Chapter-11.docx

Chapter 11 Capital Budgeting Cash Flows Instructor’s Resources Overview This chapter expands upon the capital budgeting techniques presented in the last chapter (Chapter 10). Shareholder wealth maximization relies upon selection of projects that have positive net present values. The most important and difficult aspect of the capital budgeting process is developing good estimates of the relevant cash flows. Chapter 11 focuses on the basics of determining relevant after-tax cash flows of a  project, from the initial cash cash outlay to annual cash stream stream of costs and benefits and and terminal cash flow. It also describes the special concerns facing capital budgeting for the multinational company. company. The text highlights how capital budgeting will be a critical aspect of the professional life and personal life of students upon graduation.

Suggested Answer to Opene  Question Openerr in R eview  Question The chapter opener talked about ExxonMobil’s considerable investment in long-term long-term projects and the sometimes difficult task of having projects come in on budget. How are project cash flows affected by budget overruns? In the capital budgeting process, how should financial managers account for the potential of budget overruns?

It is critical to have the best estimate of project cash flows po ssible when making a project accept/reject decision. Depending upon the scope of a project, financial managers may need to draw information from many areas of a corporation including research and development, marketing, operations, human resources, and within the various departments dealing with corporate finance. It may be possible to get some of the information directly from the project managers if they have done some of the legwork already. Budget overruns mean higher than expected costs, and therefore lower than expected cash flows. Lower than expected cash flows mean lower than expected capital budgeting outcomes (e.g., lower NPVs, PIs, IRRs, etc.). If financial managers do not adequately account for possible budget overruns in the capital  budgeting  budgeting process they are are unlikely unlikely to fully fully maximize maximize firm value. Chapter Chapter 12 consider considerss the uncertai uncertainty nty of cash flows in more detail and discusses some of the methods used by financial f inancial managers to account for the uncertainty of cash flows. In particular, ExxonMobil could generate a range or distribution of capital  budgeting  budgeting outcomes outcomes for projects projects that have have uncertain uncertain cash flows due to possible possible budget budget overruns. overruns. ExxonMobil ExxonMobil should calculate NPVs using cash flows that assume no budget overrun a nd a variety of possible budget overruns and then calculate an expected average NPV where the weights reflect the probably of each eac h  budget outcome.

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Answers to Review Questions 1. Capital budgeting budgeting projects should be evaluated evaluated using using incremental after-tax cash flows , since after-tax cash flows are what is available to the firm. When evaluating a project, concern is placed only on added cash flows expected to result from its implementation. Expansion decisions can be treated as replacement decisions in which all cash flows from the old assets are a re zero. Both expansion and replacement decisions involve purchasing new assets. Replacement decisions are more complex  because incremental cash flows flows resulting from the replacement replacement must be determined. 2. The three components of cash flow for for any project are (1) initial investment, investment, (2) operating cash flows, and (3) terminal cash flows. 3. Sunk costs are costs that have already been incurred and thus the money has already been spent. Opportunity costs  are cash flows that could be realized from the next best alternative use of an owned asset. Sunk costs are not relevant to the investment decision because they are not incremental. These costs will not change no matter what the final accept/reject decision. Opportunity costs are a relevant cost. These cash flows could be realized if the decision is made not to change the current asset structure but to utilize the owned asset for this alternative purpose. 4. To minimize long-term long-term currency risk, companies companies can finance a foreign investment investment in local capital capital markets so that the project’s revenues and costs are in the local currency rather than dollars. Techniques such as currency futures, forwards, and options market instruments protect against shortterm currency risk. Financial and operating strategies that r educe political risk include structuring the investment as a joint venture with a competent and well-connected local partner, and using debt rather than equity financing, since debt service payments are legally enforceable claims while equity returns such as dividends are not. 5. a. The cost of the new asset  is the purchase price. (Outflow)  b.  Installation costs are any added costs necessary to get an asset into operation. (Outflow) c.  Proceeds from sale of  are cash inflows resulting from the sale of an existing asset, of old asset  asset  are reduced by any removal costs. (Inflow) d. Tax on sale of old asset  is  is incurred when the replaced asset is sold due to recaptured depreciation, capital gain, or capital loss. (May be an inflow or an outflow) e. The change in net working capital  is the difference between the change in current assets and the change in current liabilities. (May be an inflow or an outflow) 6. The book value of an asset is its strict accounting value. Book value  installed cost of asset  –  accumulated  accumulated depreciation Gains and losses in the sale of an asset may have tax consequences, and hence are both key forms of taxable income. More specifically, taxable income may arise from (1) capital gain: portion of sale  price above initial purchase purchase price, taxed at the ordinary rate; (2) recaptured depreciation: portion portion of sale price in excess of book value that represents a recovery of previously taken depreciation, taxed at the ordinary rate; and (3) loss on the sale of an asset: amount by which sale price is less than book value, taxed at the ordinary rate and deducted from ordinary income if the asset is depreciable and used in business. If the asset is not depreciable or is not used in business, it is also taxed at the ordinary rate but is deductible only against capital gains.

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7. The asset may be sold (1) for more more than its book book value, (2) for the amount of its book value, or (3) at a price below book value. In the first case, taxes arise from the amount by which the sa le price exceeded the book value. In the second case, no taxes would be required. In the third case, a tax credit would occur. 8. The depreciable value value of an asset is the installed installed cost of a new asset and is based on the depreciable cost of the new project, including installation installation cost. 9. Depreciation is used to decrease the firm’s total tax liability and then is added back to net profits after taxes to determine cash flow. Table Ta ble 11.6 and Equation 3.4 (refer to the text) are equivalent ways of expressing operating cash flows. The earnings before interest and taxes in Table 11.6 is the same as the EBIT terminology in Equation 3.4. Both models then take out taxes and add back in depreciation. 10. To calculate incremental incremental operating cash cash inflow for both the existing existing situation and the proposed proposed  project, the depreciation on assets is added back to the the after-tax profits to get the cash flows flows associated with each alternative. The difference between the cash flows of the proposed and present situation, the incremental after-tax cash flows, are the relevant operating cash flows used in evaluating the proposed project. 11. The terminal cash flow is the cash flow resulting from termination and liquidation of a project at the end of its economic life. The form of calculating terminal cash flows is shown below: Terminal Cash Flow Calculation: After-tax  proceeds from sale of new asset

 – 

After-tax  proceeds from sale of old asset

 – 

Proceeds from sale of old asset  Tax on sale of old asset



Change in net working capital

=

Terminal cash flow

Extended Presentation: Proceeds from sale of new asset  Tax on sale of new asset



Change in net working capital

=

Terminal cash flow

12. The relevant cash flows  necessary for a conventional capital budgeting project are the incremental after-tax cash flows attributable to the proposed project: the initial investment, the operating cash inflows, and the terminal cash flow. The initial investment is the initial outlay required, taking into account the installed cost of the new asset, proceeds from the sale of the old asset, tax on the sale of the old asset, and any change in net working capital. The operating cash inflows are the additional cash flows received as a result of implementing a proposal. Terminal cash flow represents the aftertax cash flows expected to result from the liquidation of the project at the end of its life. These three components represent the positive or negative cash flow impact if the firm implements the project, and are depicted in the following diagram for a project lasting 5 years.

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Suggested Answer to G loba loball Focus Box: Changes May Influence Future Investments in China Although China has been actively campaigning for foreign investment, how do you think having a communist government affects its foreign investment?

Having a communist government has a negative affect on foreign direct investment (FDI). As in all investments abroad, FDI in China entails high travel and communications expenses. The differences of  political system and culture culture that exist between the country of the investor investor and the host country will will also cause problems with foreign direct investment in China. Due to its control of the economy, the communist  party has more control over employment, employment, raw materials, and repatriation repatriation of revenues to a parent firm than than found in non-communist countries. There is also the chance that a company may lose ownership of its overseas operations to a Chinese company. Hence, foreign f irms often partner with Chinese firms in their development efforts, but this requires coordination and raises the costs of FDI in China.

Suggested Answer to Focus on E thics  Box: A Question of Accuracy What would your options be when faced with the demands of an imperial chief executive officer (CEO) who expects you to t o “make it work”? Brainstorm several options.

There is a chance that you may be working for an “imperial CEO” at some point in your career. This may  be by choice choice or by chance. While the “make it work” mandate mandate may may seem like an o rder to do anything it takes to accomplish your job, you are under no obligation to do anything unethical or illegal. If that is the only way to accomplish the job, the best approach is to ask your superior directly, “Is (this) what you want me to do?”

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If the answer is that you should break the law or do something unethical, you may have three viable options other than doing something that you should not do. One option is to seek the guidance of your “mentor” if you have one in the company. He or she may be able to intervene on your behalf. Another option is to take the matter over your boss’s head (in the case of a CEO, that would be the board of directors). The third option is to evaluate your career options. You may be better served working elsewhere. Realistically, Re alistically, by offering opposition to an “imperial CEO,” you may be limiting your career in your present company. However, do not immediately assume that “do whatever it takes” or “make it work” automatically includes anything unethical or illegal. The CEO may just j ust be stating that more resources or effort need to be put into solving the problem.

Answers to Warm-Up Exercises E11-1.

Categorizing a firm’s expenditures

Answer:

In this case, the tuition reimbursement should be categorized as a capital expenditure since the outlay of funds is expected to produce benefits over a period of time greater than 1 year.

E11-2. Classification of project costs and cash flows sunk cost (irrelevant) Answer: $3.5 billion already spent —   — sunk $350 million incremental cash outflow — relevant relevant cash flow $15 million per year cash inflow — relevant relevant cash flow $450 million for satellites — opportunity opportunity cost and relevant cash flow E11-3.

Finding the initial investment

Answer:

$20,000 Purchase price of new machinery $3,000 Installation costs  $4,500 After-tax proceeds from sale of old machinery $18,500 Initial investment

E11-4.

Book value and recaptured depreciation

Answer:

Book value  $175,000  $124, 250  $50,750 Recaptured depreciation  $110,000  $50, 750  $59,250

E11-5.

Initial investment

Answer:

Initial investment  purchase price  installation costs  –  after-tax  after-tax proceeds from sale of old asset  change in net working capital  $23,750  $2,000  $40,750  $55,000  $7,500 –  $23,750

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Solutions to Problems  Note: The

MACRS depreciation percentages used in the following problems appear in Chapter 4, Table 4.2. The percentages are rounded to the nearest integer for ease in calculation. For simplification, 5-year-lived projects with 5 years of cash inflows are typically used throughout this chapter. Projects with usable lives equal to the number of years of cash inflows are also included in the end-of-chapter problems. It is important to recall from Chapter 4 that under the Tax Reform Ref orm Act of 1986, MACRS depreciation results in n  1 years of depreciation for an n-year class asset. This means that in actual practice projects will typically have at least one year of cash flow beyond their recovery period.

P11-1. Classification of expenditures LG 2; Basic

a.  b. c. d. e. f. g. h.

Operating expenditure — lease lease expires within one year Capital expenditure —   patent rights exist exist for many years Capital expenditure — research research and development benefits last many years Operating expenditure — marketable marketable securities mature in under one year Capital expenditure — machine machine will last over one year Capital expenditure —   building tool will will last over one year Capital expenditure —   building will last for more than one year Operating expenditure — market market changes require obtaining another report within a year

P11-2. Relevant cash flow and timeline depiction depiction LG 1, 2; Intermediate

a. Year

Cash Flow

This is a conventional cash flow patt ern, where the cash inflows are of equal size, which is referred to as an annuity.

 b.

This is a conventional cash flow pattern, p attern, where the subsequent cash inflows vary, which is referred to as a mixed stream.

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c.

This is a nonconventional cash flow pattern, which has several cash flow series of equal size, which is referred to as an embedded annuity.

P11-3. Expansion versus replacement cash cash flows flows LG 3; Intermediate

a. Year

Relevant Cash Flows

Initial investment 1 2 3 4 5  b.

($28,000) 4,000 6,000 8,000 10,000 4,000

An expansion project is simply a replacement decision decision in which all cash flows flows from the old asset are zero.

P11-4. Sunk costs and opportunity opportunity costs LG 2; Basic

a.

 b.

The $1,000,000 $1,000,000 development development costs should not not be considered part of the decision decision to go ahead with the new production. This money has already been spent and cannot be retrieved so it is a sunk cost. The $250,000 sale price of the existing line is an opportunity opportunity cost. If If Masters Golf Products does not proceed with the new line of clubs they will not receive the $250,000.

c.

P11-5. Sunk costs and opportunity opportunity costs LG 2; Intermediate

a.  b.

Sunk cost —  The funds for the tooling had already been expended and would not change, no  — The matter whether the new technology would be acquired or not. Opportunity cost —  The development of the computer programs can be done without  — The additional expenditures on the computers; however, the loss of the cash inflow from the leasing arrangement would be a lost opportunity to the firm.

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Opportunity cost —  Covol will not have to spend any funds for floor space but the lost cash  — Covol inflow from the rent would be a cost to the firm. Sunk cost —  The money for the storage facility has already been spent, and no matter what  — The decision the company makes there is no incremental cash flow generated or lost from the storage building.  — Forgoing Opportunity cost —  Forgoing the sale of the crane costs the firm $180,000 of potential cash inflows.

d.

e.

P11-6. Personal finance: Sunk and opportunity cash flows LG 2; Intermediate a. The sunk costs or cash cash outlays outlays are expenditures expenditures that have been made made in the past and have no no effect on the cash flows relevant to a current situation. The cash outlays done before David and Ann decided to rent out their home would be classified as sunk costs. An opportunity cost or cash flow is one that can be realized from an alternative use of an existing asset. Here, David and Ann have decided dec ided to rent out their home, and all the costs associated with getting the home in “rentable” condition would be relevant.  b. Sunk costs (cash flows): Replace water heater Replace dish washer Miscellaneous repairs and maintenance Opportunity costs cash flows: Rental income Advertising House paint and power wash

P11-7. Book value LG 3; Basic

Asset

A B C D E

Installed Cost

$ 950,000 40,000 96,000 350,000 1,500,000

Accumulated Depreciation

Book Value

$ 674,500 13,200 79,680 70,000 1,170,000

$275,500 26,800 16,320 280,000 330,000

P11-8. Book value and taxes on sale of of assets LG 3, 4; Intermediate

a.

Book value  $80,000  (0.71  $80,000)  $23,200

 b. Sale Price

Capital Gain

Tax on Capital Gain

Depreciation Recovery

Tax on Recovery

Total Tax

$100,000 56,000 23,200 15,000

$20,000 0 0 0

$8,000 0 0 0

$56,800 32,800 0 (8,200)

$22,720 13,120 0 (3,280)

$30,720 13,120 0 (3,280)

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P11-9. Tax calculations LG 3, 4; Intermediate

Current book value  $200,000  [(0.52  ($200,000)]  $96,000 (a)

Capital gain Recaptured depreciation Tax on capital gain Tax on depreciation Recovery Total tax

(b)

(c)

(d)

$ 20,000 104,000 8,000

$0 54,000 0

$0 0 0

$0 (16,000) 0

41,600 $ 49,600

21,600 $21,600

0 $0

(6,400) ($6,400)

P11-10. Change in net working capital calculation LG 3; Basic

a. Current Assets

Cash Accounts receivable Inventory  Net change

Current Liabilities $15,000 150,000

Accounts payable Accruals

10,000 $155,000

$90,000 

40,000



$130,000

 Net working capital  current assets  current liabilities  NWC  $155,000  $130,000  NWC  $25,000

 b. c.

Analysis of the purchase of of a new machine reveals an increase in net net working capital. This This increase should be treated as an initial outlay and is a cost of acquiring the new machine. Yes, in computing the terminal terminal cash flow, the the net working capital increase should should be reversed.

P11-11. Calculating Calculating initial investment LG 3, 4; Intermediate

a.  b.

Book value  $325,000  (1 0.20 –  0.32)  0.32)  $325,000  0.48  $156,000 Sales price of old equipment $200,000 Book value of old equipment 156,000 Recapture of depreciation $ 44,000 Taxes on recapture of depreciation  $44,000  0.40  $17,600 After-tax proceeds  $200,000  $17,600  $182,400

c.

Cost Cost of new machine Less sales price of old machine Plus tax on recapture of depreciation Initial investment

$ 500,000 (200,000) 17,600 $ 317,600

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P11-12. Initial investment —   basic calculation  —  LG 3, 4; Intermediate

Installed cost of new asset  Cost of new asset  Installation costs Total installed cost (depreciable value) After-tax proceeds from sale of old asset  Proceeds from sale of old asset  Tax on sale of old asset Total after-tax proceeds — old old asset Initial investment Book value of existing machine

$ 35,000 5,000 $40,000 ($25,000) 7,680 ($17,320) $22,680

 $20,000  (1  (0.20  0.32  0.19))  $5,800

Recaptured depreciation

 $20,000  $5,800

 $14,200

Capital gain

 $25,000  $20,000  $5,000

Tax on recaptured depreciation  $14,200  (0.40)   $5,680 Tax on capital gain  $5,000  (0.40)   2,000 Total tax

 

$7,680

P11-13. Initial investment at various sale prices LG 3, 4; Intermediate (a)

Installed cost of new asset: Cost of new asset  Installation cost Total installed cost After-tax proceeds from sale of old asset Proceeds from sale of old asset *  Tax on sale of old asset Total after-tax proceeds Initial investment

(b)

(c)

(d)

$24,000 2,000 26,000

$24,000 2,000 26,000

$24,000 2,000 26,000

$24,000 2,000 26,000

(11,000) 3,240 (7,760) $18,240

(7,000) 1,640 (5,360) $20,640

(2,900) 0 (2,900) $23,100

(1,500) (560) (2,060) $23,940

Book value of existing machine  $10,000  [1  (0.20  0.32 0.19)]  $2,900 *

Tax Calculations: a.

 b. c.

Recaptured depreciation

 

$10,000  $2,900



$7,100

Capital gain

 

$11,000  $10,000

 

$1,000

Tax on ordinary gain

 

$7,100  (0.40)

 

$2,840

Tax on capital gain

 

$1,000  (0.40)

 

400

Total tax

 

Recaptured depreciation

 

$7,000  $2,900

 

$4,100

Tax on ordinary gain

 

$4,100  (0.40)

 

$1,640

$3,240

0 tax liability

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d.

Loss on sale of existing asset

 

$1,500  $2,900

Tax benefit

 $

1,400  (0.40)

  

($1,400) $ 560

P11-14. Calculating Calculating initial investment LG 3, 4; Challenge

a.

Book value  ($60,000  0.31)  $18,600

 b.

Sales price of old equipment equipment Book value of old equipment Recapture of depreciation

$35,000 18,600 $16,400

Taxes on recapture of depreciation  $16,400  0.40  $6,560 Sale price of old roaster $35,000 Tax on recapture of depreciation (6,560) After-tax proceeds from sale of old roaster $28,440 c.

Changes in current asset accounts Inventory Accounts receivable  Net change

$ 50,000 70,000 $ 120,000

Changes in current liability accounts Accruals $ (20,000) Accounts payable 40,000  Notes payable 15,000 $ 35,000

 Net change Change in net working capital d.

Cost of new roaster

$ 85,000 $130,000

Less after-tax proceeds from sale of old roaster 28,440 Plus change in net working capital 85,000 Initial investment $186,560 P11-15. Depreciation LG 5; Basic Depreciation Schedule Year

1 2 3 4 5 6

Depreciation Expense

$68,000 68,000 68,000 68,000 68,000 68,000

     

0.20  $13,600 0.32  21,760 0.19  12,920 0.12  8,160 0.12  8,160 0.05  3,400

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P11-16. Incremental operating cash inflows LG 5; Intermediate

a.

Incremental profits before depreciation and tax

  $1,200,000  $480,000  $720,000

each year

 b. Year

(1)

(2)

(3)

(4) ( 4)

(5)

(6)

PBDT Depr.  NPBT Tax  NPAT

$720,00 $720 ,000 0 400,000 320,000 128,000 192,000

$720,000 640,000 640,000 80,000 32,000 48,000

$720,000 $720,000 380,000 340,000 136,000 204,000

$720,000 240,000 480,000 192,000 288,000

$720,000 240,000 480,000 192,000 288,000

$720,000 100,000 620,000 248,000 372,000

c. Cash flow

(1) $592,000

(2) $688,000

(3) $584,000

(4) $528,000

(5) $528,000

(6) $472,000

(NPAT  depreciation) PBDT  Profits before depreciation and taxes  NPBT  Net profits before taxes  NPAT  Net profits after taxes P11-17. Personal finance: Incremental operating cash inflows LG 5; Challenge Richard and Linda Thomson Incremental Operating Cash Flows Replacement of John Deere Riding Mower

Savings from new and improved mower Annual maintenance cost Depreciation

*

Savings (loss) before taxes Taxes (40%) Savings (loss) after taxes Depreciation Depreci ation Incremental operating cash flow

Year 1 $500

Year 2 Year 3 $ 500 $500

Year 4 $500

Year 5 $500

Year 6  — 

120

120

120

120

120

0

360

576

342

216

216

90

20

(196)

38

164

164

(90)

8

(78)

15

66

66

(36)

12

(118)

23

98

98

(54)

342 $365

216 $314

216 $314

360 $372

576 $ 458

*

MACRS Depreciation Schedule Year Base MACRS Year 1 $1,800 20.0% Year 2 1,800 32.0% Year 3 1,800 19.0% Year 4 1,800 12.0% Year 5 1,800 12.0% Year 6 1,800 5.0%

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Depreciation $360 576 342 216 216 90

90 $ 36

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P11-18. Incremental operating cash inflows — expense expense reduction LG 5; Intermediate Year

(1)

(2)

(3)

(4)

(5)

$16,000

$16,000

$16,000

$16,000

$16,000

$0

16,000 9,600

16,000 15,360

16,000 9,120

16,000 5,760

16,000 5,760

0 2,400

6,400

640

6,880

10,240

10,240

2,400

Taxes

2,560

256

2,752

4,096

4,096

960

 Net profits after taxes

3,840

384

4,128

6,144

6,144

1,440

13,440

15,744

13,248

11,904

11,904

960

Incremental expense savings Incremental profits  before dep. and taxes* Depreciation  Net profits  before taxes

Operating cash inflows**

(6)

*

Incremental profits before depreciation depreciation and taxes will increase the same amount as the decrease in expenses.  Net profits after taxes plus depreciation expense.

**

P11-19. Incremental operating cash inflows LG 5; Intermediate

a. Expenses (excluding depreciation Revenue and interest)

Year New Lathe 1 2 3 4 5 6 Old Lathe 1 – 5

 b.

Profits before Depreciation and Taxes

Depreciation

$40,000 41,000 42,000 43,000 44,000 0

$30,000 30,000 30,000 30,000 30,000 0

$10,000 11,000 12,000 13,000 14,000 0

$2,000 3,200 1,900 1,200 1,200 500

$35,000

$25,000

$10,000

0

Net Profits before Taxes

Taxes

$8,000 $3,200 7,800 3,120 10,100 4,040 11,800 4,720 12,800 5,120 (500) (200) $10,000

$4,000

Calculation of incremental cash inflows Year

1 2 3 4 5 6

New Lathe

Old Lathe

$6,800 7,880 7,960 8,280 8,880 200

$6,000 6,000 6,000 6,000 6,000 0

Incremental Cash Flows

$800 1,880 1,960 2,280 2,880 200

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Net Operating Profits Cash after Tax Inflows

$4,800 4,680 6,060 7,080 7,680 (300)

$6,800 7,880 7,960 8,280 8,880 200

$6,000

$6,000

Chapter 11

Capital Budgeting Cash Flows

c.

P11-20. Determining incremental operating cash flows LG 5; Intermediate Year 1

Revenues: (000)  New buses $1,850 Old buses 1,800 Incremental revenue $50 Expenses: (000)  New buses $460 Old buses 500 Incremental expense $ (40) Depreciation: (000)  New buses $ 600 Old buses 324 Incremental depr. $276 Incremental depr. tax savings @40% 110 Net Incremental Cash Flows Cash flows: (000) Revenues $50 Expenses 40 Less taxes @40% (36) Depr. tax savings 110  Net operating cash inflows $164

2

3

4

5

6

$1,850 1,800 $50

$1,830 1,790 $40

$1,825 1,785 $40

$1,815 1,775 $40

$1,800 1,750 $50

$460 510 $ (50)

$468 520 $ (52)

$472 520 $ (48)

$485 530 $ (45)

$500 535 $ (35)

$ 960 135 $825

$ 570 0 $570

$ 360 0 $360

$ 360 0 $360

$ 150 0 $150

330

228

144

144

60

$50 50 (40) 330

$40 52 (37) 228

$40 48 (35) 144

$40 45 (34) 144

$50 35 (34) 60

$390

$283

$197

$195

$111

P11-21. Terminal cash flows — various various lives and sale prices LG 6; Challenge

a. After-tax proceeds from sale of new asset Proceeds from sale of proposed asset *  Tax on sale of proposed asset Total after-tax proceeds — new new  Change in net working capital Terminal cash flow



3-Year*  $10,000

5-Year*  $10,000

7-Year* $10,000

16,880

400

4,000

$26,880 30,000 $56,880

$9,600 30,000 $39,600

$ 6,000 30,000 $36,000

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*

1.

2.

3.

 b.

Book value of asset  [1 (0.20  0.32  0.19)]  $180,000  $52,200 Proceeds from sale $10,000  $52,200 $42,200  (0.40)

 $10,000

Book value of asset

 [1  (0.20  0.32  0.19  0.12  0.12)]  $180,000  $9,000

$10,000  $9,000 $1,000  (0.40)

 $1,000

Book value of asset

 $0

$10,000  $0 $10,000  (0.40)

 $10,000

 ($42,200)

loss  $16,880 tax benefit recaptured depreciation  $400 tax liability recaptured depreciation  $4,000 tax liability

If the usable life is less than the normal recovery period, the asset asset has not been depreciated fully and a tax benefit may be taken on the loss; therefore, the terminal cash flow is higher.

c. (1)

After-tax proceeds from sale of new asset Proceeds from sale of new asset *  Tax on sale of proposed asset



 Change

in net working capital Terminal cash flow 1. 2.

d.

(2)

$ 9,000 0

$170,000 (64,400)

30,000

30,000

$39,000

$135,600

Book value of the asset  $180,000  0.05  $9,000; no taxes are due Tax  ($170,000  $9,000)  0.4  $64,400.

The higher higher the sale price, price, the higher the terminal terminal cash flow.

P11-22. Terminal cash flow — replacement replacement decision LG 6; Challenge

After-tax proceeds from sale of new asset  Proceeds from sale of new machine $75,000 l (14,360)  Tax on sale of new machine   Total after-tax proceeds — new new asset  After-tax proceeds from sale of old asset Proceeds from sale of old machine (15,000) 2 6,000  Tax on sale of old machine   Total after-tax proceeds — old old asset  Change in net working capital Terminal cash flow 1

$60,640

(9,000) 25,000 $76,640

Book value of new machine at end of year 4: [1  (0.20  0.32 0.19  0.12)  ($230,000)]   $39,100

2

$75,000  $39,100



$35,900 recaptured depreciation depreciation

$35,900  (0.40)



$14,360 tax liability liability

$15,000  $0



$15,000 recaptured depreciation depreciation

$15,000  (0.40)

 $6,000

Book value of old machine at end of year 4: $0 tax benefit

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P11-23. Relevant cash flows for f or a marketing campaign ca mpaign LG 3, 4, 5, 6; Challenge Marcus Tube Calculation of Relevant Cash Flow ($000) Calculation of Net Profits after Taxes and Operating Cash Flow: with Marketing Campaign 2013

Sales CGS (@ 80%) Gross profit Less: Operating expenses General and administrative (10% of sales) Marketing campaign Depreciation Total operating expenses  Net profit  before taxes Less: Taxes 40%  Net profit after taxes  Depreciation Operating CF

2014

2015

2016

2017

$20,500 16,400 $ 4,100

$21,000 16,800 $ 4,200

$21,500 17,200 $ 4,300

$22,500 18,000 $ 4,500

$23,500 18,800 $ 4,700

$ 2,050 150 500

$ 2,100 150 500

$ 2,150 150 500

$ 2,250 150 500

$ 2,350 150 500

2,700

2,750

2,800

2,900

3,000

$ 1,400 560

$ 1,450 580

$ 1,500 600

$ 1,600 640

$ 1,700 680

$ 840 500 $ 1,340

$ 870 500 $ 1,370

$ 900 500 $ 1,400

$ 960 500 $ 1,460

$ 1,020 500 $ 1,520

Without Marketing Campaign Years 2013 – 2017 2017

 Net profit after taxes  Depreciation Operating cash flow

$ 900 500 $1,400 Relevant Cash Flow ($000)

Year

2013 2014 2015 2016 2017

With Marketing Campaign

$1,340 1,370 1,400 1,460 1,520

Without Marketing Incremental Campaign Cash Flow

$1,400 1,400 1,400 1,400 1,400

$(60) (30) 0 60 120

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P11-24. Relevant cash flows — no no terminal value LG 3, 4, 5; Challenge

a.

Installed cost of new asset Cost of new asset $76,000 4,000  Installation costs Total cost of new asset asset  After-tax proceeds from sale of old asset Proceeds from sale of old asset (55,000) * 16,200  Tax on sale of old asset   Total proceeds, sale of old asset Initial investment *

$80,000

(38,800) $41,200

Book value of old machine:

[1  (0.20  0.32  0.19)]  $50,000

 

$14,500

$55,000  $14,500



$40,500 gain on asset

$35,500 recaptured depreciation  0.40

 

$14,200

$5,000 capital gain  0.40

 

2,000

Total tax on sale of asset

 

$16,200

 b. Calculation of Operating Cash Flow Year

(1)

(2)

(3)

(4)

(5)

Old Machine PBDT Depreciation  NPBT Taxes  NPAT Depreciation Cash flow

$14,000 6,000 $ 8,000 3,200 $ 4,800 6,000 $10,800

$16,000 6,000 $10,000 4,000 $ 6,000 6,000 $12,000

$20,000 2,500 $17,500 7,000 $10,500 2,500 $13,000

$18,000 0 $18,000 7,200 $10,800 0 $10,800

$14,000 0 $14,000 5,600 $ 8,400 0 $ 8,400

$0 0 0 0 $0 0 $0

New Machine PBDT Depreciation  NPBT Taxes  NPAT Depreciation Cash flow

$30,000 16,000 $14,000 5,600 $ 8,400 16,000 $24,400

$30,000 25,600 $ 4,400 1,760 $ 2,640 25,600 $28,240

$30,000 15,200 $14,800 5,920 $ 8,880 15,200 $24,080

$30,000 9,600 $20,400 8,160 $12,240 9,600 $21,840

$30,000 9,600 $20,400 8,160 $12,240 9,600 $21,840

$0 4,000 $4,000 1,600 $2,400 4,000 $1,600

Incremental After-tax cash flows

$13,600

$16,240

$11,080

$11,040

$13,440

$1,600

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237

c.

P11-25. Integrative — determining determining relevant cash flows LG 3, 4, 5, 6; Challenge

a.

Initial investment: Installed cost of new asset  Cost of new asset  Installation costs Total cost of new asset

$105,000 5,000 $110,000

 After-tax

proceeds from sale of old asset  Proceeds from sale of old asset *  Tax on sale of old asset   Total proceeds from sale of old asset  Change in working capital Initial investment *

(70,000) 16,480 (53,520) 12,000 $ 68,480

Book value of old asset: [1  (0.20  0.32)]  $60,000

  $28,800

$70,000  $28,800  $41,200 gain on sale of asset $31,200 recaptured depreciation  0.40   $12,480 $10,000 capital gain  0.40

 

4,000

Total tax of sale of asset

  $16,480

 b. Calculation of Operating Cash Inflows

Year

Profits before Depreciation Net Profits Net Profits and Taxes Depreciation before Taxes Taxes after Taxes

New Grinder 1 $43,000 2 43,000 3 43,000 4 43,000 5 43,000 6 0

Operating Cash Inflows

$22,000 35,200 20,900 13,200 13,200 5,500

$21,000 7,800 22,100 29,800 29,800 5,500

$8,400 3,120 8,840 11,920 11,920 2,200

$12,600 4,680 13,260 17,880 17,880 3,300

$34,600 39,880 34,160 31,080 31,080 2,200

$11,400 7,200 7,200 3,000 0 0

$14,600 16,800 14,800 17,000 18,000 0

$5,840 6,720 5,920 6,800 7,200 0

$8,760 10,080 8,880 10,200 10,800 0

$20,160 17,280 16,080 13,200 10,800 0

Existing Grinder

1 2 3 4 5 6

$26,000 24,000 22,000 20,000 18,000 0

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Calculation of Incremental Cash Inflows Year

1 2 3 4 5 6 c.

New Grinder Existing Grinder

$34,600 39,880 34,160 31,080 31,080 2,200

Incremental Operating Cash Flow

$20,160 17,280 16,080 13,200 10,800 0

$14,440 22,600 18,080 17,880 20,280 2,200

Terminal cash flow: After-tax proceeds from sale of new asset  Proceeds from sale of new asset 

Tax on sale sale of new asset*  Total proceeds from sale of new asset

After-tax proceeds from from sale of old asset asset  Proceeds from sale of old asset  Tax on sale of old asset Total proceeds from sale of old asset  Change in net working capital Terminal cash flow

$29,000 (9,400) 19,600



*

d.

0 0 0 12,000 $31,600

Book value of asset asset at end end of of year year 5  $5,500 $29,000  $5,500



$23,500  0.40

 $9,400

Year 5 relevant cash flow: Operating cash flow Terminal cash flow Total inflow

$23,500 recaptured depreciation

$20,280 31,600 $51,880

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Capital Budgeting Cash Flows

239

P11-26. Personal finance: Determining relevant cash flows for a cash budget LG 3, 4, 5, 6; Challenge Jan and Deana Cash Flow Budget Purchase of Boat

a. Initial investment Total cost of new boat Add: Taxes (6.5%) Initial investment . Operating cash flows Maint. & repair 12 months at $800 Docking fees 12 months at $500 Operating cash flows

$(70,000) (4,550) $(74,550) Year 1 $(9,600) $(6,000) $(15,600)

Year 2 $(9,600) $(6,000) $(15,600)

Year 3 $(9,600) $(6,000) $(15,600)

. Terminal cash flow — end end of year 4 Proceeds from the sale of boat . Summary of cash flows Year zero End of year 1 End of year 2 End of year 3 End of year 4

Year 4 $(9,600) $(6,000) $(15,600)

$40,000 Cash Flow $(74,550) $(15,600) $(15,600) $(15,600) $24,400

e. The ownership of the boat is is virtually just an annual annual outflow of money. Across the four years, $96,950 will be spent in excess of the anticipated sales price in year 4. Over the same time  period, the disposable income income is only $96,000. Consequently, Consequently, if the costs exceed the expected disposable income. If cash flows were adjusted for their timing, and noting that the proceeds from the sale of the new boat comes in first at the end of year 4, Jan and Deana are in a  position where they will will have to increase their disposable disposable income in order order to accommodate  boat ownership. If a loan is needed, needed, the monthly interest interest payment would be another another burden. However, there is no attempt here to measure satisfaction of ownership. P11-27. Integrative — determining determining relevant cash flows LG 3, 4, 5, 6; Challenge

a. Initial Investment

A

Installed cost of new asset Cost of new asset  Installation costs Total proceeds, sale of new asset  After-tax proceeds from sale of old asset Proceeds from sale of old asset *  Tax on sale of old asset Total proceeds, sale of old asset  Change in working capital Initial investment *

Book value of old asset:

B

$ 40,000 8,000 48,000

$ 54,000 6,000 60,000

(18,000) 3,488 (14,512) 4,000 $37,488

(18,000) 3,488 (14,512) 6,000 $51,488

[1  (0.20  0.32  0.19)]  ($32,000)  $9,280

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 b. Calculation of Operating Cash Inflows

Year

Profits before Depreciation and Taxes

Depreciation

Net Profits before Taxes

$21,000 21,000 21,000 21,000 21,000 0

$9,600 15,360 9,120 5,760 5,760 2,400

$22,000 24,000 26,000 26,000 26,000 0 $14,000 14,000 14,000 14,000 14,000 0

Hoist A 1 2 3 4 5 6

Taxes

Net Profits after Taxes

Operating Cash Inflows

$11,400 5,640 5,640 11,880 15,240 15,240 2,400

$4,560 2,256 4,752 6,096 6,096 960

$6,840 3,384 7,128 9,144 9,144 1,440

$16,440 18,744 16,248 14,904 14,904 960

$12,000 19,200 11,400 7,200 7,200 3,000

$10,000 4,800 4,800 14,600 18,800 18,800 3,000

$4,000 1,920 5,840 7,520 7,520 1,200

$6,000 2,880 8,760 11,280 11,280 1,800

18,000 22,080 20,160 18,480 18,480 1,200

$3,840 3,840 1,600 0 0 0

$10,160 10,160 12,400 14,000 14,000 0

$4,064 4,064 4,960 5,600 5,600 0

$6,096 6,096 7,440 8,400 8,400 0

$9,936 9,936 9,040 8,400 8,400 0

Hoist B

1 2 3 4 5 6 Existing Hoist

1 2 3 4 5 6

Calculation of Incremental Cash Inflows Year

Hoist A

Hoist B

Existing Hoist

Incremental Hoist A

1 2 3 4 5

$16,440 18,744 16,248 14,904 14,904

$18,000 22,080 20,160 18,480 18,480

$9,936 9,936 9,040 8,400 8,400

$6,504 8,808 7,208 6,504 6,504

$8,064 12,144 11,120 10,080 10,080

6

960

1,200

0

960

1,200

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Cash Flow Hoist B

Chapter 11

c.

Capital Budgeting Cash Flows

Terminal cash flow: (A)

After-tax proceeds form sale of new asset Proceeds from sale of new asset l  Tax on sale of new asset Total proceeds — new new asset  After-tax proceeds from sale of old asset Proceeds from sale of old asset 2  Tax on sale of old asset Total proceeds — old old asset  Change in net working capital Terminal cash flow

$12,000 (3,840) 8,160

$20,000 (6,800) 13,200

(1,000) 400 (600) 4,000 $11,560

(1,000) 400 (600) 6,000 $18,600

1

 Book value of Hoist A at end of year 5  $2,400 $12,000  $2,400



$9,600 recaptured depreciation

$9,600  0.40



$3,840 tax

Book value of Hoist B at en d of year 5  $3,000 $20,000  $3,000



$17,000 recaptured depreciation

$17,000  0.40



$6,800 tax

2

 Book value of existing hoist at end of year 5  $0 $1,000  $0



$1,000 recaptured depreciation

$1,000  0.40



$400 tax

(B)

Year 5 relevant cash flow — Hoist Hoist A: Operating cash flow Terminal cash flow Total inflow

$ 6,504 11,560 $18,064

Year 5 relevant cash flow — Hoist Hoist B: Operating cash flow Terminal cash flow Total inflow

$10,080 18,600 $28,680

d.

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P11-28. Integrative — complete complete investment decision LG 1, 2, 3, 4, 5, 6; Challenge

a.

Initial investment: Installed cost of new press  Cost of new press  After-tax proceeds from sale of old asset Proceeds from sale of existing press *  Taxes on sale of existing press   Total after-tax proceeds from sale Initial investment

$2,200,000 (1,200,000) 480,000 (720,000) $1,480,000

*

Book value  $0 $1,200,000  $0  $1,200,000 income from sale of existing press $1,200,000 income from sale  (0.40)  $480,000

 b. Calculation of Operating Cash Flows Year Revenues

Expenses

1 2 3 4 5 6

$800,000 800,000 800,000 800,000 800,000 0

c.

$1,600,000 1,600,000 1,600,000 1,600,000 1,600,000 0

Net Profits Depreciation before Taxes

$440,000 704,000 418,000 264,000 264,000 110,000

$360,000 96,000 382,000 536,000 536,000 110,000

Taxes

$144,000 38,400 152,800 214,400 214,400 44,000

Net Profits after Taxes

$216,000 57,600 229,200 321,600 321,600 66,000

Payback period  2 years  ($62,400  $647,200)  2.1 years

d.  PV  of  of cash inflows: CF0  $1,480,000, CF1  $656,000, CF2  $761,600, CF 3  $647,200, CF4  $585,600, CF5  585,600, CF6  $44,000 Set I  11 Solve for NPV  $959,152 Year

1 2 3 4 5 6

CF  

PVIF11%,n

 PV 

$656,000 761,600 647,200 585,600 585,600 44,000

0.901 0.812 0.731 0.659 0.593 0.535

$ 591,056 618,419 473,103 385,910 347,261 23,540 $2,439,289

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Cash Flow

$656,000 761,600 647,200 585,600 585,600 44,000

Chapter 11

$0 

e.

$65 $656,000 ,000 (1  IRR)1



$761 761,600 ,600 (1  IRR )2



$647 $647,20 ,200 0 (1  IRR)3



$585 $585,60 ,600 0 (1  IRR)4



Capital Budgeting Cash Flows

$585 $585,60 ,600 0 (1  IR I RR )5



$44,00 44,000 0 (1 IRR )6



243

$1, 480, 000

IRR  35% Calculator solution: 35.04% The NPV is a positive positive $959,289 and and the IRR of 35% is well above the cost of capital of 11%. Based on both decision criteria, the project should be accepted.

P11-29. Integrative — investment investment decision LG 1, 2, 3, 4, 5, 6; Challenge

a.

Initial investment: Installed cost of new asset  Cost of the new machine 

$1,200,000

Installation costs Total cost of new machine

150,000 $1,350,000

 After-tax

proceeds from sale of old asset  Proceeds from sale of existing machine *  Tax on sale of existing machine   Total after-tax proceeds from sale  Increase in net working capital Initial investment

(185,000) (79,600) (264,600) 25,000 $1,110,400

*

Book value  $384,000

$185,000  $384,000  $199,000 loss from sale of existing press $199,000 loss from sale  (0.40)  $79,600

Calculation of Operating Cash Flows New Machine Reduction in Year Operating Costs

1 2 3 4 5 6

$350,000 350,000 350,000 350,000 350,000 0

Net Profits Depreciation before Taxes

$270,000 432,000 256,500 162,000 162,000 67,500

$80,000 82,000 93,500 188,000 188,000 67,500

Taxes

Net Profits after Taxes

$32,000 32,800 37,400 75,200 75,200 27,000

$48,000 49,200 56,100 112,800 112,800 40,500

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Cash Flow

$318,000 382,800 312,600 274,800 274,800 27,000

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Existing Machine Year

1 2 3 4 5 6

Depreciation

$152,000 96,000 96,000 40,000 0 0

Net Profits before Taxes

Taxes

$152,000

$60,800

96,000

38,400

96,000

38,400

40,000

16,000

0 0

0 0

Net Profits after Taxes

Cash Flow

$91,200 57,600 57,600 24,000 0 0

$60,800 38,400 38,400 16,000 0 0

Incremental Operating Cash Flows Year

1 2 3 4 5 6

New Machine

Existing Machine

Incremental Cash Flow

$60,800 38,400 38,400 16,000 0 0

$257,200 344,400 274,200 258,800 274,800 27,000

$318,000 382,800 312,600 274,800 274,800 27,000

Terminal cash flow: After-tax proceeds from sale of new asset  Proceeds from sale of new asset *  Tax on sale of new asset   Total proceeds — sale sale of new asset  After-tax proceeds from sale of old asset  Change in net working capital Terminal cash flow

$200,000 (53,000) $147,000 0 25,000 $172,000

*

Book value of new machine at the end of year 5 is $67,500 200,000  $67,500  $132,500 income from sale of old machine 132,500  0.40  $53,000 tax liability

 b.

CF0  $1,110,400, CF 1  257,200, CF2  $344,400, CF3  $274,200, CF4  $258,800, CF5  $274,800  172,000  $446,800 Set I  9% Solve for NPV = $100,900.39

c.

$0 

d. e.

$257 $257,20 ,200 0 (1  IR I RR)1



$344 $344,40 ,400 0 (1  IRR) 2



$274 274,200 ,200 (1  IRR) 3



$258 258,80 ,800 (1  IR I RR) 4



$446 446,80 ,800 (1  IRR)5



$1,110, 400

IRR  12.2% Calculator solution: 12.24% Since the NPV  0 and the IRR  cost of capital, the new machine should be purchased. 12.24%. The criterion is that the IRR must equal or exceed exceed the cost cost of capital; capital; therefore, 12.24% is the lowest acceptable IRR.

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Capital Budgeting Cash Flows

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P11-30. Ethics Ethics problem LG 2; Intermediate The person who came up with the idea for a new investment may have an selfish interest in seeing the project approved, or may simply be emotionally vested in the project. In either case, this individual may have an incentive to make overly optimistic cash flow projections. It is best to have a n objective third party be responsible for cash flow projections.

Case Case studies are available on www.myfinancelab.com.

Developing Relevant Cash Flows for Clark Upholstery Company’s Machine Renewal or Replacement Decision Clark Upholstery is faced with a decision to either renew its major piece of machinery or to replace the machine. The case tests the students’ understanding of the c oncepts of initial investment and relevant cash flows. a.

Initial Investment:

Installed cost of new asset Cost of asset  Installation costs Total proceeds, sale of new asset  After-tax proceeds from sale of old asset Proceeds from sale of old asset *  Tax on sale of old asset Total proceeds, sale of old asset  Change in working capital Initial investment *

Book value of old asset

 0

$20,000  $0

 $20,000

$20,000  (0.40)

 $8,000

Alternative 1

Alternative 2

$90,000 0 90,000

$100,000 10,000 110,000

0 0 0 15,000 $105,000

(20,000) 8,000 (12,000) 22,000 $120,000

recaptured depreciation

tax

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 b. Calculation of Operating Cash Inflows Profits before Depreciation and Taxes

Year Alternative 1 1 2 3 4 5 6 Alternative 2 1 2 3 4 5 6

Operating Cash Net Profits after Taxes Inflows

Depreciation

Net Profits before Taxes

$198,500 290,800 381,900 481,900 581,900 0

$18,000 28,800 17,100 10,800 10,800 4,500

$180,500 262,000 364,800 471,100 571,100 4,500

$72,200 $108,300 104,800 157,200 145,920 218,880 188,440 282,660 228,440 342,660 1,800 2,700

$126,300 186,000 235,980 293,460 353,460 1,800

$235,500 335,200 385,100 435,100 551,100 0

$22,000 35,200 20,900 13,200 13,200 5,500

$213,500 300,000 364,200 421,900 537,900 5,500

$85,400 $128,100 120,000 180,000 145,680 218,520 168,760 253,140 215,160 322,740 2,200 3,300

$150,100 215,200 239,420 266,340 335,940 2,200

Taxes

Calculation of Incremental Cash Inflows Incremental Cash Flow Year

1 2 3 4 5 6

Alternative 1

$126,300 186,000 235,980 293,460 353,460 1,800

Alternative 2

Existing

Alt. 1

Alt. 2

$150,100 215,200 239,420 266,340 335,940 2,200

$100,000 150,000 200,000 250,000 320,000 0

$26,300 36,000 35,980 43,460 33,460 1,800

$50,100 65,200 39,420 16,340 15,940 2,200

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Chapter 11

c.

Capital Budgeting Cash Flows

Terminal Cash Flow: Alternative 1

After-tax proceeds from sale of new asset  Proceeds from sale of new asset asset *  Tax on sale of new asset Total proceeds, sale of new asset  After-tax proceeds from sale of old asset Proceeds from sale of old asset **  Tax on sale of old asset Total proceeds, sale of old asset  Change in working capital Terminal cash flow *

Book value value of Alternative 1 at end of year 5: $8,000  $4,500



$3,500  (0.40)

 $1,400

 

Alternative 2

$8,000 (1,400) 6,600

$25,000 (7,800) 17,200

(2,000) 800 (1,200) 15,000 $20,400

(2,000) 800 (1,200) 22,000 $38,000



$4,500

$3,500 recaptured recaptured depreciation tax

Book value of Alternative 2 at end of year 5:

 

$5,500

$25,000  $5,500  $19,500 recaptured depreciation depreciation $19,500  (0.40) **

 $7,800

tax

Book value of old asset at end of year 5:  $0 $2,000  $0



$2,000 recaptured recaptured depreciation

$2,000  (0.40)

 $800

tax

Alternative 1 Year 5 relevant cash flow:

Alternative 2 Year 5 relevant cash flow:

Operating cash flow: Terminal cash flow Total cash inflow

$33,460 20,400 $53,860

Operating cash flow: Terminal cash flow Total cash inflow

$15,940 38,000 $53,940

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d.

Alternative 1

e.

Alternative 2 appears appears to be slightly slightly better because it has the larger larger incremental incremental cash flow amounts amounts in the early years. Assuming a 9% discount rate, the NPV of Alternative 1 is $43,005.50, while the  NPV of Alternative 2 is $57,913.27. $57,913.27. The IRR of Alternative Alternative 2, 27.77%, is also higher than the the IRR of Alternative 1, which is 22.04%.

Spreadsheet Exercise The answer to Chapter 11’s Damon Corporation spreadsheet problem is located on the Instructor’s Resource Center at www.pearsonhighered.com/irc under the Instructor’s Manual .

Group Exercise Group exercises are available on www.myfinancelab.com.

Capital investment is revisited in this chapter. A long-term investment project will be detailed across this and the following two chapters. Students are warned that while this chapter’s exercise is apparently brie f, the work is vital to the work in the following chapters. The first task is to design two mutually exclusive investment projects. The design should focus on why these investments should each be undertaken. After establishing the “why” for each project, t he process of rigorous numerical analysis is begun. Cash flows are to be estimated and students should be encouraged to use simple round numbers when estimating the initial investment and operating/terminal cash flows. All numbers should be organized on an annual basis. Each group is asked to design a timeline with a minimum of 5 years for each project’s numbers. The most feasible estimates will run from 5– 10 years. A payback period, net present value, and internal rate of return are estimated for both projects. If the  projects have different sizes, sizes, it may be possible for the smaller smaller project to have a higher higher internal rate of return but a lower net present value. Giving groups a variety of discount rates to use in the analysis also adds to the richness of the project.

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