## How do firms compute weightedaverage costs of capital

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Here's the WACC formula one more time:

The WACC is the expected rate of return on the portfolio of debt and equity securities issued by the firm. The required rate of return on each security is weighted by its proportion of the firm's total market value (not book value). Since interest payments reduce the firm's income tax bill, the required rate of return on debt is measured after tax, as rdebt x (1 - Tc).

This WACC formula is usually written assuming the firm's capital structure includes just two classes of securities, debt and equity. If there is another class, say preferred stock, the formula expands to include it. In other words, we would estimate rpreferred, the rate of return demanded by preferred stockholders, determine P/V, the fraction of market value accounted for by preferred, and add rpreferred x P/V to the equation. Of course the weights in the WACC formula always add up to 1.0. In this case D/V + P/V + E/V = 1.0.

How are the costs of debt and equity calculated?

The cost of debt (rdebt) is the market interest rate demanded by bondholders. In other words, it is the rate that the company would pay on new debt issued to finance its investment projects. The cost of preferred (rpreferred) is just the preferred dividend divided by the market price of a preferred share.

The tricky part is estimating the cost of equity (requity), the expected rate of return on the firm's shares. Financial managers use the capital asset pricing model to estimate expected return. But for mature, steady-growth companies, it can also make sense to use the constant-growth dividend discount model. Remember, estimates of expected return are less reliable for a single firm's stock than for a sample of comparable-risk firms. Therefore, some managers also consider WACCs calculated for industries.

What happens when capital structure changes?

The rates of return on debt and equity will change. For example, increasing the debt ratio will increase the risk borne by both debt and equity investors and cause them to demand higher returns. However, this does not necessarily mean that the overall WACC will increase, because more weight is put on the cost of debt, which is less than the cost of equity. In fact, if we ignore taxes, the overall cost of capital will stay constant as the fractions of debt and equity change.

Should WACC be adjusted for the costs of issuing securities to finance a project?

No. If acceptance of a project would require the firm to issue securities, the flotation costs of the issue should be added to the investment required for the project. This reduces project NPV dollar for dollar. There is no need to adjust WACC.

RELATED Web www.geocities.com/WallStreet/Market/1839/irates.html Incorporating risk premiums into the cost of capital

Key TERMS capital structure weighted-average cost of capital (WACC)

Quiz

1. Cost of Debt. Micro Spinoffs, Inc., issued 20-year debt a year ago at par value with a coupon rate of 9 percent, paid annually. Today, the debt is selling at \$1,050. If the firm's tax bracket is 35 percent, what is its after-tax cost of debt?

2. Cost of Preferred Stock. Micro Spinoffs also has preferred stock outstanding. The stock pays a dividend of \$4 per share, and the stock sells for \$40. What is the cost of preferred stock?

3. Calculating WACC. Suppose Micro Spinoffs's cost of equity is 12.5 percent. What is its WACC if equity is 50 percent, preferred stock is 20 percent, and debt is 30 percent of total capital?

4. Cost of Equity. Reliable Electric is a regulated public utility, and it is expected to provide steady growth of dividends of 5 percent per year for the indefinite future. Its last dividend was \$5 per share; the stock sold for \$60 per share just after the dividend was paid. What is the company's cost of equity?

5. Calculating WACC. Reactive Industries has the following capital structure. Its corporate tax rate is 35 percent. What is its WACC?

Security Market Value Required Rate of Return

Debt \$20 million 8%

Preferred stock \$10 million 10%

Common stock \$50 million 15%

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 investment will have to be raised by a stock issue. The issue would incur flotation costs of \$1.2 million. Should the project be undertaken?

### Practice Problems

8. WACC. The common stock of Buildwell Conservation & Construction, Inc., has a beta of .80. The Treasury bill rate is 4 percent and the market risk premium is estimated at 8 percent. BCCI's capital structure is 30 percent debt paying a 5 percent interest rate, and 70 percent 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 initiate 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 million 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, and the current dividend yield is 2 percent. Its beta is 1.2, the market risk premium is 8 percent, 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 Products, 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.

 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 computer 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 Treasury 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.

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?

### Challenge Problems

19. Changes in Capital Structure. Look again at our calculation of Big Oil's WACC. Suppose Big Oil is excused from paying taxes. How would its WACC change? Now suppose Big Oil 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 finance some projects. This might lead it to reject some projects that would have seemed attractive if evaluated at the lower cost of debt. Comment on this reasoning.

Hot Rocks's 4 million common shares are worth \$40 million. Its market value balance sheet is:

Assets Liabilities and Shareholders' Equity

Value \$90 Value \$90

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 x \$4 = \$24 million. The debt is selling for 80 percent of book, or \$20 million. The market value balance sheet is:

Assets Liabilities and Shareholders' Equity

Value \$44_Value \$44_

WACC = (.45 x 14%) + (.55 x 20%) = 17.3% Note that this question ignores taxes.

Solutions to

Self-Test

### Questions

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.)

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

4 For Hot Rocks,

WACC = [.56 x 9 x (1 - .35)] + (.44 x 17) = 10.76% For Burg Associates,

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

6 From the CAPM:

requity rf + Pequity (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.

Bernice Mountaindog was glad to be back at Sea Shore Employees were treated well. When she had asked a year ago for a leave of absence to complete her degree in finance, top management promptly agreed. When she returned with an honors degree, she was promoted from administrative assistant (she had been secretary to Joe-Bob Brinepool, the president) to treasury analyst.

Bernice thought the company's prospects were good. Sure, table salt was a mature business, but Sea Shore Salt had grown steadily at the expense of its less well-known competitors. The company's brand name was an important advantage, despite the difficulty most customers had in pronouncing it rapidly.

Bernice started work on January 2, 2000. The first two weeks went smoothly. Then Mr. Brinepool's cost of capital memo assigned her to explain Sea Shore Salt's weighted-average cost of capital to other managers. The memo came as a surprise to Bernice, so she stayed late to prepare for the questions that would surely come the next day.

Bernice first examined Sea Shore Salt's most recent balance sheet, summarized in Table 4.14. Then she jotted down the following additional points:

• The company's bank charged interest at current market rates, and the long-term debt had just been issued. Book and market values could not differ by much.

• But the preferred stock had been issued 35 years ago, when

TABLE 4.14

Sea Shore Salt's balance sheet, taken from the company's 1999 balance sheet (figures in millions)

TABLE 4.14

Sea Shore Salt's balance sheet, taken from the company's 1999 balance sheet (figures in millions)

Assets

Liabilities and Net Worth

Working capital

\$200

Bank loan

\$120

Plant and equipment

360

Long-term debt

80

Other assets

40

Preferred stock

100

Common stock, including retained earnings

300

Total

\$600

Total

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.

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.

interest rates were much lower. The preferred stock was now trading for only \$70 per share.

• The common stock traded for \$40 per share. Next year's earnings per share would be about \$4.00 and dividends per share probably \$2.00. Sea Shore Salt had traditionally paid out 50 percent of earnings as dividends and plowed back the rest.

• Earnings and dividends had grown steadily at 6 to 7 percent per year, in line with the company's sustainable growth rate:

Sustainable = return x plowback growth rate = on equity ratio

• Sea Shore Salt's beta had averaged about .5, which made sense, Bernice thought, for a stable, steady-growth business. She made a quick cost of equity calculation using the capital asset pricing model (CAPM). With current interest rates of about 7 percent, and a market risk premium of 8 percent,

CAPM cost of equity = rE = rf + P(rm - rf) = 7% + .5(8%) = 11%

This cost of equity was significantly less than the 16 percent decreed in Mr. Brinepool's memo. Bernice scanned her notes apprehensively. What if Mr. Brinepool's cost of equity was wrong? Was there some other way to estimate the cost of equity as a check on the CAPM calculation? Could there be other errors in his calculations?

Bernice resolved to complete her analysis that night. If necessary, she would try to speak with Mr. Brinepool when he arrived at his office the next morning. Her job was not just finding the right number. She also had to figure out how to explain it all to Mr. Brinepool.

Sea Shore Salt Company Spring Vacation Beach, Florida

CONFIDENTIAL MEMORANDUM

DATE: January 15, 2000

TO: S.S.S. Management

FROM: Joe-Bob Brinepool,

SUBJECT: Cost of Capital

### President

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.

The weighted-average cost of capital is simply a blend of the rates of return expected by investors in our company. These investors include banks, bond holders, and preferred stock investors in addition to common stockholders. Of course many of you are, or soon will be, stockholders of our company.

The following table summarizes the composition of Sea Shore Salt's financing.

Amount (in millions) Percent of Total Rate of Return

Bank loan Bond issue Preferred stock Common stock

\$120 B0 100 300

\$600

100%

The rates of return on the bank loan and bond issue are of course just the interest rates we pay. However, interest is tax-deductible, so the after-tax interest rates are lower than shown above. For example, the after-tax cost of our bank financing, given our 35% tax rate, is 8(1 - .35) = 5.2%.

The rate of return on preferred stock is 6%. Sea Shore Salt pays a \$6 dividend on each \$100 preferred share.

Our target rate of return on equity has been 16% for many years. I know that some newcomers think this target is too high for the safe and mature salt business. But we must all aspire to superior profitability.

Once this background is absorbed, the calculation of Sea Shore Salt's weighted-average cost of capital (WACC) is elementary:

WACC = 8(1 - ,35)(.2) + 7.75(1 - ,35)(.133) + 6(.167) + 16(.50) = 10.7%

The official corporate hurdle rate is therefore 10.7%.

If you have further questions about these calculations, please direct them to our new Treasury Analyst, Ms. Bernice Mountaindog. It is a pleasure to have Bernice back at Sea Shore Salt after a year's leave of absence to complete her degree in finance.

Project Analysis

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### Responses

• Martin
How firms estimate interest rate for the WACC?
7 years ago
• rose
How do firms financial work incapital by using bankloan?
7 years ago