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CHAPTER 15 B - 1
CHAPTER 15
CAPITAL STRUCTURE: LIMITS TO THE
USE OF DEBT
Answers to Concept Questions
1. Direct costs are potential legal and administrative costs. These are the costs associated with the
litigation arising from a liquidation or bankruptcy. These costs include lawyers’ fees, courtroom costs,
and expert witness fees. Indirect costs include the following: 1) Impaired ability to conduct business.
Firms may suffer a loss of sales due to a decrease in consumer confidence and loss of reliable supplies
due to a lack of confidence by suppliers. 2) Incentive to take large risks. When faced with projects of
different risk levels, managers acting in the stockholders’ interest have an incentive to undertake high-
risk projects. Imagine a firm with only one project, which pays $100 in an expansion and $60 in a
recession. If debt payments are $60, the stockholders receive $40 (= $100 – 60) in the expansion but
nothing in the recession. The bondholders receive $60 for certain. Now, alternatively imagine that the
project pays $110 in an expansion but $50 in a recession. Here, the stockholders receive $50 (= $110
2. The statement is incorrect. If a firm has debt, it might be advantageous to stockholders for the firm to
undertake risky projects, even those with negative net present values. This incentive results from the
3. The firm should issue equity in order to finance the project. The tax-loss carry-forwards make the
firm’s effective tax rate zero. Therefore, the company will not benefit from the tax shield that debt
provides. Moreover, since the firm already has a moderate amount of debt in its capital structure,
4. Stockholders can undertake the following measures in order to minimize the costs of debt: 1) Use
protective covenants. Firms can enter into agreements with the bondholders that are designed to
decrease the cost of debt. There are two types of protective covenants. Negative covenants prohibit
5. Modigliani and Miller’s theory with corporate taxes indicates that, since there is a positive tax
advantage of debt, the firm should maximize the amount of debt in its capital structure. In reality,
however, no firm adopts an all-debt financing strategy. MM’s theory ignores both the financial distress
and agency costs of debt. The marginal costs of debt continue to increase with the amount of debt in
6. There are two major sources of the agency costs of equity: 1) Shirking. Managers with small equity
holdings have a tendency to reduce their work effort, thereby hurting both the debt holders and outside
equity holders. 2) Perquisites. Since management receives all the benefits of increased perquisites but
7. The more capital intensive industries, such as airlines, building construction, hotels, and utilities, tend
to use greater financial leverage. Also, industries with less predictable future earnings, such as
computers or drugs, tend to use less financial leverage. Such industries also have a higher
concentration of growth and startup firms. Overall, the general tendency is for firms with identifiable,
8. One answer is that the right to file for bankruptcy is a valuable asset, and the financial manager acts
in shareholders’ best interest by managing this asset in ways that maximize its value. To the extent
that a bankruptcy filing prevents “a race to the courthouse steps,” it would seem to be a reasonable use
9. As in the previous question, it could be argued that using bankruptcy laws as a sword may be the best
use of the asset. Creditors are aware at the time a loan is made of the possibility of bankruptcy, and
the interest charged incorporates it.
10. One side is that Continental was going to go bankrupt because its costs made it uncompetitive. The
bankruptcy filing enabled Continental to restructure and keep flying. The other side is that Continental
abused the bankruptcy code. Rather than renegotiate labor agreements, Continental abrogated them to
the detriment of its employees. In this, and the last several, questions, an important thing to keep in
manager’s duty to do so. As the case of Continental illustrates, the code can be changed if socially
undesirable outcomes are a problem.
CHAPTER 15 B - 3
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
Basic
1. a. Using M&M Proposition I with taxes, the value of a levered firm is:
VL = [EBIT(1 – tC)/R0] + tCB
VL = [$460,000(1 – .35)/.132] + .35($950,000)
b. The CFO may be correct. The value calculated in part a does not include the costs of any non-
marketed claims, such as bankruptcy or agency costs.
The company needs a cash infusion of $1.4 million. If the company issues debt, the annual
interest payments will be:
Interest = $1,400,000(.08)
Interest = $112,000
The cash flow to the owner will be the EBIT minus the interest payments, or:
40 hour week cash flow = $475,000 – 112,000
If the company issues equity, the company value will increase by the amount of the issue. So, the
current owners’ equity interest in the company will decrease to:
Tom’s ownership percentage = $3,200,000/($3,200,000 + 1,400,000)
CHAPTER 15 B - 4
more under this form of financing since the payments to bondholders are fixed. Under an equity
issue, new investors share proportionally in his hard work, which will reduce his propensity for
this additional work.
c. The direct cost of both issues is the payments made to new investors. The indirect costs to the
debt issue include potential bankruptcy and financial distress costs. The indirect costs of an equity
issue include shirking and perquisites.
3. a. The interest payments each year will be:
Interest payment = .06($310,000)
Interest payment = $18,600
b. At growth rate of 2 percent, the earnings next year will be:
Earnings next year = $18,600(1.02)
Earnings next year = $18,972
So, the cash available for shareholders is:
Payment to shareholders = $18,972 – 18,600
Payment to shareholders = $372
Since there is no risk, the required return for shareholders is the same as the required return on
the company’s debt. The payments to stockholders will increase at the growth rate of 2 percent
(a growing perpetuity), so the value of these payments today is:
Value of equity = $372/(.06 – .02)
Earnings next year = $18,600(1.04)
Earnings next year = $19,344
So, the cash available for shareholders is:
Payment to shareholders = $19,344 – 18,600
CHAPTER 15 B - 5
Since there is no risk, the required return for shareholders is the same as the required return on
the company’s debt. The payments to stockholders will increase at the growth rate of 6 percent
(a growing perpetuity), so the value of these payments today is:
4. According to M&M Proposition I with taxes, the value of the levered firm is:
VL = VU + tCB
VL = $11,400,000 + .35($2,650,000)
VL = $12,327,500
We can also calculate the market value of the firm by adding the market value of the debt and equity.
Using this procedure, the total market value of the firm is:
5. The president may be correct, but he may also be incorrect. It is true the interest tax shield is valuable,
and adding debt can possibly increase the value of the company. However, if the company’s debt is
increased beyond some level, the value of the interest tax shield becomes less than the additional costs
Intermediate
6. a. The total value of a firm’s equity is the discounted expected cash flow to the firm’s stockholders.
If the expansion continues, each firm will generate earnings before interest and taxes of $2.9
million. If there is a recession, each firm will generate earnings before interest and taxes of only
$950,000. Since Steinberg owes its bondholders $825,000 at the end of the year, its stockholders
Steinberg’s bondholders will receive $825,000 whether there is a recession or a continuation of
the expansion. So, the market value of Steinberg’s debt is:
BSteinberg = [.80($825,000) + .20($825,000)]/1.14
BSteinberg = $723,684
Since Dietrich owes its bondholders $1.3 million at the end of the year, its stockholders will
receive $1.6 million (= $2,900,000 – 1,300,000) if the expansion continues. If there is a recession,
SDietrich = [.80($1,600,000) + .20($0)]/1.14
SDietrich = $1,122,807
is a recession. So, the market value of Dietrich’s debt is:
Steinberg is:
VSteinberg = B + S
VSteinberg = $1,478,070 + 723,684
VSteinberg = $2,201,754
And value of Dietrich is:
VDietrich = B + S
times the value in that state of the economy. Since this is the only project for the company, the
company value will be the same as the project value, so:
Low-volatility project value = .50($7,000) + .50($7,700)
Low-volatility project value = $7,350
the low-volatility project is undertaken, the firm’s equity will be worth $0 if the economy is bad
and $700 if the economy is good. Since each of these two scenarios is equally probable, the
expected value of the firm’s equity is
CHAPTER 15 B - 7
Expected value of equity with low-volatility project = .50($0) + .50($700)
Expected value of equity with low-volatility project = $350
c. Risk-neutral investors prefer the strategy with the highest expected value. Thus, the company’s
stockholders prefer the high-volatility project since it maximizes the expected value of the
company’s equity.
d. In order to make stockholders indifferent between the low-volatility project and the high-
volatility project, the bondholders will need to raise their required debt payment so that the
expected value of equity if the high-volatility project is undertaken is equal to the expected value
of equity if the low-volatility project is undertaken. As shown in part b, the expected value of
equity if the low-volatility project is undertaken is $350. If the high-volatility project is
undertaken, the value of the firm will be $6,300 if the economy is bad and $8,300 if the economy
is good. If the economy is bad, the entire $6,300 will go to the bondholders and stockholders will
8. a. The expected payoff to bondholders is the face value of debt or the value of the company,
whichever is less. Since the value of the company in a recession is $39 million and the required
debt payment in one year is $48 million, bondholders will receive the lesser amount, or $39
million.
b. The promised return on debt is:
Promised return = (Face value of debt/Market value of debt) – 1
Promised return = ($48,000,000/$41,000,000) – 1
Promised return = .1707, or 17.07%
bondholders will receive the entire $48 million promised payment since the market value of the
company is greater than the payment. So, the expected value of debt is:
Expected payment to bondholders = .60($48,000,000) + .40($39,000,000)
Expected payment to bondholders = $44,400,000
Expected return = (Expected value of debt/Market value of debt) – 1
Expected return = ($44,400,000/$41,000,000) – 1
CHAPTER 15 B - 8
9. a. In their no tax model, MM assume that tC, tB, and C(B) are all zero. Under these assumptions, VL
= VU, signifying that the capital structure of a firm has no effect on its value. There is no optimal
debt-equity ratio.
b. In their model with corporate taxes, MM assume that tC > 0 and both tB and C(B) are equal to
zero. Under these assumptions, VL = VU + tCB, implying that raising the amount of debt in a firm’s
capital structure will increase the overall value of the firm. This model implies that the debt-
c. If the costs of financial distress are zero, the value of a levered firm equals:
VL = VU + {1 – [(1 – tC)/(1 – tB)}] × B
Therefore, the change in the value of this all-equity firm that issues debt and uses the proceeds
to repurchase equity is:
Change in value = {1 – [(1 – tC)/(1 – tB)}] × B
VL = VU + {1 – [(1 – tC)/(1 – tB)]} × B
Therefore, the change in the value of an all-equity firm that issues $1 of perpetual debt instead
of $1 of perpetual equity is:
Change in value = {1 – [(1 – tC)/(1 – tB)]} × $1
VU = EBIT(1 – tC)/R0
VU = $795,000(1 – .35)/.14
CHAPTER 15 B - 9
VU = $3,691,071.43
VL = VU + {1 – [(1 – tC)/(1 – tB)}] × B
VL = $3,691,071.43 + {1 – [(1 – .35)/(1 – .25)]} × $1,700,000
VL = $3,917,738.10
forced into bankruptcy. So, the value of the levered firm with bankruptcy would be:
VL = VU + {1 – [(1 – tC)/(1 – tB)}] × B – C(B)
VL = ($3,691,071.43 + {1 – [(1 – .35)/(1 – .25)]} × $1,700,000) – $425,000
VL = $3,492,738.10
