Solution for Chapter 15

CHAPTER 15 THE MANAGEMENT OF CAPITAL

Problems

15-1. Carter Savings Association has forecast the following performance ratios for the year ahead. How fast can Carter allow its assets to grow without reducing its ratio of equity capital to total assets, assuming its performance holds reasonably steady over it planning period? Profit Margin of Net Income Over Operating Revenue Asset Utilization Equity Multiplier Net Earnings Retention Ratio

Internal Capital Growth Rate =

= =

8.30% 9.25% 15.22x 45.00%

Profit Margin * Asset Utilization * Equity Multiplier * Retention Ratio 0.0830 * 0.0925 * 15.22 * 0.450 0.0526 or 5.26%

Its assets cannot grow any faster than 5.26 percent in order to avoid reducing its ratio of equity capital to total assets.

15-2. Using the formulas developed in this chapter and in chapter 6 and the information that follows, calculate the ratios of total capital to total assets for the banking firm listed below. What relationship among these institution’s return on assets, return on equity capital, and capital to assets ratios did you observe? What implications or recommendations would you draw for the management of each of these institutions? Name of Bank First National Bank of Hopkins Safety National Bank Ilsher State Bank Mercantile Bank and Trust Company Lakeside National Trust

Net Income/Total Assets (ROA) 0.016 0.013 0.0095 0.0083

Net Income/Total Equity Capital (ROE) 0.15 0.13 0.10 0.09

-0.0043

-0.05

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The basic relationship needed in this problem is ROE

=

Net Income After Taxes Equity Capital

= Net Income After Taxes Total Assets =

ROA

*

*

Total Assets Equity Capital Total Assets Equity Capital

in which case: Total Assets Equity Capital

=

ROE ROA

and

Equity Capital Total Assets

=

ROA ROE

Therefore the ratio of total capital to total assets for the banks named in the problem must be: First National Bank of Hopkins = 0.016/0.15 = 0.1067 or 10.67%. Safety National Bank = 0.013/0.13 = 0.1000 or 10.00% Ilsher State Bank = 0.0095/0.100 = 0.0950 or 9.50% Mercantile Bank and Trust Company = 0.0083/0.09 = 0.0922 or 9.22% Lakeside National Bank = -0.0043/-0.0500 = 0.086 = 8.60% None of the banks appear to have a serious capital deficiency problem. However, the bank with the lowest capital to total assets ratio is also the one with a negative return on assets and return on equity. The negative earnings may be eroding the capital position of this bank.

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15-3 Using the following information for Sun-Up National Bank, calculate that bank’s ratio of total capital to risk weighted assets under the terms of the Basel I agreement. Does the bank have sufficient capital? On Balance Sheet Items (Assets) Cash $ 3.5 million

U.S Treasury securities

25.6

Deposit balances due from other banks Loans secured by first lines on residential property (1-4 family dwellings) Loans to corporations Total assets

4.0

Off Balance Sheet Items Standby letters of $ 18.1 million credit backing municipals and corporate borrowing Long term binding 40.2 commitments to corporate customers Total of all off balance $ 58.3 million sheet items

19.7

105.3 $158.1 million

Total capital

$11.8 million

Sun-Up National Bank's required level of capital under the new international capital standards would be determined from: Standby Credit Letter: $18.1 million * 1.00 = $18.1 million Long-Term Credit Commitments: $40.2 million * 0.50 = 20.1 million 0% Risk-Weighting Category Cash U.S. Treasury Securities

$ 3.5 million 25.6 million $ 29.1 * 0 = $0 million

20% Risk Weighting Category Balances at Domestic Banks Credit Equivalent Amounts of Standby Credits

$ 4.0 million 18.1 million $ 22.1 million * 0.20 = $4.42 million

50% Risk Weighting Category Residential Real Estate Loans

$ 19.7 million x 0.50 = $9.85 million

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100% Risk Weighting Category Loans to Corporations Credit Equivalents of Long-Term Commitments Total Risk-Weighted Assets

$105.3 million $20.1 million $125.4 million * 1.0 = $125.4 million $139.67 million

The bank's capital ratio is: Total Capital/Risk-Weighted Assets = $ 11.800 million = 8.45% $ 139.67 million which is just above the minimum total capital (Tier One + Tier Two) requirement of 8 percent.

15-4 Top of the Mountain Savings has been told by examiners that it needs to raise an additional $8 million in long-term capital. Its outstanding common equity shares total 7.5 million, each bears a par value of $1. This thrift institution currently holds assets of nearly $2 billion, with $105 million in equity. During the coming year, the thrift’s economist has forecast operating revenues of $175 million, of which operating expenses are $25 million plus 70 percent of operating revenue.

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Among the options for raising capital considered by management are: (a) selling $8 million in new common stock, or 320,000 shares at $25 per share; (b) selling $8 million in preferred stock bearing a 9 percent annual dividend yield at $12 per share; or (c) selling $8 million worth of 10-year capital notes with a 10 percent coupon rate. Which option would be of most benefit to the stockholders? (Assume a 35% tax rate) What happens if operating revenue increases more than expected (200 million rather than 175 million)? What happens if there is a slower than expected volume of revenues (only $125 million instead of $175 million). Please explain. (a) Sale of Common Stock at $25 per share

(b) Sale of 9% Preferred Stock at $12 per share

(c) Sale of 10% Capital Notes

Operating Revenues Operating Expenses Net Revenues Interest on Capital Notes

$175,000,000 147,500,000 $ 27,500,000 -------------------

$175,000,000 147,500,000 $ 27,500,000 -------------------

$175,000,000 147,500,000 $ 27,500,000 800,000

Before-Tax Income Estimated Income Taxes

$27,500,000 9,350,000

$27,500,000 9,350,000

$26,700,000 9,078,000

18,150,000

$ 18,150,000

$ 17,622,000

----------------------

720,000

---------------------

After-Tax Income Preferred Stock Dividends Net Income for Common Stockholders Shares of Common Stock Outstanding Earnings Per Share of Common Stock

$

$

18,150,000

$

17,430,000

$

17,622,000

7,820,000

7,500,000

7,500,000

$ 2.32

$ 2.32

$ 2.35

In this case sale of the debt would yield the highest EPS for the bank's shareholders Because of the dilution effect of issuing stock.

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If operating revenue rose to $200 million the situation would be the following: (a) Sale of Common Stock at $25 per share

(b) Sale of 9% Preferred Stock at $12 per share

(c) Sale of 10% Capital Notes

Operating Revenues Operating Expenses Net Revenues Interest on Capital Notes

$200,000,000 165,000,000 $ 35,000,000 -------------------

$200,000,000 165,000,000 $ 35,000,000 -------------------

$200,000,000 165,000,000 $ 35,000,000 800,000

Before-Tax Income Estimated Income Taxes

$35,000,000 11,900,000

$35,000,000 11,900,000

$34,200,000 11,628,000

23,100,000

$ 23,100,000

$ 22,572,000

----------------------

720,000

---------------------

After-Tax Income Preferred Stock Dividends Net Income for Common Stockholders Shares of Common Stock Outstanding Earnings Per Share of Common Stock

$

$

23,100,000

$

22,380,000

$

22,572,000

7,820,000

7,500,000

7,500,000

$ 2.95

$ 2.98

$ 3.01

And again the capital notes would be the best option, although the preferred stock comes closer this time.

208

If operating revenues drop to $125 million, then the situation would be the following: (a) Sale of Common Stock at $25 per share

(b) Sale of 9% Preferred Stock at $12 per share

(c) Sale of 10% Capital Notes

Operating Revenues Operating Expenses Net Revenues Interest on Capital Notes

$125,000,000 112,500,000 $ 12,500,000 -------------------

$125,000,000 112,500,000 $ 12,500,000 -------------------

$125,000,000 112,500,000 $ 12,500,000 800,000

Before-Tax Income Estimated Income Taxes

$12,500,000 4,250,000

$12,500,000 4,250,000

$11,700,000 3,978,000

8,250,000

$ 8,250,000

$ 7,722,000

----------------------

720,000

---------------------

After-Tax Income Preferred Stock Dividends Net Income for Common Stockholders Shares of Common Stock Outstanding Earnings Per Share of Common Stock

$

$

8,250,000

$

7,530,000

$

7,722,000

7,820,000

7,500,000

7,500,000

$ 1.05

$1.00

$ 1.03

In this case issuing the common stock is the best alternative from the point of view of the common stockholders.

15-5. Please calculate New River National Bank’s total risk weighted assets, based on the following items that the bank reported on its latest balance sheet. Does the bank appear to have a capital deficiency? The risk-weighted assets of New River National Bank would be calculated as follows:

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Off-Balance-Sheet Items: Standby Credit Letters = $95 mill. * 1.00 = $95 mill. Long-Term Corporate Credit Commitments = $190 mill. * 0.50 = 95 mill. On-Balance-Sheet Items and Credit-Equivalent Off-Balance Sheet Items: Asset Items

Risk-Weight

Cash U.S. Government Securities Domestic Interbank Deposits Standby Credit Letters Residential Real Estate Loans Commercial Loans Long-Term Corporate Credit Commitments Total Risk-Weighted Assets

$95 miIl. * 0 $320 mill. * 0 $240 mill. * 0.20 $95 mill. * 0.20 $370 mill. * 0.50 $520 mill. * 100%

= = = = = =

0 0 48 mill. 19 mill. 185 mill. 520 mill.

$95 mill. * 1.00

= =

95 mill. $867 mill.

Willow River's overall capital-to-assets ratio is: Total Capital Total Risk-Weighted Assets

=

$105 million $867 million

=

0.1211 or 12.11 percent

Overall, it does not appear from the information given above that Willow River has a capital deficiency.

15-6. Suppose that New River National Bank whose balance sheet is given in problem 5, reports the forms of capital shown in the following table as of the date of its latest financial statement. What is the total dollar volume of the bank’s Tier 1 capital? Tier 2 capital? According to the data given in problems 5 and 6, does New River have a capital deficiency? New River National Bank has the following Tier 1 and Tier 2 Capital items and totals: Tier 1 Capital Common Stock (Par) Surplus Undivided Profit Total Tier 1 Capital

$8 million $17 million $35 million $60 million

Tier 1 Capital Total Risk-Weighted Assets

=

Tier 2 Capital Allowance for Loan Loss Subordinated Debt Capital Intermediate Term Preferred Stock Total Tier 2 Capital

$60 million $867 million

=

$25 million $15 million $5 million $45 million

0..0692 or 6.92 percent

This bank has sufficient Tier 1 capital and since its Tier 2 capital amount is less than its Tier 1 capital amount it satisfies the requirements of Basel I.

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15-7. Please indicate which items appearing on the following inancial statements would be classified under the terms of the Basel Agreement as Tier 1 capital and Tier 2 capital.

Tier 1 Qualifying Noncumulative Preferred Stock Common Stock Undivided Profits Minority Interest in the Equity Accounts of Consolidated Subsidiaries

Tier 2 Allowance for Loan and Lease Losses Intermediate Term Preferred Stock Cumulative Perpetual Preferred Stock with Unpaid Dividends Subordinated Debt Capital Instrument with an Original Maturity of at Least 5 Years Equity Notes Mandatory Convertible Debt

15-8. Under the terms of the Basel Agreement, what risk weights apply to the following on balance sheet and off balance sheet items? The items which would appear in the 0%, 20%, 50% and 100% risk weight categories are the following: 0% Cash U.S. Treasury Securities

GNMA Mortgage Backed Securities Short Term Loan Commitments Reserves on Deposit at the Federal Reserve

20 % Deposits held at Other Domestic Banks Federal Agency Securities

Municipal General Obligation Bonds FNMA or FHLMC Issued or Guaranteed Securities Standby Letters of Credit for Municipal Bonds

50 % Residential Real Estate Loans Long Term Commitments to Make Corporate Loans Currency Derivative Contracts Interest Rate Derivative Contracts Municipal Revenue Bonds

100 % Commercial Loans Standby Credit Letters for Commercial Paper

Investments in Subsidiaries Credit Card Loans

Bank Real Estate

Bankers’ Acceptances

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