Chapter: Chapter 13: Estimating the Cost of Capital
1. A firm has a target debt-to-equity ratio of 1. Its cost of equity equals 12 percent, the cost of
debt is 8 percent, and the tax rate is 30 percent. What is the weighted average cost of capital
(WACC)?
a) 10.0 percent.
b) 10.8 percent.
c) 9.8 percent.
d) 8.8 percent.
2. A firm has a target debt-to-equity ratio of 3. Its cost of equity equals 12 percent, its cost of
debt is 9 percent, and the tax rate is 34 percent. What is the WACC?
a) 7.46 percent.
b) 8.97 percent.
d) 10.00 percent.
d) 10.49 percent.
3. A firm has 1,200,000 shares of stock outstanding with a price per share equal to $14. There
are 10,000 bonds outstanding, priced at $1,125 each. The cost of equity is 14 percent, the cost
of debt is 8 percent, and the corporate tax rate is 40 percent. What is the WACC?
a) 10.3 percent.
b) 10.8 percent.
c) 9.8 percent.
d) 8.8 percent.
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Response: [V = (1,200,000 * $14) + (10,000 * $1,125) = $28,050,000
The weights are:
E/V = 16,800,000/28,050,000 = 0.60
D/V = 11,250,000/28,050,000 = 0.40
WACC = {0.40 * 8% * (1 – 0.40)} + (0.60 * 14%) = 10.31%]
4. A firm has 4,000,000 shares of stock outstanding with a price per share equal to $22. There
are 200,000 bonds outstanding each priced at $995 each. The cost of equity is 14 percent, the
cost of debt is 8 percent, and the corporate tax rate is 34 percent. What is the WACC?
a) 10.3 percent.
b) 9.8 percent.
c) 8.0 percent.
d) 8.8 percent.
5. An analyst should use the pretax cost of equity and the pretax cost of debt to estimate the
cost of capital.
6. The cost of capital must include the cost of capital for all investors—debt, preferred stock,
and common stock.
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Response: [Since free cash flow is available to all investors, it must include the cost of capital for
all investors.]
Short Answer
7. Briefly explain the two methods of estimating market returns.
Ans: [The first method looks backward using historical market returns. But given that past
True/False
8. One should create a synthetic risk-free rate by adding the expected inflation rate to the long–
term historical average real risk-free rate for the period following the financial crisis.
9. What challenges did the financial crisis of 2008 and its aftermath pose for estimating a firm’s
cost of capital? How should one handle these challenges?
10. To estimate the risk-free rate in developed economies, the analyst should use:
a) Short-term commercial paper.
b) Short-term government discount instruments.
c) Long-term coupon-paying government bonds.
d) Long-term government zero-coupon bonds.
True/False
11. Theoretically, one should discount each year’s cash flow at a cost of equity that matches the
maturity of the cash flow. However, for practical purposes, analysts typically choose a single
yield to maturity that best matches the cash flow stream being valued.
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12. Which of the following is/are FALSE regarding risk-free rates?
I) The 30-year Treasury bonds match the cash flow streams of a company better, and therefore
should be used over 10-year bonds in estimating the risk-free rate.
II) One should use government bond yields denominated in the same currency as the
company’s cash flow to estimate the risk-free rate.
III) One should ensure that the inflation rate embedded in the cash flows is consistent with the
inflation rate embedded in the government bond rate being used.
a) I only.
b) II only.
c) III only.
d) I and III only.
13. Suppose that the median price‐to‐earnings ratio for the S&P 500 is 20. If the long‐run return
on equity is 11.5 percent and the long‐run growth in gross domestic product (GDP) is expected
to be 6 percent (3.5 percent real growth and 2.5 percent inflation), what is the cost of equity
implied by the equity-denominated key value driver formula?
a) 7.9 percent.
b) 8.4 percent.
c) 8.9 percent.
d) 9.4 percent.
True/False
14. Researchers have concluded that an appropriate range of the equity risk premium for use in
valuation models should be 10 to 12 percent.
15. Which of the following is NOT an input into the Fama-French three-factor model?
a) The difference between low book-to-market returns and high book-to-market returns.
b) The difference between growth stock returns and value stock returns.
c) The market portfolio returns.
d) The difference between small-cap returns and large-cap returns.
16. Since the factors and their measurement for use in the arbitrage pricing theory (APT) model
have become fairly standardized, the APT model is becoming a more popular alternative to the
CAPM in estimating the market risk premium.
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17. In computing the cost of equity for a firm, which of the following are recommended steps in
estimating the CAPM beta using regression analysis?
I. Use a sample size equal to or greater than 60.
II. Use daily returns.
III. Use a diversified value-weighted index.
IV. Watch for possible distortions from market bubbles.
a) I, II, and III only.
b) I, III, and IV only.
c) II and IV only.
d) II, III, and IV only.
18. Which of the following are true concerning the index recommended for use in the CAPM?
I. It should include both traded and untraded investments.
II. The S&P 500 is the most common proxy for U.S. stocks.
III. The S&P 500 and the MSCI World index will produce very different results for U.S. stocks.
IV. For less developed countries, a local market index is recommended.
a) I and II.
b) I and IV.
c) II and III.
d) III and IV.
19. Which of the following is NOT true concerning the index recommended for use in the
CAPM?
a) It should include both traded and untraded investments.
b) The S&P 500 is the most common proxy for U.S. stocks.
c) The S&P 500 and the MSCI World index will produce fairly similar results for U.S. stocks.
d) For less developed countries, a local market index is recommended.
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Ans: [d]
Response: []
20. Bloomberg’s recommended adjustment to a firm’s beta will:
a) Lower beta in all cases.
b) Increase beta in all cases.
c) Move the beta toward 1.
d) Either increase or decrease beta, but it depends on the size of the standard error of the
estimated beta.
21. To estimate a company’s beta, using an industry-derived unlevered beta relevered to the
company’s target capital structure is preferred to directly estimating a company-specific beta.
22. An analyst gathers the following information for Firm A and Firm B. Using the information to
compute the industry unlevered beta, what is the appropriate beta for each company for use in
the WACC? (Assume that the debt beta for each firm equals zero.)
Firm A: CAPM beta = 0.9; debt-to-equity ratio = 0.4
Firm B: CAPM beta = 1.2; debt-to-equity ratio = 2
a) 0.73; 1.56
b) 0.90; 1.20
c) 0.52; 0.52
d) 1.12; 1.65
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23. An analyst gathers the following information for Firm A and Firm B. Use the information to
compute the industry unlevered beta and the appropriate beta for Firm B to use in the WACC.
Firm A: CAPM beta = 1.6; debt-to-equity ratio = 1.2
Firm B: CAPM beta = 1.0; debt-to-equity ratio = 0.8
The appropriate beta for Firm B is closest to:
a) 1.026
b) 1.154
c) 1.170
d) 1.163
24. Which of the following practices are appropriate in estimating a firm’s cost of debt?
I. Use the coupon rate on outstanding debt that is investment grade.
II. Use the yield to maturity on outstanding debt that is investment grade.
III. Use the yield to maturity on outstanding debt that is below investment grade.
IV. Use the adjusted present value (APV) method to value firms that have debt that is below
investment grade.
a) I and IV only.
b) III and IV only.
c) II and III only.
d) II and IV only.
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25. Which of the following most accurately describes the types of companies where the yield to
maturity on outstanding bonds is an appropriate proxy for the cost of debt?
a) All companies with outstanding bonds.
b) Only companies whose bonds are rated investment grade.
c) All companies whose bonds are rated investment grade or below investment grade but not in
default.
d) The yield to maturity is not an appropriate proxy for the cost of debt for any company
because of the reinvestment rate assumption.
26. Yield to maturity should be calculated on liquid, option-free, short-term debt.
27. While estimating the cost of debt for a firm, one should always use market prices for
publicly traded debt.
28. You are analyzing a distressed bond with one year to maturity. If the probability of default
rises for this bond, the yield to maturity will likely increase, while the cost of debt will likely
decrease.
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Ans: [False]
Response: [Both the yield to maturity and the cost of debt will likely increase.]
Multiple Choice
29. The weights to use in the WACC should reflect the:
a) Current book values.
b) Current market values.
c) Target-market-based values.
d) Book values in the case of bonds and market values in the case of equity.
30. If an observable market value is not readily available, book value of debt can be used to
calculate capital structure.
31. If interest rates have changed since the company’s last valuation or if the company has
entered into financial distress, book value is a reasonable approximation of market value.
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Multiple Choice
32. Which of the following is NOT a property necessary for a consistent estimate of the WACC?
a) It uses book-value-based weights.
b) It includes the opportunity cost of all investors.
c) It includes related costs/benefits such as the interest tax shield.
d) The duration of the securities used in estimating the WACC equals the duration of the free
cash flows.