Chapter 13
1. Business risk is the equity risk arising from the nature of the firm’s operating activity, and is directly related to the systematic risk of the firm’s assets. Financial risk is the equity risk that is due entirely to the firm’s chosen capital structure. As financial leverage, or the use of debt financing, increases, so does financial risk and hence the overall risk of the equity. Thus, Firm B could have a higher cost of equity if it uses greater leverage.
2. No, it doesn’t follow. While it is true that the equity and debt costs are rising, the key thing to remember is that the cost of debt is still less than the cost of equity. Since we are using more and more debt, the WACC does not necessarily rise.
3. Because many relevant factors such as bankruptcy costs, tax asymmetries, and agency costs cannot easily be identified or quantified, it’s practically impossible to determine the precise debt/equity ratio that maximizes the value of the firm. However, if the firm’s cost of new debt suddenly becomes much more expensive, it’s probably true that the firm is too highly leveraged.
4. The more capital intensive industries, such as airlines, cable television, and electric utilities, tend to use greater financial leverage. Also, industries with less predictable future earnings, such computers or drugs, tend to use less. Such industries also have a higher concentration of growth and startup firms. Overall, the general tendency is for firms with identifiable, tangible assets and relatively more predictable future earnings to use more debt financing. These are typically the firms with the greatest need for external financing and the greatest likelihood of benefiting from the interest tax shelter.
5. It’s called leverage (or “gearing” in the UK) because it magnifies gains or losses.
6. Homemade leverage refers to the use of borrowing on the personal level as opposed to the corporate level.
7. 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 alternative to complicated and expensive litigation.
8. As in the previous question, it could be argued that using bankruptcy laws as a sword may simply 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 this possibility.
9. 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 simply abrogated them to the detriment of its employees. It is important thing to keep in mind that the bankruptcy code is a creation of law, not economics. A strong argument can always be made that making the best use of the bankruptcy code is no different from, for example, minimizing taxes by making best use of the tax code. Indeed, a strong case can be made that it is the financial manager’s duty to do so. As the case of Continental illustrates, the code can be changed if socially undesirable outcomes are a problem.
10. As with any management decision, the goal is to maximize the value of shareholder equity. To accomplish this with respect to the capital structure decision, management attempts to choose the capital structure with the lowest cost of capital.
Solutions to Questions and Problems
NOTE: All endofchapter 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. A table outlining the income statement for the three possible states of the economy is shown below. The EPS is the net income divided by the 4,500 shares outstanding. The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy.



Recession

Normal

Expansion



EBIT

$10,500

$15,000

$18,000



Interest

0

0

0



NI

$10,500

$15,000

$18,000



EPS

$2.33

$3.33

$4.00



%EPS

–30%



+20%

b. If the company undergoes the proposed recapitalization, it will repurchase:
Share price = Equity / Shares outstanding
Share price = $90,000/4,500
Share price = $20
Shares repurchased = Debt issued / Share price
Shares repurchased = $45,000/$20
Shares repurchased = 2,250
The interest payment each year under all three scenarios will be:
Interest payment = $45,000(.05)
Interest payment = $2,250
The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy under the proposed recapitalization.



Recession

Normal

Expansion



EBIT

$10,500

$15,000

$18,000



Interest

2,250

2,250

2,250



NI

$8,250

$12,750

$15,750



EPS

$3.67

$ 5.67

$7.00



%EPS

–35.29

–

+23.53

2. a. A table outlining the income statement with taxes for the three possible states of the economy is shown below. The share price is still $60, and there are still 2,500 shares outstanding. The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy.



Recession

Normal

Expansion



EBIT

$10,500

$15,000

$18,000



Interest

0

0

0



Taxes

3,675

5,250

6,370



NI

$6,825

$9,750

$11,830



EPS

$1.52

$2.18

$4.73



%EPS

–30

–

+20

b. A table outlining the income statement with taxes for the three possible states of the economy and assuming the company undertakes the proposed capitalization is shown below. The interest payment and shares repurchased are the same as in part b of Problem 1.



Recession

Normal

Expansion



EBIT

$10,500

$15,000

$18,000



Interest

2,250

2,250

2,250



Taxes

2,888

4,463

5,513



NI

$5,363

$8,288

$10,238



EPS

$2.38

$3.68

$4.55



%EPS

–35.29

–

+23.53

Notice that the percentage change in EPS is the same both with and without taxes
3. a. Since the company has a markettobook ratio of 1.0, the total equity of the firm is equal to the market value of equity. Using the equation for ROE:
ROE = NI/$90,000
The ROE for each state of the economy under the current capital structure and no taxes is:



Recession

Normal

Expansion



ROE

.1167

.1667

.2000



%ROE

–30

–

+20

The second row shows the percentage change in ROE from the normal economy.
b. If the company undertakes the proposed recapitalization, the new equity value will be:
Equity = $90,000 – 45,000
Equity = $45,000
So, the ROE for each state of the economy is:
ROE = NI/$45,000



Recession

Normal

Expansion



ROE

.1833

.28.33

.3500



%ROE

–30

–

+20

c. If there are corporate taxes and the company maintains its current capital structure, the ROE is:


ROE

.0758

.1083

.1300



%ROE

–60

–––

+30

If the company undertakes the proposed recapitalization, and there are corporate taxes, the ROE for each state of the economy is:


ROE

.1192

.1842

.2275



%ROE

–35.29

–

+23.53

Notice that the percentage change in ROE is the same as the percentage change in EPS. The percentage change in ROE is also the same with or without taxes.
4. a. Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax. The EPS under this capitalization will be:
EPS = $1,500,000/800,000 shares
EPS = $1.88
Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so:
NI = $1,500,000 – .10($10,000,000)
NI = $500,000
And the EPS will be:
EPS = $500,000/320,000 shares
EPS = $1.56
Plan I has the higher EPS when EBIT is $1,500,000.
b. Under Plan I, the net income is $5,000,000 and the EPS is:
EPS = $5,000,000/800,000 shares
EPS = $6.25
Under Plan II, the net income is:
NI = $5,000,000 – .10($10,000,000)
NI = $4,000,000
And the EPS is:
EPS = $4,000,000/320,000 shares
EPS = $12.50
Plan II has the higher EPS when EBIT is $5,000,000.
c. To find the breakeven EBIT for two different capital structures, we simply set the equations for EPS equal to each other and solve for EBIT. The breakeven EBIT is:
EBIT/800,000 = [EBIT – .10($10,000,000)]/320,000
EBIT = $1,666,666.67
5. We can find the price per share by dividing the amount of debt used to repurchase shares by the number of shares repurchased. Doing so, we find the share price is:
Share price = $10,000,000/(800,000 – 320,000)
Share price = $20.83 per share
The value of the company under the allequity plan is:
V_{ }= $20.83(800,000 shares)
V = $16,666,666.67
And the value of the company under the levered plan is:
V = $20.83(320,000 shares) + $10,000,000 debt
V = $16,666,666.67
6. a. The income statement for each capitalization plan is:


 I 
II

Allequity



EBIT

$5,000

$5,000

$5,000



Interest

4,000

2,000

0



NI

$1,000

$3,000

$5,000



EPS

$ 0.50

$ 0.75

$ 0.83

Plan I has the lowest EPS; the allequity plan has the highest EPS.
b. The breakeven level of EBIT occurs when the capitalization plans result in the same EPS. The EPS is calculated as:
EPS = (EBIT – R_{D}D)/Shares outstanding
This equation calculates the interest payment (R_{D}D) and subtracts it from the EBIT, which results in the net income. Dividing by the shares outstanding gives us the EPS. For the allequity capital structure, the interest term is zero. To find the breakeven EBIT for two different capital structures, we simply set the equations equal to each other and solve for EBIT. The breakeven EBIT between the allequity capital structure and Plan I is:
EBIT/6,000 = [EBIT – .10($40,000)]/2,000
EBIT = $6,000
And the breakeven EBIT between the allequity capital structure and Plan II is:
EBIT/6,000 = [EBIT – .10($20,000)]/4,000
EBIT = $6,000
The breakeven levels of EBIT are the same because of M&M Proposition I.
c. Setting the equations for EPS from Plan I and Plan II equal to each other and solving for EBIT, we get:
[EBIT – .10($40,000)]/2,000 = [EBIT – .10($20,000)]/4,000
EBIT = $6,000
This breakeven level of EBIT is the same as in part b again because of M&M Proposition I.
d. The income statement for each capitalization plan with corporate income taxes is:


 I 
II

Allequity



EBIT

$5,000

$5,000

$5,000



Interest

4,000

2,000

0



Taxes

380

1,140

1,900



NI

$ 620

$1,860

$3,100



EPS

$ 0.31

$ 0.47

$ 052

Plan II still has the highest EPS; the allequity plan still has the lowest EPS.
We can calculate the EPS as:
EPS = [(EBIT – R_{D}D)(1 – t_{C})]/Shares outstanding
This is similar to the equation we used before, except now we need to account for taxes. Again, the interest expense term is zero in the allequity capital structure. So, the breakeven EBIT between the allequity plan and Plan I is:
EBIT(1 – .38)/6,000 = [EBIT – .10($40,000)](1 – .38)/2,000
EBIT = $6,000
The breakeven EBIT between the allequity plan and Plan II is:
EBIT(1 – .38)/6,000 = [EBIT – .10($20,000)](1 – .38)/4,000
EBIT = $6,000
And the breakeven between Plan I and Plan II is:
[EBIT – .10($40,000)](1 – .38)/2,000 = [EBIT – .10($20,000)](1 – .38)/4,000
EBIT = $6,000
The breakeven levels of EBIT do not change because the addition of taxes reduces the income of all three plans by the same percentage; therefore, they do not change relative to one another.
7. To find the value per share of the stock under each capitalization plan, we can calculate the price as the value of shares repurchased divided by the number of shares repurchased. So, under Plan I, the value per share is:
P = $40,000/4,000 shares
P = $10 per share
And under Plan II, the value per share is:
P = $20,000/2,000 shares
P = $10 per share
This shows that when there are no corporate taxes, the stockholder does not care about the capital structure decision of the firm. This is M&M Proposition I without taxes.
8. a. The earnings per share are:
EPS = $3,000/1,200 shares
EPS = $2.50
Since all earnings are paid as dividends, the cash flow for the investors will be:
Cash flow = $2.50(100 shares)
Cash flow = $250
b. To determine the cash flow to the shareholder, we need to determine the EPS of the firm under the proposed capital structure. The market value of the firm is:
V = $90(1,200)
V = $108,000
Under the proposed capital structure, the firm will raise new debt in the amount of:
D = 0.30($108,000)
D = $32,400
in debt. This means the number of shares repurchased will be:
Shares repurchased = $32,400/$90
Shares repurchased = 360
Under the new capital structure, the company will have to make an interest payment on the new debt. The net income with the interest payment will be:
NI = $3,000 – .08($32,400)
NI = $408
This means the EPS under the new capital structure will be:
EPS = $408/(1,200 – 360)
EPS = $0.49
Since all earnings are paid as dividends, the shareholder will receive:
Shareholder cash flow = $0.49(100 shares)
Shareholder cash flow = $48.57
c. To replicate the proposed capital structure, the shareholder should sell 30 percent of their shares, or 30 shares, and lend the proceeds at 8 percent. The shareholder will have an interest cash flow of:
Interest cash flow = 30($90)(.08)
Interest cash flow = $216
The shareholder will receive dividend payments on the remaining 60 shares, so the dividends received will be:
Dividends received = $0.49(70 shares)
Dividends received = $34
The total cash flow for the shareholder under these assumptions will be:
Total cash flow = $216 + 34
Total cash flow = $250
This is the same cash flow we calculated in part a.
d. The capital structure is irrelevant because shareholders can create their own leverage or unlever the stock to create the payoff they desire, regardless of the capital structure the firm actually chooses.
9. a. The total value of the company is the share price times the number of shares, so:
V = $100($2,000)
NI = $200,000
The investor will receive dividends in proportion to the percentage of the company’s share they own. The total dividends received by the shareholder will be:
Dividends received = $29,000($16,000/$200,000)
Dividends received = $2,320
b. Under the proposed capital structure, the firm will raise new debt in the amount of:
D = 0.40($200,000)
D = $80,000
in debt. This means the number of shares repurchased will be:
Shares repurchased = $80,000/$100
Shares repurchased = 800
Under the new capital structure, the company will have to make an interest payment on the new debt. The net income with the interest payment will be:
NI = $29,000 – .07($80,000)
NI = $23,400
This means the EPS under the new capital structure will be:
EPS = $23,400/(2,000 – 800)
EPS = $19.50
The number of shares owned by the shareholder is the dollar amount invested divided by the share price, so:
Shares owned = $16,000 / 100
Shares owned = 160
Since all earnings are paid as dividends, the shareholder will receive:
Shareholder cash flow = $19.50(160 shares)
Shareholder cash flow = $3,120
c. To replicate the proposed capital structure, the shareholder should sell 40 percent of their shares, or 64 shares, and lend the proceeds at 7 percent. The shareholder will have an interest cash flow of:
Interest cash flow = 64($100)(.07)
Interest cash flow = $448
The shareholder will receive dividend payments on the remaining 96 shares, so the dividends received will be:
Dividends received = $19.50(96 shares)
Dividends received = $1,872
The total cash flow for the shareholder under these assumptions will be:
Total cash flow = $448 + 1,872
Total cash flow = $2,320
This is the same cash flow we calculated in part a.
d. The capital structure is irrelevant because shareholders can create their own leverage or unlever the stock to create the payoff they desire, regardless of the capital structure the firm actually chooses.
10. A debtequity ratio of 1 implies 50 percent debt and 50 percent equity. Using M&M Proposition I with taxes, the value of the firm is:
V_{L} = V_{U} + T_{C}D
V_{L} = $45,000,000 + .40($22,500,000)
V_{L} = $54,000,000
A debtequity ratio of 2 implies 67 percent debt, so the value of the firm is:
V_{L} = V_{U} + T_{C}D
V_{L} = $45,000,000 + .40($30,000,000)
V_{L} = $57,000,000
11. With no debt, the value is unchanged at $45 million. With a debtequity ratio of 1, the firm value is:
V_{L} = V_{U} + T_{C}D
V_{L} = $45,000,000 + .30($22,500,000)
V_{L} = $51,750,000
And with a debtequity ratio of 2, the firm value is:
V_{L} = V_{U} + T_{C}D
V_{L} = $45,000,000 + .30($30,000,000)
V_{L} = $54,000,000
Debt will increase the value of the firm more when the corporate tax rate is higher.
12. a. With the information provided, we can use the equation for calculating WACC to find the cost of equity. The equation for WACC (assuming no taxes) is:
WACC = (E/V)R_{E} + (D/V)R_{D}
The company has a debtequity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the weight of equity is 1/2.5, so
WACC = .11 = (1/2.5)R_{E} + (1.5/2.5)(.06)
R_{E} = .1850 or 18.50%
b. To find the cost of equity under different capital structures, we can again use the WACC equation. With a debtequity ratio of 2, the cost of equity is:
.11 = (1/3)R_{E} + (2/3)(.06)
R_{E} = .2100 or 21.00%
With a debtequity ratio of 0.5, the cost of equity is:
.11 = (1/1.5)R_{E} + (0.5/1.5)(.06)
R_{E} = .1350 or 13.50%
And with a debtequity ratio of 0, the cost of equity is:
.11 = (1)R_{E} + (0)(.06)
R_{E} = WACC = .1100 or 11.00%
13. a. For an allequity financed company:
WACC = R_{E} = .10 or 10%
b. To find the cost of equity for the company with leverage, we need to use M&M Proposition I with no taxes, so:
R_{E} = R_{A} + (R_{A} – R_{D})(D/E)
R_{E} = .10 + (.10 – .07)(.30/.70)
R_{E} = .1129 or 11.29%
c. Using M&M Proposition I with no taxes again, we get:
R_{E} = R_{A} + (R_{A} – R_{D})(D/E)
R_{E} = .10 + (.10 – .07)(.60/.40)
R_{E} = .1450 or 14.50%
d. The WACC with 30 percent debt is:
WACC = (E/V)R_{E} + (D/V)R_{D}
WACC = .70(.1129) + .30(.07)
WACC = .1000 or 10.00%
And the WACC with 50 percent debt is:
WACC = (E/V)R_{E} + (D/V)R_{D}
WACC = .40(.1450) + .60(.07)
WACC = .1000 or 10.00%
14. Using M&M Proposition I with taxes, the value of the levered firm is:
V_{L} = V_{U} + T_{C}D
V_{L} = $480,000 + .35($90,000)
V_{L} = $511,500
15. The interest tax shield is the total interest paid times the tax rate, so:
Interest tax shield = Interest paid(t_{C})
Interest tax shield = $28,000,000(.38)
Interest tax shield = $10,640,000
The interest tax shield represents the tax savings in current income due to the deductibility of a firm’s qualified debt expenses.
Intermediate
16. M&M Proposition I with no taxes states the value of the levered firm is equal to the value of the unlevered firm. So, with no taxes, the value of the firm is it issues the debt is:
V_{U} = V_{L} = $120,000,000
With corporate taxes, we need to use M&M Proposition I with taxes, so the value of the firm is:
V_{L} = V_{U} + T_{C}D
V_{L} = $120,000,000 + .40($35,000,000)
V_{L} = $134,000,000
17. The value of the firm is the value of the debt plus the value of the equity. We can use this relationship to find the value of equity in each case. So, the debtequity ratio with no taxes is:
V = E + D
$120,000,000 = E + 35,000,000
E = $85,000,000
So, the debtequity ratio is:
Debtequity ratio = $35,000,000/$85,000,000
Debtequity ratio = .41
With taxes, the debtequity ratio becomes:
V = E + D
$134,000,000 = E + 35,000,000
E = $99,000,000
So, the debtequity ratio is:
Debtequity ratio = $35,000,000/$99,000,000
Debtequity ratio = .35
18. When the company is allequity financed, the cost of equity is:
WACC = R_{E} = .12 or 12%
Using M&M Proposition I with no taxes, the cost of equity will be:
R_{E} = R_{A} + (R_{A} – R_{D})(D/E)
R_{E} = .12 + (.12 – .065)(1)
R_{E} = .1750 or 17.50%
And the new WACC will be:
WACC = (E/V)R_{E} + (D/V)R_{D}
WACC = (.50).1750 + (.50)(.065)
WACC = .1200 or 12.00%
19. With no debt, we are finding the value of an unlevered firm, so:
V = EBIT(1 – t_{C})/R_{U}
V = $23,000(1 – .38)/.16
V = $89,125.00
With debt, we simply need to use the equation for the value of a levered firm. With 50 percent debt, onehalf of the firm value is debt, so the value of the levered firm is:
V_{L} = V_{U } + t_{C}D
V_{L} = $89,125 + .38(.50)V_{L}
V_{L} = $110,030.86
And with 100 percent debt, the value of the firm is:
V_{L} = V_{U } + t_{C}D
V_{L} = $89,125 + .38(V_{L})
V_{L} = $143,750.00 