6. Company versus Project Discount Rates. Geothermal™s WACC is 11.4 percent. Executive

Fruit™s WACC is 12.3 percent. Now Executive Fruit is considering an investment in geother-

mal power production. Should it discount project cash flows at 12.3 percent? Why or why

not?

7. Flotation Costs. A project costs $10 million and has NPV of $+2.5 million. The NPV is

computed by discounting at a WACC of 15 percent. Unfortunately, the $10 million invest-

ment will have to be raised by a stock issue. The issue would incur flotation costs of $1.2

million. Should the project be undertaken?

8. WACC. The common stock of Buildwell Conservation & Construction, Inc., has a beta of

Practice .80. The Treasury bill rate is 4 percent and the market risk premium is estimated at 8 per-

Problems cent. BCCI™s capital structure is 30 percent debt paying a 5 percent interest rate, and 70 per-

cent equity. What is BCCI™s cost of equity capital? Its WACC? Buildwell pays no taxes.

9. WACC and NPV. BCCI (see the previous problem) is evaluating a project with an internal

rate of return of 12 percent. Should it accept the project? If the project will generate a cash

flow of $100,000 a year for 7 years, what is the most BCCI should be willing to pay to ini-

tiate the project?

10. Calculating WACC. Find the WACC of William Tell Computers. The total book value of the

firm™s equity is $10 million; book value per share is $20. The stock sells for a price of $30

per share, and the cost of equity is 15 percent. The firm™s bonds have a par value of $5 mil-

lion and sell at a price of 110 percent of par. The yield to maturity on the bonds is 9 percent,

and the firm™s tax rate is 40 percent.

11. WACC. Nodebt, Inc., is a firm with all-equity financing. Its equity beta is .80. The Treasury

bill rate is 5 percent and the market risk premium is expected to be 10 percent. What is

Nodebt™s asset beta? What is Nodebt™s weighted-average cost of capital? The firm is exempt

from paying taxes.

12. Cost of Capital. A financial analyst at Dawn Chemical notes that the firm™s total interest

payments this year were $10 million while total debt outstanding was $80 million, and he

concludes that the cost of debt was 12.5 percent. What is wrong with this conclusion?

13. Cost of Equity. Bunkhouse Electronics is a recently incorporated firm that makes electronic

entertainment systems. Its earnings and dividends have been growing at a rate of 30 percent,

The Cost of Capital 457

and the current dividend yield is 2 percent. Its beta is 1.2, the market risk premium is 8 per-

cent, and the risk-free rate is 4 percent.

a. Calculate two estimates of the firm™s cost of equity.

b. Which estimate seems more reasonable to you? Why?

14. Cost of Debt. Olympic Sports has two issues of debt outstanding. One is a 9 percent coupon

bond with a face value of $20 million, a maturity of 10 years, and a yield to maturity of 10

percent. The coupons are paid annually. The other bond issue has a maturity of 15 years, with

coupons also paid annually, and a coupon rate of 10 percent. The face value of the issue

is $25 million, and the issue sells for 92.8 percent of par value. The firm™s tax rate is 35

percent.

a. What is the before-tax cost of debt for Olympic?

b. What is Olympic™s after-tax cost of debt?

15. Capital Structure. Examine the following book-value balance sheet for University Prod-

ucts, Inc. What is the capital structure of the firm based on market values? The preferred

stock currently sells for $15 per share and the common stock for $20 per share. There are

one million common shares outstanding.

BOOK VALUE BALANCE SHEET

(all values in millions)

Assets Liabilities and Net Worth

Cash and short-term securities $1 Bonds, coupon = 8%, paid $10.0

annually (maturity = 10 years,

current yield to maturity = 9%)

Accounts receivable 3 Preferred stock (par value $20 2.0

per share)

Inventories 7 Common stock (par value $.10) .1

Plant and equipment 21 Additional paid in stockholders™ 9.9

capital

Retained earnings 10.0

Total $32 Total $32.0

16. Calculating WACC. Turn back to University Products™s balance sheet from the previous

problem. If the preferred stock pays a dividend of $2 per share, the beta of the stock is .8,

the market risk premium is 10 percent, the risk-free rate is 6 percent, and the firm™s tax rate

is 40 percent, what is University™s weighted-average cost of capital?

17. Project Discount Rate. University Products is evaluating a new venture into home com-

puter systems (see problems 15 and 16). The internal rate of return on the new venture

is estimated at 13.4 percent. WACCs of firms in the personal computer industry tend to

average around 14 percent. Should the new project be pursued? Will University Products

make the correct decision if it discounts cash flows on the proposed venture at the firm™s

WACC?

18. Cost of Capital. The total market value of Okefenokee Real Estate Company is $6 million,

and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock

currently is 1.5 and that the expected risk premium on the market is 10 percent. The Trea-

sury bill rate is 4 percent.

a. What is the required rate of return on Okefenokee stock?

b. What is the beta of the company™s existing portfolio of assets? The debt is perceived to

be virtually risk-free.

458 SECTION FOUR

c. Estimate the weighted-average cost of capital assuming a tax rate of 40 percent.

d. Estimate the discount rate for an expansion of the company™s present business.

e. Suppose the company wants to diversify into the manufacture of rose-colored glasses.

The beta of optical manufacturers with no debt outstanding is 1.2. What is the required

rate of return on Okefenokee™s new venture?

19. Changes in Capital Structure. Look again at our calculation of Big Oil™s WACC. Suppose

Challenge Big Oil is excused from paying taxes. How would its WACC change? Now suppose Big Oil

Problems makes a large stock issue and uses the proceeds to pay off all its debt. How would the cost

of equity change?

20. Changes in Capital Structure. Refer again to problem 19. Suppose Big Oil starts from the

financing mix in Table 4.13, and then borrows an additional $200 million from the bank. It

then pays out a special $200 million dividend, leaving its assets and operations unchanged.

What happens to Big Oil™s WACC, still assuming it pays no taxes? What happens to the cost

of equity?

21. WACC and Taxes. “The after-tax cost of debt is lower when the firm™s tax rate is higher;

therefore, the WACC falls when the tax rate rises. Thus, with a lower discount rate, the firm

must be worth more if its tax rate is higher.” Explain why this argument is wrong.

22. Cost of Capital. An analyst at Dawn Chemical notes that its cost of debt is far below that

of equity. He concludes that it is important for the firm to maintain the ability to increase its

borrowing because if it cannot borrow, it will be forced to use more expensive equity to fi-

nance some projects. This might lead it to reject some projects that would have seemed at-

tractive if evaluated at the lower cost of debt. Comment on this reasoning.

1 Hot Rocks™s 4 million common shares are worth $40 million. Its market value balance sheet

Solutions to is:

Self-Test Assets Liabilities and Shareholders™ Equity

Questions Assets $90 Debt $50 (56%)

Equity 40 (44%)

Value $90 Value $90

WACC = (.56 — 9%) + (.44 — 17%) = 12.5%

We use Hot Rocks™s pretax return on debt because the company pays no taxes.

2 Burg™s 6 million shares are now worth only 6 million — $4 = $24 million. The debt is sell-

ing for 80 percent of book, or $20 million. The market value balance sheet is:

Assets Liabilities and Shareholders™ Equity

Assets $44 Debt $20 (45%)

Equity 24 (55%)

Value $44 Value $44

WACC = (.45 — 14%) + (.55 — 20%) = 17.3%

Note that this question ignores taxes.

The Cost of Capital 459

3 Compare the two income statements, one for Criss-cross Industries and the other for a firm

with identical EBIT but no debt in its capital structure. (All figures in millions.)

Criss-cross Firm with No Debt

EBIT $10.0 $10.0

Interest expense 2.0 0.0

Taxable income 8.0 10.0

Taxes owed 2.8 3.5

Net income 5.2 6.5

Total income accruing to debt & equity holders 7.2 6.5

Notice that Criss-cross pays $.7 million less in taxes than its debt-free counterpart. Ac-

cordingly, the total income available to debt plus equity holders is $.7 million higher.

4 For Hot Rocks,

WACC = [.56 — 9 — (1 “ .35)] + (.44 — 17) = 10.76%

For Burg Associates,

WACC = [.45 — 14 — (1 “ .35)] + (.55 — 20) = 15.1%

5 WACC measures the expected rate of return demanded by debt and equity investors in the

firm (plus a tax adjustment capturing the tax-deductibility of interest payments). Thus the

calculation must be based on what investors are actually paying for the firm™s debt and eq-

uity securities. In other words, it must be based on market values.

6 From the CAPM:

requity = rf + βequity (rm “ rf)

= 6% + 1.20(9%) = 16.8%

WACC = .3(1 “ .35) 8% + .7(16.8%) = 13.3%

7 Jo Ann™s boss is wrong. The ability to borrow at 8 percent does not mean that the cost of

capital is 8 percent. This analysis ignores the side effects of the borrowing, for example, that

at the higher indebtedness of the firm the equity will be riskier, and therefore the equity-

holders will demand a higher rate of return on their investment.

MINICASE

Bernice Mountaindog was glad to be back at Sea Shore Salt. went smoothly. Then Mr. Brinepool™s cost of capital memo as-

Employees were treated well. When she had asked a year ago for signed her to explain Sea Shore Salt™s weighted-average cost of

a leave of absence to complete her degree in finance, top man- capital to other managers. The memo came as a surprise to Ber-

agement promptly agreed. When she returned with an honors de- nice, so she stayed late to prepare for the questions that would

gree, she was promoted from administrative assistant (she had surely come the next day.

been secretary to Joe-Bob Brinepool, the president) to treasury Bernice first examined Sea Shore Salt™s most recent balance

analyst. sheet, summarized in Table 4.14. Then she jotted down the fol-

Bernice thought the company™s prospects were good. Sure, lowing additional points:

table salt was a mature business, but Sea Shore Salt had grown

steadily at the expense of its less well-known competitors. The • The company™s bank charged interest at current market rates,

company™s brand name was an important advantage, despite the and the long-term debt had just been issued. Book and market

difficulty most customers had in pronouncing it rapidly. values could not differ by much.

Bernice started work on January 2, 2000. The first two weeks • But the preferred stock had been issued 35 years ago, when

460 SECTION FOUR

TABLE 4.14

Assets Liabilities and Net Worth

Sea Shore Salt™s balance

sheet, taken from the Working capital $200 Bank loan $120

company™s 1999 balance Plant and equipment 360 Long-term debt 80

sheet (figures in millions) Other assets 40 Preferred stock 100

Common stock, including retained earnings 300

Total $600 Total $600

Notes:

1. At year-end 1999, Sea Shore Salt had 10 million common shares outstanding.

2. The company had also issued 1 million preferred shares with book value of $100 per share. Each share

receives an annual dividend of $6.00.

asset pricing model (CAPM). With current interest rates of

interest rates were much lower. The preferred stock was now

about 7 percent, and a market risk premium of 8 percent,

trading for only $70 per share.

• The common stock traded for $40 per share. Next year™s earn- CAPM cost of equity = rE = rf + β(rm “ rf)

ings per share would be about $4.00 and dividends per share

= 7% + .5(8%) = 11%

probably $2.00. Sea Shore Salt had traditionally paid out 50

This cost of equity was significantly less than the 16 percent

percent of earnings as dividends and plowed back the rest.

decreed in Mr. Brinepool™s memo. Bernice scanned her notes ap-

• Earnings and dividends had grown steadily at 6 to 7 percent

prehensively. What if Mr. Brinepool™s cost of equity was wrong?

per year, in line with the company™s sustainable growth rate:

Was there some other way to estimate the cost of equity as a

Sustainable return plowback

— check on the CAPM calculation? Could there be other errors in

=

growth rate on equity ratio

his calculations?

= 4.00/30 — .5

Bernice resolved to complete her analysis that night. If neces-

= .067, or 6.7%

sary, she would try to speak with Mr. Brinepool when he arrived

at his office the next morning. Her job was not just finding the

• Sea Shore Salt™s beta had averaged about .5, which made

right number. She also had to figure out how to explain it all to

sense, Bernice thought, for a stable, steady-growth business.

Mr. Brinepool.

She made a quick cost of equity calculation using the capital

The Cost of Capital 461

Sea Shore Salt Company

Spring Vacation Beach, Florida

CONFIDENTIAL MEMORANDUM

DATE: January 15, 2000

TO: S.S.S. Management

FROM: Joe-Bob Brinepool, President

SUBJECT: Cost of Capital

This memo states and clarifies our company™s long-standing policy regarding hurdle rates

for capital investment decisions. There have been many recent questions, and some evident

confusion, on this matter.

Sea Shore Salt evaluates replacement and expansion investments by discounted cash flow.

The discount or hurdle rate is the company™s after-tax weighted-average cost of capital.