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and the market risk premium is 6 percent.
structure can affect the weighted average cost of capital and free cash flows. Answer: See Chapter 15 Mini
Case Show
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Mini Case Show
(3.) Show the operating break even point if a company has fixed costs of $200, a sales price of $15, and
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A B C D E F G H I
10/28/2015
Situation
30% 8.5%
40% 10.0%
50% 12.0%
P = $15 0$0 $200 $200
V = $10 80 $1,200 $200 $1,000
Chapter 15. Mini Case
If the company were to recapitalize, debt would be issued, and the funds received would be used to
b. (1.) What is business risk? What factors influence a firm’s business risk? Answer: See Chapter 15 Mini
Case Show
(2.) What is operating leverage, and how does it affect a firm’s business risk? Answer: See Chapter 15
Assume you have just been hired as a business manager of PizzaPalace, a regional pizza restaurant chain.
The company’s EBIT was $50 million last year and is not expected to grow. The firm is currently financed
with all equity and it has 10 million shares outstanding. When you took your corporate finance course, your
instructor stated that most firms’ owners would be financially better off if the firms used some debt. When
you suggested this to your new boss, he encouraged you to pursue the idea. As a first step, assume that you
obtained from the firm’s investment banker the following estimated costs of debt for the firm at different
capital structures:
Operating Leverage
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Q BE = 40 Units.
A B C D E F G H I
Q BE = FC / (P – VC)
Q BE = F÷(P – VC)
Q BE = $200 ÷$15.00 – $10.00
In words, the quantity at which a firm breaks even is found as the difference between
Price and Variable costs divided by Fixed costs.
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Vop = [FCF(1+g)]/(WACC-g)
Vop = $250
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A B C D E F G H I
Beta, b = 1.0
rRF = 6.0%
RPM = 6.0%
rs= rRF + b(RPM) = 12%
Shares outstanding, n = 10
P = $25
Current Valuation
Value of equity (S)
$250
Number of shares
10
P $25
(1.) For each capital structure under consideration, calculate the levered beta, the cost of equity, and the
WACC.
h. With the above points in mind, now consider the optimal capital structure for PizzaPalace.
g. What does does the empirical evidence say about capital structure theory? What are the implications for
managers? Answer: See Chapter 15 Mini Case Show
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Vop = [FCF(1+g)]/(WACC-g)
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Equity = S = ws Vop = $212.77
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A B C D E F G H I
rs= rRF + b(RPM) = 12.90%
b = bU [1 + (1-T)(wd/ws)]
For example:
WACC = wd(1-T)rd + wsrs = 11.28%
The betas, cost of equity, and WACC at each debt level are shown in the table above.
Vop = $265.96
Debt = DNew = wd Vop = $53.19
Consider a recap to 20% debt.
After Debt
P $25.00 $26.60 $26.60
Value of stock
$250.00 $265.96 $212.77
0 0 $53.19
Wealth of shareholders
$250.00 $265.96 $265.96
+ Cash distributed in
Here b is the leveraged beta, bU is the beta that the firm would have if it used no debt, T is the marginal tax
rate, wd is the percentage of the firm financed by debt (based on market values), and ws is the percentage of
the firm financed by equity (based on market values).
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A B C D E F G H I
S =(1- wd) (VopNew)
For wd = 20%: S = $212.77
nPost = nPrior ´ [(VopNew – DNew)/(VopNew-DOld)
For wd = 20%: nPost = 8.00
PPost = (VopNew − DOld)/nPrior
For wd = 20%: PPost = $26.60
Black-Scholes Option Pricing Model
Total Value of Firm 4.00 Analogous to the stock price from the BSOPM
Face Value of Debt 2.00 Analogous to the exercise price
Standard Dev. 0.60 This is the standard dev. of the total value of the firm, not just the stock.
d11.5552
d20.9552
N(d1) 0.9401
N(d2) 0.8303
Debt yield
=
(Face
Value
/Market Value)(1/N)-1
j. Suppose there is a large probability that L will default on its debt. For the purpose of this example, assume
that the value of L’s operations is $4 million (the value of its debt plus equity). Assume also that its debt
consists of 1-year, zero coupon bonds with a face value of $2 million. Finally, assume that L’s volatility, σ is
0.60 and that the risk-free rate rRF is 6%.
If L’s debt is risky, then its equity is like a call option and can be valued with the Black-Scholes Option
Pricing Model (OPM). See Chapter 8 for details of the OPM.
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A B C D E F G H I
Debt yield
= 10.888%
Value of Stock and Debt for Different Volatilities
Equity Debt Debt yield
Volatility $ 2.20 $ 1.80 10.888%
0.20
2.12 1.88 6.18%
0.25
2.12 1.88 6.20%
0.30
2.12 1.88 6.27%
0.35
2.12 1.88 6.48%
0.40
2.13 1.87 6.89%
0.45 2.14 1.86 7.53%
0.50 2.16 1.84 8.41%
0.75 2.28 1.72 16.23%
0.80 2.31 1.69 18.40%
0.85 2.34 1.66 20.77%
0.90 2.38 1.62 23.33%
0.95 2.41 1.59 26.08%
l. How do companies manage the maturity structure of their debt? Answer: See below and the Chapter 15
Mini Case Show.
k. What is the value of L‘s stock for volatilities between 0.20 and 0.95? What incentives might the manager
of L have if she understands this relationship? What might debtholders do in response? Answer: See
below and the Chapter 15 Mini Case Show.
2.00
2.50
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