Solutions-Chapter14

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Solutions-Chapter14

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Chapter 14: Capital Structure in a Perfect Market
14-1. Consider a project with free cash flows in one year of $130,000 or $180,000, with each outcome being equally likely. The initial investment required for the project is $100,000, and the project’s cost of capital is 20%. The risk-free interest rate is 10%.
a. b.
a.
b.
What is the NPV of this project?
Suppose that to raise the funds for the initial investment, the project is sold to investors as an all-equity firm. The equity holders will receive the cash flows of the project in one year. How much money can be raised in this way—that is, what is the initial market value of the unlevered equity?
E(CF)1130,000180,000155,000,
2
1
1
155, 000 1.20
100,000129,167100,000$29,167 Equity value  PV (CF )  155, 000  129,167
1.20
NPV 
14-10. Explain what is wrong with the following argument: “If a firm issues debt that is risk free, because there is no possibility of default, the risk of the firm’s equity does not change. Therefore, risk-free debt allows the firm to get the benefit of a low cost of capital of debt without raising its cost of capital of equity.”
Any leverage raises the equity cost of capital. In fact, risk-free leverage raises it the most (because it does not share any of the risk).
14-11. Consider the entrepreneur described in Section 14.1 (and referenced in Tables 14.1– 14.3). Suppose she funds the project by borrowing $750 rather than $500.
a. According to MM Proposition I, what is the value of the equity? What are its cash flows if the economy is strong? What are its cash flows if the economy is weak?
b. What is the return of the equity in each case? What is its expected return?
c. What is the risk premium of equity in each case? What is the sensitivity of the levered equity return to systematic risk? How does its sensitivity compare to that of unlevered equity? How does its risk premium compare to that of unlevered equity?
d. What is the debt-equity ratio of the firm in this case?
e. What is the firm’s WACC in this case?
a. E = 1000 – 750 = 250. CF = (1400,900) – 750 (1.05) = (612.5,112.5). See class notes.
b. re = (145%, – 55%), E[Re] = 45%, Risk premium = 45% – 5% = 40%. See class notes.
c. Return sensitivity = 145% – (–55%) = 200%. This sensitivity is 4x the sensitivity of unlevered equity (50%). Its risk premium is also 4× that of unlevered equity (40% vs. 10%). See class notes.
750
d.  3 250
e. 25% (45%) + 75% (5%) = 15%

14-12. Hardmon Enterprises is currently an all-equity firm with an expected return of 12%. It is considering a leveraged recapitalization in which it would borrow and repurchase existing shares.
a. Suppose Hardmon borrows to the point that its debt-equity ratio is 0.50. With this amount of debt, the debt cost of capital is 6%. What will the expected return of equity be after this transaction?
b. Suppose instead Hardmon borrows to the point that its debt-equity ratio is 1.50. With this amount of debt, Hardmon’s debt will be much riskier. As a result, the debt cost of capital will be 8%. What will the expected return of equity be in this case?
c. A senior manager argues that it is in the best interest of the shareholders to choose the capital structure that leads to the highest expected return for the stock. How would you respond to this argument?
a. r r D(r r ) =12%+0.50(12%–6%)=15% EUEUD
b. re =12%+1.50(12%–8%)=18%
c. Returns are higher because risk is higher—the return fairly compensates for the risk. There is no free lunch.
14-13. Suppose Visa Inc. (V) has no debt and an equity cost of capital of 9.2%. The average debt-to-value ratio for the credit services industry is 13%. What would its cost of equity be if it took on the average amount of debt for its industry at a cost of debt of 6%?
At a cost of debt of 6%:
r r D(r r )0.0920.13(0.0920.06)0.09689.68%. E U EU D 0.87
14-14. Global Pistons (GP) has common stock with a market value of $200 million and debt with a value of $100 million. Investors expect a 15% return on the stock and a 6% return on the debt. Assume perfect capital markets.
a. Suppose GP issues $100 million of new stock to buy back the debt. What is the expected return of the stock after this transaction?
b. Suppose instead GP issues $50 million of new debt to repurchase stock.
i. If the risk of the debt does not change, what is the expected return of the stock after this transaction?
ii. If the risk of the debt increases, would the expected return of the stock be higher or lower than in part (i)?
21
a. wacc (15%) (6%)12%r .
33
b. i. r r D(r r )12%150 (12%-6%)18%
u
E U EU D 150
ii. if rd is higher, re is lower. The debt will share some of the risk.

14-16. Hartford Mining has 50 million shares that are currently trading for $4 per share and $200 million worth of debt. The debt is risk free and has an interest rate of 5%, and the expected return of Hartford stock is 11%. Suppose a mining strike causes the price of Hartford stock to fall 25% to $3 per share. The value of the risk-free debt is unchanged. Assuming there are no taxes and the risk (unlevered beta) of Hartford’s assets is unchanged, what happens to Hartford’s equity cost of capital?
11 200
ru wacc 11% 5%8%. re 8% 8%5%12%
22 150
14-18. In mid-2015, Qualcomm Inc. had $11 billion in debt, total equity capitalization of $89 billion, and an equity beta of 1.43 (as reported on Yahoo! Finance). Included in Qualcomm’s assets was $21 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 3% and the market risk premium is 4%.
a. What is Qualcomm’s enterprise value?
b. What is the beta of Qualcomm’s business assets?
c. What is Qualcomm’s WACC?
a. EnterpriseValue=E+D–Cash=89+11–21=79billion
b. Because the debt is risk free,   E  UEDE
c. r WACC
 89 (1.43) 79
 1.61
r E[R ]r 3%1.614%9.4%
f Mkt f
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