16
CAPITAL CHAPTER STRUCTURE DECISIONS: THE BASICS
True/False
Easy:
(16.1) Bankruptcy costs
1
.
Answer: a
Different borrowers have different risks of bankruptcy, and bankruptcy
is costly to lenders. Therefore, lenders charge higher rates to
borrowers judged to be more at risk of going bankrupt.
a.
b.
True
False
(16.2) Business risk
2
.
Answer: b
True
False
(16.2) Financial risk
.
Answer: a
True
False
(16.2) Financial risk
.
Answer: b
True
False
(16.2) Financial risk
.
Answer: a
True
False
(16.2) Financial leverage
.
EASY
A firms capital structure does not affect its calculated free cash
flows, because FCF reflects only operating cash flows.
a.
b.
6
EASY
As the text indicates, a firm's financial risk has identifiable market
risk and diversifiable risk components.
a.
b.
5
EASY
Financial risk refers to the extra risk stockholders bear as a result of
using debt as compared with the risk they would bear if no debt were used.
a.
b.
4
EASY
A firm's business risk is largely determined by the financial
characteristics of its industry, especially by the amount of debt the
average firm in the industry uses.
a.
b.
3
EASY
Answer: a
EASY
Whenever a firm borrows money, it is using financial leverage.
a.
b.
True
False
Chapter 16: Cap Structure: Basics
True/False
Page 225
(16.2) Use of financial leverage
7
.
True
False
(16.2) Operating and financial leverage
.
EASY
True
False
(16.3) Trade-off theory
.
Answer: b
Provided a firm does not use an extreme amount of debt, financial
leverage typically affects both EPS and EBIT, while operating leverage
only affects EBIT.
a.
b.
9
EASY
The graphical probability distribution of ROE for a firm that uses
financial leverage would tend to be more peaked than the distribution if
the firm used no leverage, other things held constant.
a.
b.
8
Answer: b
Answer: a
EASY
The trade-off theory states that the capital structure decision involves
a tradeoff between the costs and benefits of debt financing.
a.
b.
True
False
Medium:
(16.2) Use of debt in financing
10
.
True
False
(16.2) Financial leverage
.
Answer: b
True
False
(16.2) Business risk
.
MEDIUM
Firm A has a higher degree of business risk than Firm B. Firm A can
offset this by using less financial leverage. Therefore, the
variability of both firms' expected EBITs could actually be identical.
a.
b.
12
MEDIUM
If a firm utilizes debt financing, an X% decline in earnings before
interest and taxes (EBIT) will result in a decline in earnings per share
that is larger than X.
a.
b.
11
Answer: a
Answer: b
MEDIUM
Two firms, although they operate in different industries, have the same
expected earnings per share and the same standard deviation of expected
EPS. Thus, the two firms must have the same business risk.
a.
b.
Page 226
True
False
True/False
Chapter 16: Cap Structure: Basics
(16.2) Operating and financial leverage
13
.
True
False
(16.3) Bankruptcy costs
.
MEDIUM
It is possible that two firms could have identical financial and
operating leverage, yet have different degrees of risk as measured by
the variability of EPS.
a.
b.
14
Answer: a
Answer: a
MEDIUM
If Miller and Modigliani had incorporated the costs of bankruptcy into
their model, it is unlikely that they would have concluded that 100%
debt financing is optimal.
a.
b.
True
False
Multiple Choice: Conceptual
Easy:
(16.2) Business risk
15
.
Answer: a
An increase in the debt ratio will generally have no effect on which of
these items?
a.
b.
c.
d.
e.
Business risk.
Total risk.
Financial risk.
Market risk.
The firm's beta.
(16.2) Business risk
16
.
Answer: d
Demand variability.
Sales price variability.
The extent to which operating costs are fixed.
The extent to which interest rates on the firm's debt fluctuate.
Input price variability.
(16.3) Target debt ratio
.
EASY
Business risk is affected by a firm's operations. Which of the following
is NOT associated with (or does not contribute to) business risk?
a.
b.
c.
d.
e.
17
EASY
Answer: a
EASY
Which of the following events is likely to encourage a company to raise
its target debt ratio, other things held constant?
a.
b.
c.
d.
e.
An increase in the corporate tax rate.
An increase in the personal tax rate.
An increase in the companys operating leverage.
The Federal Reserve tightens interest rates in an effort to fight
inflation.
The company's stock price hits a new high.
Chapter 16: Cap Structure: Basics
True/False
Page 227
(16.3) Leverage and capital structure
18
.
Answer: b
Which of the following would increase the likelihood that a company
would increase its debt ratio, other things held constant?
a.
b.
c.
d.
e.
An increase in costs incurred when filing for bankruptcy.
An increase in the corporate tax rate.
An increase in the personal tax rate.
The Federal Reserve tightens interest rates in an effort to fight
inflation.
The company's stock price hits a new low.
(16.5) Capital structure and WACC
19
.
Answer: d
b.
c.
d.
e.
Since debt financing raises the firm's financial risk, increasing a
companys debt ratio will always increase its WACC.
Since debt financing is cheaper than equity financing, raising a
companys debt ratio will always reduce its WACC.
Increasing a companys debt ratio will typically reduce the
marginal cost of both debt and equity financing. However, this
action still may raise the companys WACC.
Increasing a companys debt ratio will typically increase the
marginal cost of both debt and equity financing. However, this
action still may lower the companys WACC.
Since a firm's beta coefficient it not affected by its use of
financial leverage, leverage does not affect the cost of equity.
(16.5) Optimal capital structure
.
Answer: d
b.
c.
d.
e.
The capital structure that maximizes
the price per share of common stock.
The capital structure that minimizes
maximizes the expected EPS.
The capital structure that minimizes
also maximizes the stock price.
The capital structure that minimizes
price per share of common stock.
The capital structure that gives the
also maximizes the stock price.
expected EPS also maximizes
the interest rate on debt also
the required return on equity
the WACC also maximizes the
firm the best credit rating
(16.5) Optimal capital structure
.
EASY
Which of the following statements is CORRECT?
a.
21
EASY
Which of the following statements is CORRECT?
a.
20
EASY
Answer: c
EASY
Based on the information below, what is Ezzel Enterprises' optimal
capital structure?
a.
b.
c.
d.
e.
Page 228
Debt
Debt
Debt
Debt
Debt
=
=
=
=
=
40%;
50%;
60%;
80%;
70%;
Equity
Equity
Equity
Equity
Equity
=
=
=
=
=
60%;
50%;
40%;
20%;
30%;
EPS
EPS
EPS
EPS
EPS
=
=
=
=
=
$2.95;
$3.05;
$3.18;
$3.42;
$3.31;
True/False
Stock
Stock
Stock
Stock
Stock
price
price
price
price
price
=
=
=
=
=
$26.50.
$28.90.
$31.20.
$30.40.
$30.00.
Chapter 16: Cap Structure: Basics
(16.5) Optimal capital structure
22
.
b.
c.
d.
e.
The optimal capital structure is the mix of debt, equity, and
preferred stock that maximizes the companys earnings per share (EPS).
The optimal capital structure is the mix of debt, equity, and
preferred stock that maximizes the companys stock price.
The optimal capital structure is the mix of debt, equity, and
preferred stock that minimizes the companys cost of equity.
The optimal capital structure is the mix of debt, equity, and
preferred stock that minimizes the companys cost of debt.
The optimal capital structure is the mix of debt, equity, and
preferred stock that minimizes the companys cost of preferred stock.
(16.5) Financial leverage and EPS
.
EASY
Which of the following statements best describes the optimal capital
structure?
a.
23
Answer: b
Answer: a
EASY
Volga Publishing is considering a proposed increase in its debt ratio,
which would also increase the companys interest expense. The plan
would involve issuing new bonds and using the proceeds to buy back
shares of its common stock. The companys CFO thinks the plan will not
change total assets or operating income, but that it will increase
earnings per share (EPS). Assuming the CFOs estimates are correct,
which of the following statements is CORRECT?
a.
b.
c.
d.
e.
Since the proposed plan increases Volgas financial risk, the
companys stock price still might fall even if EPS increases.
If the plan reduces the WACC, the stock price is also likely to
decline.
Since the plan is expected to increase EPS, this implies that net
income is also expected to increase.
If the plan does increase the EPS, the stock price will
automatically increase at the same rate.
Under the plan there will be more bonds outstanding, and that will
increase their liquidity and thus lower the interest rate on the
currently outstanding bonds.
Easy/Medium:
(16.5) Optimal capital structure
24
.
Answer: e
EASY/MEDIUM
Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
As a rule, the optimal capital structure is found by determining
the debt-equity mix that maximizes expected EPS.
The optimal capital structure simultaneously maximizes EPS and
minimizes the WACC.
The optimal capital structure minimizes the cost of equity, which
is a necessary condition for maximizing the stock price.
The optimal capital structure simultaneously minimizes the cost of
debt, the cost of equity, and the WACC.
The optimal capital structure simultaneously maximizes stock price
and minimizes the WACC.
Chapter 16: Cap Structure: Basics
True/False
Page 229
(16.5) Target capital structure
25
.
Answer: e
The firms target capital structure should be consistent with which of
the following statements?
a.
b.
c.
d.
e.
Maximize the earnings per share (EPS).
Minimize the cost of debt (rd).
Obtain the highest possible bond rating.
Minimize the cost of equity (rs).
Minimize the weighted average cost of capital (WACC).
(Comp: 16.2,16.5) Business & fin. risk & cap. struc.
26
.
EASY/MEDIUM
Answer: b
EASY/MEDIUM
Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
A firms business risk is determined solely by the financial
characteristics of its industry.
The factors that affect a firms business risk are affected by
industry characteristics and economic conditions. Unfortunately,
these factors are generally beyond the control of the firm's
management.
One of the benefits to a firm of being at or near its target
capital structure is that this eliminates any risk of bankruptcy.
A firms financial risk can be minimized by diversification.
The amount of debt in its capital structure can under no
circumstances affect a companys business risk.
Medium:
(16.2) Operating leverage
27
.
Answer: e
a.
b.
c.
d.
e.
normally
normally
normally
expected
normally
normally
lead to
lead to
lead to
EBIT.
lead to
lead to
an increase in its fixed assets turnover ratio.
a decrease in its business risk.
a decrease in the standard deviation of its
a decrease in the variability of its expected EPS.
a reduction in its fixed assets turnover ratio.
(16.2) Use of financial leverage
28
.
MEDIUM
Which of the following statements is CORRECT? As a firm increases the
operating leverage used to produce a given quantity of output, this will
Answer: d
MEDIUM
If debt financing is used, which of the following is CORRECT?
a.
b.
c.
d.
e.
Page 230
The percentage change in net operating income will be greater than
a given percentage change in net income.
The percentage change in net operating income will be equal to a
given percentage change in net income.
The percentage change in net income relative to the percentage
change in net operating income will depend on the interest rate
charged on debt.
The percentage change in net income will be greater than the
percentage change in net operating income.
The percentage change in sales will be greater than the percentage
change in EBIT, which in turn will be greater than the percentage
True/False
Chapter 16: Cap Structure: Basics
change in net income.
(16.2) Leverage and capital structure
29
.
b.
c.
d.
e.
Firms whose assets are relatively liquid tend to have relatively low
bankruptcy costs, hence they tend to use relatively little debt.
An increase in the personal tax rate is likely to increase the debt
ratio of the average corporation.
If changes in the bankruptcy code make bankruptcy less costly to
corporations, then this would likely reduce the debt ratio of the
average corporation.
An increase in the companys degree of operating leverage is likely
to encourage a company to use more debt in its capital structure.
An increase in the corporate tax rate is likely to encourage a
company to use more debt in its capital structure.
(16.2) Leverage and capital structure
.
MEDIUM
Its sales become less stable over time.
The costs that would be incurred in the event of bankruptcy increase.
Management believes that the firms stock has become overvalued.
Its degree of operating leverage increases.
The corporate tax rate increases.
(16.2) Leverage and capital structure
.
Answer: e
Other things held constant, which of the following events is most likely
to encourage a firm to increase the amount of debt in its capital
structure?
a.
b.
c.
d.
e.
31
MEDIUM
Which of the following statements is CORRECT, holding other things
constant?
a.
30
Answer: e
Answer: c
MEDIUM
Reynolds Resorts is currently 100% equity financed. The CFO is
considering a recapitalization plan under which the firm would issue
long-term debt with a yield of 9% and use the proceeds to repurchase
common stock. The recapitalization would not change the companys total
assets, nor would it affect the firms basic earning power, which is
currently 15%. The CFO believes that this recapitalization would reduce
the WACC and increase stock price. Which of the following would also be
likely to occur if the company goes ahead with the recapitalization plan?
a.
b.
c.
d.
e.
The
The
The
The
The
companys
companys
companys
companys
companys
net income would increase.
earnings per share would decline.
cost of equity would increase.
ROA would increase.
ROE would decline.
Chapter 16: Cap Structure: Basics
True/False
Page 231
(16.2) Capital structure, ROA, and ROE
32
.
Answer: e
Blemker Corporation has $500 million of total assets, its basic earning
power is 15%, and it currently has no debt in its capital structure.
The CFO is contemplating a recapitalization where it will issue debt at
a cost of 10% and use the proceeds to buy back shares of the companys
common stock, paying book value. If the company proceeds with the
recapitalization, its operating income, total assets, and tax rate will
remain unchanged. Which of the following is most likely to occur as a
result of the recapitalization?
a.
b.
c.
d.
e.
The
The
The
The
The
ROA would increase.
ROA would remain unchanged.
basic earning power ratio would decline.
basic earning power ratio would increase.
ROE would increase.
(16.5) Financial leverage and EPS
33
.
b.
c.
d.
e.
MEDIUM
Increasing financial leverage is one way to increase a firms basic
earning power (BEP).
If a firm lowered its fixed costs while increasing its variable
costs, holding total costs at the present level of sales constant,
this would decrease its operating leverage.
The debt ratio that maximizes EPS generally exceeds the debt ratio
that maximizes share price.
If a company were to issue debt and use the money to repurchase
common stock, this action would have no impact on its basic earning
power ratio. (Assume that the repurchase has no impact on the
companys operating income.)
If changes in the bankruptcy code made bankruptcy less costly to
corporations, this would likely reduce the average corporation's
debt ratio.
(16.5) Financial leverage and ratios
.
Answer: c
Which of the following statements is CORRECT?
a.
34
MEDIUM
Answer: b
MEDIUM
Companies HD and LD have identical tax rates, total assets, and basic
earning power ratios, and their basic earning power exceeds their
before-tax cost of debt, rd. However, Company HD has a higher debt
ratio and thus more interest expense than Company LD. Which of the
following statements is CORRECT?
a.
b.
c.
d.
e.
Page 232
Company
Company
Company
The two
The two
HD has a higher net income than Company LD.
HD has a lower ROA than Company LD.
HD has a lower ROE than Company LD.
companies have the same ROA.
companies have the same ROE.
True/False
Chapter 16: Cap Structure: Basics
(16.5) Financial leverage and ratios
35
.
The two companies have the same times interest earned (TIE) ratio.
Firm L has a lower ROA than Firm U.
Firm L has a lower ROE than Firm U.
Firm L has the higher times interest earned (TIE) ratio.
Firm L has a higher EBIT than Firm U.
(16.5) Financial leverage and ratios
.
d.
e.
MEDIUM
HD should have a higher return on assets (ROA) than LD.
HD should have a higher times interest earned (TIE) ratio than LD.
HD should have a higher return on equity (ROE) than LD, but its
risk, as measured by the standard deviation of ROE, should also be
higher than LD's.
Given that BEP > rd, HD's stock price must exceed that of LD.
Given that BEP > rd, LD's stock price must exceed that of HD.
(Comp: 16.2,16.3) Capital structure and WACC
.
Answer: c
Companies HD and LD have the same total assets, operating income (EBIT),
tax rate, and business risk. Company HD, however, has a much higher
debt ratio than LD. Also HDs basic earning power (BEP) exceeds its
cost of debt (rd). Which of the following statements is CORRECT?
a.
b.
c.
37
MEDIUM
Firms U and L each have the same amount of assets, and both have a basic
earning power ratio of 20%. Firm U is unleveraged, i.e., it is 100%
equity financed, while Firm L is financed with 50% debt and 50% equity.
Firm Ls debt has a before-tax cost of 8%. Both firms have positive net
income. Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
36
Answer: b
Answer: b
MEDIUM
Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
A firm can use retained earnings without paying a flotation cost.
Therefore, while the cost of retained earnings is not zero, its
cost is generally lower than the after-tax cost of debt.
The capital structure that minimizes a firms weighted average cost
of capital is also the capital structure that maximizes its stock
price.
The capital structure that minimizes the firms weighted average
cost of capital is also the capital structure that maximizes its
earnings per share.
If a firm finds that the cost of debt is less than the cost of
equity, increasing its debt ratio must reduce its WACC.
Other things held constant, if corporate tax rates declined, then
the Modigliani-Miller tax-adjusted tradeoff theory would suggest
that firms should increase their use of debt.
Chapter 16: Cap Structure: Basics
True/False
Page 233
(Comp: 16.2,16.5) Capital structure, WACC, TIE, and EPS
38
.
Answer: a
MEDIUM
Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
The capital structure that maximizes the stock price is also the
capital structure that minimizes the weighted average cost of
capital (WACC).
The capital structure that maximizes the stock price is also the
capital structure that maximizes earnings per share.
The capital structure that maximizes the stock price is also the
capital structure that maximizes the firms times interest earned
(TIE) ratio.
Increasing a companys debt ratio will typically reduce the
marginal costs of both debt and equity financing; however, this
still may raise the companys WACC.
If Congress were to pass legislation that increases the personal
tax rate but decreases the corporate tax rate, this would encourage
companies to increase their debt ratios.
Medium/Hard:
(16.2) Miscellaneous capital structure concepts
39
.
Answer: a
MEDIUM/HARD
Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
Page 234
In general, a firm with low operating leverage also has a small
proportion of its total costs in the form of fixed costs.
There is no reason to think that changes in the personal tax rate
would affect firms capital structure decisions.
A firm with high business risk is more likely to increase its use
of financial leverage than a firm with low business risk, assuming
all else equal.
If a firm's after-tax cost of equity exceeds its after-tax cost of
debt, it can always reduce its WACC by increasing its use of debt.
Suppose a firm has less than its optimal amount of debt. Increasing
its use of debt to the point where it is at its optimal capital
structure will decrease the costs of both debt and equity financing.
True/False
Chapter 16: Cap Structure: Basics
(16.2) Miscellaneous capital structure concepts
40
.
b.
c.
d.
e.
If corporate tax rates were decreased while other things were held
constant, and if the Modigliani-Miller tax-adjusted tradeoff theory
of capital structure were correct, this would tend to cause
corporations to decrease their use of debt.
A change in the personal tax rate should not affect firms capital
structure decisions.
Business risk is differentiated from financial risk by the fact
that financial risk reflects only the use of debt, while business
risk reflects both the use of debt and such factors as sales
variability, cost variability, and operating leverage.
The optimal capital structure is the one that simultaneously (1)
maximizes the price of the firms stock, (2) minimizes its WACC,
and (3) maximizes its EPS.
If changes in the bankruptcy code make bankruptcy less costly to
corporations, then this would likely reduce the debt ratio of the
average corporation.
(16.5) Leverage and capital structure
.
b.
c.
d.
e.
MEDIUM/HARD
When a company increases its debt ratio, the costs of equity and
debt both increase. Therefore, the WACC must also increase.
The capital structure that maximizes the stock price is generally
the capital structure that also maximizes earnings per share.
All else equal, an increase in the corporate tax rate would tend to
encourage a company to increase its debt ratio.
Since debt financing raises the firms financial risk, increasing a
companys debt ratio will always increase its WACC.
Since debt is cheaper than equity, increasing a companys debt
ratio will always reduce its WACC.
(16.5) Financial leverage and ratios
.
Answer: c
Which of the following statements is CORRECT?
a.
42
MEDIUM/HARD
Which of the following statements is CORRECT?
a.
41
Answer: a
Answer: c
MEDIUM/HARD
Companies HD and LD have identical amounts of assets, operating income
(EBIT), tax rates, and business risk. Company HD, however, has a much
higher debt ratio than LD. Company HDs basic earning power ratio (BEP)
exceeds its cost of debt (rd). Which of the following statements is
CORRECT?
a.
b.
c.
d.
e.
Company HD has a higher return on assets (ROA) than Company LD.
Company HD has a higher times interest earned (TIE) ratio than
Company LD.
Company HD has a higher return on equity (ROE) than Company LD, and
its risk, as measured by the standard deviation of ROE, is also
higher than LDs.
The two companies have the same ROE.
Company HDs ROE would be higher if it had no debt.
Chapter 16: Cap Structure: Basics
True/False
Page 235
Hard:
(16.4) Variations in capital structures
43
.
Answer: d
HARD
Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
Generally, debt-to-total-assets ratios do not vary much among
different industries, although they do vary among firms within a
given industry.
Electric utilities generally have very high common equity ratios
because their revenues are more volatile than those of firms in
most other industries.
Drug companies (prescription, not illegal!) generally have high
debt-to-equity ratios because their earnings are very stable and,
thus, they can cover the high interest costs associated with high
debt levels.
Wide variations in capital structures exist both between industries
and among individual firms within given industries. These
differences are caused by differing business risks and also
managerial attitudes.
Since most stocks sell at or very close to their book values, book
value capital structures are almost always adequate for use in
estimating firms' costs of capital.
Multiple Choice: Problems
Easy:
(16.2) Breakeven point--nonalgorithmic
44
.
Answer: d
EASY
Elephant Books sells paperback books for $7 each. The variable cost per
book is $5. At current annual sales of 200,000 books, the publisher is
just breaking even. It is estimated that if the authors' royalties are
reduced, the variable cost per book will drop by $1. Assume authors'
royalties are reduced and sales remain constant; how much more money can
the publisher put into advertising (a fixed cost) and still break even?
a.
b.
c.
d.
e.
Page 236
$600,000
$466,667
$333,333
$200,000
None of the above
Problems
Chapter 16: Cap Structure: Basics
Easy/Medium:
(16.2) Breakeven analysis
45
.
Answer: a
DeLong Inc. has fixed operating costs of $470,000, variable costs of
$2.80 per unit produced, and its products sell for $4.00 per unit. What
is the company's breakeven point, i.e., at what unit sales volume would
income equal costs?
a.
b.
c.
d.
e.
391,667
411,250
431,813
453,403
476,073
(16.2) Breakeven analysis
46
.
EASY/MEDIUM
Answer: c
EASY/MEDIUM
Senbet Ventures is considering starting a new company to produce
stereos. The sales price would be set at 1.5 times the variable cost
per unit; the VC/unit is estimated to be $2.50; and fixed costs are
estimated at $120,000. What sales volume would be required in order to
break even, i.e., to have an EBIT of zero for the stereo business?
a.
b.
c.
d.
e.
86,640
91,200
96,000
100,800
105,840
Medium:
(16.2) Debt's effect on ROE
47
.
Answer: a
MEDIUM
Vu Enterprises expects to have the following data during the coming
year. What is Vu's expected ROE?
Assets
D/A
EBIT
a.
b.
c.
d.
e.
$200,000
65%
$25,000
Interest rate
Tax rate
8%
40%
12.51%
13.14%
13.80%
14.49%
15.21%
Chapter 16: Cap Structure: Basics
Problems
Page 237
(16.2) Net operating income--nonalgorithmic
Page 238
Problems
Answer: b
MEDIUM
Chapter 16: Cap Structure: Basics
48
.
The Congress Company has identified two methods for producing playing
cards. One method involves using a machine having a fixed cost of
$10,000 and variable costs of $1.00 per deck of cards. The other method
would use a less expensive machine (fixed cost = $5,000), but it would
require greater variable costs ($1.50 per deck of cards). If the
selling price per deck of cards will be the same under each method, at
what level of output will the two methods produce the same net operating
income (EBIT)?
a.
b.
c.
d.
e.
5,000 decks
10,000 decks
15,000 decks
20,000 decks
25,000 decks
(16.5) Calculating the unlevered beta
49
.
Answer: e
Ang Enterprises has a levered beta of 1.10, its capital structure
consists of 40% debt and 60% equity, and its tax rate is 40%. What would
Ang's beta be if it used no debt, i.e., what is its unlevered beta?
a.
b.
c.
d.
e.
0.64
0.67
0.71
0.75
0.79
(16.5) Capital structure and value--nonalgorithmic
50
.
MEDIUM
Answer: e
MEDIUM
A consultant has collected the following information regarding Young
Publishing:
Total assets
Operating income (EBIT)
Interest expense
Net income
Share price
$3,000
$800
$0
$480
million
million
million
million
$32.00
Tax rate
Debt ratio
WACC
M/B ratio
EPS = DPS
40%
0%
10%
1.00
$3.20
The company has no growth opportunities (g = 0), so the company pays out
all of its earnings as dividends (EPS = DPS). The consultant believes
that if the company moves to a capital structure financed with 20% debt
and 80% equity (based on market values) that the cost of equity will
increase to 11% and that the pre-tax cost of debt will be 10%. If the
company makes this change, what would be the total market value (in
millions) of the firm?
a.
b.
c.
d.
e.
$3,200
$3,600
$4,000
$4,200
$4,800
Chapter 16: Cap Structure: Basics
Problems
Page 239
Medium/Hard:
(16.2) EBIT and setting the price
51
.
Answer: c
A group of venture investors is considering putting money into Lemma
Books, which wants to produce a new reader for electronic books. The
variable cost per unit is estimated at $250, the sales price would be
set at twice the VC/unit, fixed costs are estimated at $750,000, and the
investors will put up the funds if the project is likely to have an
operating income of $500,000 or more. What sales volume would be
required in order to meet this profit goal?
a.
b.
c.
d.
e.
4,513
4,750
5,000
5,250
5,513
(16.2) Differences in ROE
52
.
MEDIUM/HARD
Answer: c
MEDIUM/HARD
Firms HD and LD are identical except for their level of debt and the
interest rates they pay on debt--HD has more debt and pays a higher
interest rate on that debt. Based on the data given below, what is the
difference between the two firms' ROEs?
Applicable to Both Firms
Assets
$200
EBIT
$40
Tax rate
35%
a.
b.
c.
d.
e.
Firm HD's Data
Debt ratio
50%
Interest rate 12%
Firm LD's Data
Debt ratio
30%
Interest rate
10%
2.18%
2.29%
2.41%
2.54%
2.66%
Hard:
(16.5) levered Calculating beta and cost of equity
53
.
Answer: b
HARD
Lauterbach Corporation uses no debt, its beta is 1.10, and its tax rate
is 40%. However, the CFO is considering moving to a capital structure
with 30% debt and 70% equity. If the risk-free rate is 5.0% and the
market risk premium is 6.0%, by how much would the capital structure
shift change the firm's cost of equity?
a.
b.
c.
d.
e.
Page 240
1.53%
1.70%
1.87%
2.05%
2.26%
Problems
Chapter 16: Cap Structure: Basics
(16.5) Calculating levered beta and cost of equity
Chapter 16: Cap Structure: Basics
Problems
Answer: b
HARD
Page 241
54
.
Vafeas Inc.'s capital structure consists of 80% debt and 20% common
equity, its beta is 1.60, and its tax rate is 35%. However, the CFO
thinks the company has too much debt, and he is considering moving to a
capital structure with 40% debt and 60% equity. The risk-free rate is
5.0% and the market risk premium is 6.0%. By how much would the capital
structure shift change the firm's cost of equity?
a.
b.
c.
d.
e.
-5.20%
-5.78%
-6.36%
-6.99%
-7.69%
(16.5) Cost of equity--unlevering and relevering betas
55
.
10.95%
11.91%
12.94%
14.07%
15.29%
(16.5) Recapitalization
.
HARD
Stephens Electronics is considering a change in its target capital
structure, which currently consists of 25% debt and 75% equity. The CFO
believes the firm should use more debt, but the CEO is reluctant to
increase the debt ratio. The risk-free rate, rRF, is 5.0%, the market
risk premium, RPM, is 6.0%, and the firms tax rate is 40%. Currently,
the cost of equity, rs, is 11.5% as determined by the CAPM. What would
be the estimated cost of equity if the firm used 60% debt? (Hint: You
must first find the current beta and then the unlevered beta to solve
the problem.)
a.
b.
c.
d.
e.
56
Answer: e
Answer: b
HARD
Michaely Inc. is an all-equity firm with 200,000 shares outstanding. It
has $2,000,000 of EBIT, which is expected to remain constant in the
future. The company pays out all of its earnings, so earnings per share
(EPS) equal dividends per shares (DPS). Its tax rate is 40%.
The company is considering issuing $5,000,000 of 10.0% bonds and using
the proceeds to repurchase stock. The risk-free rate is 6.5%, the
market risk premium is 5.0%, and the beta is currently 0.90, but the CFO
believes beta would rise to 1.10 if the recapitalization occurs.
Assuming that the shares can be repurchased at the price that existed
prior to the recapitalization, what would the price be following the
recapitalization?
a.
b.
c.
d.
e.
$65.77
$69.23
$72.69
$76.33
$80.14
(16.5) Capital structure and P0--nonalgorithmic
Page 242
Problems
Answer: b
HARD
Chapter 16: Cap Structure: Basics
57
.
Dabney Electronics currently has no debt. Its operating income is $20
million and its tax rate is 40%. It pays out all of its net income as
dividends and has a zero growth rate. The current stock price is $40
per share, and it has 2.5 million shares of stock outstanding. If it
moves to a capital structure that has 40% debt and 60% equity (based on
market values), its investment bankers believe its weighted average cost
of capital would be 10%. What would its stock price be if it changes to
the new capital structure?
a.
b.
c.
d.
e.
$40
$48
$52
$54
$60
(16.5) Hamada equation and rs--nonalgorithmic
58
.
Answer: c
HARD
Simon Software Co. is trying to estimate its optimal capital structure.
Right now, Simon has a capital structure that consists of 20% debt and
80% equity, based on market values. (Its D/S ratio is 0.25.) The riskfree rate is 6% and the market risk premium, rM rRF, is 5%. Currently
the companys cost of equity, which is based on the CAPM, is 12% and its
tax rate is 40%. What would be Simons estimated cost of equity if it
were to change its capital structure to 50% debt and 50% equity?
a.
b.
c.
d.
e.
13.00%
13.64%
14.35%
14.72%
15.60%
(16.5) Opt cap struc, Hamada equation--nonalgorithmic
Chapter 16: Cap Structure: Basics
Problems
Answer: d
HARD
Page 243
59
.
Aaron Athletics is trying to determine its optimal capital structure.
The companys capital structure consists of debt and common stock. In
order to estimate the cost of debt, the company has produced the
following table:
Percent financed
with debt (wd)
Percent financed
with equity (wc)
0.10
0.20
0.30
0.40
0.50
0.90
0.80
0.70
0.60
0.50
Debt-to-equity ratio
(D/S)
0.10/0.90
0.20/0.80
0.30/0.70
0.40/0.60
0.50/0.50
=
=
=
=
=
0.11
0.25
0.43
0.67
1.00
Bond
rating
Before-tax
cost of debt
AAA
AA
A
BBB
BB
7.0%
7.2
8.0
8.8
9.6
The company uses the CAPM to estimate its cost of common equity, rs.
The risk-free rate is 5% and the market risk premium is 6%. Aaron
estimates that if it had no debt its beta would be 1.0. (Its unlevered
beta, bU, equals 1.0.) The companys tax rate, T, is 40%.
On the basis of this information, what is the companys optimal capital
structure, and what is the firms cost of capital at this optimal
capital structure?
a.
b.
c.
d.
e.
wc
wc
wc
wc
wc
=
=
=
=
=
0.9;
0.8;
0.7;
0.6;
0.5;
wd
wd
wd
wd
wd
=
=
=
=
=
0.1;
0.2;
0.3;
0.4;
0.5;
WACC
WACC
WACC
WACC
WACC
=
=
=
=
=
14.96%
10.96%
7.83%
10.15%
10.18%
Multi-part:
(The following data apply to Problems 60, 61, and 62. The problems MUST be
kept together, and they cannot be changed algorithmically.)
Powell Plastics, Inc. (PP) currently has zero debt. Its earnings before
interest and taxes (EBIT) are $80,000, and it is a zero growth company. PPs
current cost of equity is 10%, and its tax rate is 40%. The firm has 10,000
shares of common stock outstanding selling at a price per share of $48.00.
(16.5) WACC and recapitalization--nonalgorithmic
60
.
Answer: b
MEDIUM
PP is considering moving to a capital structure that is comprised of 30%
debt and 70% equity, based on market values. The debt would have an
interest rate of 8%. The new funds would be used to repurchase stock. It
is estimated that the increase in risk resulting from the added leverage
would cause the required rate of return on equity to rise to 12%. If this
plan were carried out, what would be PP's new value of operations?
a.
b.
c.
d.
e.
$484,359
$487,805
$521,173
$560,748
$584,653
(16.5) Stock price, recapitalization--nonalgorithmic
Page 244
Problems
Answer: c
MEDIUM
Chapter 16: Cap Structure: Basics
61
.
Now assume that PP is considering changing from its original capital
structure to a new capital structure with 35% debt and 65% equity. This
results in a weighted average cost of capital equal to 9.4% and a new
value of operations of $510,638. Assume PP raises $178,723 in new debt
and purchases T-bills to hold until it makes the stock repurchase. What
is the stock price per share immediately after issuing the debt but
prior to the repurchase?
a.
b.
c.
d.
e.
$45.90
$48.12
$51.06
$53.33
$58.75
(16.5) Stock price, recapitalization--nonalgorithmic
62
.
Answer: c
MEDIUM
Assume that PP is considering changing from its original capital
structure to a new capital structure with 35% debt and 65% equity. This
results in a weighted average cost of capital equal to 9.4% and a new
value of operations of $510,638. Assume PP raises $178,723 in new debt
and purchases T-bills to hold until it makes the stock repurchase. PP
then sells the T-bills and uses the proceeds to repurchase stock. How
many shares remain after the repurchase, and what is the stock price per
share immediately after the repurchase?
a.
b.
c.
d.
e.
7,500;
7,000;
6,500;
6,649;
6,959;
$71.49
$59.57
$51.06
$53.33
$58.78
(The following data apply to Problems 63, 64, and 65.
Chapter 16: Cap Structure: Basics
Problems
The problems MUST be
Page 245
kept together.)
Volunteer Fabricators, Inc. (VF) currently has zero debt. It is a zero
growth company, and it has the data shown below. Now the company is
considering using some debt, moving to the market value capital structure
indicated below. The money raised would be used to repurchase stock. It is
estimated that the increase in risk resulting from the additional leverage
would cause the required rate of return on equity to rise somewhat, as
indicated below.
EBIT =
Growth =
Orig cost of equity, rs =
New cost of equity = rs =
Tax rate =
$80,000
0%
10.0%
11.0%
40%
New Debt/Value =
New Equity/Value =
No. of shares =
Price per share =
Interest rate = rd =
(16.5) WACC and recapitalization
63
.
Answer: a
WACC
9.64%
9.83%
10.03%
10.23%
10.74%
Value
$497,925
$507,884
$518,041
$528,402
$538,970
(16.5) Stock price, recapitalization
.
MEDIUM
If this plan were carried out, what would be VF's new WACC and its new
value of operations?
a.
b.
c.
d.
e.
64
20%
80%
10,000
$48.00
7.0%
Answer: b
MEDIUM
Now assume that VF is considering changing from its original zero debt
capital structure to a new capital structure with even more debt. This
results in changes in the cost of debt and equity, and thus to a new
WACC and a new value of operations. Assume VF raises the amount of new
debt indicated below and uses the funds to purchase and hold T-bills
until it makes the stock repurchase. What is the stock price per share
immediately after issuing the debt but prior to the repurchase?
Debt/Value =
Equity/Value=
a.
b.
c.
d.
e.
Page 246
40%
60%
Value of new debt =
New WACC =
$213,333
9.0%
$50.67
$53.33
$56.00
$58.80
$61.74
Problems
Chapter 16: Cap Structure: Basics
(16.5) Stock price, recapitalization
65
.
Answer: d
MEDIUM
Based on the data in the previous two problems, what would the stock
price be if VF issued the new debt and immediately used the proceeds to
repurchase stock?
a.
b.
c.
d.
e.
$49.43
$50.70
$52.00
$53.33
$56.00
(The following data apply to Problems 66, 67, and 68. The problems MUST be
kept together, and they cannot be changed algorithmically.)
Barnes Baskets, Inc. (BB) currently has zero debt. Its earnings before
interest and taxes (EBIT) are $100,000, and it is a zero growth company. BBs
current cost of equity is 13%, and its tax rate is 40%. The firm has 20,000
shares of common stock outstanding selling at a price per share of $23.08.
(16.5) WACC and recapitalization--nonalgorithmic
66
.
$498,339
$512,188
$525,237
$540,239
$590,718
(16.5) Stock price, recapitalization--nonalgorithmic
.
MEDIUM
BB is considering moving to a capital structure that is comprised of 20%
debt and 80% equity, based on market values. The debt would have an
interest rate of 7%. The new funds would be used to repurchase stock.
It is estimated that the increase in risk resulting from the additional
leverage would cause the required rate of return on equity to rise to
14%. If this plan were carried out, what would BB's new value of
operations be?
a.
b.
c.
d.
e.
67
Answer: a
Answer: d
MEDIUM
Now assume that BB is considering changing from its original capital
structure to a new capital structure with 45% debt and 55% equity. This
results in a weighted average cost of capital equal to 10.4% and a new
value of operations of $576,923. Assume BB raises $259,615 in new debt
and purchases T-bills to hold until it makes the stock repurchase. What
is the stock price per share immediately after issuing the debt but
prior to the repurchase?
a.
b.
c.
d.
e.
$14.42
$19.36
$23.91
$28.85
$35.62
Chapter 16: Cap Structure: Basics
Problems
Page 247
(16.5) Stock price, recapitalization--nonalgorithmic
Page 248
Problems
Answer: a
MEDIUM
Chapter 16: Cap Structure: Basics
68
.
Now assume that BB is considering changing from its original capital
structure to a new capital structure with 45% debt and 55% equity. This
results in a weighted average cost of capital equal to 10.4% and a new
value of operations of $576,923. Assume BB raises $259,615 in new debt
and purchases T-bills to hold until it makes the stock repurchase. BB
then sells the T-bills and uses the proceeds to repurchase stock. How
many shares remain after the repurchase, and what is the stock price per
share immediately after the repurchase?
a.
b.
c.
d.
e.
11,001;
12,711;
13,901;
15,220;
17,105;
$28.85
$35.62
$42.57
$54.31
$89.67
(The following data apply to Problems 69, 70, 71, and 72. The problems MUST
be kept together, and they cannot be changed algorithmically.)
The A. J. Croft Company (AJC) currently has $200,000 market value (and book
value) of perpetual debt outstanding carrying a coupon rate of 6%. Its
earnings before interest and taxes (EBIT) are $100,000, and it is a zero
growth company. AJC's current cost of equity is 8.8%, and its tax rate is
40%. The firm has 10,000 shares of common stock outstanding selling at a
price per share of $60.00.
(16.5) Market value and WACC--nonalgorithmic
69
.
$600,000;
$600,000;
$800,000;
$800,000;
$800,000;
7.5%
8.0%
7.0%
7.5%
8.0%
(16.5) WACC and recapitalization--nonalgorithmic
.
MEDIUM
What is AJC's current total market value and weighted average cost of
capital?
a.
b.
c.
d.
e.
70
Answer: d
Answer: b
HARD
The firm is considering moving to a capital structure that is comprised
of 40% debt and 60% equity, based on market values. The new funds would
be used to replace the old debt and to repurchase stock. It is
estimated that the increase in risk resulting from the additional
leverage would cause the required rate of return on debt to rise to 7%,
while the required rate of return on equity would rise to 9.5%. If this
plan were carried out, what would be AJC's new WACC and total value?
a.
b.
c.
d.
e.
7.38%;
7.38%;
7.50%;
7.50%;
7.80%;
$800,008
$813,008
$813,008
$790,008
$790,008
(16.5) Stock price, recapitalization--nonalgorithmic
Chapter 16: Cap Structure: Basics
Problems
Answer: e
HARD
Page 249
71
.
Now assume that AJC is considering changing from its original capital
structure to a new capital structure with 50% debt and 50% equity. If
it makes this change, its resulting market value would be $820,000.
What would be its new stock price per share?
a.
b.
c.
d.
e.
$58
$59
$60
$61
$62
(16.5) No. shares repurchased--nonalgorithmic
72
.
Answer: c
HARD
Now assume that AJC is considering changing from its original capital
structure to a new capital structure that results in a stock price of
$64 per share. The resulting capital structure would have a $336,000
total market value of equity and a $504,000 market value of debt. How
many shares would AJC repurchase in the recapitalization?
a.
b.
c.
d.
e.
Page 250
4,250
4,500
4,750
5,000
5,250
Problems
Chapter 16: Cap Structure: Basics
CHAPTER 16
ANSWERS AND SOLUTIONS
Chapter 16: Cap Structure: Basics
Answers
Page 251
1.
(16.1) Bankruptcy costs
Answer: a
EASY
2.
(16.2) Business risk
Answer: b
EASY
3.
(16.2) Financial risk
Answer: a
EASY
4.
(16.2) Financial risk
Answer: b
EASY
5.
(16.2) Financial risk
Answer: a
EASY
6.
(16.2) Financial leverage
Answer: a
EASY
7.
(16.2) Use of financial leverage
Answer: b
EASY
8.
(16.2) Operating and financial leverage
Answer: b
EASY
9.
(16.3) Trade-off theory
Answer: a
EASY
10.
(16.2) Use of debt in financing
Answer: a
MEDIUM
11.
(16.2) Financial leverage
Answer: b
MEDIUM
12.
(16.2) Business risk
Answer: b
MEDIUM
13.
(16.2) Operating and financial leverage
Answer: a
MEDIUM
If one firm's sales and earnings were more volatile than those of the other, it could have greater EPS variability in
spite of identical financial and operating leverage.
14.
(16.3) Bankruptcy costs
Answer: a
15.
(16.2) Business risk
Answer: a
EASY
16.
(16.2) Business risk
Answer: d
EASY
17.
(16.3) Target debt ratio
Answer: a
EASY
18.
(16.3) Leverage and capital structure
Answer: b
EASY
19.
(16.5) Capital structure and WACC
Answer: d
EASY
20.
(16.5) Optimal capital structure
Answer: d
EASY
21.
(16.5) Optimal capital structure
Answer: c
EASY
22.
(16.5) Optimal capital structure
Answer: b
EASY
23.
(16.5) Financial leverage and EPS
Answer: a
EASY
24.
(16.5) Optimal capital structure
Answer: e
EASY/MEDIUM
25.
(16.5) Target capital structure
Answer: e
EASY/MEDIUM
26.
(Comp: 16.2,16.5) Business & fin. risk & cap. struc.
Answer: b
EASY/MEDIUM
27.
(16.2) Operating leverage
Answer: e
MEDIUM
MEDIUM
More operating leverage generally means a greater use of automation, which means more fixed assets. If fixed
assets increase, but sales do not, then the fixed asset turnover (S/FA) will decline.
28.
(16.2) Use of financial leverage
Answer: d
MEDIUM
29.
(16.2) Leverage and capital structure
Answer: e
MEDIUM
30.
(16.2) Leverage and capital structure
Answer: e
MEDIUM
31.
(16.2) Leverage and capital structure
Answer: c
MEDIUM
32.
(16.2) Capital structure, ROA, and ROE
Answer: e
MEDIUM
33.
(16.5) Financial leverage and EPS
Answer: c
MEDIUM
34.
(16.5) Financial leverage and ratios
Answer: b
MEDIUM
35.
(16.5) Financial leverage and ratios
Answer: b
MEDIUM
36.
(16.5) Financial leverage and ratios
Answer: c
MEDIUM
37.
(Comp: 16.2,16.3) Capital structure and WACC
Answer: b
MEDIUM
38.
(Comp: 16.2,16.5) Capital structure, WACC, TIE, and EPS
Answer: a
MEDIUM
39.
(16.2) Miscellaneous capital structure concepts
Answer: a
MEDIUM/HARD
40.
(16.2) Miscellaneous capital structure concepts
Answer: a
MEDIUM/HARD
41.
(16.5) Leverage and capital structure
Answer: c
MEDIUM/HARD
42.
(16.5) Financial leverage and ratios
Answer: c
MEDIUM/HARD
43.
(16.4) Variations in capital structures
Answer: d
HARD
44.
(16.2) Breakeven point--nonalgorithmic
Answer: d
EASY
$7(200,000) $5(200,000) F = 0; F = $400,000.
$7(200,000) $4(200,000) F = 0; F = $600,000.
$600,000 $400,000 = $200,000.
45.
(16.2) Breakeven analysis
Answer: a
EASY/MEDIUM
Answer: c
EASY/MEDIUM
Fixed operating costs
$470,000
Variable costs per unit
$2.80
Sales price per unit
$4.00
Breakeven volume (units) = FC/(P VC) = 391,667
46.
(16.2) Breakeven analysis
VC/unit
$2.50
Price multiple over VC
1.50
Price
$3.75
Fixed costs
$120,000
Breakeven volume (units) = FC/(P VC) = 96,000
47.
(16.2) Debt's effect on ROE
Assets
D/A
EBIT
$200,000
65%
$25,000
Answer: a
MEDIUM
Interest rate
Tax rate
EBIT
Interest
EBT
Tax
NI
8%
40%
$25,000
10,400
$14,600
5,840
$ 8,760
ROE = NI avail to common/Common equity
ROE = 12.51%
48.
(16.2) Net operating income--nonalgorithmic
Answer: b
MEDIUM
Answer: e
MEDIUM
Answer: e
MEDIUM
Total cost Method 1 = $1.00Q + $10,000.
Total cost Method 2 = $1.50Q + $5,000.
Set equal and solve for Q:
Q + $10,000 = $1.50Q + $5,000; $5,000 = $0.5Q; 10,000 = Q.
49.
(16.5) Calculating the unlevered beta
bL
D/A
Tax rate
D/E = (D/A) / (1-D/A)
bU = bL/(1 + (D/E) (1 T))
50.
1.10
0.40
40%
0.67
0.79
(16.5) Capital structure and value--nonalgorithmic
Step 1: Find the new WACC:
WACC = wcrs + wd(1 T)rd = (0.8(0.11)) + (0.2(1 0.4)0.10) = 0.10.
Step 2: Find the free cash flow: Because there is no growth, there is no investment in capital, hence FCF is equal
to NOPAT:
FCF = NOPAT Investment in capital = EBIT(1 T) 0 = $800(1 0.4) = $480 million.
Step 3: Find the new value of the firm:
V = FCF/(WACC g) = $480/0.10 = $4,800 million.
51.
(16.2) EBIT and setting the price
Answer: c
MEDIUM/HARD
Answer: c
MEDIUM/HARD
VC/unit
$250
Price multiple over VC
2
Price
$500
Fixed costs
$750,000
Profit target
$500,000
Volume (units) to meet profit goal = (FC + Profit)/(P VC) =
5,000
Check: Op profit = (P VC) Units FC =
$500,000
52.
(16.2) Differences in ROE
Applicable to Both Firms
Assets
$200
EBIT
$40
Tax rate 35%
Debt =
Firm HD's Data
Debt ratio 50%
Interest rate 12%
Firm LD's Data
Debt ratio 30%
Interest rate 10%
$100.0
$60.0
Interest = I =
Taxable income = EBIT I =
NI = (Taxable Income)(1 T) =
Equity = A Debt =
ROE = NI/Equity =
Difference in ROEs = 2.41%
53.
$12.0
$28.0
$18.2
$100.0
18.20%
$6.0
$34.0
$22.1
$140.0
15.79%
(16.5) Calculating levered beta and cost of equity
bU =
Target % Debt =
Target D/E =
T=
bL = bU (1+ (D/E) (1 T))
rRF =
RPM =
rsU = rRF + bU(RPM) =
rsL = rRF + bL(RPM) =
Change in equity cost =
Answer: b
HARD
1.10
30%
0.43
40%
1.38
5.00%
6.00%
11.60%
13.30%
1.70%
54.
(16.5) Calculating levered beta and cost of equity
Answer: b
HARD
55.
bL =
1.60
Current Debt%
80%
Target Debt%
40%
Current D/E = D%/(1 D%)
4.00
Target D/E = D%/(1 D%)
0.67
Tax rate =
35%
bU = bL/(1 + (D/E)(1 T))
0.4444
new bL = bU (1 + (D/E) (1 T)) 0.6370
rRF =
5.00%
RPM
6.00%
rs 80% D = rRF + b80% D(RPM) =
14.60%
rs 40% D = rRF + b40% D (RPM) =
8.82%
Change in equity cost
-5.78%
(16.5) Cost of equity--unlevering and relevering betas
Answer: e
HARD
Answer: b
HARD
Original rs
Current D/A
rRF
RPM
Tax rate
Target D/A
11.5%
25%
5%
6%
40%
60%
Original b:
rs = rRF + bL(RPM); b = (rs rRF)/RPM =
Original D/E:
D/A/(1 D/A) =
Unlevered beta:
bU = bL/(1 + (D/E)(1 T))
Target D/E =
1.50
New beta:
bL = bU (1+ (D/E)(1 T))
rs New = rRF + bL New (RPM) =
56.
1.083
0.3333
0.90
1.7153
15.29%
(16.5) Recapitalization
Shares outstanding
EBIT
Dividend payout ratio
Tax rate
Bonds issued = stock repurchased
200,000
$2,000,000
100%
40%
$5,000,000
Interest rate
Risk-free rate
Market risk premium
Beta - before recap
Beta - after recap
10%
6.5%
5.0%
0.90
1.10
Before the recapitalization
rs = rRF + bold(RPM)
DPS = EPS = (EBIT)(1 T)/Shares
P0 = DPS/rs
Shares repurchased = Bonds issued/P0
After the recapitalization
rs = rRF + bnew(RPM)
DPS = EPS = (EBIT rd Bonds)(1 T)/Shares
P0 = DPS/rs
57.
11.00%
$6.00
$54.55
91,667
12.00%
$8.31
$69.23
(16.5) Capital structure and P0--nonalgorithmic
Answer: b
HARD
Step 1: Find the new value of the firm after the recapitalization. Because growth is zero, free cash flow is equal
to NOPAT:
V = FCF/WACC = NOPAT/WACC = EBIT(1 T)/WACC = $20(1 0.4)/0.1 = $120 million.
Step 2: Find the new value of equity and debt after the recapitalization:
S = wcV = 0.6($120) = $72 million.
D = wdV = 0.4($120) = $48 million.
Step 3: Find the new price per share after the recapitalization:
P = [S + (D D0)]/n0 = [$72 + ($48 0)]/2.5 = $48.
58.
(16.5) Hamada equation and rs--nonalgorithmic
Answer: c
HARD
Facts given: rs = 12%; D/E = 0.25; rRF = 6%; RPM = 5%; T = 40%.
Step 1: Find the firms current levered beta using the CAPM:
rs = rRF + RPM(b)
12% = 6% + 5%(b)
b = 1.2.
Step 2: Find the firms unlevered beta using the Hamada equation:
b = bU[1 + (1 T)(D/E)]
1.2 = bU[1 + (0.6)(0.25)]
1.2 = 1.15bU
1.0435 = bU.
Step 3: Find the new levered beta given the new capital structure using the Hamada equation:
b = bU[1 + (1 T)(D/E)]
= 1.0435[1 + (0.6)(1)]
= 1.6696.
Step 4: Find the firms new cost of equity given its new beta and the CAPM:
rs = rRF + RPM(b)
= 6% + 5%(1.6696)
= 14.35%.
59.
(16.5) Opt cap struc, Hamada equation--nonalgorithmic
rRF = 5%; rM rRF = 6%. rs = rRF + (rM rRF)b. WACC = rd wd (1 T) + rs wc.
Answer: d
HARD
You need to use the D/E ratio given for each capital structure to find the levered beta using the Hamada equation. Then,
use each of these betas with the CAPM to find the rs for that capital structure. Use this rs and rd for each capital structure
to find the WACC. The optimal capital structure is the one that minimizes the WACC.
(D/E)
0.11
0.25
0.43
0.67
1.00
b = bU[1 + (1T)(D/E)]
1.0667
1.1500
1.2571
1.4000
1.6000
rs = rRF + (rM rRF)b
11.4005%
11.9000
12.5429
13.4000
14.6000
wc
0.9
0.8
0.7
0.6
0.5
rd
7.0%
7.2
8.0
8.8
9.6
wd
0.1
0.2
0.3
0.4
0.5
WACC
10.68%
10.38
10.22
10.15
10.18
For example, if the D/E is 0.11: b = 1.0[1 + (1 T)(D/E)] = 1.0[1 + (1 0.4)(0.1111)] = 1.0667.
rs = rRF + (rM rRF)b = 5% + 6%(1.0667) = 11.40%.
The weights are given at 0.9 and 0.1 for equity and debt, respectively, and the rd for that capital structure is given as 7%.
WACC = rd wd (1 T) + rs wc
= 7% 0.1 (1 0.4) + 11.40% 0.9 = 10.68%.
Do the same calculation for each of the capital structures and find each WACC. The optimal capital structure is
the one that minimizes the WACC, which is 10.15%. Therefore, the optimal capital structure is 40% debt and 60%
equity.
60.
(16.5) WACC and recapitalization--nonalgorithmic
Answer: b
MEDIUM
Answer: c
MEDIUM
Answer: c
MEDIUM
WACC = wcrs + wd(1 T)rd
= (0.7)(0.12) + (0.3) (10.4)(0.08) = 0.0984 = 9.84%.
V = FCF/WACC. Since g = 0, FCF = NOPAT = EBIT(1 T).
V = $80,000(1 0.4)/0.0984 = $487,804.878 $487,805.
61.
(16.5) Stock price, recapitalization--nonalgorithmic
Value of operations
+ value of T-bills
Total value
value of debt
Value of equity
Divide by # shares
Price per share
62.
$510,638
178,723
$689,361
178,723
$510,638
10,000
$51.06
(16.5) Stock price, recapitalization--nonalgorithmic
First, find the stock price after issuing debt but prior to repurchase:
Value of operations
+ value of T-bills
Total value
value of debt
Value of equity
Divide by # shares
Price per share
$510,638
178,723
$689,361
178,723
$510,638
10,000
$51.06
The price per share does not change in the repurchase, so the number of shares repurchased is equal to the amount
used to repurchase shares divided by the price per share:
Number shares repurchased = $178,723/$51.06 = 3,500.
Number shares remaining = 10,000 3,500 = 6,500.
As a check, the price per share after repurchase is:
Value of operations
+ value of T-bills
Total value
repurchase
Value of equity
Divide by # shares
Price per share
63.
$510,638
0
$510,638
178,723
$331,915
6,500
$51.06
(16.5) WACC and recapitalization
Debt/Value =
Equity/Value=
Answer: a
20%
80%
Interest rate = rd =
New cost of equity = rs =
MEDIUM
7.0%
11.0%
WACC = wd(1T)rd + wcrs = 0.84% + 8.80% = 9.64%
V = FCF/WACC. Since g = 0, FCF = NOPAT = EBIT(1 T).
V = NOPAT/WACC
V = $48,000/9.64% = $497,925
64.
(16.5) Stock price, recapitalization
Value of operations = EBIT(1T) / WACC
+ value of T-bills
Total value
value of debt
Value of equity
Divide by # shares
Price per share
65.
Answer: b
MEDIUM
Answer: d
MEDIUM
$533,333
213,333
$746,666
-213,333
$533,333
10,000
$53.33
(16.5) Stock price, recapitalization
The price per share does not change in the repurchase, so share price would be the same as in the preceding
answer.
As a check, consider the following data:
Value of operations = EBIT(1 T)/WACC
+ value of T-bills
Total value
repurchase
Value of equity
New shares = old Debt/Price =
Stock price = Equity divided by # shares
66.
$533,333
0
$533,333
-213,333
$320,000
6,000
$53.33
(16.5) WACC and recapitalization--nonalgorithmic
WACC = wcrs + wd(1 T)rd
= (0.8)(0.14) + (0.2)(0.07)(1 0.4) = 0.1204 = 12.04%.
Answer: a
MEDIUM
V = FCF/WACC. Since g = 0, FCF = NOPAT = EBIT(1 T).
V = $100,000(1 0.4)/0.1204 = $498,338.87 $498,339.
67.
(16.5) Stock price, recapitalization--nonalgorithmic
Value of operations
+ value of T-bills
Total value
value of debt
Value of equity
Divide by # shares
Price per share
68.
Answer: d
MEDIUM
Answer: a
MEDIUM
$576,923
259,615
$836,538
259,615
$576,923
20,000
$28.85
(16.5) Stock price, recapitalization--nonalgorithmic
First, find the stock price after issuing debt but prior to repurchase:
Value of operations
+ value of T-bills
Total value
value of debt
Value of equity
Divide by # shares
Price per share
$576,923
259,615
$836,538
259,615
$576,923
20,000
$28.85
The price per share does not change in the repurchase, so the number of shares repurchased is equal to the amount
used to repurchase shares divided by the price per share:
Number shares repurchased = $259,615/$28.85 = 8,999.
Number shares remaining = 20,000 8,999 = 11,001.
As a check, the price per share after repurchase is:
Value of operations
+ value of T-bills
Total value
repurchase
Value of equity
Divide by # shares
Price per share
69.
$576,923
0
$576,923
259,615
$317,308
11,001
$28.84
(16.5) Market value and WACC--nonalgorithmic
Answer: d
MEDIUM
V = Debt + Equity = $200,000 + $60(10,000) = $200,000 + $600,000
= $800,000.
WACC = wcrs + wd(1 T)rd
= (($600,000/$800,000)(0.088)) + ($200,000/$800,000)(1 0.4)(0.06)
= (0.75)(0.088) + (0.25)(0.036) = 0.075 = 7.5%.
As a check, V = FCF/WACC. Since g = 0, FCF = NOPAT = EBIT(1 T).
V = $100,000(1 0.4)/0.075 = $800,000.
70.
(16.5) WACC and recapitalization--nonalgorithmic
WACC = wcrs + wd(1 T)rd
= (0.6)(0.095) + (0.4)(1 0.4)(0.07) = 0.0738 = 7.38%.
Answer: b
HARD
V = FCF/WACC. Since g = 0, FCF = NOPAT = EBIT(1 T).
V = $100,000(1 0.4)/0.0738 = $813,008.
71.
(16.5) Stock price, recapitalization--nonalgorithmic
Answer: e
HARD
Answer: c
HARD
Step 1. Find the new value of equity and debt after the recapitalization:
S = wcV = 0.5($820,000) = $410,000.
D = wdV = 0.5($820,000) = $410,000.
Step 2. Find the new price per share after the recapitalization:
P = [S+ (DD0)]/n0 = [$410,000 + ($410,000 $200,000)]/10,000
= $62.
72.
(16.5) No. shares repurchased--nonalgorithmic
First, find the number of shares remaining:
n = S/P = $336,000/$64 = 5,250.
The number of repurchased shares is the original number of shares minus the resulting number of shares:
# repurchased = 10,000 5,250 = 4,750.
Alternatively, number of shares repurchased is equal to the debt used to repurchase stock divided by the price per
share:
# repurchased = ($504,000 $200,000)/$64 = 4,750.