current assets are usually more easily converted into cash.

C.

The firm can invest in marketable securities to increase its liquidity. However, such a policy involves committing the firm's funds to a relatively low-yielding (in comparison to fixed assets) investment.

Managing the firm's use of current liabilities A.

The greater the firm's use of current liabilities, other things being the same, the less will be the firm's liquidity.

B.

There are a number of advantages associated with the use of current liabilities for financing the firm's asset investments. 1.

Flexibility. Current liabilities can be used to match the timing of a firm's short-term financing needs exactly.

99

2. C.

III.

Interest cost. Historically, the interest cost on short-term debt has been lower than that on long-term debt.

Following are the disadvantages commonly associated with the use of shortterm debt: 1.

Short-term debt exposes the firm to an increased risk of illiquidity because short-term debt matures sooner and in greater frequency, by definition, than does long-term debt.

2.

Since short-term debt agreements must be renegotiated from year-toyear, the interest cost of each year's financing is uncertain.

Determining the appropriate level of working capital A.

Pragmatically, it is impossible to derive the "optimal" level of working capital for the firm. Such a derivation would require estimation of the potential costs of illiquidity which, to date, have eluded precise measurement.

B.

However, the "hedging principle" provides the basis for the firm's workingcapital decisions.

C.

1.

The hedging principle, or rule of self-liquidating debt involves the following: Those asset needs of the firm not financed by spontaneous sources (i.e., payables and accruals) should be financed in accordance with the following rule: Permanent asset investments are financed with permanent sources and temporary asset investments are financed with temporary sources of financing.

2.

A permanent investment in an asset is one which the firm expects to hold for a period longer than one year. Such an investment may involve current or fixed assets.

3.

Temporary asset investments comprise the firm's investment in current assets that will be liquidated and not replaced during the year.

4.

Spontaneous sources of financing include all those sources that are available upon demand (e.g., trade credit--Accounts Payable) or that arise naturally as a part of doing business (e.g., wages payable, interest payable, taxes payable, etc.).

5.

Temporary sources of financing include all forms of current or shortterm financing not categorized as spontaneous. Examples include bank loans, commercial paper, and finance company loans.

6.

Permanent sources of financing include all long-term sources such as debt having a maturity longer than one year, preferred stock, and common stock.

Although the hedging principle provides a useful guide to the firm's workingcapital decisions, no firm will follow its tenets strictly. At times a firm may rely too much on temporary financing for its cash needs or it may have excess cash as a result of excessive use of permanent financing.

100

IV.

V.

VI.

Determining the appropriate level of short-term financing A.

The hedging concept was presented as one basis for determining the firm's use of short-term debt.

B.

Hedging involves attempting to match temporary needs for funds with shortterm sources of financing and permanent needs with long-term sources.

Measuring the effectiveness of managing net working capital A.

The firm’s goal should be to minimize net working capital. This can be accomplished by: 1. faster collection of cash from sales 2. increasing inventory turns 3. slowing down disbursements to suppliers

B.

Cash conversion cycle (CCC) measures these three factors 1.

CCC = Days of sales outstanding (DSO) + Days of sales in inventory (DSI) – Days of payables outstanding (DPO)

2.

Decreasing DSO or DSI or increasing DPO will lead to a shorter cash conversion cycle.

Selecting a source of short-term financing A.

In general, there are three basic factors that should be considered in selecting a source of short-term financing: 1.

The effective cost of the credit source

2.

The availability of credit

3.

The effect of the use of a particular source of credit on the cost and availability of other sources

B.

The basic procedure used in estimating the cost of short-term credit utilizes the basic interest equation, i.e., interest = principal x rate x time.

C.

The problem faced in assessing the cost of a source of short-term financing involves estimating the annual percentage rate (APR) where the interest amount, the principal sum, and the time for which financing will be needed is known. Thus, the basic interest equation is "rearranged" as follows: interest

APR = principal D.

x

1 time

Compound interest was not considered in the simple APR calculation. To consider compounding, the following relation is used: m i APY = 1 +  - 1



m

where APY is the annual percentage yield, i is the nominal rate of interest per year, and m is the number of compounding periods within one year. The effect of compounding is thus to raise the effective cost of short-term credit.

101

VII.

Sources of short-term credit A.

B.

The two basic sources of short-term credit are unsecured and secured credit. 1.

Unsecured credit consists of all those sources that have as their security only the lender's faith in the ability of the borrower to repay the funds when due.

2.

Secured funds include additional security in the form of assets that are pledged as collateral in the event the borrower defaults in payment of principal or interest.

There are three major sources of unsecured short-term credit: trade credit, unsecured bank loans, and commercial paper. 1.

Trade credit provides one of the most flexible sources of financing available to the firm. To arrange for credit, the firm need only place an order with one of its suppliers. The supplier then checks the firm's credit and if the credit is good, the supplier sends the merchandise.

2.

Commercial banks provide unsecured short-term credit in two basic forms: lines of credit and transaction loans (notes payable). Maturities of both types of loans are usually 1 year or less with rates of interest depending on the credit-worthiness of the borrower and the level of interest rates in the economy as a whole.

3.

A line of credit is generally an informal agreement or understanding between the borrower and the bank as to the maximum amount of credit that the bank will provide the borrower at any one time. There is no "legal" commitment on the part of the bank to provide the stated credit. There is another variant of this form of financing referred to as a revolving credit agreement whereby such a legal obligation is involved. The line of credit generally covers a period of one year corresponding to the borrower's "fiscal" year.

4.

Transaction loans are another form of unsecured short-term bank credit. The transaction loan, in contrast to a line of credit, is made for a specific purpose.

5.

Only the largest and most creditworthy companies are able to use commercial paper, which consists of unsecured promissory notes sold in the money market. a.

The maturities of commercial paper are generally six months or less with the interest rate slightly lower than the prime rate on commercial bank loans. The new issues of commercial paper are either directly placed or dealer placed.

102

B.

b.

There are a number of advantages that accrue to the user of commercial paper: interest rates are generally lower than rates on bank loans and comparable sources of short-term financing; no minimum balance requirements are associated with commercial paper; and commercial paper offers the firm with very large credit needs a single source for all its shortterm financing needs. Since it is widely recognized that only the most creditworthy borrowers have access to the commercial paper market, its use signifies a firm's credit status.

c.

However, a very important "risk" is involved in using this source of short-term financing; the commercial paper market is highly impersonal and denies even the most credit-worthy borrower any flexibility in terms of repayment.

Secured sources of short-term credit have certain assets of the firm, such as accounts receivable or inventories, pledged as collateral to secure a loan. Upon default of the loan agreement, the lender has first claim to the pledged assets. 1.

2.

Generally, a firm's receivables are among its most liquid assets. Two secured loan arrangements are generally made with accounts receivable as collateral: a.

Under the arrangement of pledged accounts receivable, the amount of the loan is stated as a percentage of the face value of the receivables pledged.

b.

Factoring accounts receivable involves the outright sale of a firm's accounts receivables to a factor.

Four secured loan arrangements are generally made with inventory as collateral: a.

Under the floating lien agreement, the borrower gives the lender a lien against all its inventories.

b.

The chattel mortgage agreement involves having specific items of inventory identified in the security agreement.

c.

The field warehouse financing agreements means that the inventories used as collateral are physically separated from the firm's other inventories and are placed under the control of a third-party field warehousing firm.

d.

Terminal warehouse agreements involve transporting the inventories pledged as collateral to a public warehouse that is physically removed from the borrower's premises.

103

ANSWERS TO END-OF-CHAPTER QUESTIONS 18-l.

Working capital has traditionally been defined as the firm's investment in current assets. Current assets are comprised of all assets which the firm expects to convert into cash within one year including: cash, marketable securities, accounts receivable, and inventories. Net working capital refers to the difference in the firm's current assets and its current liabilities, i.e., net working capital = current assets - current liabilities.

18-2. The final composition of the firm's current and fixed asset investments is an important determinant of the firm's liquidity since, other things remaining the same, the greater the firm's investment in current assets the greater its liquidity. The firm may choose to invest additional funds in cash and/or marketable securities as a means of increasing its liquidity. However, this type of action involves a tradeoff between the risk of illiquidity and the firm's return on invested funds. By increasing its investment in cash and marketable securities, the firm reduces its risk of illiquidity. However, the firm has increased its investment in assets which earn little or no return. The firm can reduce its risk of illiquidity only by reducing its overall return on invested funds and vice versa. 18-3. Advantages of Short-Term Debt: (1)

The interest rate is usually lower (i.e., the term structure of interest rates is generally upward sloping) for short-term debt.

(2)

Funds are paid for only when they are used.

Disadvantages: (1)

Short-term debts must be repaid sooner; thus, there is a greater risk of illiquidity.

(2)

Interest costs on short-term debts vary from year-to-year, whereas long-term debt agreements "lock in" the cost of funds to the firm.

18-4. The use of current liabilities, or short-term debt as opposed to long-term debt, subjects the firm to a greater risk of illiquidity. That is, short-term debt by its very nature must be repaid or "rolled over" more often than long-term debt. Thus, the possibility that the firm's financial condition might deteriorate to a point where the needed funds might not be available is enhanced where short-term debt is used. 18-5. The hedging principle involves matching the maturities of the sources of financing for the firm's assets with the useful lives of the assets. To implement the hedging principle, the firm must fund all its permanent assets investments not financed by spontaneous sources (payables) with long-term sources of funds, and then, finance all its temporary asset investments not funded by spontaneous sources with shortterm sources of funds.

104

18-6. Definitions: (1)

A permanent asset investment is one which the firm expects to hold for a period longer than one year.

(2)

Temporary asset investments are comprised of the firm's investments in current assets which will be liquidated and not replaced within the current year.

(3)

Permanent sources of financing include intermediate and long-term debt, preferred stock, and common equity.

(4)

Temporary sources of financing consist of the various sources of short-term debt: including secured and unsecured bank loans, commercial paper, loans secured by accounts receivable, and loans secured by inventories.

(5)

Spontaneous sources of financing consist of the trade credit and other accounts payable which arise "spontaneously" in the firm's day-to-day operations. Examples include wages and salaries payable, accrued interest, and accrued taxes.

18-7. The important factors in selecting a source of short-term credit are as follows: (1)

the effective cost of credit.

(2)

the availability of credit.

(3)

the effect of the use of a particular source of credit on the cost and availability of other sources of credit.

18-8. The procedure used in estimating the cost of short-term credit relies on the use of the basic interest equation: i=PxRxT The problem faced in assessing the cost of a source of short-term financing, however, generally involves estimating the annual effective rate for which both the interest amount, the principal sum, and the time for which financing will be needed is known. To find the effective rate of interest, we simply solve the interest equation for the rate (APR), i.e.: APR =

i i = Px T P

x

1 T

18-9. Compound interest was not considered in the simple APR calculation. To consider the influence of compounding we can use the following relation: APY = (1 + i/m)m - 1 where i is the nominal rate of interest per year and m is the number of compounding periods within a year. This cost of credit relationship is frequently referred to as the Annual Percentage Yield, or APY.

105

18-10. The trade credit term "2/10, net 30" means that a 2 percent discount is offered for payment within 10 days or the full amount is due in 30 days: "4/20, net 60"--4 percent discount within 20 days, full amount due in 60 days; 3/15, net 45--3 percent discount within 15 days, full amount due in 45 days. 18-11. (a)

A line of credit is generally an informal agreement or understanding between the borrower and the bank as to the maximum amount of credit which the bank will provide the borrower at any one time.

(b)

Commercial paper consists of unsecured promissory notes of firms that are sold in the money market.

(c)

Compensating balance is a minimum balance that a borrower must maintain in a bank throughout a loan period.

(d)

The prime rate represents the interest rate which a bank charges its most creditworthy borrowers on short-term loans.

18-12. The four advantages of commercial paper are: (1)

Interest rate. Commercial paper rates are generally lower than rates on bank loans and comparable sources of short-term financing.

(2)

Compensating balance requirements. No minimum balance requirements are associated with commercial paper.

(3)

Amount of credit. Commercial paper offers the firm with very large credit needs a single source for all its short-term financing needs.

(4)

Prestige. Since it is widely recognized that only the most creditworthy borrowers have access to the commercial paper market, its use signifies a firm's credit status.

18-13. The "risk" involved with the firm's use of commercial paper as a source of short-term debt relates to the fact that the commercial paper market is highly impersonal and denies even the most credit-worthy borrower any flexibility in terms of repayment. 18-14. There are two basic procedures which can be used in arranging for financing on receivables--pledging and factoring. Under pledging, the borrower simply offers his accounts receivable as collateral for a loan obtained from either a commercial bank or a finance company. The amount of the loan is stated as a percent of the face value of the receivables pledged. The primary advantage of pledging as a source of short-term credit relates to the flexibility it provides the borrower. Financing is available on a continuous basis. Furthermore, the lender may provide credit services which eliminate or reduce the need for similar services within the firm. Factoring receivables involves the outright sale of a firm's accounts to a factor. The factor, in turn, bears the risk of collection and services the accounts for a fee. In addition, the factor provides advances or loans to the borrower on which interest is charged for the term of the advance.

106

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 18-1A.

The financial statements for both firms are found below:

Firm A Cash Accounts Receivable Inventories Net Fixed Assets Total

100,000 100,000 300,000 1,500,000 2,000,000

Accounts Payable Notes Payable Bonds Common Equity Total

200,000 200,000 600,000 1,000,000 2,000,000

150,000 50,000 300,000 1,500,000 2,000,000

Accounts Payable Notes Payable Current Liabilities Bonds Common Equity Total

400,000 200,000 600,000 400,000 1,000,000 2,000,000

Firm B Cash Accounts Receivable Inventories Net Fixed Assets Total

Financial measures of firm liquidity Working Capital Net Working Capital Current Ratio Acid Test Ratio Cash

Firm A 500,000 100,000 1.25 0.5 100,000

Firm B 500,000 (100,000) 0.83 0.33 150,000

Firm B is obviously the more aggressive of the two firms. Note the fact that it has negative net working capital (current liabilities exceed current assets) and both its current ratio and acid test ratio are lower. Notice that the higher level of cash for Firm B is more than offset by it more aggressive use of current liabilities.

107

18-2A. The information contained in the problem provides the basis for the following: Purchases = Discount Period = Cash Discount = Deferred Period = Maximum Credit Period = Purchases per day =

$480,000 15 days 1% 30 days 45 days 480,000 ÷ 360 = 1,333.33

a. Purchases/day x 15 day discount period b. Purchases/day x 45 day maximum credit period c. The Annual Percentage Rate for forgoing the discount

= = =

20,000.00 60,000.00 12.12%

18-3A.First we calculate the interest expense for the three month loan as follows: Interest = .12 x $100,000 x 3/12 = $3,000. Assuming that Paymaster has to leave 10% of the loan idle in a compensating balance the effective cost of credit can be calculated as follows: APR = [$3,000/($100,000 - 10,000 - 3,000)] x (12/3) = 13.79% If the company already has sufficient funds in the bank to satisfy the compensating balance requirement then the cost of credit drops to 12.37%. 18-4A. Interest expense for the commercial paper issue is calculated as follows: Interest = .11 x $20 million x (270/360) = $1,650,000 The effective rate of interest to Burlington Western (including the issue fee of $200,000) is calculated as follows: APR = [($1,650,000 + 200,000)/($20 million - 1,650,000 - 200,000)] x (360/270) = 13.59% Note that both the interest expense and the issue fee are prepaid. 18-5A. (a)

0.02 0.98

x

1 20 / 360

= 0.36734 or 36.73%

(b)

0.03 0.97

x

1 15 / 360

= 0.74226 or 74.23%

108

(c)

0.03 0.97

x

1 30 / 360

= 0.37113 or 37.11%

(d)

0.02 0.98

x

1 45 / 360

= 0.16327 or 16.33%

18-6A. Instructor’s Note: This problem can be easily solved using the exponent function (yx) on a hand calculator. Simply let y = (1+r/m) and x = m, then solve for yx. Finally subtract "1" to obtain the effective cost of credit with compounding of interest.

(a)

APY

=

(1 + i/m)m - 1

i

=

Nominal interest rate

m

=

# of compounding periods in a year

APY

= (1 +

0.3673 18 ) -1 18

= 1.4385 - 1 = .4385 or 43.85% (b)

APY

= (1+

0.7423 24 ) -1 24

= 2.0773 - 1 = 1.0773 or 107.73% (c)

APY

= (1 +

0.3711 12 ) -1 12

= 1.4412 - 1 = .4412 or 44.12% (d)

APY

= (1 +

0.1633 8 ) -1 8

= 1.1755 - 1 = .1755 or 17.55%

109

18-7A. (a) Interest

= .14 x $100,000 = $14,000

Therefore, the effective rate of interest on the loan is calculated as follows: APR

=

$14 ,000 $100 ,000 −14 ,000

x

1 360 / 360

= .1628 or 16.28% Dealer Financing Alternative APR

$16 ,300

= $100 ,000

x

1 360 / 360

= .163 or 16.3% Analysis. The costs of the two sources of financing are identical for practical purposes. The final choice can now be made based upon other nonquantitative factors. For example, the firm may find that using dealer financing is less time consuming and allows the firm to leave its credit line within the bank unchanged. Since bank credit can be used for a much wider array of financing needs than dealer financing, R. Morin would find that using dealer financing leaves the firm with greater flexibility in raising funds for its future needs. (b)

If the compensating balance becomes binding, then the effective rate on the bank loan alternative will be Interest

= .14 x $100,000 = $14,000

Compensating Balance

= .15 x $100,000 = $15,000

$14 ,000

APR = $100 ,000 −14 ,000 −15 ,000

x

= .197 or 19.7% Thus, where the 15 percent compensating balance requirement is binding on R. Morin, the cost of the bank loan rises to 19.7 percent. In this case, dealer financing is clearly less costly. Note that equipment dealers will frequently price their merchandise so as to compensate them for offering "below market" rates of interest for financing. This may well be the case here such that R. Morin should use the dealer financing unless it can negotiate a price concession equal to the value of "bargain financing."

110

18-8A. Interest

= .13 x 100,000 = $13,000 $1083/month -- interest

Compensating balance

= 100,000 x .20 = $20,000

$13 ,000

x

1 360 / 360

(a)

APR = $100 ,000

(b)

APR = $100 ,000 −20 ,000

$13 ,000

x

= 0.13 or 13% 1 360 / 360

= 0.1625 or 16.25%

Interest expense for the loan is $13,000; however, the firm gets the use of only .8 x $100,000 = $80,000. 18-9A. (a)

Interest

= .1025 x $500,000 x 180/360 = 25,625

APR

=

interest principal

APR

=

$25 ,625 +12 ,000 $500 ,000 −12 ,000 − 25 ,625

x

1 time

x

1 180 / 360

= .1627 = 16.27% (b)

The risk involved with the issue of commercial paper should be considered. This risk relates to the fact that the commercial paper market is highly impersonal and denies even the most credit-worthy borrower any flexibility in terms of when repayment is made. In addition, commercial paper is a viable source of credit to only the most credit-worthy borrowers. Thus, it may simply not be available to the firm.

18-10A.(a)

Interest = P x R x T = (400,000 x .75) x .13 x 1 = $39,000 Fee = $200,000 x .01 x 12 = $24,000 APR

=

interest principal

APR

=

$39 ,000 + 24 ,000 $400 ,000 x .75

x

1 time

111

x

1 360 / 360

= .21 or 21%

(b)

$300,000 x .15 = $45,000 (compensating balance) Since Johnson maintains a balance of $80,000 normally with the bank, the compensating balance requirement will not increase the effective cost of credit. Interest = 300,000 x (.11 + .03) x 1 = $42,000 $42 ,000 $300 ,000

(c)

18-11A.(a)

x

1 360 / 360

= 0.14 or 14%

Choose the line of credit since the effective interest is considerably lower. Note, however, that the pledging arrangement may reduce credit services to Johnson which would reduce Johnson's credit department expense. If this were the case then these savings would reduce the effective cost of that financing arrangement. Maximum Advance Face Value of Receivables (2 months credit sales) Less: Factoring Fee (1%) Reserve (9%) Interest (1 1/2% per month for 60 days)* Loan Advance (less discount interest)

$ 800,000 (8,000) (72,000) (21,600) $ 698,400

*Interest is calculated on the 90 percent of the factored accounts that can be borrowed, (.90 x $800,000 x .015 x 2 months) = $21,600 or ($800,000 8,000 - 72,000) x .015 x 2 months = $21,600. Thus, the effective cost of credit to MDM is calculated as follows: APR

=

1 $21,600 +8,000 −3,000 * * x (60 / 360 ) $698 ,400

= .2285 or 22.85% **Credit department savings for 60 days equals 2 x $1500.

112

Calculated on an annual basis, the cost of credit would be: APR

=

$129 ,600 + 48 ,000 −18 ,000 $698 ,400

x

1 360 / 360

= .2285 or 22.85%

(b)

where interest

= .015 x $720,000 x 12

= $129,600

factoring fee

= .01 x $400,000 x 12

= $48,000

credit department savings

= 12 x $1500 = $18,000

Of particular concern here is the presence of any "stigma" associated with factoring. In some industries, factoring simply is not used unless the firm's financial condition is critical. This would appear to be the case here, given the relatively high effective rate of interest on borrowing.

18-12A. (a)

Pledged Receivables (A/R): 0.80 A/R

= $500,000 loan

A/R

= $500,000/.80 = $625,000

Fee

= (0.01) ($625,000) = $6,250

Interest Cost

= (0.11) ($500,000) x 90/360 = $13,750

Effective Rate

=

1  $13 ,750 + 6,250     x   $ 500 , 000 90 / 360    

= .16 or 16% (b)

Warehousing cost = $2,000 x 3 months = $6,000 Interest cost

= 0.09 x $500,000 x 90/360 = $11,250

Effective Rate

=

1  $6,000 +11,250     x   $ 500 , 000 90 / 360    

= .138 or 13.8% The inventory loan would be preferred since its cost is lower under the conditions presented to S-J.

113

18-13A. (a)

Interest

= $20,000 x .10 x 180/360 = $1,000

APR

=

$1,000 $20 ,000

1

x (180 / 360 )

= .10 or 10% (b)

The net proceeds from the loan are now $20,000 - (.15 x $20,000) or $17,000. Thus, the effective cost of credit is APR

=

$1,000 $17 ,000

1 180 / 360

x

= .1176 or 11.76% We would have gotten the same answer by assuming that you borrow the necessary compensating balance. In that case the amount borrowed (B) is found as follows: B - .15B .85B B Interest

= = = =

$20,000 $20,000 $20,000/.85 $23,529.41

= .10 x 180/360 x $23,529.41 = $1,176.47

APR

=

$1,176 .47 $20 ,000

x

1 180 / 360

= .1176 or 11.76% (c)

In this case we assess the impact of discounted interest and the 15 percent compensating balance. As in part (b) the discounted interest serves to reduce the loan proceeds: APR

=

$1,000 $20 ,000 −3,000 −1,000

= .125 or 12.5%

114

1

x (180 / 360 )

If you borrowed enough to cover both the compensating balance requirement and discounted interest, then you would borrow (B) such that B - .15B - (.10 x 6/12)B = $20,000 .8B = $20,000 B = $25,000 Interest

= .10 x 6/12 x $25,000 = $1,250

Compensating Balance

= .15 x $25,000 = $3,750

Thus, APR

=

$1,250 $25 ,000 −1,250 −3,750

x

1 180 / 360

= .125 or 12.5% The cost of the bank loan rises once again in part (c) due to the reduction in funds available to you from the loan as a result (this time) of discounted interest. 18-14A. Calculation of the Maximum Advance Face Amount of Receivables Factored Less: Fee (.02 x $300,000) Reserve (.20 x $300,000) Interest (.01 x $234,000 x 3 months) Maximum Advance

$300,000 (6,000) (60,000) (7,020) $226,980

Calculation of the cost of credit APR

=

$7,020 + 6,000 − 6,000 * $226,980

x

12 3

= .0309 x 4 = .1237 or 12.37% * Credit department expenses reduced by $2,000 per month for 3 months.

115

18-15A. (a)

Days of Sales Outstanding (DSO) = Days of Sales in Inventory (DSI) =

DSO DSI

(b)

1999 52.2 28.0

2000 56.5 30.8

Accounts Receivable Sales/365 Inventorie s Sales/365

2001 50.0 29.6

Days of Payables Outstanding (DPO) =

2002 42.5 11.8

2003 44 6.9

Accounts Payable Sales/365

Cash Conversion Cycle (CCC) = DSO + DSI - DPO DPO CCC

1999 35.9 44.22

2000 47.0 40.3

2001 32.1 47.5

2002 48.9 5.4

2003 48.7 2.2

Generally, DSO and DSI are decreasing and DPO is increasing. This signifies that Mega PC is collecting receivables faster, turning inventory more rapidly, and paying suppliers slower. Mega PC has achieved significant improvement in its working capital management practices.

Solutions to Problem Set B 18-1B. Firm A Cash Accounts Receivable Inventories Net Fixed Assets Total

200,000 200,000 600,000 3,000,000 4,000,000

Accounts Payable Notes Payable Bonds Common Equity Total

400,000 400,000 1,200,000 2,000,000 4,000,000

200,000 400,000 400,000 3,000,000 4,000,000

Accounts Payable Notes Payable Bonds Common Equity Total

600,000 400,000 500,000 2,500,000 4,000,000

Firm B Cash Accounts Receivable Inventories Net Fixed Assets Total

116

The preceding financial statements provide the information needed to compute the following measures of liquidity for the two firms: Firm A 1,000,000 200,000 1.25 .5 200,000

Working Capital Net Working Capital Current Ratio Acid Test Ratio Cash

Firm B 1,000,000 0 1 0.6 200,000

Firm B is the more aggressive of the two firms with respect to the management of its working capital. Firm B has zero net working capital which is reflected in its lower current ratio. 18-2B. The information contained in the problem provides the basis for the following: Purchases Discount Period Cash Discount Deferred Period Maximum Credit Period Purchases per day

= = = = = =

600,000 30 days 2% 30 days 60 days 600,000 ÷ 360 = 1,666.67

a.

Purchases/day x 30 day discount period

=

50,000.00

b.

Purchases/day x 60 day maximum credit period

=

100,000.00

c.

The Annual Percentage Rate

=

24.49%

18-3B. First we calculate the interest expense for the three month loan as follows: Interest = .14 x $125,000 x 3/12 = $4,375. Assuming that Dee has to leave 10% of the loan idle in a compensating balance, the effective cost of credit can be calculated as follows: APR = [$4,375/($125,000 - 12,500 - 4,375)] x (12/3) = 16.18%

If the company already has sufficient funds in the bank to satisfy the compensating balance requirement then the cost of credit drops to 14.5%.

117

18-4B.Interest expense for the commercial paper issue is calculated as follows: Interest = .12 x $15 million x (270/360) = $1,350,000 The effective rate of interest to Duro Auto Parts (including the issue fee of $150,000) is calculated as follows: APR = [($1,350,000 + 150,000)/($15 million - 1,350,000 - 150,000)] x (360/270) = 14.81% Note that both the interest expense and the issue fee are prepaid. 18-5B. (a)

0.01 0.99

x

1 = 20 / 360

.1818 or 18.18%

(b)

0.02 0.98

x

1 = 15 / 360

.4898 or 48.98%

(c)

0.02 0.98

x

1 = 30 / 360

.2449 or 24.49%

(d)

0.03 0.97

x

1 = 45 / 360

.2474 or 24.74%

18-6B. Instructor’s Note: This problem can be easily solved using the exponent function (yx) on a hand calculator. Simply let y = (1+i/m) and x = m, then solve for y x. Finally subtract "1" to obtain the effective cost of credit with compounding of interest.

(a)

APY

= (1 + i/m)m - 1

i

= Nominal interest rate

m

= # of compounding periods in a year

APY

= (1 +

0.1818 18 ) -1 18

= .1983 or 19.83% (b)

APY

= (1+

0.4898 24 ) -1 24

= .6240 or 62.40% (c)

APY

= (1 +

0.2449 12 ) -1 12

= .2744 or 27.44% (d)

APY

= (1 +

0.2474 8 ) -1 8

118

= .2759 or 27.59% 18-7B. (a)

Interest

=

.15 x $150,000

=

$22,500

Therefore, the effective rate of interest on the loan is calculated as follows: APR

=

$22 ,500 $150 ,000 −22 ,500

x

1 360 / 360

= .1765 or 17.65% Dealer Financing Alternative APR

=

$30 ,000 1 x $150 ,000 360 / 360

= .20 or 20% In this case bank financing is preferred. (b)

If the compensating balance becomes binding, then the cost of bank loan alternative will be Interest

= .15 x $150,000 = $22,500

Compensating Balance

= .16 x $150,000 = $24,000

APR

$22 ,500

= $150 ,000 − 22 ,500 − 24 ,000

x

1 360 / 360

= .2174 or 21.74% Thus, where the 16 percent compensating balance requirement is binding on Vitra, the cost of the bank loan rises to 21.74 percent, and dealer financing is preferred.

119

18-8B. Interest

= =

100,000 x .14 x 1 $14,000

Compensating balance = $14 ,000

100,000 x .15 = 15,000 x

1 360 / 360

(a)

APR = $100 ,000

(b)

APR = $100 ,000 - 15,000

$14 ,000

x

= 0.14 or 14% 1 360 / 360

= .1647 or 16.47%

Interest expense for the loan is $14,000; however, the firm gets the use of only .85 x $100,000 = $85,000. 18-9B. (a)

(b)

APR

=

interest principal

x

1 time

Interest =

.11 x $450,000 x 180/360 = $24,750

APR

=

$24 ,750 +13 ,000 x $450 ,000 −13 ,000 − 24 ,750

=

.1831 or 18.31%

The risk involved with the issue of commercial paper should be considered. This risk relates to the fact that the commercial paper market is highly impersonal and denies even the most credit-worthy borrower any flexibility in terms of when repayment is made. In addition, commercial paper is a viable source of credit to only the most credit-worthy borrowers. Thus, it may simply not be available to the firm.

18-10B. Interest = ($500,000 x 0.80) x .13 x 1

= $52,000

Processing fee = (250,000 x .01 x 12)

= $30,000

(a)

APR

=

$52 ,000 +30 ,000 x = .205 or 20.5% $500 ,000 x .80

120

(b)

Interest = $400,000 x .14

=

$56,000

Compensating Balance = $400,000 x .15 =

$60,000

Since the firm maintains a balance of $100,000 normally with the bank, the compensating balance requirement will not increase the effective cost of credit. $56 ,000 $400 ,000

(c)

x

1 360 / 360

= 0.14 or 14%

Choose the line of credit since the effective interest is considerable lower. Note, however, that the pledging arrangement may reduce credit services to the firm which would reduce its credit department expense. If this were the case then these savings would reduce the effective cost of that financing arrangement.

18-11B. (a)

Maximum Advance Face Value of Receivables (2 months credit sales)

$ 600,000

Less:

Factoring Fee (1%) Reserve (9%) Interest (1 1/2% per month for 60 days)* Loan Advance (less discount interest)

(6,000) (54,000) (16,200) $ 523,800

*Interest is calculated on the 90 percent of the factored accounts that can be borrowed, (.90 x $600,000 x .015 x 2 months) = $16,200 or ($600,000 6,000 - 54,000) x .015 x 2 months = $16,200. Thus, the effective cost of credit to Dal Molle is calculated as follows: APR

=

$16 ,200 + 6,000 − 2,800 * * x $523 ,800

= .2222 or 22.22% **Credit department savings for 60 days equals 2 months x $1,400/month. (b)

Of particular concern here is the presence of any "stigma" associated with factoring. In some industries, factoring simply is not used unless the firm's financial condition is critical. This would appear to be the case here, given the relatively high effective rate of interest on borrowing.

121

18-12B. Pledged Receivables (A/R): 0.80 A/R

= $400,000 loan

A/R

= $400,000/.80 = $500,000

Fee

= (0.01) ($500,000) = $5,000

Interest Cost = (0.11) ($400,000) x 3/12 = $11,000 Effective Rate =

 $11,000 + 5,000   1   x   $400 ,000    3 / 12 

= .16 or 16% Inventory Loan: Warehousing cost

=

$2,000 x 3 months = $6,000

Interest cost

=

0.09 x $400,000 x 3/12 = $9,000

Effective Rate

=

 $6,000 + 9,000   1   x    $400 ,000   3 / 12 

=

.15 or 15%

The inventory loan would be preferred since its cost is lower under the conditions presented. 18-13B. (a)

Interest

APR

(b)

=

$25,000 x .11 x 180/360

=

$1,375

=

$1,375 $25 ,000

=

.11 or 11%

1

x (180 / 360 )

The net proceeds from the loan are now $25,000 - (.15 x $25,000) or $21,250. Thus, the effective cost of credit is APR

1 180 / 360

=

$1,375 $21 ,250

=

.1294 or 12.94%

x

122

We would have gotten the same answer by assuming that you borrow the necessary compensating balance. In that case the amount borrowed (B) is found as follows: B - .15B

=

.85B

= $25,000

B

=

$25,000/.85

=

$29,411.76

=

.11 x 180/360 x $29,411.76

=

$1,617.65

Interest

$25,000

Compensating Balance = .15 x 29,411.76 = 4,411.76 APR

(c)

=

$1,617 .65 $29 ,411 .76 −4,411 .76

=

.1294 or 12.94%

x

1 180 / 360

In this case we assess the impact of discounted interest and the 15 percent compensating balance. As in part (b) the discounted interest serves to reduce the loan proceeds: APR

=

$1,375 $25 ,000 −3,750 −1,375

=

.1383 or 13.83%

1

x (180 / 360 )

18-14B. Calculation of the Maximum Advance Face Amount of Receivables Factored Less: Fee (.02 x $450,000) Reserve (.15 x $450,000) Interest ( .13/12 x $373,500 x 3 months)

$450,000 (9,000) (67,500)

Maximum Advance

$361,361

Calculation of the cost of credit APR

=

$12 ,139 + 9,000 − (3 x 2000 ) 12 x $361 ,361 3

= .1676 or 16.76% 18-15B 123

(12,139)

(a)

DSO DSI (b)

Days of Sales Outstanding (DSO) =

Accounts Receivable Sales/365

Days of Sales in Inventory (DSI)

Inventorie s Sales/365

1997 59.4 46.9

=

1998 63.7 24.7

Days of Payables Outstanding (DPO) =

1999 63.6 32.8

2000 62.7 31.5

2001 60.5 26.0

Accounts Payable Sales/365

Cash Conversion Cycle (CCC) = DSO + DSI - DPO DPO CCC

1997 26.5 79.8

1998 18.9 79.5

1999 20.2 76.2

2000 19.4 74.8

2001 22.6 63.9

Although there has been some improvement in DSO, DSI, and DPO during the last 5 years, there has been little change during the most recent 2 years. Allergan should focus on collecting receivables faster and increasing inventory turns to reduce the DSO and DSI measures. This will in turn reduce the cash conversion cycle. Allergan should also try to obtain more favorable trade credit terms (i.e. lengthen payment period).

CHAPTER 19

Cash and Marketable 124

Securities Management CHAPTER ORIENTATION This chapter initiates our study of cash management, focusing on the cash flow process and the reasons why a firm holds cash balances. Cash management systems are explored, as is the topic of investing excess cash in marketable securities.

CHAPTER OUTLINE I.

Why a company holds cash A.

B.

II.

Sound cash management techniques are based on a thorough understanding of the cash flow process. 1.

Cash holdings are increased from several external sources on an irregular basis.

2.

Irregular cash outflows reduce the firm's cash balance.

3.

Other major sources of cash arising from internal operations occur on a rather regular basis, i.e., accounts receivable collections.

Three motives for holding cash balances have been identified by Keynes. 1.

The transactions motive

2.

The precautionary motive

3.

The speculative motive

Cash management objectives and decisions A.

B.

C.

The risk return trade-off 1.

Strike an acceptable balance between holding too much cash and holding too little cash.

2.

A large cash investment minimizes insolvency, but penalizes profitability.

3.

A small cash investment frees excess balances for investment in more profitable assets, which increase profitability.

The objectives 1.

On-hand cash must be sufficient to meet disbursal needs.

2.

Idle cash balances must be reduced to a minimum.

The decisions 1.

How to speed up cash collections and slow down cash outflows?

125

D. III.

2.

What should be the composition of the marketable securities portfolio?

3.

How should the investment in liquid assets be split between actual cash holdings and marketable securities?

Perspective on collection and disbursement procedures

Collection and disbursement procedures A.

Cash acceleration and deceleration techniques revolve around the concept of float. 1.

Mail float

2.

Processing float

3.

Transit float

4.

Disbursing float

B.

Float reduction can result in (l) usable funds that are released for company use and (2) increased returns produced on these freed-up balances.

C.

Several techniques are available to improve the management of the firm's cash inflows and may also provide for a reduction in float. 1.

2.

3.

The lock-box arrangement expedites cash gathering. a.

The objective is to reduce both mail and processing float.

b.

The procedure includes rental of a local post office box and authorization of a local bank, in which a demand deposit account (DDA) is maintained, to pick up remittances from the box.

c.

The arrangement provides for (l) increased working cash, (2) elimination of clerical functions, and (3) early knowledge of dishonored checks.

d.

Added costs must be evaluated.

Pre-authorized checks (PACs) also speed up the conversion of receipts into working cash. a.

The objective is to reduce mail and processing float.

b.

A PAC (l) is created with the individual's legal authorization, (2) resembles an ordinary check, and (3) does not contain the signature of the person on whose account it is being drawn.

c.

PAC systems are most useful to firms that regularly receive a large volume of payments of a fixed amount from the same customers.

Depository transfer checks (DTCs) are used in conjunction with concentration banking.

126

Major objectives of using DTCs are (1) elimination of excess cash balances held in several regional banks and (2) reduction of float. 4.

D.

IV.

Wire transfers offer the fastest method for moving funds between commercial banks. Two major communication facilities accommodate wire transfers: (1) Bank Wire, and (2) Federal Reserve Wire System.

Techniques used by firms that hope to improve the management of their cash flow 1.

Zero balance accounts (ZBAs) permit centralized control, but also allow the firm to maintain disbursing authority at the local level. The major objective is to achieve better control over cash payments. It might also increase disbursement float.

2.

Payable-through drafts (PTDs) have the physical appearance of ordinary checks but they are drawn on and paid by the issuing firm instead of the bank. a.

The objective of a PTD system is to provide for effective control of field-authorized payments.

b.

Stop payment orders can be initiated on any drafts considered inappropriate.

c.

Legal payment of individual drafts takes place after review and approval of the drafts by the company. Disbursing float is usually not increased by the use of drafts.

Electronic funds transfer systems (EFT) reduce transit, mail, and processing float. A.

Transactions are immediately reflected on the books and bank accounts of firms doing business.

B.

This ideal has not yet been fully reached.

C.

The purpose of the EFT is the elimination of the check as a method of transferring funds.

D.

Perspective on evaluating costs.

127

V.

Evaluating the costs of cash management services A.

Whether a cash management system will provide an economic benefit can be evaluated by: added costs = added benefits

B.

If the benefits exceed the costs, the system is economically feasible.

C.

On a per unit basis, this relationship can be expressed as follows: P where P

VI.

= (D) (S) (i) = increase in per-check processing cost, if new system is adopted

D

= days saved in the collection process

S

= average check size in dollars

i

= the daily, before-tax opportunity cost of carrying cash.

D.

The product of (D) x (S) x (i) must exceed P for the system to be beneficial to the firm.

E.

Perspective on the marketable securities portfolio.

Composition of marketable securities portfolio A.

B.

Five factors to consider when selecting a proper marketable securities mix 1.

Financial risk

2.

Interest rate risk

3.

Liquidity

4.

Taxability of interest income and capital gains

5.

Yield criterion

Marketable security alternatives 1.

A Treasury bill is a direct obligation of the U.S. government. a.

May be purchased in denominations of $1,000 and higher ($10,000, $15,000, $50,000, $100,000, $500,000, and $1,000,000).

b.

Currently offered with maturities of 91, 182, and 365 days.

c.

Since Treasury bills are sold on a discount basis, the investor does not receive an actual interest payment.

d.

The bills are considered risk-free and sell at lower yields than other marketable securities of like maturity.

e.

Income from Treasury bills is subject to the federal income tax and is taxed as ordinary income.

128

2.

Federal agency securities represent debt obligations of corporations and agencies that have been created to manage the various lending programs of the U.S. government.

3.

Bankers' acceptances are drafts drawn on a specific bank by an exporter in order to obtain payment for goods shipped to a customer who maintains an account with that bank.

4.

5.

6.

7.

a.

Maturities run mostly from 30 to 180 days.

b.

Acceptances are sold on a discount basis.

c.

Income generated is fully taxable at all levels.

d.

Provide investors with a higher yield than do Treasury bills.

A negotiable certificate of deposit (CD) is a marketable receipt for funds that have been deposited in a bank for a fixed time period at a fixed interest rate. a.

CDs are offered in denominations ranging from $25,000 to $10,000,000

b.

Maturities range from 1 to 18 months.

c.

Yields are higher than those of Treasury bills.

d.

Income received is taxed at all governmental levels.

Commercial paper refers to short-term, unsecured promissory notes. a.

Paper ranges from $5,000 up to $5,000,000.

b.

The notes are generally sold on a discount basis with maturities ranging from 3 to 270 days.

c.

Paper has no active trading in a secondary market.

d.

Return received is taxable at all governmental levels.

Repurchase agreements involve the actual sale of securities by a borrower to the lender, with a commitment on the part of the borrower to repurchase the securities at the contract price plus a stated interest charge. a.

These agreements are usually executed in sizes of $500,000 or more.

b.

There is a specified maturity date or time period.

c.

Yields are higher than for Treasury bills and are taxable at all governmental levels.

Money market mutual funds usually invest in a diversified portfolio of short-term, high-grade debt instruments. a.

Shares are sold to a large number of small investors.

b.

Funds offer a high degree of liquidity.

c.

Returns are usually taxable at all governmental levels. 129

IX.

Summary

ANSWERS TO END-OF-CHAPTER QUESTIONS 19-1. The procedure by which funds generated from company activity are accommodated (directed) through the firm from the time of their initial receipt until their ultimate disposition. Over the long run, accounts receivable collections account for the largest regular source of cash in the typical manufacturing company. Payment of accounts payable, payroll expenses, and the distribution of income to the owners (cash dividends) are the major forms of cash disbursal. Other sources of cash for a company may include receipts from the sale of assets, assumption of additional debt, issuance of new stock, or gains realized from investments. While these are important sources of cash to a company, the proceeds are not available on a regular basis. Major capital expenditure programs, new company acquisitions, and inventory stockpiling are examples of irregular disbursals of cash outside the normal course of everyday business. 19-2. The three classical motives for holding cash and near-cash balances are: (1) the transactions motive; (2) the precautionary motive; (3) the speculative motive. Transactions balances allow the firm to make payments that arise in the ordinary course of doing business. Precautionary balances provide a buffer stock of liquid assets that can be drawn down if unexpected demands for cash arise. Speculative balances permit the economic unit to take advantage of future profit-making situations. 19-3. Concentration banking involves the use of multiple cash collection centers and the deposit of funds in regional banks located near the collection centers. Funds are then transferred from the regional commercial banks to a concentration bank. A concentration bank is one where the firm maintains a major cash disbursing account. Concentration banking may permit the firm to: (1) operate with lower levels of excess cash; (2) maintain more effective control over the firm's cash resources; (3) make prudent decisions concerning marketable securities transactions. Moreover, concentration banking will reduce both mail float and transit float. 19-4. The "regular" depository transfer check is a pre-printed form that is filled out and mailed by a company employee in order to move demand deposit balances from one bank to another. The automated depository transfer check (ADTC) eliminates the mail delay associated with the "regular" depository transfer check. The deposit information in this latter case is telephoned by a company employee to a regional data collection center. The data collection center transmits the information to the firm's concentration bank. Ordinarily, both of these systems are used in conjunction with a concentration banking arrangement. 19-5. The firm which regularly receives a large volume of payments from the same customers will find the pre-authorized check system a useful device. Common examples are insurance companies, savings and loan associations, consumer credit firms, leasing enterprises and charitable and religious organizations.

130

19-6. The firm must: (1) maintain adequate cash balances that will permit it to meet the disbursal needs that occur in the course of doing business; (2) reduce idle cash balances to a minimum. 19-7. (1)

Choosing among various methods available for speeding up cash receipts, slowing down cash payments, and providing for more effective control over cash outflows.

(2)

Splitting the firm's liquid asset holdings among cash and marketable securities.

(3)

Choosing the appropriate marketable securities mix.

19-8. (1)

Mail float: this represents funds which are not usable to the firm because of the time necessary for a customer's remittance check to travel through the mails to a company collection center.

(2)

Processing float: this represents funds tied up due to the time needed for the company to process the remittance checks and get them ready for deposit in a demand deposit account.

(3)

Transit float: this represents funds tied up because of the time necessary for a deposited check to clear through the commercial banking system and become "good" funds to the firm.

(4)

Disbursing float: this refers to funds available in the firm's demand deposit account due to the time needed for a payment check to clear through the banking system.

19-9. In the context of cash management, financial risk is the uncertainty of future returns from a security caused by possible changes in the financial capability of the securityissuer to make future payments to the security-owner. This is sometimes called default risk. On the other hand the uncertainty related to the expected returns from a financial asset caused by changes in interest rates is called interest rate risk. 19-10. Liquidity is the ability to change a security into cash. A money market instrument that is highly liquid can be converted into cash quickly and at a price near its prevailing market price. 19-11. Commercial paper 19-12. Bills--5.90% Agencies--6.10% Paper--6.25% 19-13. (1)

Maturity periods on repurchase agreements can be individually tailored to the needs of the investor.

(2)

The price at which the repo will be liquidated is set at the time the contract is finalized.

131

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 19-1A. Average daily float

Annual Revenues Days in Year

=

=

$40 ,000 ,000 365

=

$109,589 [(Average daily float) invested [($109,589)

x

(Number of days of float reduction)]

x

[(Amount that can be invested) forgone [($767,123)

(7)] x

= Amount that can be =

$767,123

Interest rate on investment)] = Annual interest

x

(.05)]

=

$38,358

Thus, the cost of the Healthy Herbal's current billing system is: Annual interest forgone Plus: Clerical costs Cost of current system

$38,356 35,000 $73,356

And, the net annual gain from adoption of the proposed concentration banking system is: Cost of current system Less: cost of concentration banking system Net annual gain from proposed system

$73,356 40,000 $33,356

19-2A. Analysis of the two alternatives requires that the net earnings be computed for each alternative for each of the specified time periods as follows: Invest in Money Market Fund: Cash Available

Interest Rate

Holding Period

Annual Earnings

$750,000 $750,000 $750,000 $750,000

0.05 0.05 0.05 0.05

1mo. 2 mo. 6 mo. 12 mo.

$3,125 6,250 18,750 37,500

132

Annual Cost 0 0 0 0

Net Earnings $3,125 6,250 18,750 37,500

Invest directly in marketable securities: Cash Available

Interest Rate

Holding Period

Annual Earnings

Annual Cost

$750,000 $750,000 $750,000 $750,000

0.075 0.075 0.075 0.075

1mo. 2 mo. 6 mo. 12 mo.

$4,688 9,375 28,125 56,250

15000 15000 15000 15000

Net Earnings -$10,312 -5,625 13,125 41,250

Accordingly, a comparison of the net earnings of the two alternatives indicates the following: Money Market Fund 1 mo. 2 mo. 6 mo. 12 mo.

$3,125 6,250 18,750 37,500

Direct Investment -$10,312 -5,625 13,125 41,250

Recommendation Money Market Fund Money Market Fund Money Market Fund Direct Investment

19-3A. Annual collection = ($6,232,375) (12 regions) = $74,788,500 Daily collections = $74,788,500 / 365 = $204,900 Use of the lock-box system will reduce Marino Rug Company's float by 3 days according to the study done by National Bank of Miami. The value of the float reduction is found by presuming the freed funds will be added to the marketable securities portfolio and will earn the 9.75% yield noted in the text of the problem. The gross annual savings from the system are: ($204,900) (3) (.0975) = $59,933 The annual cost of operating the lock-box system is: ($325 per month) (12 regions) (12 months) = $46,800 The net annual savings are: ($59,933) - ($46,800) = $13,133 Marino's management should approve the use of the proposed lock-box system and, thereby, save $13,133 per year.

133

19-4A. (a)

The average accrued wages under the monthly payment system are: 4($ 675 ,000 ) = $1,350,000 2

This means the firm has, on average, $1,012,500 (i.e., $1,350,000 - $337,500) more to invest. This provides an annual return of ($1,012,500) (.085) = $86,063. Therefore, Mac's Tennis Racket should move to the monthly payment system since it will generate $86,063 - $50,775 = $35,288 in net annual savings. (b)

Let r = the break-even rate of return on the near cash portfolio: $1,012,500 (r) = $50,775 r = 5.01% A reasonable margin of safety favoring adoption of the monthly payment proposal is present.

19-5A. (a)

Reduction in mail float: (1.5 days) ($750,000) = + reduction in processing float: (2.0 days) ($750,000) = = Total Float Reduction

(b)

1,500,000 $2,625,000

The opportunity cost of maintaining the current banking arrangement is: (.092) ($2,625,000) =

(c)

$1,125,000

$241,500

The average number of checks to be processed each day through the lock-box arrangement is: Daily remittance s Average check size

=

$750 ,000 $3,750

= 200 checks per day

Now we can calculate the cost of the lock-box system on an annual basis as follows: (200 checks) ($0.35) (270 days) = $18,900 Next, we compute the cost of the automated depository transfer check (ADTC) system. Second National Bank will not contribute to the cost of the ADTC arrangement because it is the lead concentration bank and, thereby, receives the transferred data. Thus, James Waller will be charged for six ADTCs (or, three locations @ 2 checks each) each business day. The cost of the ADTC system is: (6 daily transfers) ($27 each) (270 days) = $43,740

134

The total cost of the proposed system will be: Lock-box cost

$18,900

ADTC cost

43,740

Total cost (d)

$62,640

Waller Nail Corp. should adopt the proposed system. The projected net annual gain will be $178,860. Projected return on freed balances Less: Cost of new system Net annual gain

$241,500 62,640 $178,860

19-6A. Initially, compute the firm's average remittance check size and daily opportunity cost of carrying cash. The average check size is: $40 ,000 ,000 15 ,000

= $2,666.67

The daily opportunity cost of carrying cash is: .09 365

= .0002466 per day

Next, the days saved in the collection process can be evaluated according to this format: Added costs = Added benefits or P = (D) (S) (i) $0.35 = (D) (2,666.67) (.0002466) 0.5322 days = D We know Mountain Furniture will experience a financial gain if it adopts the lockbox system and, thereby, speeds up its collections by more than 0.5322 days.

135

Annual revenues Days in year

19-7A.

=

$890 ,000 ,000 365

(sales per day) (assumed yield) ($2,438,35 6) (0.096)

19-8A. (a)

=

=

$2,438,356 sales per day

$234,082

First, it is necessary to compute Mustang's average remittance check size and the daily opportunity cost of carrying cash. The average check size is: $12 ,000 ,000 6,000

= $2,000 per check.

The daily opportunity cost of carrying cash is: 0.07 365

= 0.0001918 per day

Second, the days saved in the collection process can be evaluated according to the general format of Added Costs = Added Benefits or P = (D) (S) (i) 0.20 = (D) ($2,000) (0.0001918) 0.5214 days = D. Therefore, Mustang Ski-Wear will experience a financial gain if it adopts the lock-box system and speeds up its collections by more than 0.5214 days. (b)

In this situation the daily opportunity cost of carrying cash is: 0.045 365

= 0.0001233 per day

For Mustang to break even should it choose to install the lock-box system, the cash collections must be accelerated by 0.8110 days as follows: $0.20 = (D) ($2,000) (0.0001233) 0.8110 days = D.

136

(c)

The break-even cash acceleration period of 0.8110 days is greater than the 0.5214 days found in part (a). This is due to the lower yield available on near-cash assets (or 4.5 percent annually versus 7.0 percent). Since the alternative rate of return on the freed-up balances is lower in the second situation, more funds must be invested to cover the costs of operating the lock-box system. The greater cash acceleration period generates this increased level of required funds.

19-9A. The value of one day of processing float is: $18 ,000 ,000 270

= $66,667

The annual savings at 8% are: (2 days) ($66,667) (0.08) = $10,667 19-10A. Annual collections = ($5,200,000) (12) = $62,400,000 Daily collections = $62,400,000/365 = $170,959 The opportunity cost of the mail and processing float is: ($170,959) (4.0) (0.09) = $61,545 19-11A. This exercise attempts to illustrate that a change in the firm's accounts payable policy can properly be viewed as a part of the overall problem of cash management. Before evaluating the 45 day and 60 day payment alternatives it is necessary to calculate the amount of purchases that are actually discounted and the value of the annual purchase discount earned by Bradford Construction. These amounts are calculated below:

Purchases discounted ($37,500,000 annual purchases) (0.25) = $9,375,000

Purchase discounts earned ($9,375,000) (0.03) = $281,250 with $281,250 in purchase discounts earned. Bradford actually pays: ($9,375,000) - ($281,250) = $9,093,750, 10 days after purchase. The annual amount not discounted is ($37,500,000) - ($9,375,000) = $28,125,000.

137

We are now in a position to evaluate first the 45 day proposal and, second, the 60 day proposal. 45 day alternative: (1) (2) Principal Extra time amount available $ 28,125,000 9,093,750

(3) Interest rate

15 days 35 days

(4) = (1) x (2) x (3) Interest earned

0.12 ÷ 365 = $138,699 0.12 ÷ 365 = 104,640 Total added return $243,339

- $281,250 Lost discounts earned + 243,339 Total added return $ 37,911 Loss to Bradford by stretching payables to 45 days. 60 day alternative: (1) Principal amount

(2) Extra time available

$28,125,000 9,093,750

30 days 50 days

(3) Interest rate

(4) =(1)x(2)x(3) Interest earned

0.12 ÷ 365 = $277,397 0.12 ÷ 365 = 149,486 Total added return $426,883

-$281,250 Lost discounts earned +$426,883 Total added return $145,633 Gained by Bradford by stretching payables to 60 days Finally, we can evaluate the effect of the projected price increase to Bradford that is associated with the 60 day alternative. Price Increase: $37,500,000 Purchases .005 $

187,500 Price increase

$187,500 Price increase -145,633 Net added return $ 41,867 Loss to Bradford

138

Ultimately, none of the proposed courses of action would benefit the firm.

139

19-12A. 18

(a)

P =

∑

T =1

$80 (1.09)

T

+

$1,000 (1.09 )18

= $912.44

The bond can be sold for $912.44. This was developed as follows: $80 (8.7556) + $1,000 (.21199) = $912.44 (b)

$1,000 - $912.44 = $87.56

(c)

First, we find the price of the 4-year bond, which now has 2 years remaining to maturity: 2

P =

∑

T =1

$80 (1.09)

T

+

$1,000 = $982.41 (1.09 ) 2

Then we can determine the expected capital loss on the shorter-term bond as follows: $1,000 - $982.41 = $17.59 The capital loss on the shorter-term bond is much less than that suffered on the longer-term instrument. (d)

Interest rate risk.

19-13A.The easiest way to visualize the appropriate responses to all three parts of this problem is to calculate the income that would be generated if the entire $4,000,000 was invested in each separate maturity category. This is shown below:

AmountYield

Income

1. 2. 3. 4. 5. 6.

(.062) 1/12 (.064) 2/12 (.065) 3/12 (.067) 4/12 (.069) 5/12 (.070) 6/12

$4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000

Brokerage $ 20,667 $ 42,667 $ 65,000 $ 89,333 $115,000 $140,000

Net $10,000 $10,000 $10,000 $10,000 $10,000 $10,000

$ 10,667 $ 32,667 $ 55,000 $ 79,333 $105,000 $130,000

From this table we can see that the $10,000 brokerage fee is exceeded by the incremental return from the investment in all maturity categories. Since the available yield rises with each successive increase in the maturity period, investment in longer maturities increases return. Now, we can proceed to answer the specific parts of this problem. (a) Return from investing: $2,000,000 for three months $32,500 $2,000,000 for six months $70,000 - brokerage fee $10,000 $92,500 By investing half of the excess for three months and half for six months the return will be maximized at $92,500; this approach adheres to the wishes of the company president.

140

(b)

Under this circumstance all $4,000,000 should be invested in securities with maturity periods of six months. The added income will be $130,000.

(c)

This solution is developed from the table above: (1)

20 ,667 6

=

$ 3,445

(2)

42 ,667 6

=

$ 7,111

(3)

65 ,000 6

=

$10,833

(4)

89 ,333 6

=

$14,889

(5)

115 ,000 6

=

$19,167

(6)

140 ,000 6

=

$23,333

Total Brokerage fee Net

78,778 -10,000 $68,778

19-14A. (a)

The after-tax yield to Aggieland Fireworks on the BBB-rated bond is (0.09) (1-0.46) = .0486 = 4.86%. Since the yield on the tax-exempt issue is already stated on an after-tax basis, we can conclude the 5 1/2 percent return on the municipal is preferable.

(b)

r = (1 −T)

r*

0.055

r = (1 −0.46 ) =

0.055 0.54

=

141

10.185%

SOLUTION TO INTEGRATIVE PROBLEM 1.

The amount of cash balances that will be freed if New Wave Surfing Stuff, Inc. adopts the system proposed by the Bank of the U.S.: Cash balances freed due to reduction in mail float: [(Number of days eliminated) [(3.5)

x

(Average daily cash remittances)]

x

($100,000)]

=

$350,000

Cash balances freed due to reduction in processing float: [(Number of days eliminated)

x

(Average daily cash remittances)]

[(4)

x

($100,000)]

=

Total float reduction 2.

$750,000

Opportunity cost of maintaining the current banking arrangement: (Forecast yield on marketable securities portfolio) x =

(Total float reduction)

(Opportunity Cost--Interest)

[(.06)

x

Opportunity cost--interest

($750,000)]

= $45,000

$45,000

Opportunity cost--clerical expense

50,000

Total Opportunity cost 3.

$400,000

$95,000

Projected annual cost of operating the proposed system: Average number of checks to be processed each day through the lock-box arrangement: Daily remittance s Average check size

=

$100 ,000 $1,000

=

100 checks

Resulting cost of lock-box system on an annual basis: [(Average number of checks) x (Processing cost per check) x (Number of business days per year)] = Cost [(100) x

($0.25)x

(270)] =

$6,750

Next, the estimated cost of the ADTC system must be calculated. The Bank of the U.S. will not contribute to the cost of the ADTC because it is the lead concentration bank and thereby receives the transferred data. As a result, New Wave will be charged for six ADTCs (three locations @ two checks each) each business day. The ADTC system, therefore, costs:

142

[(No. of daily transfers) x (Cost per transfer) x (No. of business days per year)] = Cost [(6)

($25)

x

(270)]

=

Accordingly, the total cost of the proposed system is: Lock-box cost ADTC cost Total Cost 4.

$40,500 $ 6,750 40,500 $47,250

The net annual gain associated with adopting the proposed system is: Opportunity cost of current system [from "2" above] Less: Total cost of new system [from "3" above] Net annual gain (loss)

$95,000 47,250 $47,750

As a result, the analysis suggests the company should adopt the proposed cash receipts acceleration system.

Solutions to Problem Set B 19-1B. Annual Revenues Days in Year

Average daily float = [(Average daily float) invested [($219,178)

=

$80 ,000 ,000 = 365

x (No. of days of float reduction)] x

(5)]

[(Amount that can be invested) interest forgone [($1,095,890) x

= x

(.055)] =

$219,178

= Amount that can be

$1,095,890 (Interest rate on investment)]

= Annual

$60,274

Thus, the cost of the Sprightly Step's current billing system is: Annual interest forgone

$ 60,274

Plus: Clerical costs

50,000

Cost of current system

$110,274

And, the net annual gain from adoption of the proposed concentration banking system is: Cost of current system Less: cost of concentration banking system Net annual gain from proposed system

143

$110,274 80,000 $ 30,274

19-2B. Analysis of the two alternatives requires that the net earnings be computed for each alternative for each of the specified time periods as follows: Invest in Money Market Fund: Cash Available $1,100,000 $1,100,000 $1,100,000 $1,100,000

Interest Rate 0.055 0.055 0.055 0.055

Holding Period 1 mo. 2 mo. 6 mo. 12 mo.

Annual Earnings $5,042 10,083 30,250 60,500

Annual Cost 0 0 0 0

Net Earnings $5,042 10,083 30,250 60,500

Invest directly in marketable securities: Cash Available $1,100,000 $1,100,000 $1,100,000 $1,100,000

Interest Rate 0.08 0.08 0.08 0.08

Holding Period 1 mo. 2 mo. 6 mo. 12 mo.

Annual Earnings $7,333 14,667 44,000 88,000

Annual Cost $15,000 15,000 15,000 15,000

Net Earnings -$7,667 - 333 29,000 73,000

Accordingly, a comparison of the net earnings of the two alternatives indicates the following: Money Market Fund 1 mo. $5,042 2 mo. 10,083 6 mo. 30,250 12 mo. 60,500

Direct Investment -$7,667 -333 29,000 73,000

19-3B. (a)

Reduction in mail float: (1.5 days) ($800,000) =

$1,200,000

+ reduction in processing float: (2.0 days) ($800,000) =

1,600,000

= Total Float Reduction

$2,800,000

144

Recommendation Money Market Fund Money Market Fund Money Market Fund Direct Investment

(b)

The opportunity cost of maintaining the current banking arrangement is: (.095) ($2,800,000) =

(c)

$266,000

The average number of checks to be processed each day through the lock-box arrangement is: Daily remittance s Average check size

=

$800 ,000 = 200 checks per day $4,000

Now we can calculate the cost of the lock-box system on an annual basis as follows: (200 checks) ($0.40) (270 days) = $21,600 Next, we compute the cost of the automated depository transfer check (ADTC) system. First Citizens Bank will not contribute to the cost of the ADTC arrangement because it is the lead concentration bank and, thereby, receives the transferred data. Thus, Charles Kobrin will be charged for six ADTCs (or, three locations @ 2 checks each) each business day. The cost of the ADTC system is: (6 daily transfers) ($30 each) (270 days) = $48,600 The total cost of the proposed system will be: Lock-box cost ADTC cost Total cost (d)

$21,600 48,600 $70,200

Kobrin Door & Glass, Inc. should adopt the proposed system. The projected net annual gain will be $195,800. Projected return on freed balances Less: Cost of new system Net annual gain

$266,000 (70,200) $195,800

19-4B. Annual collections = $10,000,000 (5 regions) = $50,000,000 Daily collections = $50,000,000/365 = $136,986 The value of the 3.0 days' float reduction is found by presuming the freed balances will be added to the marketable securities portfolio and will earn 11.0% (see text of problem). The gross annual savings from the system are: ($136,986) (3.0 days) (.11) = $45,205

145

The annual cost of operating the lock-box system is: ($600 per month) (5 regions) (12 months) = $36,000 The net annual savings are:

$45,205 - 36,000 $9,205

Savings

The data indicate that Regency Components should adopt the lock-box system. 19-5B. Initially, compute the firm's average remittance check size and daily opportunity cost of carrying cash. The average check size is: $50 ,000 ,000 20 ,000

= $2,500

The daily opportunity cost of carrying cash is: .09 = .0002466 per day 365

Next, the days saved in the collection process can be evaluated according to this format: Added costs = Added benefits or P = (D) (S) (i) $0.37 = (D) (2,500) (.0002466) 0.6002 days = D We know Hallmark Technology will experience a financial gain if it adopts the lockbox system and, thereby, speeds up its collections by more than 0.6002 days. 19-6B.

Annual revenues Days in year

=

$900 ,000 ,000 365

(sales per day) (assumed yield) ($2,465,75 3) (0.095)

19-7B. (a)

=

2,465,753 sales per day

= $234,247

First, it is necessary to compute Colorado Comm's average remittance check size and the daily opportunity cost of carrying cash. The average check size is: $10 ,000 ,000 7,000

= $1,429 per check.

146

The daily opportunity cost of carrying cash is: 0.07 365

= 0.0001918 per day

Second, the days saved in the collection process can be evaluated according to the general format of Added Costs = Added Benefits or P = (D) (S) (i) 0.30 = (D) ($1,429) (0.0001918) 1.0946 days = D Therefore, Colorado Comm will experience a financial gain if it adopts the lock-box system and speeds up its collections by more than 1.0946 days. (b)

In this situation the daily opportunity cost of carrying cash is: 0.045 365

= 0.0001233 per day

For Colorado Comm to break even should it choose to install the lock-box system, the cash collections must be accelerated by 1.7027 days as follows: $0.30 = (D) ($1,429) (0.0001233) 1.7027 days = D (c)

The break-even cash acceleration period of 1.7027 days is greater than the 1.0946 days found in part (a). This is due to the lower yield available on near-cash assets (or 4.5 percent annually versus 7.0 percent). Since the alternative rate of return on the freed-up balances is lower in the second situation, more funds must be invested to cover the costs of operating the lock-box system. The greater cash acceleration period generates this increased level of required funds.

19-8B. The value of one day of processing float is: $17 ,000 ,000 270

= $62,963

The annual savings at 9% are: (2 days) ($62,963) (0.09) = $11,333

147

19-9B. (a)

The average accrued wages under the monthly payment system are: 4($ 500 ,000 ) 2

= $1,000,000

This means that the firm has, on the average, $750,000 (i.e., $1,000,000 $250,000) more to invest. This provides an annual return of ($750,000) (0.08) = $60,000. Therefore, Katz Jewelers should move to the monthly payment system since it will generate $60,000 - $40,000 = $20,000 in net annual savings. (b)

Let r = the break-even rate of return on the near-cash portfolio: $750,000

(r) = $40,000 r

=

5.33%

A reasonable margin of safety favoring adoption of the monthly payment proposal is present. 19-10B. Annual collections = ($5,000,000) (10) = $50,000,000 Daily collections = $50,000,000/365 = $136,986 The opportunity cost of the mail and processing float is: ($136,986) (4.0) (0.09) = $49,315 19-11B. This exercise attempts to illustrate that a change in the firm's accounts payable policy can properly be viewed as a part of the overall problem of cash management. Before evaluating the 45 day and 60 day payment alternatives it is necessary to calculate the amount of purchases that are actually discounted and the value of the annual purchase discount earned by Meadowbrook. These amounts are calculated below:

Purchases discounted ($40,000,000 annual purchases) (0.25) = $10,000,000 Purchase discounts earned ($10,000,000) (0.03) = $300,000 with $300,000 in purchase discounts earned. Meadowbrook actually pays: ($10,000,000) - ($300,000) = $9,700,000, 10 days after purchase. The annual amount not discounted is ($40,000,000) - ($10,000,000) = $30,000,000. We are now in a position to evaluate first the 45 day proposal and, second, the 60 day proposal. 148

45 day alternative: (1) Principal amount $30,000,000 9,700,000

(2) Extra time available

- $300,000 + 237,931 - $ 62,069

15 days 35 days

(3) Interest rate

(4) = (1) x (2) x (3) Interest earned

0.11 ÷ 365 = $135,616 0.11 ÷ 365 = 102,315 Total added return $237,931

Lost discounts earned Total added return Loss to Meadowbrook by stretching payables to 45 days.

60 day alternative: (1) Principal amount $30,000,000 9,700,000

(2) Extra time available 30 days 50 days

(3) Interest rate

(4) =(1)x(2)x(3) Interest earned

0.11 ÷ 365 = $271,233 0.11 ÷ 365 = 146,164 Total added return $417,397

-$300,000 Lost discounts earned +$417,397 Total added return $117,397 Gained by Meadowbrook by stretching payables to 60 days Finally, we can evaluate the effect of the projected price increase to Meadowbrook that is associated with the 60 day alternative. Price Increase: $40,000,000 Purchases .005 $ 200,000 Price increase $200,000 Price increase -117,397 Net added return -$ 82,603 Loss to Meadowbrook Ultimately, none of the proposed courses of action would benefit the firm.

149

19-12B. (a)

P =

18 $80 ∑ T =1 (1.09)

T

+

$1,000 (1.09 )18

= $912.44

The bond can be sold for $912.44. This was developed as follows: $80 (8.7556) + $1,000 (.21199) = $912.44 (b)

$1,000 - $912.44 = $87.56

(c)

First, we find the price of the 4-year bond, which now has 2 years remaining to maturity: P =

2 $80 ∑ T =1 (1.09)

T

+

$1,000 = $982.41 (1.09 ) 2

Then we can determine the expected capital loss on the shorter-term bond as follows: $1,000 - $982.41 = $17.59 The capital loss on the shorter-term bond is much less than that suffered on the longer-term instrument. (d)

Interest rate risk.

19-13B. The easiest way to visualize the appropriate responses to all three parts of this problem is to calculate the income that would be generated if the entire $3,500,000 was invested in each separate maturity category. This is shown below:

AmountYield

Income

1. 2. 3. 4. 5. 6.

(.062) 1/12 (.064) 2/12 (.065) 3/12 (.067) 4/12 (.069) 5/12 (.070) 6/12

$3,500,000 $3,500,000 $3,500,000 $3,500,000 $3,500,000 $3,500,000

Brokerage $ 18,083 $ 37,333 $ 56,875 $ 78,167 $100,625 $122,500

Net $15,000 $15,000 $15,000 $15,000 $15,000 $15,000

$ 3,083 $ 22,333 $ 41,875 $ 63,167 $85,625 $107,500

From this table we can see that the $15,000 brokerage fee is exceeded by the incremental return from the investment in all maturity categories. Since the available yield rises with each successive increase in the maturity period, investment in longer maturities increases return. Now, we can proceed to answer the specific parts of this problem. 150

(a)

Return from investing: $1,750,000 for three months $1,750,000 for six months - brokerage fee

$28,438 $61,250 $15,000 $74,688

By investing half of the excess for three months and half for six months the return will be maximized at $74,688; this approach adheres to the wishes of the company president.

(b)

Under this circumstance all $3,500,000 should be invested in securities with maturity periods of six months. The added income will be $107,500.

(c)

This solution is developed from the table above: (1)

18 ,083 6

=

$ 3,014

(2)

37 ,333 6

=

$ 6,222

(3)

56 ,875 6

=

$9,479

(4)

78 ,167 6

=

$13,028

(5)

100 ,625 6

=

$16,771

(6)

122 ,500 6

=

$20,417

Total Brokerage Net

68,931 -15,000 $53,931

19-14B. (a)

The after-tax yield to Ward Grocers on the BBB-rated bond is (0.08) (1-0.46) = .0432 = 4.32%. Since the yield on the tax-exempt issue is already stated on an after-tax basis, we can conclude the 5 1/2 percent return on the municipal is preferable.

(b)

r

=

r* (1 −T)

r

=

0.055 0.055 = = (1 −0.46 ) 0.54

151

10.185%

CHAPTER 20

Accounts Receivable and 152

Inventory Management CHAPTER ORIENTATION The investment of funds in accounts receivable inventory involves a trade-off between profitability and risk. For accounts receivable, this trade-off occurs as less creditworthy customers with a higher probability of bad debts are taken on to increase sales. With respect to inventory management, a larger investment in inventory leads to more efficient production and speedier delivery, hence, increased sales. However, additional financing to support the increase in inventory and increased handling and carrying costs is required. In addition, the concept of total quality management and single-sourcing have had a major impact on inventory purchasing.

CHAPTER OUTLINE I.

Accounts receivable A.

Typically, accounts receivable account for just over 20 percent of a firm's assets.

B.

The size of the investment in accounts receivable varies from industry to industry and is affected by several factors including the percentage of credit sales to total sales, the level of sales and the credit and collection policies, more specifically the terms of sale, the quality of customers and collection efforts.

C.

Although all these factors affect the size of the investment, only the credit and collection policies are decision variables under the control of the financial manager.

D.

The terms of sale are generally stated in the form a/b net c, indicating that the customer can deduct a percentage if the account is paid within b days; otherwise, the account must be paid within c days.

153

E.

If the customer decides to forgo the discount and not pay until the final payment date, the annualized opportunity cost of passing up this a% discount and withholding payment until the cth day is determined as follows: annualized opportunit y cost of forgoing the discount

=

a 1 −a

x

360 c −b

Example: Given the trade credit terms of 2/10, net 30, what is the annualized opportunity cost of passing up the 2 percent discount and withholding payment until the 30th day? Solution: Substituting the values from the example, we get 36.73% = F.

H.

x

360 30 −10

A second decision variable in determining the size of the investment in accounts receivable in addition to the trade credit terms is the type of customer. 1.

G.

0.02 1 −0.02

The costs associated with extending credit to lower-quality customers include: a.

Increased costs of credit investigation

b.

Increased probability of customer default

c.

Increased collection costs

Analyzing the credit application is a major part of accounts receivable management. 1.

Several avenues are open to the firm in considering the credit rating of an applicant. Among these are financial statements, independent credit ratings and reports, bank references, information from other companies, and past experiences.

2.

One commonly used method for credit evaluation is called credit scoring and involves the numerical evaluation of each applicant in which an applicant receives a score based upon the answers to a simple set of questions. The score is then evaluated relative to a predetermined standard, its level relative to that standard determining whether or not credit scoring should be extended to the applicant. The major advantage of credit scoring is that it is inexpensive and easy to perform.

The key to maintaining control over the collection of accounts receivable is the fact that the probability of default increases with the age of the account. 1.

One common way of evaluating the current situation is ratio analysis. a.

examining the average collection period

b.

ratio of receivables to assets

154

c. d. e.

II.

ratio of credit sales to receivables (accounts receivable turnover ratio) amount of bad debts relative to sales over time aging of accounts receivable schedule

I.

Once delinquent accounts have been identified, the third and final variable is determined by the firm’s collection policies. A direct trade-off does exist between collection expenses and lost goodwill on one hand and noncollection of accounts on the other, and this trade-off is always part of making the decision.

J.

Credit should be extended to the point that marginal profitability on additional sales equals the required rate of return on the additional costs we have to consider investment in inventories + receivables + change in cost of cash discount to generate those sales.

Inventory A.

Typically, inventory accounts for about four to five percent of a firm's assets.

B.

The purpose of carrying inventories is to uncouple the operations of the firm; that is, to make each function of the business independent of each other function.

C.

As such, the decision with respect to the size of the investment in inventory involves a basic trade-off between risk and return.

D.

The risk comes from the possibility of running out of inventory if too little inventory is held, while the return aspect of this trade-off results because increased inventory investment costs money.

E.

There are several general types of inventory. 1. Raw materials inventory consists of the basic materials that have been purchased from other firms to be used in the firm's production operations. This type of inventory uncouples the production function from the purchasing function. 2. Work in process inventory consists of partially finished goods that require additional work before they become finished goods. This type of inventory uncouples the various production operations. 3. Finished goods inventory consists of goods on which the production has been completed but the goods are not yet sold. This type of inventory uncouples the production and sales function. 4. Stock of cash inventory, already discussed in some detail in preceding chapters, serves to make the payment of bills independent of the collection of accounts due.

F.

In order to effectively manage the investment in inventory, two problems must be dealt with: the order quantity problem and the order point problem.

G.

The order quantity problem involves the determination of the optimal order size for an inventory item given its expected usage, carrying, and ordering costs. 155

H.

The economic order quantity (EOQ) model attempts to determine the order size that will minimize total inventory costs. The EOQ is given as Q* = where C

=

carrying cost per unit

O

=

ordering cost per order

S

=

total demand in units over the planning period

Q*

=

the optimal order quantity in units

I.

The order point problem attempts to answer the following question: How low should inventory be depleted before it is reordered?

J.

In answering this question two factors become important: 1.

What is the usual procurement or delivery time and how much stock is needed to accommodate this time period?

2.

How much safety stock does the management desire?

K.

Modification for safety stocks is necessary since the usage rate of inventory is seldom stable over a given timetable.

L.

This safety stock is used to safeguard the firm against changes in order time and receipt of shipped goods.

M.

The greater the uncertainty associated with forecasted demand or order time, the larger the safety stock. 1.

The costs associated with running out of inventory will also determine the safety stock levels.

2. N.

A point is reached where it is too costly to carry a larger safety stock given the associated risk. Inflation can also have an impact on the level of inventory carried. 1. Goods may be purchased in large quantities in anticipation of price rises. 2.

O.

The cost of carrying goods may increase, causing a decline in Q*, the optimal order quantity.

The just-in-time inventory control system is more than just an inventory control system; it is a production and management system. 1.

Under this system, inventory is cut down to a minimum, and the time and physical distance between the various production operations is also minimized.

156

III.

2.

Actually the just-in-time inventory control system is just a new approach to the EOQ model which tries to produce the lowest average level of inventory possible.

3.

Average inventory is reduced by locating inventory supplies in convenient locations and setting up restocking strategies that cut time and thereby reduce the needed level of safety stock.

TQM and Inventory Purchasing management. A.

The concept of total quality management has led to strong customer-supplier relationships in an effort to increase quality.

B.

In many cases firms that only a few years ago placed an upper limit of 10 or 20 percent on the purchases of any part from a single supplier now rely on a single supplier using the single-sourcing relationship.

C.

Single sourcing ties the interests of the supplier to the firm to which it supplies and allows the supplier to provide input on production techniques that might improve quality.

D.

Financially, the TQM view argues that higher quality will result in increased sales and market share and as a result the traditional economic analysis of inventory management is flawed.

ANSWERS TO END-OF-CHAPTER QUESTIONS 20-1. The size of the investment in accounts receivable is determined primarily by these factors: (1)

The percentage of credit sales to total sales. While this factor plays a major role in determining the investment in accounts receivable, it is generally not within the control of the financial manager. In essence, the nature of the business tends to determine the blend between credit sales and cash sales.

(2)

The level of sales. As sales increase, so will accounts receivable. Again, this is not an effective decision tool.

(3)

Credit and collection policies. Specifically the terms of sale, the quality of customer, and collection efforts are determinants of the level of investment in receivables that are under the control of the financial manager.

20-2. (a)

1/20 net 50 means a 1 percent discount can be taken if the account is paid within 20 days; otherwise, it can be paid within 50 days.

(b)

2/30 net 60 means a 2 percent discount can be taken if the account is paid within 30 days; otherwise, it must be paid within 60 days.

(c)

Net 30 means there are no discounts offered and the account must be paid within 30 days.

157

(d)

2/10, 1/30 net 60 means a two percent discount can be taken if the account is paid within 10 days, and if paid after 10 days but before and up to 30 days, a one percent discount can be taken; otherwise, the account must be paid within 60 days.

20-3. The purpose of an aging account is to provide a breakdown both in dollars and percentage terms of the proportion of receivables that are past due. The same function could essentially be handled through ratio analysis, provided accounts receivable were broken down according to when they were due. However, an aging account provides control over past due accounts in an extremely efficient manner. 20-4. If a credit manager experienced no bad debt losses over the past year, then credit was probably not extended to enough customers. Ideally credit should be extended to the point where marginal revenue from added sales due to increased credit is equal to the marginal costs associated with increased bad debts, costs of investigation, costs of collection, and increased required rate of return. Obviously the credit manager was nowhere near this level if no bad debts were incurred. 20-5. Credit scoring involves the numerical evaluation of credit applicants based upon their answers to simple questions. This score is then evaluated relative to a predetermined standard, many times generated through the use of multiple discriminant analysis; its level relative to the standard determining whether or not credit should be extended to the applicant. The major advantage of credit scoring is that it is inexpensive and easy to perform. Once standards are set, a computer or clerical worker without specialized training can easily evaluate applicants. 20-6. The returns associated with a more liberal credit policy come from the fact that extending credit to weaker customers or liberalizing the trade credit terms will probably increase sales, resulting in a larger profit level. The risks involved largely result from the increased possibility of extending credit that will eventually become bad debts. 20-7. The logic behind marginal analysis is to examine the incremental or marginal benefits, and incremental costs associated with any change in the credit policy; and if this change produces more benefits than costs, the change should be made. If, however, the incremental costs are greater than the incremental benefits, the proposed change should be dropped. 20-8. The purpose of carrying inventories is to uncouple the operations of the firm; that is, to make each function of the business independent of each other's function. By uncoupling the various operations of the firm, delays or shutdowns in one area no longer affect the production and sale of the final product. Raw materials inventory, for example, uncouples the production function from the purchasing function. Work in process inventory uncouples the various production operations. 20-9. Yes. The stock of cash carried by a firm is simply a special type of inventory. In terms of uncoupling the various operations of the firm, the purpose of holding cash is to make the payment of bills independent of the collection of accounts due.

158

20-10. In order to effectively control the investment in inventory, the firm must: (1) determine the optimal order size for the inventory item, given its expected usage, carrying, and ordering costs; (2) determine how low inventory should be allowed to deplete before it is reordered. 20-11. The major assumptions of the EOQ model include: (1) Constant or uniform demand. (2) Constant unit price regardless of amount ordered. (3) Constant carrying costs per unit. (4) Constant ordering costs per order regardless of the size of the order. (5) Instantaneous delivery. (6) Independent orders. 20.12. The risk associated with the inventory investment is that if the level of inventory is too low, the various functions of business will not be effectively uncoupled, and delays in production and customer delivery will result. The return aspects of this trade-off result because increased inventory investment costs money. As the size of the inventory increases, the storage and handling cost, in addition to the required rate of return on capital invested in inventory, will rise. Thus, the more inventory the firm holds, the less risk they run of stocking out of inventory and the greater are their inventory expenses. 20.13. Inflation affects the EOQ model by increasing carrying costs (C) which results in a small EOQ level. In addition, if inflation is accompanied by major periodic price increases, this may cause the EOQ model to lose its applicability and be replaced by a policy of anticipatory buying; that is, buying in anticipation of a price increase in order to secure the goods at a lower cost. 20-14. With single-sourcing, a company uses very few suppliers or, in many cases, a single supplier as a source for a particular part or material. In this way the company has a more direct influence and control over the quality performance of a supplier, since the company accounts for a larger proportion of the supplier's volume. The company and supplier can then enter into a partnership where the supplier agrees to meet the quality standards of the customer. In this way the supplier can be brought into the TQM program of the customer. 20-15. The TQM view argues that the traditional analysis is flawed in that it ignores the fact that increased sales and market share result from better quality products and that this increase in sales will more than offset the higher costs associated with increased quality. In effect, it is argued that the benefits from quality improvement are underestimated.

159

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 20-1A.

a x 1 −a

360 c −b

where a b c 0.02 1 − 0.02

x

x

= 18.37%

360 c −b

where a b c 0.02 1 − 0.02

amount of the discount the discount period the net period

360 50 −10

a x 1 −a

20-2A.

= = =

= = =

amount of the discount the discount period the net period

360 30 − 20

= 73.47%

20-3A. a x 1 −a

360 c −b

where a b c

= = =

amount of the discount the discount period the net period

(a)

0.01 1 −0.01

x

360 20 −10

=

36.36%

(b)

0.02 1 − 0.02

x

360 30 −10

=

36.73%

(c)

0.03 1 −0.03

x

360 30 −10

=

55.67%

(d)

0.03 1 −0.03

x

360 60 −10

=

22.27%

160

(e)

0.03 1 −0.03

x

360 90 −10

=

13.92%

(f)

0.05 1 −0.05

x

360 60 −10

=

37.89%

20-4A. Applicant #1 Z = Z = Z =

3.3(0.2) + 1.0(0.2) + 0.6(1.2) + 1.4(0.3) + 1.2(0.5) 0.66 + 0.2 + 0.72 + 0.42 + 0.6 2.6 < 2.7 thus, reject

Applicant #2 Z = Z = Z =

3.3(0.2) + 1.0(0.8) + 0.6(1.0) + 1.4(0.3) + 1.2(0.8) 0.66 + 0.8 + 0.6 + 0.42 + 0.96 3.44 > 2.7 thus, accept

Applicant #3 Z = Z = Z =

3.3(0.2) + 1.0(0.7) + 0.6(0.6) + 1.4(0.3) + 1.2(0.4) 0.66 + 0.7 + 0.36 + 0.42 + 0.48 2.62 < 2.7 thus, reject

Applicant #4 Z = Z = Z =

3.3(0.1) + 1.0(0.4) + 0.6(1.2) + 1.4(0.4) + 1.2(0.4) 0.33 + 0.4 + 0.72 + 0.56 + 0.48 2.49 < 2.7 thus, reject

Applicant #5 Z = Z = Z =

3.3(0.3) + 1.0(0.7) + 0.6(0.5) + 1.4(0.4) + 1.2(0.7) 0.99 + 0.7 + 0.30 + 0.56 + 0.84 3.39 > 2.7 thus, accept

Applicant #6 Z = Z = Z =

3.3(0.2) + 1.0(0.5) + 0.6(0.5) + 1.4(0.4) + 1.2(0.4) 0.66 + 0.5 + 0.30 + 0.56 + 0.48 2.5 < 2.7 thus, reject

20-5A. (a)

Sales − cost of goods sold Sales

=

Gross Profit Margin

$600,000 − Cost of goods sold $600,000

=

0.10

Cost of goods sold

=

$540,000

161

(b)

(c)

(d)

Cost of goods sold Average inventory

=

Inventory turnover ratio

$540,000 Average inventory

=

6

Average inventory

=

$90,000

Inventory turnover ratio

=

360 Average Collection

Inventory turnover

=

Inventory turnover ratio

=

9 times

Cost of goods sold Average inventory

=

9 times

$480,000 Average inventory

=

9 times

Average inventory

=

$53,333

Cost of goods sold Average inventory

=

Inventory turnover ratio

$1,150,000 Average inventory

=

5

Average inventory

=

$230,000

(1 - Gross profit margin) (Sales)

=

(0.86)($25,000,000)

Cost of Goods Sold

=

$21,500,000 cost of goods

=

8 times

$21,500,00 0 Average inventory

=

8 times

Average inventory

=

$ 2,687,500

Inventory turnover ratio =

20-6A.

Step 1:

360 45

Estimate the Change in Profit. = =

($1,000,000 x .20) - ($1,000,000 x .08) $200,000 - $80,000

162

Period

=

$120,000

Step 2: Estimate the cost of additional investment in accounts receivable and inventory. Estimate the additional investment in accounts receivable: = = =

($6,000,000 / 360) x 90 - ($5,000,000 / 360) x 60 $1,500,000 - $833,333 $666,667

Additional accounts receivable and inventory times the required rate of return: = = Step 3:

($666,667 + $50,000) .15 $107,500

Estimate the change in the cost of the cash discount =

Step 4:

$0 (no change)

Compare incremental revenues with incremental costs. = = =

Step 1 - (Step 2 + Step 3) $120,000 - $107,500 $12,500

The policy should be adopted. 20-7A.

Step 1:

Estimate the Change in Profit. = = =

($1,500,000 x .20) - ($1,500,000 x .09) $300,000 - $135,000 $165,000

Step 2: Estimate the cost of additional investment in accounts receivable and inventory. Estimate the additional investment in accounts receivable: = = =

($12,500,000 / 360) x 45 - ($11,000,000 / 360) x 30 $1,562,500 - $916,667 $645,833

Additional accounts receivable and inventory times the required rate of return:

163

= = Step 3:

($645,833 + $75,000) .15 $108,125

Estimate the change in the cost of the cash discount =

Step 4:

$0 (no change)

Compare the incremental revenues with the incremental costs. =

Step 1 - (Step 2 + Step 3) $165,000 - $108,125 $56,875

= =

The policy should be adopted. 20-8A. (a)

Q*

=

2SO C

=

2(3000 )10 0.10

=

600 ,000

= (b)

775 units

Total costs

=

S  Q   C +  Q  O 2  

Order one time:

=

 3000   3000    $.10 +   $10  2   3000 

=

$150 + $10

=

$160

Order four times: =

 750   3000    $.10 +   $10  2   750 

=

$37.50 + $40

=

$77.50

Order five times: =

 600   3000    $.10 +   $10  2   600 

164

Order ten times:

Order 15 times:

(c)

(1) (2) (3) (4) (5) (6)

(a)

Q*

=

$30.00 + $50.00

=

$80

=

 300   2

=

$15.00 + $100

=

$115

=

 200   2

=

$10 + $150

=

$160

  3000   $0.10 +   $10   300 

  3000   $0.10 +   $10   200 

constant or uniform demand constant unit price constant carrying costs constant ordering costs instantaneous delivery independent orders

20-9A. =

2SO C

=

2( 20 ,000 )50 0.25

= (b)

2828 boxes

It assumes among other things that the rolls are not perishable. assumptions include: (1) constant or uniform demand (2) constant unit price (3) constant carrying costs (4) constant ordering costs (5) instantaneous delivery (6) independent orders

165

Other

20-10A. (a)

Q*

=

2SO C

2(50 ,000 )500 75

= = (b)

816.4967 units or 816 units

Total costs

=

S  Q   C +  Q  O 2  

=

 816   2

=

$30,600 + $30,637

=

$61,237

  50 ,000   $75 +   $500   816 

Note that carrying cost ($30,600) differs from ordering cost ($30,637) due to a $37 rounding error. Recall that Q* was rounded down by .4967 units. 20-11A. (a)

Q*

=

2SO C

=

2(500 ,000 )90 .40

=

15,000 Units

(b)

500 ,000 15 ,000

(c)

Inventory order point = delivery time stock + safety stock

(d)

=

Average inventory

33 1/3 orders per year

=

1 50

=

10,000 + 15,000

=

25,000 units

=

EOQ + safety time stock 2

=

15 ,000 + 15,000 2

=

7,500 + 15,000

=

22,500 units

166

x 500,000 + 15,000

20-12A. (a)

EOQ

=

2SO C

=

2(500 ,000 )(100 ) .50

=

14,142 units: but since orders must be placed in 200-unit lots, the effective EOQ becomes 14,200 units

=

35.2 orders per year

(b)

500 ,000 14 ,200

(c)

Inventory order point = Delivery time stock + safety stock

(d-a)

EOQ

=

=

4 50

=

40,000 + 5,000

=

45,000 units

x 500,000 + 5,000

2(500 ,000 )(100 ) 2.5

=

6,324.5 =

=

6,325 units, but since orders must be placed in 200 unit lots the effective EOQ becomes 6,400

=

78.1 orders per year

(d-b)

500 ,000 6,400

(d-c)

4 x 500,000 + 5,000 50

=

40,000 + 5,000

=

45,000 units

6,325

(d-d) Yes, as carrying costs rise the EOQ level drops and the number of orders per year rises which means that on average less inventory will be kept on hand.

167

SOLUTION TO INTEGRATIVE PROBLEM Accounts Receivable 1.

2.

The size of the investment in accounts receivable is determined primarily by these factors: (a)

The percentage of credit sales to total sales. While this factor plays a major role in determining the investment in accounts receivable, it is generally not within the control of the financial manager. In essence, the nature of the business tends to determine the blend between credit sales and cash sales.

(b)

The level of sales. As sales increase, so will accounts receivable. Again, this is not an effective decision tool.

(c)

Credit and collection policies. Specifically the terms of sale, the quality of customer, and collection efforts are determinants of the level of investment in receivables that are under the control of the financial manager.

(a)

a x 1 −a

where a b c x 3.

(a)

4.

Step 1:

a x 1 −a

Step 2:

amount of the discount the discount period the net period

360 c −b

= = =

amount of the discount the discount period the net period

= 24.49% Estimate the Change in Profit. = = =

5.

= = =

= 18.18%

where a b c x

360 c −b

($1,000,000 x .25) - ($1,000,000 x .08) $250,000 - $80,000 $170,000

Estimate the cost of additional investment in account receivable and inventory. Estimate the additional investment in accounts receivable: = = =

($8,000,000 / 360) x 75 - ($7,000,000 / 360) x 60 $1,666,667 - $1,166,667 $500,000

168

Additional accounts receivable and inventory times the required rate of return: = = 6.

Step 3:

Estimate the change in the cost of the cash discount = = =

7.

Step 4:

($500,000 + $50,000) .15 $82,500 ($8,000,000 x .02 x .50) - ($7,000,000 x .01 x .50) $80,000 - $35,000 $45,000

Compare the incremental revenues with the incremental costs. = = =

Step 1 - (Step 2 + Step 3) $170,000 - ($82,500 + $45,000) $42,500

The policy should be adopted. Inventory Management 1.

EOQ

=

2SO C

=

2( 250 ,000 )100 1

= 2. 3.

4.

250 ,000 = 7,100

7,071 units or 7,100 units 35.2 orders per year

Inventory order point = Delivery time stock + safety stock

Average inventory

=

1 x 250,000 + 5,000 50

=

5,000 + 5,000

=

10,000 units

=

EOQ 2

+ Safety stock

=

7,100 2

+ 5,000

=

8,550 units

169

5.

EOQ

Elasticity of EOQ with respect to a double in sales

6.

EOQ

Elasticity of EOQ with respect to a double in carrying costs

7.

EOQ

Elasticity of EOQ with respect to a double in ordering costs

=

2(500 ,000 )100 1

=

10,000 units

=

% Δ EOQ % Δ Sales

=

Δ EOQ EOQ Δ Sales Sales

=

10 ,000 − 7,100   500 ,000 − 250 ,000    /   7,100 250 ,000    

=

.4085 1.0

=

= .4085 or 40.85%

2( 250 ,000 )100 2

=

5,000

=

% ∆ EOQ % ∆ Carrying Costs

=

5,000 − 7,100 7,100 2 −1 1

=

= -29.58%

2(250 ,000 )200 1

=

10,000

=

% ∆ EOQ % ∆ Ordering Costs

=

10 ,000 − 7,100 7,100 200 −100 100

170

= 40.85%

8.

The selling price of the item does not enter the EOQ equation and does not affect the level of EOQ. The EOQ equation attempts to minimize costs and as such the selling price does not enter into its calculation; thus the elasticity of EOQ with respect to the selling price is 0.

9.

The major assumptions of the EOQ model include: (1) (2) (3) (4) (5) (6)

Constant or uniform demand. Constant unit price regardless of amount ordered. Constant carrying costs per unit. Constant ordering costs per order regardless of the size of the order. Instantaneous delivery. Independent orders.

10.

Inflation affects the EOQ model by increasing carrying costs (C) which results in a small EOQ level. In addition if inflation is accompanied by major periodic price increases this may cause the EOQ model to lose its applicability and be replaced by a policy of anticipatory buying, that is, buying in anticipation of a price increase in order to secure the goods at a lower cost.

11.

A decrease in the average delivery time decreases the inventory order point. Inventory can be ordered when there is a lower level of inventory. Safety stock may also be reduced. The total level of inventory held will decrease in this situation.

12.

If ordering costs decrease, then it is more economical to order more often and the EOQ decreases. This in turn means that less inventory on average will be held.

Solutions to Problem Set B 20-1B.

a x 1 −a

360 c −b

where a b c 0.02 1 − 0.02

= = = x

amount of the discount the discount period the net period

360 60 −10

= 14.69%

171

a x 1 −a

20-2B.

360 c −b

where a b c x

amount of the discount the discount period the net period

= 36.73%

a x 1 −a

20-3B.

= = =

360 c −b

where a

=

amount of the discount

b

=

the discount period

c

=

the net period

(a)

0.01 360 x = 24.24% 1 −0.01 20 − 5

(b)

0.02 1 − 0.02

(c)

0.01 360 x = 4.55% 1 −0.01 100 − 20

(d)

0.04 1 − 0.04

(e)

0.05 360 x = 23.68% 1 −0.05 100 − 20

(f)

0.05 360 x = 94.74% 1 −0.05 50 − 30

x

x

360 = 10.50% 90 − 20

360 = 37.50% 50 −10

172

20-4B. Applicant #1 Z

=

3.3(0.3) + 1.0(0.4) + 0.6(1.2) + 1.4(0.3) + 1.2(0.5)

Z

=

0.99 + 0.4 + 0.72 + 0.42 + 0.6

Z

=

3.13 > 2.7 thus, accept

Z

=

3.3(0.2) + 1.0(0.6) + 0.6(1.3) + 1.4(0.4) + 1.2(0.3)

Z

=

0.66 + 0.6 + 0.78 + 0.56 + 0.36

Z

=

2.96 > 2.7 thus, accept

Z

=

3.3(0.2) + 1.0(0.7) + 0.6(0.6) + 1.4(0.3) + 1.2(0.2)

Z

=

0.66 + 0.7 + 0.36 + 0.42 + 0.24

Z

=

2.38 < 2.7 thus, reject

Z

=

3.3(0.1) + 1.0(0.5) + 0.6(1.8) + 1.4(0.5) + 1.2(0.4)

Z

=

0.33 + 0.5 + 1.08 + 0.7 + 0.48

Z

=

3.09 > 2.7 thus, accept

Z

=

3.3(0.5) + 1.0(0.7) + 0.6(0.5) + 1.4(0.4) + 1.2(0.6)

Z

=

1.65 + 0.7 + 0.30 + 0.56 + 0.72

Z

=

3.93 > 2.7 thus, accept

Z

=

3.3(0.2) + 1.0(0.4) + 0.6(0.2) + 1.4(0.4) + 1.2(0.4)

Z

=

0.66 + 0.4 + 0.12 + 0.56 + 0.48

Z

=

2.22 < 2.7 thus, reject

Applicant #2

Applicant #3

Applicant #4

Applicant #5

Applicant #6

173

20-5B. (a)

(b)

Sales − cost of goods sold Sales

=

Gross Profit Margin

$550,000 − Cost of goods sold $550,000

=

0.10

Cost of goods sold

=

$495,000

Cost of goods sold Average inventory

=

Inventory turnover ratio

$495,000 Average inventory

=

5

Average inventory

=

$99,000

Inventory turnover ratio

=

360 Average Collection

Inventory turnover

=

360 35

Inventory turnover ratio

=

10.286 times

Cost of goods sold Average inventory

=

10.286 times

$480,000 Average inventory

=

10.286 times

Average inventory

=

$46,665.37

=

Inventory turnover ratio

$1,250,000 Average inventory

=

6

Average inventory

=

$208,333

(c)

174

Period

(d)

20-6B. Step 1:

Step 2:

(1 - Gross profit margin) (Sales)

=

cost of goods

(0.85)($25,000,000)

=

$21,250,000

Inventory turnover ratio =

=

7.2 times

$21,250,00 0 Average inventory

=

7.2 times

Average inventory

=

$ 2,951,389

Estimate the Change in Profit. =

($1,000,000 x .20) - ($1,000,000 x .08)

=

$200,000 - $80,000

=

$120,000

Estimate the cost of additional investment in accounts receivable and inventory. Estimate the additional investment in accounts receivable: =

($7,000,000 / 360) x 90 - ($6,000,000 / 360) x 40

=

$1,750,000 - $666,667

=

$1,083,333

Additional accounts receivable and inventory times the required rate of return:

Step 3:

=

($1,083,333 + $40,000) .15

=

$168,500

Estimate the change in the cost of the cash discount =

Step 4:

$0 (no change)

Compare the incremental revenues with the incremental costs. =

Step 1

-

(Step 2 + Step 3)

=

$120,000 - $168,500

=

- $48,500

The policy should not be adopted.

175

20-7B. Step 1:

Estimate the Change in Profit.

Step 2:

=

($1,000,000 x .20) - ($1,000,000 x .08)

=

$200,000 - $80,000

=

$120,000

Estimate the cost of additional investment in accounts receivable and inventory. Estimate the additional investment in accounts receivable: =

($18,000,000 / 360) x 50 - ($17,000,000 / 360) x 30

=

$2,500,000 - $1,416,667

=

$1,083,333

Additional accounts receivable and inventory times the required rate of return:

Step 3:

=

($1,083,333 + $60,000) .15

=

$171,500

Estimate the change in the cost of the cash discount =

Step 4:

$0 (no change)

Compare the incremental revenues with the incremental costs. =

Step 1 - (Step 2 + Step 3)

=

$120,000 - $171,500

=

- $51,500

The change should not be made. 20-8B. (a)

Q*

=

2SO C

=

2(3500 )9 0.2

=

315 ,000

=

561.2 units

176

(b)

S Q  C +  Q  O 2  

Total costs

= 

Order one time:

=

 3500   3500    $.20 +   $9  2   3500 

=

$350 + $9

=

$359

=

 875   3500    $.20 +   $9  2   875 

=

$87.50 + $36

=

$123.50

=

 700   3500    $.20 +   $9  2   700 

=

$70.00 + $45.00

=

$115

=

 350   3500    $0.20 +   $9  2   350 

=

$35.00 + $90

=

$125

=

 234   3500    $0.20 +   $9  2   234 

=

$23.40 + $134.62

=

$158.02

Order four times:

Order five times:

Order ten times:

Order 15 times:

(c)

20-9B.

(1) (2) (3) (4) (5) (6)

constant or uniform demand constant unit price constant carrying costs constant ordering costs instantaneous delivery independent orders

(a)

Q* = =

2(21,000 )55 0.20

3,398.5 boxes

177

=

2SO C

(b)

It assumes among other things that the rolls are not perishable. assumptions include: (1) (2) (3) (4) (5) (6)

Other

constant or uniform demand constant unit price constant carrying costs constant ordering costs instantaneous delivery independent orders

20-10B. (a)

(b)

Q*

Total costs

=

2SO C

=

2(55 ,000 )500 70

=

886.40 units or 886 units

=

S  Q   C +  Q  O 2  

=

 886   55 ,000    $70 +   $500  2   886 

=

$31,010 + $31,038.37

=

$62,048.37

Note that carrying cost ($31,010) differs from ordering cost ($31,038.37) due to a $37 rounding error. 20-11B. (a)

Q*

=

2SO C

=

2(600 ,000 )90 .45

=

15,492 units or 15,400 units

=

38.96 orders per year (or about 39 orders)

(b)

600 ,000 15 ,400

(c)

Inventory order point

(d)

Average inventory

=

delivery time stock + safety stock

=

x 600,000 + 15,000

=

12,000 + 15,000

=

27,000 units EOQ + safety time stock 2

=

178

=

15 ,400 + 15,000 2

=

7,700 + 15,000

=

22,700 units

20-12B. (a)

EOQ

=

2SO C

=

2(500 ,000 )( 75 ) .45

=

12,909.90 units: but since orders must be placed in 200 unit lots, the effective EOQ becomes 13,000 units

(b)

500 ,000 13 ,000

=

38.5 orders per year

(c)

Inventory order point

=

Delivery time stock + safety stock

=

4 50

=

40,000 + 5,000

=

45,000 units

(d-a)

EOQ

= =

2(500 ,000 )( 75 ) 2.5

5,477 units, but since orders must be placed in 200 unit lots the effective EOQ becomes 5,400

(d-b)

500 ,000 = 5,400

(d-c)

4 x 500,000 + 5,000 50

(d-d)

x 500,000 + 5,000

93 orders per year

=

40,000 + 5,000

=

45,000 units

Yes. As carrying costs rise the EOQ level drops and the number of orders per year rises which means that on average less inventory will be kept on hand.

CHAPTER 21 179

Risk Management CHAPTER ORIENTATION The purpose of this chapter is to look at futures, options, and currency swaps and explain how they are used by financial managers to control risk.

CHAPTER OUTLINE I.

Futures and options can be used by the financial manager to reduce the risks associated with interest rates, and exchange rates, and commodity price fluctuations. A.

A futures contract is a contract to buy or sell a stated commodity (such as soybeans or corn) or a financial claim (such as U.S. Treasury bonds) at a specified price at some future specified time. 1.

2.

A futures contract is a specialized form of a forward contract distinguished by: (l) an organized exchange, (2) a standardized contract with limited price changes and margin requirements, (3) a formal clearinghouse and (4) daily resettlement of contracts. a.

An organized exchange provides a central trading place and encourages confidence in the futures market by allowing for effective regulation of trading.

b.

Standardized contracts lead to greater liquidity in the secondary market for that contract, which in turn draws more traders into the market.

c.

The futures clearinghouse serves to guarantee that all trades will be honored. This is done by having the clearinghouse interpose itself as the buyer to every seller and the seller to every buyer.

d.

Under the daily resettlement process, maintenance margins must be maintained.

For the financial manager financial futures provide an excellent way of controlling risk in interest rates, foreign exchange rates, and stock fluctuations.

180

B.

There are two basic types of options: puts and calls. A call option gives its owner the right to purchase a given number of shares of stock or some other asset at a specified price over a specified time period. A put gives its owner the right to sell a given number of shares of common stock or some other asset at a specified price over a given time period.

1.

The popularity of options can be explained by their leverage, financial insurance, and investment alternative expansion features.

2.

II.

a.

The leverage feature allows the financial manager the chance for unlimited capital gains with a very small investment.

b.

When a put with an exercise price equal to the current stock price is purchased, it insures the holder against any declines in the stock price over the life of the put. This is the financial insurance feature of options and can be used by portfolio managers to reduce risk exposure in portfolios.

c.

From the point of view of the investor, the use of puts, calls, and combinations of them can materially increase the set of possible investment alternatives available.

Recently, five new variations of the traditional option have appeared: the stock index option, the interest rate option, the foreign currency option, the Treasury bond futures option, and leaps. a.

Stock index options are merely options with the underlying asset being the value or price of an index of stocks -- for example, the S&P 100.

b.

Interest rate and foreign exchange currency options are also merely options with the underlying asset being the Treasury bonds or a specific foreign currency.

c.

Options on Treasury bond futures are different from other bond options in that they involve the acquisition of a futures position rather than the delivery of actual bonds. The buyer of an option on a futures contract achieves immunization against any unfavorable price movements, whereas the buyer of a futures contract achieves immunization against any price movements regardless of whether they are favorable or unfavorable.

Currency Swaps are another technique for controlling exchange rate risk available to the financial manager. Whereas options and futures contracts generally have a fairly short duration, a currency swap provides the financial manager with the ability to hedge away exchange rate risk over longer periods. It is for that reason that currency swaps have gained in popularity. A.

A currency swap is simply an exchange of debt obligations in different currencies. Interest rate swaps are used to provide long-term exchange rate

181

risk hedging. Actually, a currency swap can be quite simple, with two firms agreeing to pay each other's debt obligation. B.

The nice thing about a currency swap is that it allows the firm to engage in long-term exchange rate risk hedging since the debt obligation covers a relatively long time period.

C.

One of the more popular is the interest rate currency swap where the principal is not included in the swap. That is, only interest payment obligations in different currencies are swapped.

D.

The key to controlling risk is to get an accurate estimate on the net exposure level the firm is subjected to. Then, the firm must decide whether it feels it is prudent to subject itself to the risk associated with possible exchange rate fluctuations.

ANSWERS TO END-OF-CHAPTER QUESTIONS 21-1. Commodity and financial futures are the same other than the type of item specified in the contract, that is the item to be delivered. With a commodity future, the item to be delivered is an article of commerce such as soybeans, or wheat, while with a financial future the item to be delivered is a financial instrument such as a certificate of deposit or Eurodollars. 21-2. A manufacturer of electronic equipment might need copper in a few months and feel that the price of copper in the futures market is extremely low. As a result it might purchase a futures contract for delivery of copper in five months. If the price of copper goes up, the futures contract has saved the company money; however, if the price of copper drops, the futures contract does not allow the company to participate in the price drop. Thus, the futures contract eliminates the effect of any future price change. 21-3. A financial manager planning on issuing debt one month from now who was concerned about possible interest rate rises might wish to write a futures contract on Treasury bonds. If interest rates went up, the money made on the futures contract would offset the increase costs associated with having to issue the debt at a higher interest rate. On the other hand, if interest rates fell, the losses on the futures contracts would be offset by the gains associated with the fact that the debt could now be issued at a lower rate. In effect, the futures contract serves to lock in the current interest rate. 21-4. A call option is the option to buy stock or some other asset at a specified price over a specified time period. 21-5. A put is the option to sell a stock or some other asset at a specified price over a specified time period. 21-6. (a)

Standardization of the options contracts.

182

(b)

Creation of a regulated central marketplace.

(c)

Creation of the Options Clearinghouse Corporation.

183

(d)

Trading was made certificateless, allowing for up-to-date and continuous records of trader's positions.

(e)

The result of all this has been the creation of a liquid secondary market with dramatically decreased transactions costs.

21-7. An option on a futures contract is exactly what it sounds like. An example is an option on Treasury Bond futures. While the purchaser of a futures contract on Treasury bonds benefits from any decreases in interest rates, the purchaser is negatively affected by any increases in interest rates. With an option on Treasury Bond futures, the futures contract will only be exercised if the holder makes money. Thus, with a futures contract there is the potential for both favorable and unfavorable price movements, whereas with an option on a futures contract unfavorable price movements are limited to the cost of the option. 21-8. With either buying a call or writing a put the investor is "betting" that the stock price will rise. In the case of buying a call the purchaser has the right to purchase a given number of shares of stock at a set price. Thus, the purchaser only makes money if the stock rises in price, and the potential profits are unlimited. In the case of writing a put, the put writer receives a premium when he or she sells the put. Then if the stock price rises the put becomes worthless and the put writer profits by the amount of the premium. In this case the maximum potential profits are the premium. 21-9. A currency swap provides the financial manager with the ability to hedge away exchange rate risk over longer periods. It is for that reason that currency swaps have gained in popularity. A currency swap is simply an exchange of debt obligations in different currencies. Interest rate swaps are used to provide long-term exchange rate risk hedging.

184

ANSWERS TO END-OF-CHAPTER PROBLEMS 21-1A. (a)

Purchasing a call with an exercise price of $65 with a $9 premium. 20

Profit or Loss

15

Maximum Profits = Unlimited

10 5 0 -5

Breakeven Point = $74

10

20

30

40

50

60

70 75

Maximum loss = $9

-9

Exercise or Striking Price = $65

-10 Stock Price at Option Expiration (b)

Purchase a call with an exercise price of $70 with a $6 premium.

185

40 30 Maximum Profits = Unlimited

Pr ofit 20 or Lo 10 ss 0 -10

Breakeven Point = $76 10

} 20

30

40

50

Maximum loss = $6

-20

186

60

70

80 Exercise or Striking Price = $70

21-2A. (a)

Profit or loss graph for a call writer for a call with an exercise price of $65 and a premium of $9.

10

Breakeven Point (Exercise Price + Premium) = $74

}

Maximum Profits = $9

10

Profit or Loss

0 -10

20

30

40

50

60

70

80

Exercise or Striking Price = $65

-20

Maximum Loss = $ Unlimited

-30 -40

(b)

Profit or loss graph for a call writer for a call with an exercise price of $70 and a premium of $6. Breakeven Point (Exercise Price + Premium) = $76

10

Profit or Loss

0 -10

}Maximum Profits = $6 10

20

30

40

50

60

Exercise or Striking Price = $70

-20 -30 -40 -50

187

70

80

Maximum Loss = $ Unlimited

21-3A.

A Profit or loss graph for the purchase of a put with an exercise price of $45 and a premium of $5. 60 Maximum Profits = $40

Profit or Loss

50 40 30

Breakeven Point (Exercise Price Premium) = $40

20

-

10 MaximumLoss = $5 0 -10

}

Exercise or Striking Price = $45

-

A Profit or loss graph for writing a put with an exercise price of $45 and a premium of $5. 10 0

Exercise or Striking Price = $45

} 10

20

30

Profit or Loss

21-4A.

10 20 30 40 50 60 70 80 90

-10

40

50

60

80

Breakeven Point (Exercise Price Premium) = $40

-20 -30 -40

70

Maximum Loss = $40

-50 -60

188

90 Maximum Profits = $5

Solutions to Chapter Problems 21-1B. (a)

Purchasing a call with an exercise price of $50 with a $5 premium. 20

Profit or Loss

15

Maximum Profits = Unlimited

10

Breakeven Point = $55

5 0

-5

10

}

20

30

40

50

60

70

80

Exercise or Striking Price = $50

Maximum loss = $5 -10 Stock Price at Option Expiration (b)

Purchase a call with an exercise price of $55 with a $6 premium. 40 Maximum Profits = Unlimited

Profit or Loss

30 20

Breakeven Point = $61

10 0

-10

10

} 20

30

40

50

Maximum loss = $6

-20

189

60

70

80 Exercise or Striking Price = $55

190

21-2B. (a)

Profit or loss graph for a call writer for a call with an exercise price of $50 and a premium of $5. Breakeven Point (Exercise Price + Premium) = $55

10

} Maximum Profits = $5 10

Profit or Loss

0 -10

20

30

40

50

60

70

80

Exercise or Striking Price = $50

-20

Maximum Loss = $ Unlimited

-30 -40

(b) Profit or loss graph for a call writer for a call with an exercise price of $55 and a premium of $6. 10

Profit or Loss

0 -10 -20 -30

Breakeven Point (Exercise Price + Premium) = $61

}Maximum Profits = $6 10

20

30

40

50

60

Exercise or Striking Price = $55 Maximum loss = $ Unlimited

-40 -50

191

70

80

21-3B.

A Profit or loss graph for the purchase of a put with an exercise price of $60 and a premium of $4. 60 Maximum Profits = $56

Profit or Loss

50 40 30 20

Breakeven Point (Exercise Price – Premium) = $56

10

Maximum loss = $4

0 -10 -

20

30

40

50

60

}70

80

90

Exercise or Striking Price = $60

A Profit or loss graph for writing a put with an exercise price of $60 and a premium of $4. 10 0

Profit or Loss

21-4B.

10

Exercise or Striking Price = $60

10

20

30

40

50

60

70

}

80

-10 -20

Breakeven Point (Exercise Price – Premium) = $56

-30 -40 -50

Maximum Loss = $56

-60

192

90 Maximum Profits = $4

SOLUTION TO INTEGRATIVE PROBLEM 1.

Derivative securities allow the financial manager to eliminate the effects of interest rate, foreign exchange, and commodity price fluctuations. For example, a manufacturer of electronic equipment might need copper in a few months and feel that the price of copper in the futures market is extremely low. As a result it might purchase a futures contract for delivery of copper in five months. If the price of copper goes up, the futures contract has saved the company money; however, if the price of copper drops, the futures contract does not allow the company to participate in the price drop. Thus, the futures contract eliminates the effect of any future price change.

2.

Interest rate futures can be used to eliminate the effects of interest rate movements. For example, a financial manager planning on issuing debt one month from now who was concerned about possible interest rate rises might wish to write a futures contract on Treasury bonds. If interest rates went up, the money made on the futures contract would offset the increased costs associated with having to issue the debt at a higher interest rate. On the other hand, if interest rates fell, the losses on the futures contracts would be offset by the gains associated with the fact that the debt could now be issued at a lower rate. In effect, the futures contract serves to lock in a future interest rate. In a similar manner foreign exchange futures can be used to lock in exchange rates while stock index futures can be used to lock in stock prices.

3.

Foreign currency options can be used to lock in the exchange rate on a foreign exchange rate like the British Pound or the Japanese Yen. Currency swaps can also be used to control exchange rate risk over longer periods of time.

4.

With a futures contract, all exchange rate movements, both favorable and unfavorable are eliminated. With an option, it is only exercised if it is in the best interests of the option holder. In effect, the buyer of an option on a futures contract can achieve immunization against any unfavorable price movements, whereas the buyer of a futures contract can achieve immunization against any price movements regardless of whether they are favorable or unfavorable.

5.

An option on a futures contract is exactly what it sounds like. An example is an option on Treasury Bond futures. While the purchaser of a futures contract on Treasury bonds benefits from any decreases in interest rates, the purchaser is negatively affected by any increases in interest rates. With an option on Treasury Bond futures, the futures contract will only be exercised if the holder makes money. Thus, with a futures contract there is the potential for both favorable and unfavorable price movements, whereas with an option on a futures contract unfavorable price movements are limited to the cost of the option.

193

6.

Purchasing a call with an exercise price of $25 with a $6 premium. 20 Maximum Profits = Unlimited

Profit or Loss

15 10 5 0

Breakeven Point = $31

10

20

30

40

50

60

70 75

Maximum Loss = $6

-5

Exercise or Striking Price = $25

-6 -10

Stock Price at Option Expiration

Profit or loss graph for a call writer for a call with an exercise price of $25 and a premium of $6.

10 6 0

Profit or Loss

7.

Breakeven Point (Exercise Price + Premium) = $31

Maximum Profits = $6

} 10

20

30

40

-10 -20 -30 -40

Exercise or Striking Price = $25

Maximum Loss = $ Unlimited

194

50

60

70

80

8.

A Profit or loss graph for the purchase of a put with an exercise price of $30 and a premium of $5. 60 50

Profit or Loss

Maximum Profits = $25

40 30 20

Breakeven Point (Exercise Price – Premium) = $25

10 0 -

10

20

30

50

60

} 70

80

90

Exercise or Striking Price = $30

-10 -

A Profit or loss graph for writing a put with an exercise price of $30 and a premium of $5. 10 0

Profit or Loss

9.

40

Maximum Loss = $5

-10 -20

Exercise or Striking Price = $30

} 10

20

30

40

50

60

70

80

90

Maximum Profits = $5 Breakeven Point (Exercise Price – Premium) = $25

-30 Maximum Loss = $25 -40 -50 -60

195

10.

A currency swap provides the financial manager with the ability to hedge away exchange rate risk over longer periods. It is for that reason that currency swaps have gained in popularity. A currency swap is simply an exchange of debt obligations in different currencies. Interest rate swaps are used to provide long-term exchange rate risk hedging. If I am an American firm with much of my income coming from sales in England, I might enter in a currency swap with an English firm. The nice thing about a currency swap is that it allows the firm to engage in long-term exchange rate risk hedging since the debt obligation covers a relatively long time period.

196

Appendix to Chapter 21

Convertible Securities and Warrants APPENDIX ORIENTATION The purpose of this appendix is to explain the use of convertibles and warrants and to describe the terminology associated with them and their valuation.

CHAPTER OUTLINE I.

A convertible security is a bond or preferred stock that can be exchanged for a stated number of common shares at the option of the holder. A.

The conversion ratio is the stated number of shares that the security can be converted into.

B.

The conversion price is the face or par value of the security divided by the conversion ratio.

C.

The conversion value equals the conversion ratio times the market price of the stock when one converts.

D.

The security value of a convertible is the price the convertible debenture (or preferred stock) would sell for in the absence of its conversion feature.

E.

The conversion premium is the difference between the market price of the convertible and the higher of the security value or the conversion value.

F.

There are several reasons generally given for issuing convertibles: 1.

As a sweetening to long-term debt to make the security attractive enough to ensure a market for it

2.

As a method of delayed common stock financing a.

No dilution of earnings occurs at time of issuance.

b.

Companies expect them to be converted sometime in the future.

197

c.

3. G.

H

Less dilution of earnings occurs in the future because the conversion price is greater than the common stock price at time of issuance.

The interest rate associated with convertible debt is, to an extent, indifferent to the risk level of the issuing firm.

There are two ways in which a company can stimulate conversion: 1.

Include an acceleration clause, which periodically increases the conversion price and results in a lower conversion ratio over time.

2.

Force conversion by calling the convertible.

The value of the convertible security is twofold. 1.

The value of the common stock into which it can be converted is the first component.

2.

The value of the bond or preferred stock provides a cushion or a floor value in case the stock price does not rise significantly (Provided interest rates do not increase). security value =

where I = i= N=

$I

N

∑

t =1

(1 +i)

t

+

$M (1 + i) N

annual dollar interest paid to the investor each year market yield to maturity on straight bond of same company and with same seniority & maturity number of years to maturity

M = maturity value or par value of the debt

II.

I.

The market price of a convertible security is frequently above the higher of security value and conversion value; this difference is called the premium.

J.

Unless the conversion feature is considered worthless, the security will sell for a premium-over-security value (i.e., above the value of the security solely as a bond or preferred stock).

K.

In comparing the two premiums, one finds an inverse relationship between them. In the extremes, the convertible security is selling either as a common stock or a bond equivalent.

Warrants are a "sweetener" added to a bond or debt issue. Warrants entitle the holder to purchase a specified number of shares of stock at a stated price. A.

The exercise price can be either fixed or "stepped up" over time.

B.

A warrant usually has a fixed expiration date.

C.

A detachable warrant can be sold separately in the marketplace.

D.

A nondetachable warrant can only be exercised by the bondholder and cannot be sold on its own.

198

E.

Warrants are issued for two major reasons: 1.

Warrants are attached to debt issues as sweeteners to increase the marketability of these issues.

2.

Warrants provide an additional cash inflow when they are exercised. Convertible securities do not.

F.

The minimum price of a warrant is equal to the price of the common stock less the exercise price times the exercise ratio.

G.

The premium on a warrant is the amount above the minimum price for which the warrant sells.

ANSWERS TO END-OF-CHAPTER QUESTIONS 21A-1. (a)

The conversion ratio is the number of shares of common stock for which the convertible security can be exchanged.

(b)

The conversion value of a convertible security is the market value of the common stock for which the convertible can be exchanged.

(c)

The conversion premium is the difference between the convertible's market price and the higher of its security value or its conversion value.

21A-2. The major reason for issuing convertibles is, that interest rates on convertibles are indifferent to the issuing firm’s risks level. Several reasons why firms choose to issue convertibles include "sweetening" the long-term debt issue to make it more attractive, delayed equity financing, raising temporarily inexpensive funds, and financing corporate mergers. 21A-3. Investors are willing to pay a premium over value in order to have the possibility of capital gains from stock price advances, coupled with the security of the fixed interest payments associated with a debenture. 21A-4. If the price of the underlying common stock goes up, the convertible will be valued as common stock, while if the price of the underlying common stock goes down, the convertible will be valued as a bond and not fall accordingly. Graphically this is illustrated in Figure 21A.1. If interest rates rise, the security value will fall, lowering the bond floor on the convertible. On the other hand, if interest rates fall, the security value will rise, increasing the value of the convertible as a bond. 21A-5. If the convertible is never exercised, then the cost of the convertible will be lower than nonconvertible debt. If the convertible is converted, its cost becomes interest payments while it was not converted and dividends after it is. In this case, the cost of the convertible depends upon the conversion ratio, the common stock dividends, and the time at which the security is converted. In any case, while the cost of convertibles many times is less than the nonconvertible debt, the limitations it imposes on the firm's financing flexibility must also be considered. Thus, the issuance of convertibles involves a trade-off between cost and future financing flexibility. 199

21A-6. A convertible security is a debenture or preferred stock that can be converted into common stock at the owner's discretion. A warrant, on the other hand, is similar to a long-term right, in that it is merely an option to purchase common stock at a stated price. When a convertible is exercised, it is exchanged directly for common stock; however, with a warrant, both money and the warrant are exchanged for the common stock. 21A-7. The minimum price of a warrant is equal to zero until the price of the stock rises above the warrant's exercise price. After that, the warrant's minimum price takes on positive values. The degree to which the warrant price rises with increases in the common stock price depends upon the exercise ratio. In addition, investors are willing to pay a premium for warrants because only a small loss is possible, in that the warrant price is less than that of the common stock and has large return possibilities. 21A-8. Several factors affect the size of the warrant premium including: (1)

The stock price/exercise price-ratio. As the ratio of the stock price to the exercise price climbs, the warrant premium falls, because the leverage ability of the warrant declines.

(2)

The time left to the warrant expiration date. As the expiration date approaches the size of the warrant premium shrinks.

(3)

Investors' expectations concerning the capital gains potential of the stock. If investors feel favorably about the stock, the warrant premium is larger.

(4)

The degree of price volatility on the underlying common stock. The more volatile the common stock, the higher the warrant premium.

SOLUTIONS TO END-OF-APPENDIX PROBLEMS Solutions To Set A 21A-1A. (a)

Conversion ratio

=

Par value of convertibl e security conversion price

=

$1,000 $40

=

25 shares

200

(b)

Conversion value

(c)

(d)

=

 Market value    (Conversion ratio) x  pershare of the   common stock 

=

25 shares x $27.25/share

=

$681.25

=

Conversion premium in absolute dollars

$60

20

∑

t =1

(1 +0.09)

t

+

$1,000 (1 + 0.09)

20

=

$60 (9.129) + $1,000(0.178)

=

$547.74 + $178

=

$725.74

=

 Market price of   Higher of the   the convertible   security value and      bond    conversion value 

=

$840.25 - $725.74

=

$114.51

=

Par value of convertibl e security conversion price

21A-2A. (a)

(b)

Conversion ratio

Conversion value

=

$25 $27

=

0.9259

=

 Market value  (Conversion ratio) x  per share of the   common stock 

=

(0.9259) x ($13.25)

=

$12.27

201

(c)

Value as straight preferred stock = Conversion premium (in absolute dollars)

$1.25 0.08

=

$15.63

 Market price of   the convertible   preferred stock   

=

 Higher of the security   value and conversion    value   =

$17.75 - $15.63

=

$2.12

=

 Market price of − Exercise   Exercise   common stock  x  ratio  price    

=

($25 - $30) x 1.0

=

-$5

21A-3A. (a)

Minimum price

Thus, the minimum price on this warrant is considered to be zero, because things simply do not sell for negative prices. (b)

Warrant premium

=

Market price of warrant - Minimum price of warrant

=

$4 - $0

=

$4

21A-4A. (a)

Minimum price

=

 Market price of − Exercise   Exercise   common stock  x  ratio  price    

=

($10.00 - 11.71) x 1.0

=

-$1.71

Thus, the minimum price on this warrant is considered to be zero, because things simply do not sell for negative prices. Warrant premium warrant

=

Market price of warrant - Minimum price of

202

(b)

Minimum price

=

$3 - 0

=

$3

=

 Market price of − Exercise   common stock price  x 

 Exercise   ratio 

Warrant premium

=

($16.375 - $11.71) x 1.0

=

$4.665

=

 Market price - Minimum price   of warrant of warrant  

=

$9.75 - $4.665

=

$5.085

=

 Market price of − Exercise   Exercise   common stock price  x  ratio  

=

($7.25 - $22.94) x 3.1827

=

(-$15.69) (3.1827)

=

-$49.94

21A-5A. Minimum price

Thus, the minimum price on this warrant is considered zero, because things simply do not sell for negative prices. Warrant premium

21A-6A.

=

 Market price − Minimum price   of warrant  of warrant  

=

$6.25 - 0

=

$6.25

The gain on the warrants is 100($7.50-$3.00)

=

$450 for a return of

$450 300

=

150%

If $300 had been invested in stock, 7.5 shares could have been purchased and those shares would have risen in price by $5 per share for a return of $37.50 or 12.50%.

203

204

Solutions to Problem Set B 21A-1B. (a)

(b)

(c)

(d)

Conversion ratio

Conversion value

Security Value

=

Par value of convertibl e security conversion price

=

$1,000 $45

=

22.22 shares

=

 Market value    (Conversion ratio) x  per share of the   common stock 

=

22.22 shares x $26.00/share

=

$577.72

=

$70

20

∑

t =1

(1 +0.09)

t

+

$1,000 (1 + 0.09 ) 20

=

$70 (9.129) + $1,000(0.178)

=

$639.03 + $178

=

$817.03

Conversion premium in absolute dollars

 Market price of   the convertible   bond  

=

 Higher of the   security value and     conversion value  =

$840.25 - $817.03

=

$23.22

=

Par value of convertibl e security conversion price

=

$25 $28

=

0.8929

21A-2B. (a)

Conversion ratio

205

(b)

(c)

Conversion value

=

 Market value    (Conversion ratio) x  per share of the   common stock 

=

(0.8929) x ($14.00)

=

$12.50

Value as straight preferred stock = = Conversion premium (in absolute dollars)

$18.75

 Market price of   the convertible   preferred stock   

=

 Higher of the security   value and conversion    value   =

$20.00 - $18.75

=

$1.25

=

 Market price of − Exercise   common stock price  x 

=

($24 - $32) x 1.0

=

-$8

21A-3B. (a)

Minimum price

 Exercise   ratio 

Thus, the minimum price on this warrant is considered to be zero, because things simply do not sell for negative prices. (b)

Warrant premium

=

 Market price − Minimum price   of warrant  of warrant  

=

$5 - $0

=

$5

206

21A-4B. (a)

Minimum price

=

 Market price of − Exercise   Exercise   common stock price  x  ratio  

=

($9.00 - 11.75) x 1.0

=

-$2.75

The minimum price on this warrant is considered to be zero, because things simply do not sell for negative prices. Warrant premium

Minimum price

Warrant premium

=

 Market price Minimum price  −   of waranet  of warrant 

=

($4.00 - 0)

=

$4.00

=

Market price of common stock

=

($15.375 - $11.75) × 1.0

=

$3.625

=

 Market price Minimum price  −   of waranet  of warrant 

=

($7.00 - $3.625)

=

$3.375

−

Exercise price

21A-5B Minimum price Minimum price

=

 Market price of Exercise  Exercise      common stock − price ×  ratio   

=

($8.00 - $22.94)

=

$63.60

The minimum price on this warrant is considered to be zero because things simply do not sell for negative prices. Warrant premium

=

 Marketpric e − Minimumpri ce   ofwarrant ofwarrant  

207

=

($6.75 – 0)

=

$6.75

=

$400 for a return of

21A-6B. The gain on the warrants is 100($6.75-$2.75)

$400 275

= 145.45%

If $275 had been invested in stock, 7.86 shares could have been purchased and those shares would have increased in value by $5 each for a gain of $39.30 or 14.29%.

CHAPTER 22 208

International Business Finance CHAPTER ORIENTATION This chapter introduces some of the financial techniques and strategies necessary to the efficient operations of an international business. Problems inherent to these firms include multiple currencies, differing legal and political environments, differing economic and capital markets, and internal control problems. The difficulties arising from multiple currencies are stressed here, including the dimensions of foreign exchange risk and strategies for reducing this risk. We also cover multinational working capital management and direct foreign investment for international firms.

CHAPTER OUTLINE I.

The globalization of product and financial markets A.

World trade has grown faster over the last few decades than has aggregate world GNP.

B.

In less-developed countries, long-run overseas investments of the United States' companies have yielded high returns.

C.

Many American multinational corporations (MNC) have significant assets, sales, and profits attributable to foreign investments.

D.

Many foreign MNCs have significant operations in the United States.

E.

Many firms, investment companies, and individuals invest in the capital markets of foreign companies to receive

F.

1.

Higher returns than those available in domestic capital markets

2.

Reduced portfolio risk through international diversification

Companies are increasingly turning to the Eurodollar market to raise funds.

209

II.

Exchange rates A.

B.

C.

Recent history of exchange rates 1.

Exchange rates between the major currencies were fixed from 1949 and 1970.

2.

Countries were required to set a parity rate with the U.S. dollar, around which the daily exchange rate could narrowly fluctuate.

3.

In order to effect a major adjustment, a currency either had to undergo a devaluation (reducing the cost relative to the dollar) or an upvaluation/revaluation (increasing the cost relative to the U.S. dollar).

4.

Since 1973, a floating rate international currency system has operated, wherein the currencies are allowed to fluctuate freely.

5.

Two major types of transactions now occur in the foreign exchange markets: spot and forward transactions.

The Euro 1.

Beginning January 1, 1999, 11 countries in the European Union introduced a single currency, the Euro.

2.

This should make it easier for goods and services to cross borders, and, as a result, economies should flourish.

3.

It also eliminates the uncertainty associated with currency fluctuations.

4.

For the United States, it also means that competition should be stronger.

Spot exchange rates 1.

The rate at which one currency can be immediately exchanged for another currency

2.

Direct quote expresses the exchange rate in the units of home currency required to buy one unit of foreign currency. For example, 1.4845 U.S. dollars per pound.

3.

Indirect quotes indicate the number of foreign currency units needed to purchase one unit of home currency. For example, .6691 pounds per U.S. dollar. EXAMPLE Using the rates listed above, how many dollars would a U.S. manufacturer pay for a part costing 250 pounds? 250 (pounds) x 1.4845 ($/pound) = $371.13

210

4.

The direct and indirect quotes should have a reciprocal relationship. In formula 1

Direct Quote = Indirect Quote or 1

Indirect Quote = Direct Quote

D.

5.

When these quotes are not equal, arbitrage will occur, where a trader (or arbitrager) makes a riskless profit, by exchanging currency in two markets.

6.

The asked rate is the rate which the bank or foreign exchange trader "asks" the buyer to pay for the foreign currency.

7.

The bid rate is the rate which the bank or foreign exchange trader buys the foreign currency from the customer.

8.

The spread is the difference in the bid and the asked rates.

9.

The narrower the spread, the greater is the efficiency in the spot exchange market.

10.

A cross rate is the result of an indirect computation of one currency's exchange rate from the exchange rate of two other currencies. For example, the calculation of marks per pound from U.S. dollars per pound and marks per U.S. dollars.

11.

Triangular arbitrage will occur when the cross rates calculated are not equal to the exchange rates offered.

Forward exchange rates 1.

A forward exchange rate specifies today the rate at which currencies will be exchanged at in the future, usually 30, 90, or 180 days from today.

2.

Rates are quoted in both the direct and indirect form.

3.

Forward rates are often quoted at a premium or a discount to the existing spot rate. This is also referred to as the forward-spot differential.

4.

These differentials may be stated either in absolute terms or as an annualized percent premium or discount.

5.

The use of forward contracts allows for risk reduction in that future cash outlays are known with certainty.

211

III.

The interest parity theory A.

Theorem states that the forward premium or discount should be equal and opposite in sign to the difference in the national interest rates for securities of the same maturity (except for the effects of small transaction costs). Notationally, this is expressed as P(or D)

=

- =

where P(or D)

=

the percent-per-annum premium or discount on the forward rate

If

=

the annual interest rate on a foreign instrument having the same maturity as the forward contract

Id

=

the annualized interest rate on a domestic instrument having the same maturity as the forward contract

EXAMPLE The premium (P) on 30-day forward mark contracts is 4.368 percent. If the 30-day T-Bill is yielding 10 percent, what must the 30-day German instrument yield?

B

IV.

P

=

.04368

=

If

=

If − I d 1 + If I f − .10 1 + If

.1502 or 15.02%

If the forward differentials are not those predicted by the interest parity theorem, then covered interest arbitrage can occur and be profitable at no risk.

Purchasing power parity A.

According to purchasing power parity, exchange rates will adjust over time so that the currencies of different countries will have the same purchasing power. The exchange rates will adjust to cover the inflation rate differential between the two countries.

212

B.

Purchasing power parity can be demonstrated by the equation St + 1

=

St (l + Pd) / (l + Pf ) n

=

S t ( 1 + P d - P f )n

=

units of domestic currency per unit of the foreign

where St

currency at time t Pf

=

the foreign inflation rate

Pd

=

the domestic inflation rate

n

=

the number of time periods

EXAMPLE The inflation rate in Great Britain is 6% and in the United States it is 10%. The current spot rate of the pound is $2.00. According to purchasing power parity, what will be the expected value of the pound at the end of the year? S

C.

=

$2.00 (1 + .10 + -.06)1

=

$2.00 (l.04)1

=

$2.08

The law of one price The law of one price underlies purchasing power parity. This law suggests that where there are no transportation costs or barriers to trade, the same good sold in different countries should sell for the same price if all the different prices are expressed in terms of the same currency.

D.

International Fisher effect 1.

According to the Fisher effect, interest rates reflect not only the real rate of return but the expected inflation rate.

2.

The Fisher effect can be expressed as I

=

P + Ir + (P) (Ir)

I

=

the nominal interest rate

Ir

=

the real rate of return

P

=

the expected inflation rate

where

213

IV.

3.

The international Fisher effect suggests that the exchange rate adjusts to cover the interest rate differential between two countries.

4.

This theory suggests that in efficient markets, with rational expectations, the forward rate is an unbiased forecast of the future spot rate.

Exchange Rate Risk A.

Risk arises from not knowing the value of the future spot rate today.

B.

Types of exchange risk

C.

D.

1.

Risk in international trade contracts—when an agreement exists to purchase some good at a future date in foreign currency, uncertainty exists as to the future cash outlay.

2.

Risk in foreign portfolios - because of exchange rate fluctuations in foreign securities the returns are more variable and thus more risky than investment in domestic securities.

3.

Risk in direct foreign investment (DFI)—the balance sheet and income statement are denominated in foreign currency. Thus, for the parent company, risk arises from both the fluctuations in the asset's value and the profit streams.

Exposure to exchange rate risk 1.

Transaction exposure refers to the net total foreign currency transactions whose monetary value was fixed at a time different from when the transactions are actually completed. Examples of transactions exposed to this kind of risk are receivables, payables, and fixed price sales or purchase contracts. Fluctuations in exchange rates can affect the value of these assets and liabilities.

2.

Translation exposure is actually a paper gain or loss. Translation exposure refers to gains or losses caused by the translation of foreign currency assets and liabilities into the currency of the parent company for accounting purposes.

3.

Economic exposure refers to the extent to which the economic value of a company can decline due to exchange rate changes. It is the overall impact of exchange rate changes on the value of the firm. A decline in value can be attributed to an exchange rate induced decline in the level of expected cash flows and/or by an increase in the riskiness of these cash flows.

Hedging strategies 1.

The standard procedure to hedge is to match the amount and the duration of the asset (liability) position.

2.

The money market hedge offsets the exposed position in a foreign currency by borrowing or lending in the foreign and domestic money markets. This may be costly for small or infrequent users. 214

V.

3.

The forward market hedge matches the asset (liability) position with an offsetting forward contract of equal value and maturity. Generally, this is less costly than the money market hedge.

4.

Foreign currency futures contracts and foreign currency options are two relatively new instruments used for hedging. Futures contracts are similar to forward contracts in that they provide a fixed price for the required delivery of foreign currency. Options, on the other hand, permit a fixed price anytime before their expiration date. Options and futures both differ from forward contracts in that they are traded in standardized amounts with standardized maturity dates and are traded through organized exchanges and individual dealers. The difference between the futures contract and the currency option is that the option requires delivery only if it is exercised. The option can be exercised any time before its maturity date; this can provide additional flexibility for a company.

Multinational working capital management A.

The MNC must be careful to make decisions concerning working capital management that are optimal for the corporation as a whole and not just the best for the individual entities.

B.

Leading and lagging are important risk reduction techniques for a MNC's working capital management. 1.

2.

C.

When holding an asset in a: a.

Strong (appreciating) currency, we should lag (delay) conversion to the domestic currency.

b.

Weak (depreciating) currency, we should lead (expedite) conversion to the domestic currency.

When holding a liability in a: a.

Strong currency, we should lead (expedite) payment of the liability.

b.

Weak currency, we should lag (delay) payment of the liability.

Cash management 1.

A MNC may wish to position funds in a specific subsidiary in another country such that the foreign exchange exposure and the tax liability of the MNC are minimized as a whole. This strategy may not, however, be the optimal strategy for the specific subsidiary.

2.

The transfer of funds is effected by royalties, fees, and transferpricing. The transfer price is the price charged for goods or services transferred from a subsidiary or parent company to another subsidiary.

215

VI.

International Financing Decisions A.

A multinational corporation (MNC) may have a lower cost of capital than a domestic firm due to its ability to tap a larger number of financial markets. 1.

A multinational company has access to financing sources in the countries in which it operates.

2.

VII.

Host countries often provide access to low-cost subsidized financing to attract foreign investment. 3. A MNC may enjoy preferential credit treatment due to its size and investor preference for its home currency. 4. A MNC may be able to access third country capital markets. 5. A MNC has access to external currency markets variously known as Eurodollar, Eurocurrency, or Asian dollar markets. These markets are unregulated and because of their lower spread, can offer attractive rates for financing and investment. B. To increase their visibility in foreign capital markets, MNCs are increasingly listing their stocks in the foreign capital markets. C. A MNC's capital structure should reflect its wider access to financial markets, the ability to diversify economic and political risks, and several of its other advantages over domestic firms. Direct foreign investment A. Risk in international capital budgeting 1. Political risk arises from operating a business in a different and possibly less stable business climate than the United States. 2. Exchange risk incorporates changes in the future earnings stream because of currency fluctuations, possibly in both foreign and domestic currencies. 3. Business risk is affected by the response of business and the MNC to economic conditions within the foreign country. 4. Financial risk arises from the financial structure of the firm and its effect on the profit stream. B. Cash flows must be estimated considering the potential effects of exchange rate changes, governmental policy, and other items that determine product demand and sales. C. A foreign investment can be evaluated from either a parent or a local firm perspective. If a firm uses a local perspective the initial investment and all of its cash flows should be discounted at a rate that reflects the local inflation rate and the riskiness of the project. When using the parent company perspective, the discount rate should reflect the expected inflation rate in the parent currency and foreign currency cash flows should be converted to the parent currency cash flows using projected exchange rates.

216

D.

VIII

The net present value (NPV) must be calculated using the above factors. 1. If NPV is greater than zero, generally accept direct foreign investments. 2. If NPV is less than zero, the MNC may decide to a. Reject direct foreign investment. b. Establish a sales office in the foreign country. c. License a local company to manufacture the product, where the MNC receives royalty payments. How financial managers use this material.

IX.

Summary.

ANSWERS TO END-OF-CHAPTER QUESTIONS 22-1. The additional factors that must be considered in international finance relate to: multiple currencies, different legal requirements, institutional restrictions, and internal control problems. These issues are discussed in the introduction to the chapter. 22-2. The different types of businesses that operate in the international environment are: one time (or occasional) exporters and importers, exporters and importers that do business (continually) with one foreign country, exporters and importers that conduct business in many countries, companies that have a production plant or subsidiary abroad and multinational corporations with many subsidiaries in different countries. The techniques and strategies open to these firms differ mainly due to the differing exposure to risk. Firms with plants abroad are subject to political risk of expropriation. Firms doing import or export business do not have much risk of expropriation. The ideas of exchange risk apply to all these firms. The relevant measures of exchange risk differ between businesses due to the amount of foreign exchange diversification that they have. 22-3. Arbitrage profits are the riskless profits made without investing funds. These profits are generated when certain assets are not priced according to an equilibrium relationship. For example, arbitrage profits are possible in the spot and forward exchange markets if the indirect quote or cross quote relationships are out of line. The respective arbitrage processes are called simple and triangular arbitrage. Arbitrage opportunities exist if the money market rates differ from the forward market rates. This is referred to as: Covered Interest Arbitrage. 22-4.(a)

Simple Arbitrage is possible when the quoted rates in a foreign market for a single currency are not the inverse of the rates quoted in the home market. For example, the dollar quote in Frankfurt should be the inverse of the DM quote in New York. Otherwise, arbitrage opportunities would prevail. See Problem 22-5 and its solution in this regard. Simple arbitrage is also possible

217

in the forward quotes. (b)

Triangular Arbitrage is possible when the cross rate is out of line. For example, if the pound rate in Frankfurt (quoted as DM/pound) is different  DM   $   x   rate, then an arbitrageur could sell and buy  $   Pound 

from the 

different currencies in Frankfurt, London, and New York to turn an arbitrage profit. 22-5. Purchasing power parity suggests that exchange rates will adjust so that each currency will have the same purchasing power. Differences in forward and spot rates are explained by differences in inflation rates between two countries. Interest-rate parity theory suggests that current spot rates and forward rates differ because of an interest-rate differential between two countries. The Fisher effect contends that the nominal interest rate is a function of the real rate of interest and an expected inflation rate. Thus, spot and forward rates between countries will differ depending on the inflation rate and the real rate of return in those countries. 22-6. (a)

Exchange Risk: Refers to the change in value of a profit stream or the economic value of an asset due to changes in the exchange rate.

(b)

Political Risk: Refers to the risks associated with direct foreign investment due to changes in political climate or structure in the foreign country. These risks are due to expropriation, lack of compensation or other unanticipated governmental controls that are imposed on the multinational corporation.

22-7. The proper measurement of exchange risk involves the measurement of economic exposure. This is difficult to measure. However, the net asset (liability) exposure in a currency measures the exchange risk (at least, of short-term assets) quite well. 22-8. Exposure to foreign currency losses is often placed into three categories as follows: (a)

Transaction Exposure: This is the net total of foreign currency transactions whose monetary value was fixed at a time different from when the given transactions were actually completed. Accounts receivable and payable are typical examples of such transactions.

(b)

Translation Exposure: This is the net total of exposed assets less exposed liabilities. The asset or liability is exposed in this sense if the foreign currency value is to be translated (i.e., altered) into the parent company currency using the exchange rate in effect on the balance sheet date. This is primarily a bookkeeping exercise with no impact on taxable income.

(c)

Economic Exposure: This is the extent to which the economic value of a company can decline because of exchange rate fluctuations.

For practical purposes it is fair to say that these risks can be managed, but they should not be reduced to zero. For example, economic exposure could only be reduced to zero by doing business in the domestic country and, thereby, giving up the potential benefits of operating in the foreign environment.

218

22-9. Short-term exchange risk can be covered by the money market or the forward market hedge. The hedge should be constructed so that the net asset (liability) position in a foreign currency is zero. In addition to the amount of hedge, the maturity of the hedge should also be matched. This ensures that the risk of foreign exchange exposure is eliminated. 22-10. The money market hedge is implemented by borrowing or lending in the home or the foreign money market against the foreign currency asset or liability position. In the forward market hedge a forward contract is bought or sold to exactly offset the foreign currency net asset or liability position. The hedges differ in the markets utilized for covering the exposed positions. The types of hedge may also differ in the costs of hedge. The money market hedge may be cheaper for the hedge on large amounts of exposure. 22-11. Since the forward market for the Indian Rupee does not exist, a trader can effect a hedge via the money markets in the U.S. and India. Other ways of covering an exposed position in rupees are by bilateral swap arrangements with other companies in India. 22-12. A forward exchange contract requires delivery, at a specified future date, of one currency for a specified amount of another currency. The exchange rate for the future transaction is agreed upon today. The physical transaction takes place at the future date. Futures contracts (like forward exchange contracts) provide fixed prices for the required delivery of a foreign currency at maturity. Options, on the other hand, permit fixed (strike) price foreign currency transactions anytime prior to maturity. Futures contracts and options are traded in standardized amounts with standardized maturity dates. These instruments are traded on organized security exchanges. The individual traders deal with the exchange-based clearing organization rather than the direct parties to the foreign currency transaction. Forward contracts are quite different. Typically they are written by banks and the firm deals directly with the banking institution rather than the organized security exchange. 22-13. Leading and lagging are two useful working capital management techniques. Leading and lagging techniques are useful because they reduce the exchange risk. Leading and lagging are not useful as hedging techniques, since exchange risk cannot be totally eliminated by these techniques. Leading and lagging techniques are profitable when the potential appreciation (depreciation) in the foreign currency is correctly anticipated.

219

22-14. The multinational corporation enjoys access to more financing sources than the domestic company. Specifically the MNC: a. May have access to low-cost subsidized financing provided by the host country. b. May enjoy preferential credit standards. c. May tap third-country capital markets. d. May tap the (1) Eurodollar, (2) Eurocurrency, or (3) Asian dollar markets. Probably the MNC operates at a lower cost of capital because of the financing flexibility available to it. 22-15. The risks associated with direct foreign investment are: business risk, financial risk, exchange risk, and political risk. The direct foreign investment has the additional factors of exchange and political risk compared to domestic investment. The exchange risk is due to the fact that the profit stream and the value of the subsidiary fluctuate due to changes in the exchange rate. The political risk arises from the fact that the political system and laws in many foreign countries are not as stable as in the U.S. 22-16. The direct foreign investment problem is a capital budgeting problem. All the relevant risks like business risk, financial risk, exchange risk and political risk are to be considered. The cash flow estimates should take into account the risks and demand related factors. The choice of the appropriate discount rate should include the following: the risks of the investment, and the choice of the "correct" component costs of financing. Finally, the net present value of the project is calculated and the project is accepted if the NPV is positive. 22-17. If direct foreign investment is not a profitable way of entering a foreign market, a corporation has the choice of establishing either a sales office or a licensing arrangement. Typically, if the sales volume is expected to be low, then a sales office is profitable. Production is done elsewhere and the finished product is exported to the foreign country for sales. If the sales volume is expected to be large, but not large enough to support DFI, then a licensing arrangement is beneficial. 22-18. A sales office is an acceptable alternative when the volume of sales is not very high. This corresponds to a low cash flow situation. A licensing arrangement is beneficial when the affiliate's required return is less than the MNC's required rate of return. This situation arises since the affiliate typically faces less political and exchange risk than a subsidiary. Consequently, the required return for the owner of the licensing company is less than that of the MNC.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

220

Solutions to Problem Set A 22-1A. (a)

10,000 (Canadian $) x . 8437 (U.S. $/Canadian $) = $8,437

(b)

2,000,000 (Yen) x .004684 ($/Yen) = $ 9,368

(c)

50,000 (Swiss-franc) x .5139 ($/Swiss franc) = $25,695.

(a)

10,000 ($) x 1/.004684 (Yen/$) = 2,134,927.41 Yen

(b)

15,000 ($) x 1/.5139 (Swiss franc/$) = 29,188.56 Swiss franc

(c)

20,000 ($) x 1/.8437 (Canadian $/U.S. $) = 23,705.11 Canadian $.

22-2A.

22-3A. Recall that the indirect quote = (1/Direct Quote). The results are tabulated below: Foreign Currency/$ Spot 1.1853 30 day 1.1881 90 day 1.1912

Canadian - dollar

Japan - Yen

Spot 30 day 90 day

213.4927 211.9992 209.1613

Swiss - franc

Spot 30 day 90 day

1.9459 1.9346 1.8815

22-4A. Recall that the direct asked quote is greater than the direct bid quote. Consequently, the direct bid quote for Yen is 98% of the asked quote. The bid quotes for Canadian dollars and Swiss francs are, respectively, 97% and 95% of the selling quotes. The results are tabulated below:

Canadian - dollar

Bid Quotes for Foreign Currency Spot .8437 × .97 30 day .8417 × .97 90 day .8395 × .97

= = =

$/Foreign Currency .8184 .8165 .8143

Japan - Yen

Spot 30 day 90 day

.004684 × .98 .004717 × .98 .004781 × .98

= = =

.004590 .004623 .004685

Swiss - franc

Spot 30 day 90 day

.5139 × .95 .5169 × .95 .5315 × .95

= = =

.4882 .4910 .5049

221

222

22-5A. The Tokyo rate is 216.6743 Yen/$ The (indirect) New York rate is 1/.004684 = 213.4927 Yen/$. Assuming no transaction costs, the rate between Tokyo and New York are out of line. Arbitrage profits are possible. Yen is cheaper in Tokyo. Buy Yen for $10,000. $10,000 x 216.6743 = 2,166,743 Yen. Sell the Yen in New York at the prevailing rate. 2,166,743 x .004684 = $10,149.02 Your net gain is $10,149.02 - $10,000 = $149.02 22-6A. (a)

(b)

(Canadian dollar/Yen) =

(Yen/Swiss franc)

 Canadian dollar    U.S. dollar 

($/Yen) × 

=

.004684 × (1/.8437)

=

.00555

=

($/Swiss franc) × 

=

.5139 × (1/.004684)

=

109.7139

 Yen    $ 

SOLUTIONS TO INTEGRATIVE PROBLEM 1..

The additional factors that must be considered in international finance relate to: multiple currencies, different legal requirements, institutional restrictions, and internal control problems. These issues are discussed in the introduction to the chapter.

2.

Arbitrage profits are the riskless profits made without investing funds. These profits are generated when certain assets are not priced according to an equilibrium relationship. For example, arbitrage profits are possible in the spot and forward exchange markets if the indirect quote or cross quote relationships are out of line. The respective arbitrage processes are called simple and triangular arbitrage. Arbitrage opportunities exist if the money market rates differ from the forward market rates. This is referred to as: Covered Interest Arbitrage.

223

3.

Short-term exchange risk can be covered by the money market or the forward market hedge. The hedge should be so constructed that the net asset (liability) position in a foreign currency is zero. In addition to the amount of hedge, the maturity of the hedge should also be matched. This ensures that the risk of foreign exchange exposure is eliminated.

4.

A forward exchange contract requires delivery, at a specified future date, of one currency for a specified amount of another currency. The exchange rate for the future transaction is agreed upon today. The physical transaction takes place at the future date. Futures contracts (like forward exchange contracts) provide fixed prices for the required delivery of a foreign currency at maturity. Options, on the other hand, permit fixed (strike) price foreign currency transactions anytime prior to maturity. Futures contracts and options are traded in standardized amounts with standardized maturity dates. These instruments are traded on organized security exchanges. The individual traders deal with the exchange-based clearing organization rather than the direct parties to the foreign currency transaction. Forward contracts are quite different. Typically, they are written by banks and the firm deals directly with the banking institution rather than the organized security exchange.

5.

6.

7.

(a)

15,000 (Canadian $) x . 8450 (U.S. $/Canadian $) = $12,675

(b)

1,500,000 (Yen) x .004700 ($/Yen) = $ 7,050

(c)

55,000 (Swiss-franc) x .5150 ($/Swiss franc) = $28,325.

(a)

20,000 ($) x 1/.004700 (Yen/$) = 4,255,319.15 Yen

(b)

5,000 ($) x 1/.5150 (Swiss franc/$) = 9,708.74 Swiss franc

(c)

15,000 ($) x 1/.8450 (Canadian $/U.S. $) = 17,751.48 Canadian $.

Recall that the indirect quote = (1/Direct Quote). The results are tabulated below: Foreign Currency / $ Spot 1.1834 30 day 1.1884 90 day 1.1919

Canadian - dollar

8.

The Tokyo rate is 216.6752 Yen/$. The (indirect) New York rate is 1/.004700 = 212.7660 Yen/$. Assuming no transaction costs, the rate between Tokyo and New York are out of line. Arbitrage profits are possible. Yen is cheaper in Tokyo. Buy Yen for $10,000.

224

$10,000 x 216.6752 = 2,166,752 Y. Sell the Yen in New York at the prevailing rate. 2,166,752 x .004700 = $10,183.73 Your net gain is $10,183.73 - $10,000 = $183.73 9.

(Canadian dollar/Yen)

 Canadian dollar    U.S. dollar 

=

($/Yen) × 

=

.004700 × (1/.8450)

=

.00556

Solutions to Problem Set B 22-1B. (a)

15,000 (Canadian $) x . 8439 (U.S. $/Canadian $) = $12,65850

(b)

1,500,000 (Yen) x .004680 ($/Yen) = $ 7,020

(c)

55,000 (Swiss-franc) x .5140 ($/Swiss franc) = $28,270.

22-2B. (a)

20,000 ($) x 1/.004680 (Yen/$) = 4,273,504.27 Yen

(b)

5,000 ($) x 1/.5140 (Swiss franc/$) = 9,728.63 Swiss franc

(c)

15,000 ($) x 1/.8439 (Canadian $/U.S. $) = 17,774.62 Canadian $.

22-3B. Recall that the indirect quote = (1/Direct Quote). The results are tabulated below: Canadian - dollar

Foreign Currency/$ Spot 1.1850 30 day 1.1891 90 day 1.1919

Japan - Yen

Spot 30 day 90 day

213.6752 211.8644 208.8991

Swiss - franc

Spot 30 day 90 day

1.9455 1.9309 1.8744

225

22-4B. Recall that the direct asked quote is greater than the direct bid quote. Consequently, the direct bid quote for Yen is 96% of the asked quote. The bid quotes for Canadian dollars and Swiss francs are, respectively, 97% and 94% of the selling quotes. The results are tabulated below:

Canadian - dollar

Bid Quotes for Foreign Currency Spot .8439 × .97 30 day .8410 × .97 90 day .8390 × .97

= = =

&/Foreign Currency .8186 .8158 .8138

Japan - Yen

Spot 30 day 90 day

.004680 × .96 .004720 × .96 .004787 × .96

= = =

.004493 .004531 .004596

Swiss - franc

Spot 30 day 90 day

.5140 × .94 .5179 × .94 .5335 × .94

= = =

.4832 .4868 .5015

22-5B. The Tokyo rate is 216.6752 Yen/$ The Yen rate in New York is 0.00468 $/Yen. Assuming no transaction costs, the rate between Tokyo and New York are out of line. Arbitrage profits are possible. Buy Yen for $10,000. $10,000 x 216.6752 = 2,166,752 Yen. Sell the Yen in New York at the prevailing rate. 2,166,752 x .004680 = $10,140.40 Your net gain is $10,140.40 - $10,000 = $140.40 22-6B. (a)

(b)

(Canadian dollar/Yen)

(Yen/Swiss franc)

=

 Canadian dollar    U.S. dollar 

($/Yen) × 

=

.004680 × (1/.8439)

=

.0055457

=

($/Swiss franc) × 

 Yen    $ 

= .5140 × (1/.004680) = 109.8291

226

CHAPTER 23

Corporate Restructuring: Combinations and Divestitures CHAPTER ORIENTATION Corporate restructuring comes through combining assets (mergers and acquisitions) and uncombining assets (divestitures). This chapter examines how mergers and acquisitions can create shareholder wealth and the methods used to value a potential merger candidate. Firms may also increase shareholder wealth by divesting themselves of some portion of its current operations. This chapter discusses the different divestiture options available to a firm.

CHAPTER OUTLINE I.

II.

There are two principal ways by which a firm may grow: A.

Internally, through the acquisition of specific assets which are financed by the retention of earnings and/or external financing, or

B.

Externally, through the combination with another company. We turn now to a discussion of external growth through mergers with, and acquisition of, other firms.

There have been five identifiable time periods where the number and amount of mergers and acquisitions were particularly accentuated. A.

End of the 19th century and beginning of the 20th century. During this time, many industries were merged. The resulting firms had enormous economic power. Example firms include U.S. Steel, American Tobacco, and Standard Oil.

B.

The decade of the 1920s. This merger wave was closely related to the creation of oligopolies (industries dominated by a few firms), such as IBM, General Foods, and Allied Chemical. During this time, the developments in transportation, communications, and merchandising fostered the growth.

227

C.

III.

Between the 1950s and the 1970s. No longer permitted by the Federal Trade Commission to acquire firms in their own industry, companies actively began acquiring companies outside their own industries. The bringing together of these dissimilar firms into one corporate entity came to be known as the conglomerate. 1.

The creation of a conglomerate was thought to be an efficient way of monitoring individual businesses by subjecting them to regular quantitative evaluations by the central office.

2.

With hindsight we now see that conglomerate acquisitions have, for the most part, proven unsuccessful.

D.

The 1980s. In this period, the pattern became that of acquiring a conglomerate, breaking it up into its individual business units, and selling off the segments to large corporations in the same businesses. The 1980s merger activity came to an end, however, largely because the huge amounts of debt financing used to fund many of the acquisitions dried up.

E.

The 1990s. During the 90s the financial services and telecommunication industries went through a period of consolidation resulting in some of the largest mergers ever recorded.

Why mergers create value. For a merger to create wealth it has to provide shareholders with something they get for free by merely holding the individual shares of the two firms. Such benefits might include: A.

Tax benefits: If a merger were to result in a reduction of taxes that is not otherwise possible, then wealth is created by the merger. This can be the case with a firm that has lost money and thus generated tax credits, but does not currently have a level of earnings sufficient to utilize those tax credits.

B.

Reduction of agency costs: An agency problem is a result of the separation of management and the ownership in the firm. A merger, particularly when it results in a holding company or conglomerate organizational form may reduce the significance of this problem, because top management is created to monitor the management of the individual companies making up the conglomerate. Alternatively, it can be argued that the creation of a conglomerate might result in increased agency costs. This might occur as shareholders in conglomerates feel they have less control over the firm's mangers, as a result of the additional layers of management between them and the decision makers.

C.

The release of free cash flows to the owners: A merger can create wealth by allowing the new management to distribute the free cash flow out to the shareholders, thus allowing them to earn a higher return on these cash flows than would have been earned by the firm.

D.

Economies of scale: Wealth can be created in a merger through economies of scale. Redundant functions of the combined firms, such as accounting, computer operations, and management, provide opportunities to reduce staffing and its associated costs or to increase productivity.

228

IV.

E.

Unused debt potential: Assuming the acquired firm has unused debt capacity, a new management can increase debt financing, and reap the tax benefits associated with the increased debt.

F.

Complementary financial slack: It may be possible to create wealth by combining cash-rich bidders and cash-poor targets, with wealth being created as a result of the positive NPV projects taken by the merged firm that the cash-poor firm would have passed up.

G.

Removal of ineffective management: If a firm with ineffective management can be acquired, it may be possible to replace the current management with a more efficient management team, and thereby create wealth.

H.

Increased market power: The merger of two firms can result in an increase in the market or monopoly power of the two firms. While this can result in increased wealth, it may also be illegal.

I.

Reduction in bankruptcy costs: Presuming that bankruptcy costs exist, a merger that reduces the possibility of bankruptcy creates wealth.

J.

The creation of "chop shop" value: It may be less expensive to purchase assets through an acquisition than it is to obtain those assets in any other way.

Determining a firm's value A.

The value of a firm depends not only on its earnings capabilities but also on the operating and financial characteristics of the acquired firm. To determine an acceptable price of a corporation, a number of factors must be carefully evaluated. The final objective of this valuation process is to maximize the stockholders' wealth (stock price) of both firms.

B.

The value of a firm may be represented in a number of ways including (l) book value, (2) appraisal value, (3) chop-shop value, and (4) the free cash flow value. 1.

The book value of a firm's net worth is the depreciated value of the company's assets less its outstanding liabilities. Book value alone is not a significant measure of the worth of a company but should be used as a starting point to be compared with other analyses.

2.

Appraisal value, acquired from an independent appraisal firm, may be useful in conjunction with other methods. Advantages include a.

The reduction of accounting goodwill by increasing the recognized worth of specific assets.

b.

A test of the reasonableness of results obtained through other evaluation methods.

c.

The discovery of strengths and weaknesses that otherwise might not be recognized.

229

V.

3.

The "chop shop" approach to valuation attempts to identify multiindustry companies that are undervalued and would be worth more if separated into their parts. As such, this approach encompasses the idea of attempting to buy assets below their replacement cost.

4.

The free cash-flow approach to merger valuation requires that we estimate the incremental net cash flows available to the bidding firm as a result of the merger or acquisition. The present value of these cash flows will then be determined, and this will be the maximum amount that should be paid for the target firm. The initial outlay can then be subtracted out to calculate the net present value from the merger.

Divestitures A.

Divestitures, or "reverse mergers," have become an important factor in restructuring corporations.

B.

A successful divestiture allows the firm's assets to be used more efficiently, and therefore, be assigned a higher value by the market forces.

C.

The different types of divestitures may be summarized as follows: 1.

Selloff. A selloff is the sale of a subsidiary, division, or product line by one company to another.

2.

Spinoff. A spinoff involves the separation of a subsidiary from its parent, with no change in the equity ownership.

3.

Liquidation. A liquidation in this context is not a decision to shut down or abandon an asset. Rather, the assets are sold to another company and the proceeds are distributed to the stockholders.

4.

Going private. Going private results when a company, whose stock is traded publicly, is purchased by a small group of investors and the stock is no longer bought and sold on a public exchange.

5.

Leveraged buyout. The leveraged buyout is a special case of going private. The existing shareholders sell their shares to a small group of investors. The purchasers of the stock use the firm's unused debt capacity to borrow the funds to pay for the stock.

230

ANSWERS TO END-OF-CHAPTER QUESTIONS 23-1. Clearly, for a merger to create wealth it would have to provide shareholders with something they could not get for free by merely holding the individual shares of the two firms. Restating the question: What benefits are there to shareholders from mergers and acquisitions? Potential benefits would include the following: a.

If a merger were to result in a reduction of taxes that is not otherwise possible, then wealth is created by the merger.

b.

As a result of agency problems, stockholders and bondholders impose a premium on funds supplied to the firm to compensate them for this inefficiency in management. A merger, particularly when it results in a holding company or conglomerate organizational form, may reduce the significance of this problem, because top management is created to monitor the management of the individual companies making up the conglomerate. As a result, management of the individual companies can be effectively monitored without any forced public announcement of proprietary information, such as new product information that might aid competitors. If investors recognize this reduction in the agency problem as being material in scope, they may provide funds to the firm at a reduced cost, no longer charging as large of an "agency problem premium." Alternatively, it can be argued that the creation of a conglomerate might result in increased agency costs. This might occur as shareholders in conglomerates feel they have less control over the firm's mangers, as a result of the additional layers of management between them and the decision makers.

c.

Free cash flow should be paid out to shareholders; otherwise it would be invested in projects returning less than the required rate of return. Unfortunately, managers may not wish to pass these funds to the shareholders, because they may feel that their power would be reduced. Moreover, if they return these surplus funds they may, at a later date, be forced to go outside for financing if more profitable investment opportunities are identified. This situation is a form of the agency problem, but these actions may be more a result of the corporate management culture than of any attempt by the managers to maintain their own position as opposed to maximizing shareholder wealth. A merger can create wealth by allowing the new management to pay this free cash flow out to the shareholders, thus allowing them to earn a higher return on this excess than would have been earned by the firm.

d.

Wealth can be created in a merger through economies of scale. For example, administrative expenses including accounting, computing, or simply top-management costs, may fall as a percent of total sales as a result of sharing these resources.

231

e.

Some firms simply do not exhaust their debt capacity. If a firm with unused debt potential is acquired, the new management can then increase debt financing, and reap the tax benefits associated with the increased debt.

f.

It may be possible to create wealth by combining cash-rich bidders and cash-poor targets, with wealth being created as a result of the positive NPV projects taken by the merged firm that the cash-poor firm would have passed up.

g.

If a firm with ineffective management can be acquired, it may be possible to replace the current management with a more efficient management team, and thereby create wealth.

h.

The merger of two firms can result in an increase in the market or monopoly power of the two firms. While this can result in increased wealth, it may also be illegal.

i.

Firm diversification, when the earnings from the two firms are less than perfectly positively correlated, can reduce the chance of bankruptcy. Since costs are associated with bankruptcy, reduction of the chance of bankruptcy has a very real value to it.

23-2. The basic function of book value is to establish the costs as set forth by accounting principles, not to determine value. These costs may bear little relationship to the value of the organization or to its ability to produce earnings. 23-3. The advantages of an independent appraisal include: (1)

Accounting goodwill may be reduced by increasing the recognized worth of specific assets.

(2)

The reasonableness of the results obtained through other valuation methods are tested.

(3)

Strengths and weaknesses may be uncovered that otherwise might not be recognized.

23-4. The "chop-shop" approach to valuation attempts to identify multi-industry companies that are undervalued and would be worth more if separated into their parts. As such, this approach encompasses the idea of attempting to buy assets below their replacement cost. 23-5. The NPV, or free cash flow valuation model, is familiar to us, since it merely involves finding the present value of cash flows, as we did in our studies in capital budgeting. Using the cash-flow approach to merger valuation requires that we estimate the incremental net cash flows available to the bidding firm as a result of the merger or acquisition. The present value of these cash flows will then be determined, and this will be the maximum amount that should be paid for the target firm. The initial outlay can then be subtracted out to calculate the net present value from the merger. While this is very similar to what was proposed when we examined the capital budgeting problem, there are differences, particularly when estimating the initial outlay.

232

23-6. Types of divestitures include: (1)

Selloff. A selloff is the sale of a subsidiary, division, or product line by one company to another.

(2)

Spinoff. A spinoff involves the separation of a subsidiary from its parent with no change in the equity ownership.

(3)

Liquidation. A liquidation in this context is not a decision to shut down or abandon an asset. Rather, the assets are sold to another company, and the proceeds are distributed to the stockholders.

(4)

Going private. Going private results when a company whose stock is traded publicly is purchased by a small group of investors, and the stock is no longer bought and sold on a public exchange.

(5)

Leveraged buyout. The leveraged buyout is a special case of going private. The existing shareholders sell their shares to a small group of investors. The purchasers of the stock use the firm's unused debt capacity to borrow the funds to pay for the stock.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Solutions to Problem Set A 23-1A.

Aramus, Inc. - Chop shop valuation (In Thousands) Business Segment Sunglasses distribution Reading glasses distribution Technical products Total Value

Capital-toSales 1.0 0.9 1.2

Segment Sales 3,500 2,000 6,500

Theoretical Values $3,500 1,800 7,800 $13,100

Business Segment Sunglasses distribution Reading glasses distribution Technical products Total Value

Capital-toAssets 0.8 0.8 1.0

Segment Sales 1,000 1,500 8,500

Theoretical Values $ 800 1,200 8,500 $10,500

233

Business Segment Sunglasses distribution Reading glasses distribution Technical products Total Value

Capital-toOperating Income 8.0 10.0 7.0

Segment Sales 350 250 1,200

Theoretical Values $2,800 2,500 8,400 $13,700

Average Theoretical Value 23-2A.

$12,433

Argo Corporation (numbers expressed in millions)

Year Sales Cost of goods sold Admin. & selling costs Depreciation Earnings before taxes Taxes (34%) Earnings after taxes Depreciation Capital expenditures Free cash flows

2004 $200.00 120.00 15.00 10.00 $55.00 18.70 $36.30 10.00 12.00 $34.30

2005 $225.00 135.00 20.00 15.00 $55.00 18.70 $36.30 15.00 13.00 $38.30

2006 $240.00 144.00 27.00 17.00 $52.00 17.68 $34.32 17.00 15.00 $36.32

2007 $250.00 150.00 28.00 20.00 $52.00 17.68 $34.32 20.00 17.00 $37.32

Beyond 2007 $275.00 165.00 30.00 24.00 $56.00 19.04 $36.96 24.00 20.00 $40.96

Weighted cost of capital: (.30) x 8% + (.70) x 18% = 15% $29.83

$28.96

Total present value Cost of acquisition ($250 paid + $40 debt assumed) Net present value

*

$23.88

$21.34

$156.13

*

$260.14 290.00 -$29.86

 $40 .96   /(1+.15)4 = $156.13  .15 

=

234

23-3A.

Prime Corporation - Free cash flow valuation (In Millions) Beyond Year 2004

2005

2006

2007

2007

Sales Cost of Goods Sold Admin.& selling Depreciation Earnings before tax Taxes (34%)

$300.00 180.00

$335.00 201.00

$370.00 222.00

$400.00 240.00

$425.00 255.00

40.00 25.00 $55.00 18.70

50.00 30.00 $54.00 18.36

58.00 35.00 $55.00 18.70

62.00 38.00 $60.00 20.40

65.00 40.00 $65.00 22.10

Earnings after tax. Depreciation

$36.30 25.00

35.64 30.00

$36.30 35.00

$39.60 38.00

$42.90 40.00

Capital expenditures Free Cash Flows

30.00 $31.30

37.00 $28.64

45.00 $26.30

48.00 $29.60

50.00 $32.90

Weighted Cost of Capital

. 4(10%) + .6(20%) = 16% $26.98

$21.28

Total Present Value

$16.85

$16.35

$113.56

*

$195.02

Cost of Acquisition

180.00

($150 paid + $30 debt assumed) Net Present Value

*

$15.02

 $32 .90   /(1+.16)4 = $113.56  .16 

=

235

Solutions to Problem Set B 23-1B.

Cornutt, Inc. - Chop-shop valuation (In Thousands) Business Segment Consumer wholesale Specialty services Retirement centers Total value

Capital-toSales 0.75 1.10 1.00

Segment Sales $1,500 800 2,000

Theoretical Values $1,125 880 2,000 $4,005

Business Segment Consumer wholesale Specialty services Retirement centers Total value

Capital-toAssets 0.60 0.90 0.60

Segment Assets $750 700 3,000

Theoretical Values $450 630 1,800 $2,880

Segment Income $100 150 600

Theoretical Values $1,000 1,050 3,600 $5,650 $4,178

Business Capital-toSegment Operating Income Consumer wholesale 10.00 Specialty services 7.00 Retirement centers 6.00 Total value Average theoretical value 23-2B

Wrongway, Inc. - Chop-shop valuation (In Thousands) Business Segment Sunglasses distribution Reading glasses distribution Technical products Total value Business Segment Sunglasses distribution Reading glasses distribution Technical products Total value Business Segment Sunglasses distribution Reading glasses distribution Technical products Total Value

Capital-toSales 0.8 1.2 1.2

Segment Sales 2,200 1,000 3,500

Theoretical Values 1,760 1,200 4,200 $7,160

Capital-toAssets

Segment Assets

Theoretical Values

1.0 0.9 1.1 Capital-toOperating Income 8.0 10.0 12.0

236

600 700 5,000 Segment Income 200 150 500

600 630 5,500 $6,730 Theoretical Values 1,600 1,500 6,000 $9,100

Average Theoretical Value

$7,663

237

23-3B.

Brown Corporation. - Free cash flow valuation (In Millions) Year 2004 Sales $260.00 Cost of goods sold (50%) 130.00 Admin. & selling costs 25.00 Depreciation 15.00 Earnings before taxes $90.00 Taxes (34%) 30.60 Earnings after taxes $59.40 Depreciation 15.00 Capital expenditures 22.00 Free cash flows $52.40

2005 $265.00 132.50 25.00 17.00 $90.50 30.77 $59.73 17.00 18.00 $58.73

2006 $280.00 140.00 25.00 18.00 $97.00 32.98 $64.02 18.00 18.00 $64.02

2007 $290.00 145.00 30.00 23.00 $92.00 31.28 $60.72 23.00 20.00 $63.72

Beyond 2007 $300.00 150.00 30.00 30.00 $90.00 30.60 $59.40 30.00 22.00 $67.40

Weighted average cost of capital = .25 x 8% + .75 x 22% = 18.50% $44.22

$41.82

$38.47

Total present value Cost of acquisition ($225 paid plus $75 debt assumed) Net present value

*

 $67 .40   /(1+.185)4 = $184.76  .185 

=

238

$32.32 $184.76 $341.59 300.00 $41.59 *

23-4B. Little Corporation - Free cash flow valuation (In Millions) Beyond

Year

2004 2005 2006 2007 2007 Sales Cost of goods sold Admin. & selling Depreciation Earnings before tax Taxes (34%) Earnings after tax Depreciation Capital expend. Free Cash Flows

$200.00 140.00 30.00 18.00 $12.00 4.08 $7.92 18.00 20.00 $5.92

$220.00 154.00 35.00 20.00 $11.00 3.74 $7.26 20.00 22.00 $5.26

$245.00 171.50 38.00 22.00 $13.50 4.59 $8.91 22.00 25.00 $5.91

$275.00 $300..00 192.50 210.00 40.00 45.00 25.00 30.00 $17.50 $15.00 5.95 5.10 $11.55 $9.90 25.00 30.00 28.00 30.00 $8.55 $9.90

$3.65

$3.42

$4.12 $23.87 * $39.99 37.00

Weighted Cost of Capital: .5 (15%) + .5 (25%) = 20% $4.93 Total Present Value Cost of Acquisition ($25 paid + $12 debt assumed) Net Present Value

$2.99

CHAPTER 24 **

*

 $9.90   /(1+.20)4 = $23.87  .20 

=

239

Term Loans and Leases CHAPTER ORIENTATION The first section of this chapter provides an overview of the major sources of term loans and their characteristics. The second section of the chapter provides an overview of lease financing, including a discussion of leasing arrangements, the accounting treatment of financial leases, the lease versus purchase decision, and the potential benefits from leasing.

CHAPTER OUTLINE I.

Term loans

A.

In general, term loans have maturities from one to 10 years and are repaid in periodic installments over the life of the loan. Term loans are usually secured by a chattel mortgage on equipment or a mortgage on real property. The principal suppliers of term credit include commercial banks, insurance companies and, to a lesser extent, pension funds.

B.

The common attributes of term loans include the following: 1.

2.

The maturities of term loans are usually as follows: a.

Commercial banks: 1 to 5 years.

b.

Insurance companies: 5 to 15 years.

c.

Pension funds: 5 to 15 years.

The collateral backing term loans: a.

Shorter maturity loans are usually secured with a chattel mortgage on machinery and equipment or securities such as stocks and bonds.

b.

Longer maturity loans are frequently secured by mortgages on real estate.

240

3.

II.

In addition to collateral, the lender on a term loan agreement will often require restrictive covenants that are designed to maintain the borrower's financial condition on a par with that which existed at the time the loan was made. a.

Working capital restrictions involve maintaining a minimum current ratio that reflects the norm for the borrower's industry, as well as the lender's desires.

b.

Additional borrowing restrictions prevent the borrower from increasing the amount of debt financing outstanding without the lender's approval.

c.

A third covenant that is very popular requires that the borrower supply periodic financial statements to the lender.

d.

Term loan agreements often include a key-man provision that the borrower requires that the lender approve major personnel changes and insure the lives of "key" personnel with the lender named as the beneficiary.

4.

Term loans are generally repaid in periodic installments in accordance with repayment schedules established by the lender. Each installment includes both an interest and a principal component.

5.

Frequently a bank will have demand for loans that exceeds its lending capacity. In order to satisfy the demand, the bank will share the loan demand with other participating banks. The participating banks receive a certificate of participation and a commitment from the lead bank to pay a portion of the loan cash flows as they are received.

6.

Eurodollar loans are intermediate term loans made by major international banks to businesses based on foreign deposits denominated in dollars. The rate of the loan is an amount greater than the London Interbank Offered Rate. The Eurodollar loan market is governed by a limited number of regulations.

Leasing A.

There are three major lease agreements: direct leasing, sale and leaseback, and leveraged leasing. 1.

In a direct lease the firm acquires the services of an asset it did not previously own. Direct leasing is available through a number of financial institutions, including manufacturers, banks, finance companies, independent leasing companies, and special-purpose leasing companies. Basically, direct leasing involves the purchase of the asset by the lessor from a vendor and leasing the asset to the lessee.

2.

A sale and leaseback arrangement occurs when a firm sells land, buildings, or equipment that it already owns to a financial institution and simultaneously enters into an agreement to lease the property

241

back for a specified period under specific terms. The lessee firm receives cash in the amount of the sales price of the asset sold and the use of the asset over the term of the lease. In return, the firm must make periodic rental payments throughout the term of the lease to the lessor. 3.

B.

In a leveraged lease a third participant is added who finances the acquisition of the asset to be leased for the lessor. From the lessee's standpoint, this lease is no different from the two lease arrangements discussed above. But with a leveraged lease, specific consideration is given to the financing arrangement used by the lessor in acquiring the asset to be leased.

The accounting profession through Financial Accounting Statement No. 13 requires the capitalization of any lease that meets one or more of the following criteria: 1.

The lease transfers ownership of the property to the lessee by the end of the lease term.

2.

The lease contains a bargain repurchase option.

3.

The lease term is equal to 75 percent or more of the estimated economic life of the leased property.

4.

The present value of the minimum lease payments equals or exceeds 90% of the excess of the fair value of the property over any related investment tax credit retained by the lessor.

C.

The lease–versus-purchase decision requires a standard capital budgeting type of analysis, as well as an analysis of two alternative "packages" of financing. Two models are used to evaluate the lease versus purchase decision.

1.

The first model computes the net present value of the purchase option which can be defined as follows:

n

A Ct F ∑t = 1 ( 1+ K t) - IO

NPV (P)

=

where ACFt

= the annual after-tax cash flow resulting from the asset’s purchase in period t

K

= the firm's cost of capital applicable to the project being analyzed and the particular mix of financing used to acquire the project

IO

= the initial cash outlay required to purchase the asset in period zero (now)

n

= the productive life of the project

242

2.

In the second model a net advantage to lease (NAL) over purchase equation is used that indicates the more favorable (least expensive) method of financing. The equation used to arrive at NAL is as follows:

n

NAL =

Ot ( 1- T -)R t ( 1- T -)T t I- T tD ∑t = 1 ( 1+ r )t b -

Vn (1 + K s ) n

+ IO

where Ot

=

any operating cash flows incurred in period t that are incurred only when the asset is purchased. Most often this consists of maintenance expenses and insurance that would be paid by the lessor.

Rt

=

the annual rental for period t.

T

=

the marginal tax rate on corporate income.

It

=

the tax deductible interest expense foregone in period t if the lease option is adopted. This level of interest expense was set equal to that which would have been paid on a loan equal to the full purchase price of the asset.

Dt

=

depreciation expense in period t for the asset.

Vn

=

the after-tax salvage value of the asset expected in year n.

Ks

=

the discount rate used to find the present value of Vn. This rate should reflect the risk inherent in the estimated Vn. For simplicity, the after-tax cost of capital is often used as a proxy for this rate.

IO

=

the purchase price of the asset which is not paid by the firm in the event the asset is leased.

rb

=

the after-tax rate of interest on borrowed funds. This rate is used to discount the relatively certain after-tax cash flow savings accruing through leasing the asset.

If NAL is positive, there would be a positive cost advantage to lease financing. If NAL is negative, then purchasing the asset and financing with a debt plus equity package would be the preferred alternative. However, we would lease or purchase the asset in accordance with the value of NAL in only two circumstances:

243

D.

a.

If NPV(P) is positive, then the asset should be acquired through the preferred financing method as indicated by NAL.

b.

If NPV(P) is negative, then the asset's services should be acquired via the lease alternative only if NAL is positive and greater in absolute value than NPV(P). That is, the asset should be leased only if the cost advantage of leasing (NAL) is great enough to offset the negative NPV(P). In effect, if a positive NAL were to more than offset a negative NPV(P), then the net present value through lease would be positive.

Over the years a number of potential benefits have been offered for lease financing. Some of the more frequently cited advantages are enumerated and commented upon here. 1.

Flexibility and convenience. It is often argued that lease financing is more convenient than other forms of financing because smaller amounts of funds can be raised at lower cost. In addition, it is often argued that lease payment schedules can be made to coincide with cash flows generated by the asset. These may or may not be real advantages. It depends on the actual circumstances faced by the lessee firm.

2.

Lack of restrictions. It has been argued that leases require fewer restrictions on the lessee than do debt agreements.

3.

Avoiding the risk of obsolescence. This argument is generally conceded to be fallacious because the lessor includes his or her estimated cost of obsolescence in the lease terms.

4.

Conservation of working capital. Here it is argued that leasing involves no down payment. However, the borrower could obtain the same effect by borrowing the down payment.

5.

100-percent financing. The lease involves 100% financing but purchasing the asset would surely involve some equity. As we noted above, the down payment could be borrowed to produce 100% financing via a loan. In addition, it is not clear that 100% lease financing is desirable because it represents 100% non-owner financing. Finally the lease agreement does not entitle the lessee to the asset's salvage value. Thus, the lease provides 100% financing for the "use value" of the asset but not its "salvage value."

6.

Tax savings. The difference in tax shelters between leasing and other forms of financing can only be evaluated by using a net advantage of lease model as we discussed earlier.

7.

Ease of obtaining credit. Lease financing may be more or less difficult to obtain than other forms of financing. This advantage (or disadvantage) can only be evaluated on a case-by-case basis.

244

ANSWERS TO END-OF-CHAPTER QUESTIONS 24-1. Intermediate-term financing includes all those financing arrangements with final maturities longer than one year and with a maximum of ten years. Short-term financing is for a period of less than one year and long-term financing generally involves a period of more than ten years. 24-2. The major types of restrictions usually found in the covenants of term loan agreements include: (1)

Working capital requirement. This restriction involves maintaining a minimum amount of working capital. Very often this restriction takes the form of a minimum current ratio such as 2 to 1 or 3 1/2 to 1, or a minimum level of net working capital such as $200,000.

(2)

Additional borrowing. Generally, this type of restriction will require the approval of the lender before any additional debt is issued. The restriction is often extended to long-term lease agreements.

(3)

Periodic financial statements. A standard covenant in most term-loan agreements involves supplying the lender with periodic financial statements. These usually include annual or quarterly-income statements and balance sheets.

(4)

Management. Term-loan agreements will sometimes include a provision requiring prior approval by the lender of major personnel changes. In addition, the borrower may be required to insure the lives of certain "key" personnel with the lender named as beneficiary.

24-3. (1)

In a direct leasing agreement the firm acquires the services of an asset it did not previously own. The lease basically involves purchase of the asset by the lessor from a vendor and leasing it to the lessee.

(2)

Sale and leaseback arrangements arise when a firm sells land, buildings, or equipment which it already owns to a financial institution and simultaneously enters into an agreement to lease the property back for a specified period under specific terms.

(3)

A net-net lease requires that the lessee maintain the leased asset and return it to the lessor at the end of the lease term with a value equal to a preestablished amount.

(4)

An operating lease constitutes a cancelable contractual commitment on the part of the firm leasing the asset (the lessee) to make a series of payments to the firm which actually owns the asset (the lessor) for use of the asset.

245

24-4. Prior to January, 1977, most financial leases were not included in the balance sheets of lessee firms. They were instead reported in the footnotes to the balance sheet in accordance with APB Opinions 5 and 31. In November, 1976, the accounting profession reversed its long standing position with Statement of Financial Account Standards No. 13 entitled "Accounting for Leases." Specifically, Statement 13 requires that any lease which meets one or more of the following criteria be included in the body of the balance sheet of the lessee: (1)

The lease transfers ownership of the property to the lessee by the end of the lease term.

(2)

The lease contains a bargain repurchase option.

(3)

The lease term is equal to 75 percent or more of the estimated economic life of the leased property.

(4)

The present value of the minimum lease payments equals or exceeds 90 percent of the excess of the fair value of the property over any related investment tax credit retained by the lessor.

24-5. The potential benefits from lease financing include: (1)

Flexibility and convenience. First, it is argued that leasing provides the firm with flexibility because it allows for piece-meal financing of relatively small asset acquisitions. Second, leasing may allow a division or subsidiary manager to acquire equipment without the approval of the corporate capital budgeting committee. Third, some lease payment schedules may be structured to coincide with the revenues generated by the asset, or they may be timed to match seasonal fluctuations in a given industry. Arguments for the greater convenience of leasing may take many forms. It is sometimes stated that leasing simplifies bookkeeping for tax purposes because it eliminates the need to prepare time-consuming depreciation tables and subsidiary fixed asset schedules. It is also pointed out that the fixed payment nature of lease rentals allows more accurate forecasting of cash needs. Finally, it is frequently noted that leasing allows the firm to avoid the "problems" and "headaches" associated with ownership.

(2)

Lack of restrictions. Lease contracts generally do not contain protectivecovenant restrictions. Furthermore, it is sometimes possible to exclude lease payments from the firm's debt commitments in calculating financial ratios under existing covenants.

(3)

Avoiding the risk of obsolescence. This argument states that a lease is advantageous because it allows the firm to avoid the risk that the equipment will become obsolete. In actuality, the risk of obsolescence is passed on to the lessee in any financial lease, except in cases of operating cancelable operating leases, in which it is sometimes possible to avoid the risk of obsolescence.

246

(4)

Conservation of working capital. The argument for conservation is that a lease does not require an immediate outflow of cash to cover the full purchase price of the asset and, therefore, the funds are retained in the business.

(5)

100 percent financing. Another alleged benefit of leasing is embodied in the argument that a lease provides the firm with 100 percent financing. It is pointed out that the borrow-and-buy alternative generally involves a down payment, whereas leasing does not.

(6)

Tax savings. It is also argued that leasing offers an economic advantage in that the tax shield generated by the lease payments usually exceeds the tax shield from depreciation that would be available if the asset were purchased.

(7)

Ease of obtaining credit. This alleged advantage of leasing concerns assertion that firms with poor credit ratings are able to obtain assets through leases when they are unable to finance the acquisitions with debt capital.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS Solutions to Problem Set A 24-1A. Interest Rate Face Amount Year 0 1 2 3 4 5

10.0% $325,000.00

Payment

Interest

Principal

50,000.00 50,000.00 50,000.00 50,000.00 268,160.75

32,500.00 30,750.00 28,825.00 26,707.50 24,378.25

17,500.00 19,250.00 21,175.00 23,292.50 243,782.50

Balance 325,000.00 307,500.00 288,250.00 267,075.00 243,782.50 0

Thus, the fifth year balloon payment will equal the principal remaining at the end of that year of $243,782.50 plus interest for the year of $24,378.25 for a total of $268,160.75. 24-2A. Interest Rate Equipment Price Number of Payments Rental Payment

12.0% 100,000.00 10 15,802.16

Present Value of the 247

Rental Payments

$100,000.00

5

24-3A. $100,000 = Payment Payment =

1

∑ t t =1 (1.18 )

$100 ,000 3.127

= $31,979.53

24-4A. Year 1 2 3 4 5

Payment $31,979.53 31,979.53 31,979.53 31,979.53 31,979.53

Interest $18,000.00 15,483.68 12,514.43 9,010.71 4,876.33

Principal $13,979.53 16,495.85 19,465.10 22,968.82 27,103.20

Remaining Balance $86,020.47 69,524.62 50,059.52 27,090.70 (12.50)

Rounding errors produced a $12.50 difference in the remaining balance and principal portion of the fifth year payment. 5

24-5A. (a)

$200,000 = $59,663

1

∑ t t =1 (1 + r)

where r = the effective annual rate on the computer sales firm loan. 5

1

∑ t t =1 (1 + r)

$200 ,000 59 ,663

=

=

3.352

Looking in the annuity present value table we find that an r of 15% for a five year loan is 3.352. Thus, the effective rate on the loan is 15%. 5

(b )

(c)

$250,000

= Payment

Payment

=

$250,000

= $385,080

1 (1 + r)

Thus, (d)

5

r

= =

1

∑ t t =1 (1.16 )

$250 ,000 = 3.274

$250 ,000 $385 ,080

$76,359.19

1 (1 + r) 5

= .6492

9%.

The effective rate of interest is lowest on the insurance company loan. In addition, the insurance company loan does not require an interim principal or interest payment during the five-year period.

248

24-6A. Bank Loan Alternative: Cost = 14% Manufacturer Financing Alternative: The cost of this alternative is not immediately apparent and must be calculated. We know that the following relationship holds for any equal payment installment loan: n 1 Loan Amount = Payment ∑ t t =1 (1 + k) where n is the term of the loan and k is the rate of interest charged on the remaining loan balance. Using this relationship we can define 4

$400,000 4

Therefore,

1

∑ t t =1 (1 + k)

1

∑ t t =1 (1 + k)

= $140,106

$400 ,000 $140 ,106

=

= 2.855

We now know the present value of an annuity factor that corresponds to a four-year period and the rate of interest on the loan (k). Looking up this factor in the annuity present value table, we find that k = 15 percent. Therefore, the bank loan alternative is preferred. 24-7A.(a)

Evaluating the purchase alternative: IO = $20,000 Annual net cash flows: Annual cash savings Less: depreciation

Book profits $6,000 (4,000)

Cash flows $6,000

2,000 (1,000)

6,000 (1,000)

Net revenues before taxes Less: taxes (50%) Plus: salvage value

$5,000 4,000

Annual after-tax cash flow (4)

$9,000

4

NPV

= $5,000

1

∑ t + t =1 (1.12)

$4,000

1 (1.12 ) 4

- $20,000

= $5,000 (3.037 )+ $4,000 (0.636) - $20,000 = $15,185 + $2,544 - $20,000 = $17,729 - $20,000 = $-2,271 Thus, the asset should not be purchased.

249

(b)

Evaluating the lease alternative: Calculating principal and interest on a loan of $20,000 at 10%. 4

Annual payment = $20,000 / Year 0 1 2 3 4

1

∑ t = t =1 (1.10)

$6,309.15

Payment

Interest

Principal

$6,309.15 6,309.15 6,309.15 6,309.15

$2,000.00 1,569.09 1,095.08 573.67

$4,309.15 4,740.06 5,214.07 5,735.48

Remaining Balance $20,000.00 15,690.85 10,950.79 5,736.72 1.24

Rounding errors produced a $1.24 difference in the remaining balance and principal portion of the fourth year payment. 4

(1)

Year 1 2 3 4

Solving for

∑ t =1

Ot(1-T) - R(1-T) $500 500 500 500

$3,000 3,000 3,000 3,000

-

O t (1 − T) − R t (1 − T) − I t T − D t T (Term one) (1 + rb ) t ItT $1,000 785 548 287

Vn (1 + k s ) n

-

DtT $2,000 2,000 2,000 2,000

= SUM -$5,500 - 5,285 - 5,048 - 4,787

Discount Present Factor Value 5% 0.952 -$ 5,236 0.907 - 4,794 0.864 - 4,361 0.823 - 3,940

(Term one)

=

-$18,331

(Term two)

=

-2,544

(2)

Solving for -

(3)

Adding IO

20,000

(4)

Net advantage of leasing

($875)

Since the asset's NAL is negative, the asset should not be leased.

250

24-8A.(a) The basic analytical relationship needed to solve for installment payments is found below: n

Loan Amount

1

∑ t t =1 (1 + k)

= Payment

Thus, for the first part of this exercise 10

$100,000

1

∑ t t =1 (1.15)

= Payment

or 10

Payment

= $100,000 ÷ ( ∑ t =1

1 (1.15)

10

We recognize the summation term

t

)

1

∑ t as a present t =1 (1.15)

value annuity factor which is found in Appendix E. Thus, Payment

= $100,000 ÷ 5.019 = $19,924.29

(b)

In this problem we must recall the procedure for quarterly compounding. In general, the payment relationship in (a) becomes mn

Loan Amount

= Payment

1

∑ t t =1 (1 + k/m)

where m is the number of compounding periods in a year (e.g., m = 4 for quarterly compounding). Thus, 20

$100,000

= Payment

1

∑ t =1 (1.0375)

t

Since the tables in Appendix E do not have fractional rates we must solve for the present value annuity interest factor algebraically. Payment

= $100,000 ÷ 13.8962 = $7,196.21

251

(c)

This problem requires that we first solve for the annual installment payments for each of the next five years based upon a 30-year installment period, i.e., 30

Payment

= Loan amount ÷

1

∑ (1 +.15) t

t =1

or Payment

= $100,000 ÷ 6.566 = $15,229.97

Next, we have to calculate the outstanding or remaining balance of the loan at the end of the fifth year where five annual installments of $15,229.97 have been made. To do this, we must go through the calculations outlined in Table 24-1. Remaining

Year Loan Payment

Interest

Principal Balance

0 $100,000.00 1 $15,229.97 $15,000.00 $ 229.97 99,770.03 2 15,229.97 14,965.50 264.47 99,505.56 3 15,229.97 14,925.83 304.14 99,201.42 4 15,229.97 14,880.21 349.76 98,851.66 5 113,679.41 14,827.75 98,851.66 0 Thus, the fifth year balloon payment will equal the principal remaining at the end of that year of $98,851.66 plus interest for the year of $14,827.75 for a total of $113,679.41. This type of loan agreement is frequently used by homeowners who give buyers a second loan on a home purchase. The loan will usually be amortized or have installment payments calculated over a 30-year period but require full repayment in a 5- or 10-year period.

252

SOLUTION TO INTEGRATIVE PROBLEM (a)

Initial outlay (IO) = $60,000 Computing annual net cash flows Annual cash savings Less: depreciation

Book profits $27,000 (12,500)

Cash flows $27,000

14,500 (7,250)

27,000 (7,250)

Net revenues before taxes Less: taxes (50%)

Annual after-tax cash flows (1-3) Plus: salvage value

$19,750 10,000

Annual after-tax cash flow (4)

$29,750

Years 1-3 Year 4

Calculating NPV (P): 4

NPV(P)

= $19,750

1

∑ t t =1 (1.12)

+ $10,000 - $60,000

= $19,750(3.037) + $10,000(0.636) - $60,000 = $59,980.75 + $6,360 - $60,000 = $6,340.75 Thus, the computer should be acquired via normal purchase financing, as it has a positive NPV(P) of $6,340.75.

(b)

Calculating principal and interest components of a loan equal to the full $60,000 purchase price of the asset: 4

Loan payment = $60,000 ÷ Year 0 1 2 3 4

1

∑ t = t =1 (1.08)

$18,115.94

Payment

Principal

Interest

$18,115.94 18,115.94 18,115.94 18,115.94

$13,315.94 14,381.22 15,531.71 16,774.25

$4,800.00 3,734.72 2,584.23 1,341.69

Remaining Balance $60,000.00 46,684.06 32,302.84 16,771.13 (3.12)

Rounding errors produced a $3.12 difference in the remaining balance and principal portion of the fourth year payment.

253

254

4

(1)

Year

After-tax operating expenses paid by lessor Ot(1-T)

1 2 3 4

Solving for

After-tax rental expenses -

1,000 1,000 1,000 1,000

Rt(1-T)

∑ t =1

O t (1 − T) − R t (1 − T) − I t T − D t T (Term one) (1 + rb ) t

Tax Shelter on loan (interest lost by leasing) -

$9,000 9,000 9,000 9,000

ItT

Depreciation Tax Shelter -

$2,400 1,868 1,292 671

TDt

Total SUM

=

$6,250 6,250 6,250 6,250

Discount Factor 4% x

-$16,650 -16,118 - 15,542 - 14,921 (Term one)

591

Vn

Solving for: -

(3)

Adding: IO:

(4)

Net Advantage of Leasing (NAL)

(1 + k s )

n

= -

10 ,000

(2)

(1.12 ) 4

= (Term two) (Term three)

DF 0.962 0.925 0.889 0.855

=

Present Value =

PV -$16,017 - 14,909 - 13,817 - 12,757 - $57,500

=

- 6,360

=

60,000 $ (3,860)

(c) The NAL is negative, indicating that lease financing is not preferred to normal purchase financing. That is, the net present value of the asset, if leased, is equal to NPV(P) + NAL or $6,340 - $3,860 = $2,480. The asset should not be leased.

Solutions to Problem Set B 24-1B. Interest Rate Face Amount Year 0 1 2 3 4 5

12.0% $300,000.00

Payment

Interest

60,000.00 60,000.00 60,000.00 60,000.00 207,531.67

Principal

36,000.00 33,120.00 29,894.40 26,281.73 22,235.54

24,000.00 26,880.00 30,105.60 33,718.27 185,296.13

Balance 300,000.00 276,000.00 249,120.00 219,014.40 185,296.13 0

Thus, the fifth year balloon payment will equal the principal remaining at the end of that year of $185,296.13 plus interest for the year of $22,235.54 for a total of $207,531.67. 24-2B. Interest Rate Equipment Price Number of Payments Rental Payment

15.0% 250,000.00 10 43,315.67

Present Value of the Rental Payments 7

24-3B. $100,000 = PAYMENT

$250,000.00

1

∑ t t =1 (1.16)

Payment = $24,761.27 24-4B. Year 1 2 3 4 5 6 7

Payment $24,758.60 24,758.60 24,758.60 24,758.60 24,758.60 24,758.60 24,758.60

Interest $16,000.00 14,598.62 12,973.03 11,087.34 8,899.93 6,362.55 3,419.18

Principal $8,758.60 10,159.98 11,785.57 13,671.26 15,858.67 18,396.05 21,339.42

Remaining Balance $91,241.40 81,081.42 69,295.85 55,624.59 39,765.92 21,369.87 30.45

Rounding errors produced a $30.45 difference in the remaining balance and principal portion of the seventh year payment.

80

81

24-5B. 5

(a)

1

∑ t t =1 (1 + r)

$250,000

= $69,000

where r

= the effective annual rate on the loan.

5

1

∑ t t =1 (1 + r)

=

$250 ,000 69 ,000

= 3.623

Looking in the annuity present value table we find that an r of 12% for a five-year loan is 3.605. Thus, the effective rate on the loan is approximately 12%. Actually, it is 11.79% (found using the Rate function in a financial spreadsheet). 5

(b )

(c)

= Payment

Payment

= $91,631.03

$300,000

= $425,000

1 (1 + r)

Thus, r (d)

5

=

1

∑ t t =1 (1.16)

$300,000

$300 ,000 $425 ,000

1 (1 + r) 5

= .7059

= 7.21%.

The effective rate of interest is lowest on the insurance loan.

24-6B. Bank Loan Alternative: Cost = 14% Manufacturer Financing Alternative: The cost of this alternative is not immediately apparent and must be calculated. We know that the following relationship holds for any equal payment installment loan: n

Loan Amount

= Payment

1

∑ t t =1 (1 + r)

where n is the term of the loan and r is the rate of interest charged on the remaining loan balance.

82

Using this relationship we can define 4

$500,000 4

Therefore,

= $175,000

1

$500 ,000

∑ t t =1 (1 + r)

1

∑ t t =1 (1 + r)

= $175 ,000

= 2.857

We now know the present value of an annuity factor that corresponds to a fouryear period and the rate of interest on the loan (r). Looking up this factor in the annuity present value table, we find that r = 15 percent. Therefore, bank loan alternative is preferred. 24-7B. (a)

IO = $25,000 Annual net cash flows: Annual cash savings Less: depreciation

Book profits $7,000 (5,000)

Cash flows $7,000

2,000 (1,000)

7,000 (1,000)

Net revenues before taxes Less: taxes (50%) Annual after-tax Cash flows Plus: salvage value

$6,000 5,000

Annual after-tax cash flow (4) 4

NPV

= $6,000

1

∑ t t =1 (1.13)

$11,000

+ $5,000

1 (1.13 ) 4

= $6,000 (2.974) + $5,000 (0.613) - $25,000

= -$4,091.00

Thus, the asset should not be purchased.

83

- $25,000

Years 1-3 Year 4

(b)

Calculating principal and interest on a loan of $25,000 at 10%. 4

Annual payment = $25,000/ Year 0 1 2 3 4

Payment

Interest

$8,058.16 8,058.16 8,058.16 8,058.16

$2,750.00 2,166.10 1,517.98 798.56 4

(1) Year 1

Ot(1-T) 625.00

Solving for

∑ t =1

1

∑ t = t =1 (1.11)

$8,058.16

Principal $5,308.16 5,892.06 6,540.18 7,259.60

Remaining Balance $25,000.00 19,691.84 13,799.78 7,259.60 0.00

O t (1 - T) - R(1 - T) - I t T - D t T (1 + rb )t

R(1-T) ItT DtT 3,500 1,375.00 2,500.00

= SUM -6,750.00

PV Factor .9479

PV -6,398.32

2

625.00

3,500

1,083.05

2,500.00

-6,458.05

.8985

-5,802.56

3

625.00

3,500

758.99

2,500.00

-6,133.99

.8516

-5,223.71

4

625.00

3,500

399.28

2,500.00

-5,774.28

.8072

-4,661.00

Term one= (Term two)

=

22,085.59

(2)

Solving for -

-3,065.00

(3)

Adding IO

25,000.00

(4)

Net advantage of leasing

- $ 150.59

Since the asset's NAL is negative, the asset should not be leased. 24-8B. (a)

The basic analytical relationship needed to solve for installment payments is found below: Loan Amount

n

1

t =1

(1 + k) t

= Payment ∑

84

Thus, for the first part of this exercise $125,000

1

12

= Payment ∑

(1.13)

t =1

t

or Payment

1

12

= $125,000 ÷ ∑

(1.13)

t =1

1

12

We recognize the summation term ∑

t =1

t

(1.13)

t

as a present

value annuity factor which is found in Appendix E. Thus, Payment

= $125,000 ÷ 5.918 = $21,122.00

(b)

In this problem we must recall the procedure for quarterly compounding. In general, the payment relationship in (a) becomes mn

Loan Amount = Payment ∑

t =1

1 (1 + k/m)

t

where m is the number of compounding periods in a year (e.g., m = 4 for quarterly compounding). Thus, $125,000

24

= Payment ∑

t =1

1 (1.0325)

t

Since the tables in Appendix E do not have fractional rates we must solve for the present value annuity interest factor algebraically or using the "payment" function in a financial spreadsheet software package. Payment

= $7,581.11

85

(c)

This problem requires that we first solve for the annual installment payments for each of the next five years based upon a 30-year installment period, i.e., 30

Payment

= Loan amount ÷

∑ t =1

1 (1 + .13)

t

or Payment

= $125,000 ÷ 7.496 = $16,675.56

Next, we have to calculate the outstanding or remaining balance of the loan at the end of the fifth year where five annual installments of $16,675.56 have been made. To do this, we must go through the calculations outlined in Table 24-1. Remaining

YearLoan Payment Interest 0 1 3 4 5

$16,675.56 16,675.56 16,675.56 16,675.56 138,917.82

$16,250.00 16,194.68 16,132.16 16,061.52 15,981.70

Principal $

425.56 480.88 543.40 614.04 122,936.12

Balance $125,000.00 124,574.44 124,093.56 123,550.16 122,936.12 0.00

Note that the fifth year balloon payment will equal the principal remaining at the end of that year of $122,936.12 plus interest for the year of $15,981.70 for a total of $138,917.82. This type of loan agreement is frequently used by homeowners who give buyers a second loan on a home purchase. The loan will usually be amortized or have installment payments calculated over a 30-year period but require full repayment in a 5- or 10-year period.

86

24-9B. (a)

Initial outlay (IO) = $65,000 Computing annual net cash flows Annual cash savings Less: depreciation

Book profits $29,000 (14,250)

Cash flows $29,000

14,750 (7,375)

29,000 (7,375)

Net revenues before taxes Less: taxes (50%) Annual after-tax cash flows (1-3)

$21,625

Plus: salvage value

Years 1-3

8,000

Annual after-tax cash flow (4)

$29,625

Year 4

Calculating NPV (P): NPV(P)

1

4

= $21,625 ∑

t =1

(1.14)

t

+ $8,000

1 (1.14 ) 4

- $65,000

= $21,625 (2.914) + $8,000 (0.592) - $65,000 = $2,751.25 Thus, the computer should be acquired via normal purchase financing, as it has a positive NPV(P) of $2,745.67.

(b)

Calculating principal and interest components of a loan equal to the full $65,000 purchase price of the asset: 4

Loan payment = $65,000 / ∑

t =1

Year 0 1 2 3 4

1 (1.08)

t

= $19,624.85

Payment

Principal

Interest

$19,624.85 19,624.85 19,624.85 19,624.85

$14,424.85 15,578.84 16,825.15 18,171.16

$5,200.00 4,046.01 2,799.70 1,453.69

87

Remaining Balance $65,000.00 50,575.15 34,996.31 18,171.16 0.00

O t (1 − T) − R t (1 − T) − I t T − D t T (1 + rb ) t

4

(1)

Solving for

∑

t =1

Year

After-tax Discount operating expenses Factor paid by lessor Total Ot(1-T) SUM

1 $18,600.00 2 18,023.01 3 17,399.85 4 16,726.85

After-tax

Tax Shelter

rental Present expenses 4%

on loan (interest

Depreciation

lost by leasing) Value

Tax Shelter

x

1,125 0.962 1,125 0.925 1,125 0.889 1,125 0.855

Rt(1-T) DF

=

$10,000 -$17,893 10,000 - 16,671 10,000 - 15,468 10,000 - 14,301

ItT PV

-

TDt

=

$2,600.00

$7,125

-

2,023.01

7,125

-

1,399.85

7,125

-

726.85

7,125

-

599

(Term = -

one) $64,333 (2)

Solving for - = -

8,000 (1.14 ) 4

two) 4,736 (3)

Adding: IO: three)

(4)

Net Advantage of Leasing (NAL)

=

(Term

=

(Term = 65,000 $

(4,069) (c)

The NAL is negative, indicating that lease financing is not preferred to normal purchase financing. 88

89