Answers and Solutions: 15 – 1
Chapter 15
Capital Structure Decisions
ANSWERS TO END-OF-CHAPTER QUESTIONS
15-1 a. Capital structure is the manner in which a firm’s assets are financed; that is, the right–
hand side of the balance sheet. Capital structure is normally expressed as the
percentage of each type of capital used by the firm—debt, preferred stock, and
common equity. Business risk is the risk inherent in the operations of the firm, prior
to the financing decision. Thus, business risk is the uncertainty inherent in a total risk
sense, future operating income, or earnings before interest and taxes (EBIT).
Business risk is caused by many factors. Two of the most important are sales
variability and operating leverage. Financial risk is the risk added by the use of debt
financing. Debt financing increases the variability of earnings before taxes (but after
interest); thus, along with business risk, it contributes to the uncertainty of net income
and earnings per share. Business risk plus financial risk equals total corporate risk.
c. Reserve borrowing capacity exists when a firm uses less debt under “normal”
conditions than called for by the tradeoff theory. This allows the firm some
flexibility to use debt in the future when additional capital is needed.
15-2 Business risk refers to the uncertainty inherent in projections of future ROIC = ROEU.
15-4 Operating leverage affects EBIT and, through EBIT, EPS. Financial leverage has no
effect on EBIT—it only affects EPS, given EBIT.
15-5 If sales tend to fluctuate widely, then cash flows and the ability to service fixed charges
will also vary. Such a firm is said to have high business risk. Consequently, there is a
15-6 Public utilities place greater emphasis on long-term debt because they have more stable
sales and profits as well as more fixed assets. Also, utilities have fixed assets which can
15-7 EBIT depends on sales and operating costs. Interest is deducted from EBIT. At high debt
15-8 The tax benefits from debt increase linearly, which causes a continuous increase in the
firm’s value and stock price. However, financial distress costs get higher and higher as
Answers and Solutions: 15 – 3
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
15-1 QBE = F/(P – V) = $500,000/($75 – $50) = 20,000.
15-2 If wd = 0.2, then wce = 1 – 0.2 = 0.8. So D/S = wd/we = 0.2/0.8.
15-3 If the company had no debt, its required return would be:
rs,U = rRF + bU RPM = 5.5% + 1.0(6%) = 11.5%.
15-4 S = (1 – wd)(Vop) = (1 – 0.4)($500) = $300 million.
15-7 a. Here are the steps involved:
(1) Determine the variable cost per unit at present, V:
Profit = P(Q) – FC – V(Q)
$500,000 = ($100,000)(50) – $2,000,000 – V(50)
50(V) = $2,500,000
V = $50,000.
Answers and Solutions: 15 – 4
(4) Estimate the approximate rate of return on new investment:
Return = Profit/Investment = $850,000/$4,000,000 = 21.25%.
Since the return exceeds the 15 percent cost of equity, this analysis suggests that the
firm should go ahead with the change.
c. It is impossible to state unequivocally whether the new situation would have more or
less business risk than the old one. We would need information on both the sales
probability distribution and the uncertainty about variable input cost in order to make
this determination. However, since a higher breakeven point, other things held
constant, is more risky. Also the percentage of fixed costs increases:
15-8 a. Original value of the firm (D = $0):
We are given that the book value of assets is equal to the market value of assets, so
the value is $3,000,000. Alternatively, we can calculate the value as the sum of the
debt (which is zero) and the stock (200,000 shares at a price of $15 per share):
V = D + S = 0 + ($15)(200,000) = $3,000,000.
Because growth is zero, FCF is equal to EBIT(1-T). The value of operations is:
Vop =
.286.214,348,3$
0896.0
)40.01)(000,500($
WACC
)T1)(EBIT(
WACC
FCF =
−
=
−
=
Increasing the financial leverage by adding $900,000 of debt results in an increase in
b. Using its target capital structure of 30% debt, the company must have debt of:
D = wd V = 0.30($3,348,214.286) = $1,004,464.286.
Therefore, its value of equity is:
Answers and Solutions: 15 – 6
c. The number of shares repurchased, X, is:
X = (D – D0)/P = $1,004,464.286 / $16.741 = 60,000.256 60,000.
Thus, by adding debt, the firm increased its EPS by $0.342.
d. 30% debt: TIE =
I
EBIT
=
5.312,70$
EBIT
.
Probability TIE
0.10 ( 1.42)
0.20 2.84
Answers and Solutions: 15 – 7
15-9 a. Present situation (50% debt):
WACC = wd rd(1-T) + wcers
= (0.5)(10%)(1-0.15) + (0.5)(14%) = 11.25%.
V =
1125.0
)15.01)(24.13($
WACC
)T1)(EBIT(
WACC
FCF −
=
−
=
= $100 million.
15-10 a. BEA’s unlevered beta is bU=b/(1+ (1-T)(D/S))=1.0/(1+(1-0.40)(20/80)) = 0.870.
b. b = bU (1 + (1-T)(D/S)).
At 40 percent debt: bL = 0.87 (1 + 0.6(40%/60%)) = 1.218.
rS = 6 + 1.218(4) = 10.872%
1114.0
)15.01)(24.13($
WACC
)T1)(EBIT(
WACC
FCF −
=
−
=
Answers and Solutions: 15 – 8
15-11 Tax rate = 40% rRF = 5.0%
bU = 0.8 rM – rRF = 6.0%
From data given in the problem and table we can develop the following table:
wd
wce
D/S
rd
rd(1 – T)
Levered
betaa
rsb
WACCc
0
100%
0.00
6.0%
3.60%
0.80
9.80%
9.80%
Notes:
a These beta estimates were calculated using the Hamada equation,
b = bU[1 + (1 – T)(D/S)].
b These rs estimates were calculated using the CAPM, rs = rRF + (rM – rRF)b.
0.25
7.0%
4.20%
0.92
9.26%
0.67
8.0%
4.80%
1.12
8.95%
1.50
9.0%
5.40%
1.52
8.89%
4.00
10.0%
6.00%
2.72
9.06%
Answers and Solutions: 15 – 9
SOLUTION TO SPREADSHEET PROBLEM
Mini Case: 15 – 10
MINI CASE
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:
% Financed With Debt rd
0% —
20 8.0%
30 8.5
40 10.0
50 12.0
If the company were to recapitalize, debt would be issued, and the funds received would be
used to repurchase stock. PizzaPalace is in the 40 percent state-plus-federal corporate tax
bracket, its beta is 1.0, the risk-free rate is 6 percent, and the market risk premium is 6
percent.
a. Using the free cash flow valuation model, show the only avenues by which
capital structure can affect value.
Answer: The basic definitions are:
(1) V = Value of Firm
Mini Case: 15 – 11
b. (1) What is business risk? What factors influence a firm’s business risk?
Answer: Business risk is uncertainty about EBIT. Factors that influence business risk include:
b. (2) What is operating leverage, and how does it affect a firm’s business risk? Show
the operating break even point if a company has fixed costs of $200, a sales price
of $15, and variables costs of $10.
Answer: Operating leverage is the change in EBIT caused by a change in quantity sold. The
higher the proportion of fixed costs within a firm’s overall cost structure, the greater
c. Now, to develop an example which can be presented to PizzaPalace’s
management to illustrate the effects of financial leverage, consider two
hypothetical firms: Firm U, which uses no debt financing, and Firm L, which
uses $10,000 of 12 percent debt. Both firms have $20,000 in assets, a 40 percent
tax rate, and an expected EBIT of $3,000.
Mini Case: 15 – 12
1. Construct partial income statements, which start with EBIT, for the two firms.
Answer: Here are the fully completed statements:
Firm U Firm L
c. 2. Now calculate ROE for both firms.
Answer: Firm U Firm L
c. 3. What does this example illustrate about the impact of financial leverage on
ROE?
Answer: Conclusions from the analysis:
• The firm’s basic earning power, BEP = EBIT/total assets, is unaffected by financial
leverage.
Mini Case: 15 – 13
d. Explain the difference between financial risk and business risk.
Answer: Business risk increases the uncertainty in future EBIT. It depends on business factors
e. What happens to ROE for Firm U and Firm L if EBIT falls to $2,000? What does this
imply about the impact of leverage on risk and return?
Answer:
Firm U
Firm L
EBIT
$2,000
$2,000
Interest
$1,200
EBT
$2,000
Taxes
$1,200
ROIC
ROE
Mini Case: 15 – 14
f. What does capital structure theory attempt to do? What lessons can be learned
from capital structure theory? Be sure to address the MM models.
Answer: MM theory begins with the assumption of zero taxes. MM prove, under a very
restrictive set of assumptions, that a firm’s value is unaffected by its financing mix:
VL = VU.
MM theory ignores bankruptcy (financial distress) costs, which increase as more
leverage is used. At low leverage levels, tax benefits outweigh bankruptcy costs. At
high levels, bankruptcy costs outweigh tax benefits. An optimal capital structure
exists that balances these costs and benefits. This is the trade-off theory.
Mini Case: 15 – 15
A second agency problem is the potential for “underinvestment”. Debt increases risk
of financial distress. Therefore, managers may avoid risky projects even if they have
positive NPVs.
g. What does the empirical evidence say about capital structure theory? What are
the implications for managers?
Answer: Tax benefits are important. At the optimal capital structure, $1 debt adds about $0.10
to $0.20 to value on average. For the average firm financed with 25% to 30% debt,
this adds about 3% to 6% to the total value. Bankruptcies are costly– costs can be up
Mini Case: 15 – 16
attitudes.
h. With the above points in mind, now consider the optimal capital structure for
PizzaPalace.
h. (1) For each capital structure under consideration, calculate the levered beta, the
cost of equity, and the WACC.
Answer: MM theory implies that beta changes with leverage. bu is the beta of a firm when it
has no debt (the unlevered beta.) Hamada’s equation provides the beta of a levered
firm: bL = bU [1 + (1 – T)(D/S)]. For example, to find the cost of equity for wd = 20%,
Mini Case: 15 – 17
h. (2) Now calculate the corporate value.
Answer: For example the corporate value for wd = 20% is:
V = FCF(1+g) / (WACC-g)
Using these values, V = $30(1+0) / (0.1128 − 0) = $2,65.96 million.
Mini Case: 15 – 18
i. Describe the recapitalization process and apply it to PizzaPalace. Calculate the
resulting the value of the debt that will be issued, the resulting market value of
equity, the price per share, the number of shares repurchased, and the
remaining shares. Considering only the capital structures under analysis, what is
PizzaPalace’s optimal capital structure?
Answer:
First, find the dollar value of debt. For example, for wd = 20%, the dollar value of
debt is:
d = wd V = 0.2 ($2,659,574) = $53.19.
Mini Case: 15 – 19
The situation before the recap is:
The stock price is $25 and the total wealth of shareholders is $2,500,000.
Now consider the situation if the firm moves to a capital structure with wd = 20% by
issuing $53.1915 in debt but has not yet repurchased equity. The firm’s value of
operations increases because its WACC decreases. The firm also temporarily has
$531,915 in short-term investments.
Mini Case: 15 – 20
The repurchase itself will not change the stock price. If investors thought that the
repurchase would increase the stock price, they would all purchase stock the day
before, which would drive up its price. If investors thought that the repurchase would
decrease the stock price, they would all sell short the stock the day before, which
would drive down the stock price.
Before
Debt
After
Debt,
Before
Rep.
After Rep.
Vop
$250
$265.9574
$265.9574
+ ST Inv.
0
53.1915
0
$250
$319.1489
$265.9574
0
53.1915
53.1915
$250
$265.9574
$212.7660
$250
$265.9574
$212.7660
0
0
53.1915
$250
$265.9574
$265.9574
Mini Case: 15 – 21
There are some shortcuts we can take to find the values of S, P, and n after the
repurchase:
We apply these relationships for each possible capital structure:
wd
0%
20%
30%
40%
50%
rd
0.0%
8.0%
8.5%
10.0%
12.0%
ws
100%
80%
70%
60%
50%
b
1.150
13.54%
11.01%
$81.74
S
n
P
$27.25
$27.17
The optimal capital structure is for wd = 30%. This gives the highest corporate value,
the lowest WACC, and the highest stock price per share. But notice that wd = 40% is
very similar to the optimal solution; in other words, the optimal range is pretty flat.