Chapter 14
Capital Structure in a Perfect Market
14–1. Consider a project with free cash flows in one year of $137,022 or $188,017, with each outcome
being equally likely. The initial investment required for the project is $100,655, and the project’s
cost of capital is 20%. The risk-free interest rate is 11%.
a. What is the NPV of this project?
b. 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?
c. Suppose the initial $100,655 is instead raised by borrowing at the risk-free interest rate.
What are the cash flows of the levered equity, and what is its initial value according to MM?
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14–6. Suppose Alpha Industries and Omega Technology have identical assets that generate identical
cash flows. Alpha Industries is an all-equity firm, with 14 million shares outstanding that trade
for a price of $24 per share. Omega Technology has 22 million shares outstanding as well as debt
of $100 million.
a. According to MM Proposition I, what is the stock price for Omega Technology?
b. Suppose Omega Technology stock currently trades for $15 per share. What arbitrage
opportunity is available? What assumptions are necessary to exploit this opportunity?
14–7. Cisoft is a highly profitable technology firm that currently has $5 billion in cash. The firm has
decided to use this cash to repurchase shares from investors, and it has already announced these
plans to investors. Currently, Cisoft is an all-equity firm with 6 billion shares outstanding. These
shares currently trade for $20 per share. Cisoft has issued no other securities except for stock
options given to its employees. The current market value of these options is $10 billion.
a. What is the market value of Cisoft’s non-cash assets?
b. With perfect capital markets, what is the market value of Cisoft’s equity after the share
repurchase? What is the value per share?
4.750
14–8. Schwartz Industry is an industrial company with 103.5 million shares outstanding and a market
capitalization (equity value) of $4.41 billion. It has $1.21 billion of debt outstanding.
Management have decided to delever the firm by issuing new equity to repay all outstanding
debt.
Chapter 14/Capital Structure in a Perfect Market 199
a. How many new shares must the firm issue?
b. Suppose you are a shareholder holding 100 shares, and you disagree with this decision.
Assuming a perfect capital market, describe what you can do to undo the effect of this
decision.
14–9. Zetatron is an all-equity firm with 270 million shares outstanding, which are currently trading
for $23.64 per share. A month ago, Zetatron announced it will change its capital structure by
borrowing $921 million in short-term debt, borrowing $820 million in longterm debt, and issuing
$1,015 million of preferred stock. The $2,756 million raised by these issues, plus another $94
million in cash that Zetatron already has, will be used to repurchase existing shares of stock. The
transaction is scheduled to occur today. Assume perfect capital markets.
a. What is the market value balance sheet for Zetatron
i. Before this transaction?
ii. After the new securities are issued but before the share repurchase?
iii. After the share repurchase?
b. At the conclusion of this transaction, how many shares outstanding will Zetatron have, and
what will the value of those shares be?
23.64 =
149.44 =
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.”
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?
200 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
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?
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 5%. 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 7%. 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?
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%:
()
0.13
0.092 (0.092 0.06)
0.87
0.0968
9.68%.
E U U D
E
D
r r r r
E
r
= + −
= + −
=
=
14-14. Global Pistons (GP) has common stock with a market value of $470 million and debt with a value
of $299 million. Investors expect a 13% return on the stock and a 5% return on the debt. Assume
perfect capital markets.
a. Suppose GP issues $299 million of new stock to buy back the debt. What is the expected
return of the stock after this transaction?
Chapter 14/Capital Structure in a Perfect Market 201
b. Suppose instead GP issues $71 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)?
470 299
14-15. Hubbard Industries is an all-equity firm whose shares have an expected return of 10.9%.
Hubbard does a leveraged recapitalization, issuing debt and repurchasing stock, until its debt–
equity ratio is 0.66. Due to the increased risk, shareholders now expect a return of 17.1%.
Assuming there are no taxes and Hubbard’s debt is risk-free, what is the interest rate on the
debt?
3 2 3 2
10.9% 17.1% 10.9% 17.1% 1.6%
5 5 5 5
= = = + = − = =
u
wacc r x x x x
14-16. Hartford Mining has 90 million shares that are currently trading for $2 per share and $160
million worth of debt. The debt is risk free and has an interest rate of 4%, and the expected
return of Hartford stock is 11%. Suppose a mining strike causes the price of Hartford stock to
fall 25% to $1.50 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?
( ) ( )
180 160
11 4 7.7%
340 340
= = + =
u
wacc r
.
( )
160
7.7% 7.7% 4% 12.09%
135
= + − =
e
r
14-17. Mercer Corp. is a firm with 10 million shares outstanding and $84 million worth of debt
outstanding. Its current share price is $73. Mercer’s equity cost of capital is 8.5%. Mercer has
just announced that it will issue $354 million worth of debt. It will use the proceeds from this
debt to pay off its existing debt, and use the remaining $270 million to pay an immediate
dividend. Assume perfect capital markets.
a. Estimate Mercer’s share price just after the recapitalization is announced, but before the
transaction occurs.
b. Estimate Mercer’s share price at the conclusion of the transaction. (Hint: Use the market
value balance sheet.)
c. Suppose Mercer’s existing debt was risk free with a 4.39% expected return, and its new debt
is risky with a 4.93% expected return. Estimate Mercer’s equity cost of capital after the
transaction.
202 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
c. Ru = (730/814) 8.5% + (84/814) 4.39% = 8.08%
Re = 8.08% + 354/460(8.08% – 4.93%) = 10.50%
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?
Chapter 14/Capital Structure in a Perfect Market 203
repurchasing the rest of the outstanding equity by issuing debt due in one year. Assume the debt
is zero-coupon and will pay it’s face value in one year.
a. What is the market value of the new debt that must be issued?
b. Suppose OpenStart issues risk-free debt with a face value of $75 million. How much of its
outstanding equity could it repurchase with the proceeds from the debt? What fraction of
the remaining equity would Jim still not own?
c. Combine the fraction of the equity Jim does not own with the risk-free debt. What are the
payoffs of this combined portfolio? What is the value of this portfolio?
d. What face value of risky debt would have the same payoffs as the portfolio in (c)?
e. What is the yield on the risky debt in (d) that will be required to take the company private?
f. If the two outcomes are equally likely, what is OpenStart’s current WACC (before the
transaction)?
g. What is OpenStart’s debt and equity cost of capital after the transaction? Show that the
WACC is unchanged by the new leverage.
19.71%
14–21. Yerba Industries is an all-equity firm whose stock has a beta of 0.70 and an expected return of
18.50%. Suppose it issues new risk-free debt with a 6.50% yield and repurchases 5% of its stock.
Assume perfect capital markets.
a. What is the beta of Yerba stock after this transaction?
b. What is the expected return of Yerba stock after this transaction?
Suppose that prior to this transaction, Yerba expected earnings per share this coming year of
$4.50, with a forward P/E ratio (that is, the share price divided by the expected earnings for the
coming year) of 10.
c. What is Yerba’s expected earnings per share after this transaction? Does this change benefit
shareholders? Explain.
d. What is Yerba’s forward P/E ratio after this transaction? Is this change in the P/E ratio
reasonable? Explain.
204 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition
©2017 Pearson Education, Ltd.
a.
( )
5
1 / 0.70 1 0.737
95
= + = + =
ude
e
b.
( )
( )
17.5 6.5 15.71% 6.5 0.737 15.71 18.08%
0.70
−
= + − − = = = + =
e f m f m f e
r r r r r r r
from the
CAPM, or
( )
( )
5
/ 17.5 17.5 6.5 18.08%
95
= + − = + − =
e u u d
r r d e r r
c. P = 10(4.50) = $45. Borrow 5%(45) = 2.25, interest = 6.5%(2.25) = 0.14625. Earnings = 4.50 –
0.14625 = 4.35375, per share
4.35375 4.58.
0.95
==
No benefit; risk is higher. The stock price does not change.
d.
45 9.83
4.58
==PE
. It falls due to higher risk.
14–22. You are CEO of a high-growth technology firm. You plan to raise $160 million to fund an
expansion by issuing either new shares or new debt. With the expansion, you expect earnings
next year of $31 million. The firm currently has 9 million shares outstanding, with a price of $67
per share. Assume perfect capital markets.
a. If you raise the $160 million by selling new shares, what will the forecast for next year’s
earnings per share be?
b. If you raise the $160 million by issuing new debt with an interest rate of 8%, what will the
forecast for next year’s earnings per share be?
c. What is the firm’s forward P/E ratio (that is, the share price divided by the expected
earnings for the coming year) if it issues equity? What is the firm’s forward P/E ratio if it
issues debt? How can you explain the difference?
160 2.388
