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 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, 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 use of the process.
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 it.
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. In this, and the last several, questions, an important thing to keep in mind is 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. The basic goal is to minimize the value of non-marketed claims.
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. 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 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 | $5,600 | $14,000 | $18,200 | ||
| Interest | 0 | 0 | 0 | ||
| NI | $5,600 | $14,000 | $18,200 | ||
| EPS | $ 2.24 | $ 5.60 | $ 7.284 | ||
| %DEPS | –60 | ––– | +30 |
b. If the company undergoes the proposed recapitalization, it will repurchase:
Share price = Equity / Shares outstanding
Share price = $150,000/2,500
Share price = $60
Shares repurchased = Debt issued / Share price
Shares repurchased =$60,000/$60
Shares repurchased = 1,000
The interest payment each year under all three scenarios will be:
Interest payment = $60,000(.05) = $3,000
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 | $5,600 | $14,000 | $18,200 | ||
| Interest | 3,000 | 3,000 | 3,000 | ||
| NI | $2,600 | $11,000 | $15,200 | ||
| EPS | $1.73 | $ 7.33 | $10.13 | ||
| %DEPS | –76.36 | ––– | +38.18 |
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 | $5,600 | $14,000 | $18,200 | ||
| Interest | 0 | 0 | 0 | ||
| Taxes | 1,960 | 4,900 | 6,370 | ||
| NI | $3,640 | $9,100 | $11,830 | ||
| EPS | $1.46 | $3.64 | $4.73 | ||
| %DEPS | –60 | ––– | +30 |
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 | $5,600 | $14,000 | $18,200 | ||
| Interest | 3,000 | 3,000 | 3,000 | ||
| Taxes | 910 | 3,850 | 5,320 | ||
| NI | $1,690 | $7,150 | $9,880 | ||
| EPS | $1.13 | $4.77 | $6.59 | ||
| %DEPS | –76.36 | ––– | +38.18 |
Notice that the percentage change in EPS is the same both with and without taxes.
3. a. Since the company has a market-to-book 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/$150,000
The ROE for each state of the economy under the current capital structure and no taxes is:
| Recession | Normal | Expansion | |||
| ROE | .0373 | .0933 | .1213 | ||
| %DROE | –60 | ––– | +30 |
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 = $150,000 – 60,000
Equity = $90,000
So, the ROE for each state of the economy is:
ROE = NI/$90,000
| Recession | Normal | Expansion | |||
| ROE | .0222 | .1156 | .1622 | ||
| %DROE | –76.36 | ––– | +38.18 |
c. If there are corporate taxes and the company maintains its current capital structure, the ROE is:
| ROE | .0243 | .0607 | .0789 | ||
| %DROE | –60 | ––– | +30 |
If the company undertakes the proposed recapitalization, and there are corporate taxes, the ROE for each state of the economy is:
| ROE | .0144 | .0751 | .1054 | ||
| %DROE | –76.36 | ––– | +38.18 |
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 = $200,000/150,000 shares
EPS = $1.33
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 = $200,000 – .10($1,500,000)
NI = $50,000
And the EPS will be:
EPS = $50,000/60,000 shares
EPS = $0.83
Plan I has the higher EPS when EBIT is $200,000.
b. Under Plan I, the net income is $700,000 and the EPS is:
EPS = $700,000/150,000 shares
EPS = $4.67
Under Plan II, the net income is:
NI = $700,000 – .10($1,500,000)
NI = $550,000
And the EPS is:
EPS = $550,000/60,000 shares
EPS = $9.17
Plan II has the higher EPS when EBIT is $700,000.
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/150,000 = [EBIT – .10($1,500,000)]/60,000
EBIT = $250,000
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 = $1,500,000/(150,000 – 60,000)
Share price = $16.67 per share
The value of the company under the all-equity plan is:
V = $16.67(150,000 shares) = $2,500,000
And the value of the company under the levered plan is:
V = $16.67(60,000 shares) + $1,500,000 debt = $2,500,000
6. a. The income statement for each capitalization plan is:
| I | II | All-equity | |||
| EBIT | $10,000 | $10,000 | $10,000 | ||
| Interest | 1,650 | 2,750 | 0 | ||
| NI | $8,350 | $7,250 | $10,000 | ||
| EPS | $7.59 | $ 8.06 | $ 7.14 |
Plan II has the highest EPS; the all-equity plan has the lowest EPS.
b. The breakeven level of EBIT occurs when the capitalization plans result in the same EPS. The EPS is calculated as:
EPS = (EBIT – RDD)/Shares outstanding
This equation calculates the interest payment (RDD) and subtracts it from the EBIT, which results in the net income. Dividing by the shares outstanding gives us the EPS. For the all-equity 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 all-equity capital structure and Plan I is:
EBIT/1,400 = [EBIT – .10($16,500)]/1,100
EBIT = $7,700
And the breakeven EBIT between the all-equity capital structure and Plan II is:
EBIT/1,400 = [EBIT – .10($27,500)]/900
EBIT = $7,700
The break-even 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($16,500)]/1,100 = [EBIT – .10($27,500)]/900
EBIT = $7,700
This break-even 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 | All-equity | |||
| EBIT | $10,000 | $10,000 | $10,000 | ||
| Interest | 1,650 | 2,750 | 0 | ||
| Taxes | 3,340 | 2,900 | 4,000 | ||
| NI | $5,010 | $4,350 | $6,000 | ||
| EPS | $4.55 | $ 4.83 | $ 4.29 |
Plan II still has the highest EPS; the all-equity plan still has the lowest EPS.
We can calculate the EPS as:
EPS = [(EBIT – RDD)(1 – tC)]/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 all-equity capital structure. So, the breakeven EBIT between the all-equity plan and Plan I is:
EBIT(1 – .40)/1,400 = [EBIT – .10($16,500)](1 – .40)/1,100
EBIT = $7,700
The breakeven EBIT between the all-equity plan and Plan II is:
EBIT(1 – .40)/1,400 = [EBIT – .10($27,500)](1 – .40)/900
EBIT = $7,700
And the breakeven between Plan I and Plan II is:
[EBIT – .10($16,500)](1 – .40)/1,100 = [EBIT – .10($27,500)](1 – .40)/900
EBIT = $7,700
The break-even 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 = $11,000/200 shares
P = $55 per share
And under Plan II, the value per share is:
P = $27,500/500 shares
P = $55 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 = $16,000/2,000 shares
EPS = $8.00
So, the cash flow for the company is:
Cash flow = $8.00(100 shares)
Cash flow = $800
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 = $70(2,000)
V = $140,000
Under the proposed capital structure, the firm will raise new debt in the amount of:
D = 0.40($140,000)
D = $56,000
in debt. This means the number of shares repurchased will be:
Shares repurchased = $56,000/$70
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 = $16,000 – .08($56,000)
NI = $11,520
This means the EPS under the new capital structure will be:
EPS = $11,520/1,200 shares
EPS = $9.60
Since all earnings are paid as dividends, the shareholder will receive:
Shareholder cash flow = $9.60(100 shares)
Shareholder cash flow = $960
c. To replicate the proposed capital structure, the shareholder should sell 40 percent of their shares, or 40 shares, and lend the proceeds at 8 percent. The shareholder will have an interest cash flow of:
Interest cash flow = 40($70)(.08)
Interest cash flow = $224
The shareholder will receive dividend payments on the remaining 60 shares, so the dividends received will be:
Dividends received = $9.60(60 shares)
Dividends received = $576
The total cash flow for the shareholder under these assumptions will be:
Total cash flow = $224 + 576
Total cash flow = $800
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 rate of return earned will be the dividend yield. The company has debt, so it must make an interest payment. The net income for the company is:
NI = $73,000 – .10($300,000)
NI = $43,000
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 = $43,000($30,000/$300,000)
Dividends received = $4,300
So the return the shareholder expects is:
R = $4,300/$30,000
R = .1433 or 14.33%
b. To generate exactly the same cash flows in the other company, the shareholder needs to match the capital structure of ABC. The shareholder should sell all shares in XYZ. This will net $30,000. The shareholder should then borrow $30,000. This will create an interest cash flow of:
Interest cash flow = .10($30,000)
Interest cash flow = –$3,000
The investor should then use the proceeds of the stock sale and the loan to buy shares in ABC. 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 = $73,000($60,000/$600,000)
Dividends received = $7,300
The total cash flow for the shareholder will be:
Total cash flow = $7,300 – 3,000
Total cash flow = $4,300
The shareholders return in this case will be:
R = $4,300/$30,000
R = .1433 or 14.33%
c. ABC is an all equity company, so:
RE = RA = $73,000/$600,000
RE = .1217 or 12.17%
To find the cost of equity for XYZ we need to use M&M Proposition II, so:
RE = RA + (RA – RD)(D/E)(1 – tC)
RE = .1217 + (.1217 – .10)(1)(1)
RE = .1433 or 14.33%
d. To find the WACC for each company we need to use the WACC equation:
WACC = (E/V)RE + (D/V)RD(1 – tC)
So, for ABC, the WACC is:
WACC = (1)(.1217) + (0)(.10)
WACC = .1217 or 12.17%
And for XYZ, the WACC is:
WACC = (1/2)(.1433) + (1/2)(.10)
WACC = .1217 or 12.17%
When there are no corporate taxes, the cost of capital for the firm is unaffected by the capital structure; this is M&M Proposition I without taxes.
10. With no taxes, the value of an unlevered firm is the interest rate divided by the unlevered cost of equity, so:
V = EBIT/WACC
$35,000,000 = EBIT/.13
EBIT = .13($35,000,000)
EBIT = $4,550,000
11. If there are corporate taxes, the value of an unlevered firm is:
VU = EBIT(1 – tC)/RU
Using this relationship, we can find EBIT as:
$35,000,000 = EBIT(1 – .35)/.13
EBIT = $7,000,000
The WACC remains at 13 percent. Due to taxes, EBIT for an all-equity firm would have to be higher for the firm to still be worth $35 million.
12. a. With the information provided, we can use the equation for calculating WACC to find the cost of equity. The equation for WACC is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
The company has a debt-equity 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 = .12 = (1/2.5)RE + (1.5/2.5)(.12)(1 – .35)
RE = .1830 or 18.30%
b. To find the unlevered cost of equity we need to use M&M Proposition II with taxes, so:
RE = RU + (RU – RD)(D/E)(1 – tC)
.1830 = RU + (RU – .12)(1.5)(1 – .35)
RU = .1519 or 15.19%
c. To find the cost of equity under different capital structures, we can again use the WACC equation. With a debt-equity ratio of 2, the cost of equity is:
.12 = (1/3)RE + (2/3)(.12)(1 – .35)
RE = .2040 or 20.40%
With a debt-equity ratio of 1.0, the cost of equity is:
.12 = (1/2)RE + (1/2)(.12)(1 – .35)
RE = .1620 or 16.20%
And with a debt-equity ratio of 0, the cost of equity is:
.12 = (1)RE + (0)(.12)(1 – .35)
RE = WACC = .12 or 12%
13. a. For an all-equity financed company:
WACC = RU = RE = .12 or 12%
b. To find the cost of equity for the company with leverage we need to use M&M Proposition II with taxes, so:
RE = RU + (RU – RD)(D/E)(1 – tC)
RE = .12 + (.12 – .08)(.25/.75)(.65)
RE = .1287 or 12.87%
c. Using M&M Proposition II with taxes again, we get:
RE = RU + (RU – RD)(D/E)(1 – tC)
RE = .12 + (.12 – .08)(.50/.50)(1 – .35)
RE = .1460 or 14.60%
d. The WACC with 25 percent debt is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
WACC = .75(.1287) + .25(.08)(1 – .35)
WACC = .1095 or 10.95%
And the WACC with 50 percent debt is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
WACC = .50(.1460) + .50(.08)(1 – .35)
WACC = .0990 or 9.90%
14. a. The value of the unlevered firm is:
V = EBIT(1 – tC)/RU
V = $95,000(1 – .35)/.22
V = $280,681.82
b. The value of the levered firm is:
V = VU + tCD
V = $280,681.82 + .35($60,000)
V = $301,681.82
15. We can find the cost of equity using M&M Proposition II with taxes. Doing so, we find:
RE = RU + (RU – RD)(D/E)(1 – t)
RE = .22 + (.22 – .11)($60,000/$241,681.82)(1 – .35)
RE = .2378 or 23.78%
Using this cost of equity, the WACC for the firm after recapitalization is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
WACC = .2378($241,681.82/$301,681.82) + .11(1 – .35)($60,000/$301,681.82)
WACC = .2047 or 20.47%
When there are corporate taxes, the overall cost of capital for the firm declines the more highly leveraged is the firm’s capital structure. This is M&M Proposition I with taxes.
Intermediate
16. To find the value of the levered firm we first need to find the value of an unlevered firm. So, the value of the unlevered firm is:
VU = EBIT(1 – tC)/RU
VU = ($35,000)(1 – .35)/.14
VU = $162,500
Now we can find the value of the levered firm as:
VL = VU + tCD
VL = $162,500 + .35($70,000)
VL = $187,000
Applying M&M Proposition I with taxes, the firm has increased its value by issuing debt. As long as M&M Proposition I holds, that is, there are no bankruptcy costs and so forth, then the company should continue to increase its debt/equity ratio to maximize the value of the firm.
17. With no debt, we are finding the value of an unlevered firm, so:
V = EBIT(1 – tC)/RU
V = $9,000(1 – .35)/.17
V = $34,411.76
With debt, we simply need to use the equation for the value of a levered firm. With 50 percent debt, one-half of the firm value is debt, so the value of the levered firm is:
V= VU + tCD
V = $34,411.76 + .35($34,411.76/2)
V = $40,433.82
And with 100 percent debt, the value of the firm is:
V= VU + tCD
V = $34,411.76 + .35($34,411.76)
V = $46,455.88
Challenge
18. M&M Proposition II states:
RE = RA + (RA – RD)(D/E)(1 – tC)
And the equation for WACC is:
WACC = (E/V)RE + (D/V)RD(1 – tC)
Substituting the M&M Proposition II equation into the equation for WACC, we get:
WACC = (E/V)[RA + (RA – RD)(D/E)(1 – tC)] + (D/V)RD(1 – tC)
Rearranging and reducing the equation, we get:
WACC = RA[(E/V) + (E/V)(D/E)(1 – tC)] + RD(1 – tC)[(D/V) – (E/V)(D/E)]
WACC = RA[(E/V) + (D/V)(1 – tC)]
WACC = RA[{(E+D)/V} – tC(D/V)]
WACC = RA[1 – tC(D/V)]
19. The return on equity is net income divided by equity. Net income can be expressed as:
NI = (EBIT – RDD)(1 – tC)
So, ROE is:
RE = (EBIT – RDD)(1 – tC)/E
Now we can rearrange and substitute as follows to arrive at M&M Proposition II with taxes:
RE = [EBIT(1 – tC)/E] – [RD(D/E)(1 – tC)]
RE = RAVU/E – [RD(D/E)(1 – tC)]
RE = RA(VL – tCD)/E – [RD(D/E)(1 – tC)]
RE = RA(E + D – tCD)/E – [RD(D/E)(1 – tC)]
RE = RA + (RA – RD)(D/E)(1 – tC)
20. M&M Proposition II, with no taxes is:
RE = RA + (RA – Rf)(D/E)
Note that we use the risk-free rate as the return on debt. This is an important assumption of M&M Proposition II. The CAPM to calculate the cost of equity is expressed as:
RE = bE(RM – Rf) + Rf
We can rewrite the CAPM to express the return on an unlevered company as:
RA = bA(RM – Rf) + Rf
We can now substitute the CAPM for an unlevered company into M&M Proposition II. Doing so and rearranging the terms we get:
RE = bA(RM – Rf) + Rf + [bA(RM – Rf) + Rf – Rf](D/E)
RE = bA(RM – Rf) + Rf + [bA(RM – Rf)](D/E)
RE = (1 + D/E)bA(RM – Rf) + Rf
Now we set this equation equal to the CAPM equation to calculate the cost of equity and reduce:
bE(RM – Rf) + Rf = (1 + D/E)bA(RM – Rf) + Rf
bE(RM – Rf) = (1 + D/E)bA(RM – Rf)
bE = bA(1 + D/E)
21. Using the equation we derived in Problem 20:
bE = bA(1 + D/E)
The equity beta for the respective asset betas is:
| Debt-equity ratio | Equity beta | |
| 0 | 1(1 + 0) = 1 | |
| 1 | 1(1 + 1) = 2 | |
| 5 | 1(1 + 5) = 6 | |
| 20 | 1(1 + 20) = 21 |
The equity risk to the shareholder is composed of both business and financial risk. Even if the assets of the firm are not very risky, the risk to the shareholder can still be large if the financial leverage is high. These higher levels of risk will be reflected in the shareholder’s required rate of return RE, which will increase with higher debt/equity ratios.
1. Dividend policy deals with the timing of dividend payments, not the amounts ultimately paid. Dividend policy is irrelevant when the timing of dividend payments doesn’t affect the present value of all future dividends.
2. A stock repurchase reduces equity while leaving debt unchanged. The debt ratio rises. A firm could, if desired, use excess cash to reduce debt instead. This is a capital structure decision.
3. The chief drawback to a strict dividend policy is the variability in dividend payments. This is a problem because investors tend to want a somewhat predictable cash flow. Also, if there is information content to dividend announcements, then the firm may be inadvertently telling the market that it is expecting a downturn in earnings prospects when it cuts a dividend, when in reality its prospects are very good. In a compromise policy, the firm maintains a relatively constant dividend. It increases dividends only when it expects earnings to remain at a sufficiently high level to pay the larger dividends, and it lowers the dividend only if it absolutely has to.
4. Friday, December 29 is the ex-dividend day. Remember not to count January 1 because it is a holiday, and the exchanges are closed. Anyone who buys the stock before December 29 is entitled to the dividend, assuming they do not sell it again before December 29.
5. No, because the money could be better invested in stocks that pay dividends in cash which benefit the fundholders directly.
6. The change in price is due to the change in dividends, not due to the change in dividend policy. Dividend policy can still be irrelevant without a contradiction.
7. The stock price dropped because of an expected drop in future dividends. Since the stock price is the present value of all future dividend payments, if the expected future dividend payments decrease, then the stock price will decline.
8. The plan will probably have little effect on shareholder wealth. The shareholders can reinvest on their own, and the shareholders must pay the taxes on the dividends either way. However, the shareholders who take the option may benefit at the expense of the ones who don’t (because of the discount). Also as a result of the plan, the firm will be able to raise equity by paying a 10% flotation cost (the discount), which may be a smaller discount than the market flotation costs of a new issue for some companies.
9. If these firms just went public, they probably did so because they were growing and needed the additional capital. Growth firms typically pay very small cash dividends, if they pay a dividend at all. This is because they have numerous projects available, and they reinvest the earnings in the firm instead of paying cash dividends.
10. It would not be irrational to find low-dividend, high-growth stocks. The trust should be indifferent between receiving dividends or capital gains since it does not pay taxes on either one (ignoring possible restrictions on invasion of principal, etc.). It would be irrational, however, to hold municipal bonds. Since the trust does not pay taxes on the interest income it receives, it does not need the tax break associated with the municipal bonds. Therefore, it should prefer to hold higher yield, taxable bonds.
11. The stock price drop on the ex-dividend date should be lower. With taxes, stock prices should drop by the amount of the dividend, less the taxes investors must pay on the dividends. A lower tax rate lowers the investors’ tax liability.
12. With a high tax on dividends and a low tax on capital gains, investors, in general, will prefer capital gains. If the dividend tax rate declines, the attractiveness of dividends increases.
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. The aftertax dividend is the pretax dividend times one minus the tax rate, so:
Aftertax dividend = $6.00(1 – .15) = $5.10
The stock price should drop by the aftertax dividend amount, or:
Ex-dividend price = $80 – 5.10 = $74.90
2. a. The shares outstanding increases by 10 percent, so:
New shares outstanding = 10,000(1.10) = 11,000
New shares issued = 1,000
Since the par value of the new shares is $1, the capital surplus per share is $24. The total capital surplus is therefore:
Capital surplus on new shares = 1,000($24) = $24,000
| Common stock ($1 par value) | $ 11,000 | |
| Capital surplus | 204,000 | |
| Retained earnings | 561,500 | |
| $776,500 |
b. The shares outstanding increases by 25 percent, so:
New shares outstanding = 10,000(1.25) = 12,500
New shares issued = 2,500
Since the par value of the new shares is $1, the capital surplus per share is $24. The total capital surplus is therefore:
Capital surplus on new shares = 2,500($24) = $60,000
| Common stock ($1 par value) | $ 12,500 | |
| Capital surplus | 240,000 | |
| Retained earnings | 524,000 | |
| $776,500 |
3. a. To find the new shares outstanding, we multiply the current shares outstanding times the ratio of new shares to old shares, so:
New shares outstanding = 10,000(4/1) = 40,000
The equity accounts are unchanged except the par value of the stock is changed by the ratio of new shares to old shares, so the new par value is:
New par value = $1(1/4) = $0.25 per share.
b. To find the new shares outstanding, we multiply the current shares outstanding times the ratio of new shares to old shares, so:
New shares outstanding = 10,000(1/5) = 2,000.
The equity accounts are unchanged except the par value of the stock is changed by the ratio of new shares to old shares, so the new par value is:
New par value = $1(5/1) = $5.00 per share.
4. To find the new stock price, we multiply the current stock price by the ratio of old shares to new shares, so:
a. $65(3/5) = $39.00
b. $65(1/1.15) = $56.52
c. $65(1/1.425) = $45.61
d. $65(7/4) = $113.75
e. To find the new shares outstanding, we multiply the current shares outstanding times the ratio of new shares to old shares, so:
a: 150,000(5/3) = 250,000
b: 150,000(1.15) = 172,500
c: 150,000(1.425) = 213,750
d: 150,000(4/7) = 85,714
5. The stock price is the total market value of equity divided by the shares outstanding, so:
P0 = $175,000 equity/5,000 shares = $35.00 per share
Ignoring tax effects, the stock price will drop by the amount of the dividend, so:
PX = $35.00 – 1.50 = $33.50
The total dividends paid will be:
$1.50 per share(5,000 shares) = $7,500
The equity and cash accounts will both decline by $7,500.
6. Repurchasing the shares will reduce shareholders’ equity by $4,025. The shares repurchased will be the total purchase amount divided by the stock price, so:
Shares bought = $4,025/$35.00 = 115
And the new shares outstanding will be:
New shares outstanding = 5,000 – 115 = 4,885
After repurchase, the new stock price is:
Share price = $170,975/4,885 shares = $35.00
The repurchase is effectively the same as the cash dividend because you either hold a share worth $35.00, or a share worth $33.50 and $1.50 in cash. Therefore, you participate in the repurchase according to the dividend payout percentage; you are unaffected.
7. The stock price is the total market value of equity divided by the shares outstanding, so:
P0 = $360,000 equity/15,000 shares = $24 per share
The shares outstanding will increase by 25 percent, so:
New shares outstanding = 15,000(1.25) = 18,750
The new stock price is the market value of equity divided by the new shares outstanding, so:
PX = $360,000/18,750 shares = $19.20
8. With a stock dividend, the shares outstanding will increase by one plus the dividend amount, so:
New shares outstanding = 350,000(1.12) = 392,000
The capital surplus is the capital paid in excess of par value, which is $1, so:
Capital surplus for new shares = 42,000($19) = $798,000
The new capital surplus will be the old capital surplus plus the additional capital surplus for the new shares, so:
Capital surplus = $1,650,000 + 798,000 = $2,448,000
The new equity portion of the balance sheet will look like this:
| Common stock ($1 par value) | $ 392,000 | |
| Capital surplus | 2,448,000 | |
| Retained earnings | 2,160,000 | |
| $5,000,000 |
9. The only equity account that will be affected is the par value of the stock. The par value will change by the ratio of old shares to new shares, so:
New par value = $1(1/5) = $0.20 per share.
The total dividends paid this year will be the dividend amount times the number of shares outstanding. The company had 350,000 shares outstanding before the split. We must remember to adjust the shares outstanding for the stock split, so:
Total dividends paid this year = $0.70(350,000 shares)(5/1 split) = $1,225,000
The dividends increased by 10 percent, so the total dividends paid last year were:
Last year’s dividends = $1,225,000/1.10 = $1,113,636.36
And to find the dividends per share, we simply divide this amount by the shares outstanding last year. Doing so, we get:
Dividends per share last year = $1,113,636.36/350,000 shares = $3.18
10. The equity portion of capital outlays is the retained earnings. Subtracting dividends from net income, we get:
Equity portion of capital outlays = $1,200 – 480 = $720
Since the debt-equity ratio is .80, we can find the new borrowings for the company by multiplying the equity investment by the debt-equity ratio, so:
New borrowings = .80($720) = $576
And the total capital outlay will be the sum of the new equity and the new debt, which is:
Total capital outlays = $720 + 576 =$1,296.
11. a. The payout ratio is the dividend per share divided by the earnings per share, so:
Payout ratio = $0.80/$7
Payout ratio = .1143 or 11.43%
b. Under a residual dividend policy, the additions to retained earnings, which is the equity portion of the planned capital outlays, is the retained earnings per share times the number of shares outstanding, so:
Equity portion of capital outlays = 7M shares ($7 – .80) = $43.4M
The debt-equity ratio is the new borrowing divided by the new equity, so:
D/E ratio = $18M/$43.4M = .4147
12. a. Since the company has a debt-equity ratio of 3, they can raise $3 in debt for every $1 of equity. The maximum capital outlay with no outside equity financing is:
Maximum capital outlay = $180,000 + 3($180,000) = $720,000.
b. If planned capital spending is $760,000, then no dividend will be paid and new equity will be issued since this exceeds the amount calculated in a.
c. No, they do not maintain a constant dividend payout because, with the strict residual policy, the dividend will depend on the investment opportunities and earnings. As these two things vary, the dividend payout will also vary.
13. a. We can find the new borrowings for the company by multiplying the equity investment by the debt-equity ratio, so we get:
New debt = 2($56M) = $112M
Adding the new retained earnings, we get:
Maximum investment with no outside equity financing = $56M + 2($56M) = $168M
b. A debt-equity ratio of 2 implies capital structure is 2/3 debt and 1/3 equity. The equity portion of the planned new investment will be:
Equity portion of investment funds = 1/3($72M) = $24M
This is the addition to retained earnings, so the total available for dividend payments is:
Residual = $56M – 24M = $32M
This makes the dividend per share:
Dividend per share = $32M/12M shares = $2.67
c. The borrowing will be:
Borrowing = $72M – 24M = $48M
Alternatively, we could calculate the new borrowing as the weight of debt in the capital structure times the planned capital outlays, so:
Borrowing = 2/3($72M) = $48M
The addition to retained earnings is $24M, which we calculated in part b.
d. If the company plans no capital outlays, no new borrowing will take place. The dividend per share will be:
Dividend per share = $56M/12M shares = $4.67
Intermediate
14. The price of the stock today is the PV of the dividends, so:
P0 = $0.70/1.15 + $40/1.152 = $30.85
To find the equal two year dividends with the same present value as the price of the stock, we set up the following equation and solve for the dividend (Note: The dividend is a two year annuity, so we could solve with the annuity factor as well):
$30.85 = D/1.15 + D/1.152
D = $18.98
We now know the cash flow per share we want each of the next two years. We can find the price of stock in one year, which will be:
P1 = $40/1.15 = $34.78
Since you own 1,000 shares, in one year you want:
Cash flow in Year one = 1,000($18.98) = $18,979.07
But you’ll only get:
Dividends received in one year = 1,000($0.70) = $700.00
Thus, in one year you will need to sell additional shares in order to increase your cash flow. The number of shares to sell in year one is:
Shares to sell at time one = ($18,979.07 – 700)/$34.78 = 525.52 shares
At Year 2, you cash flow will be the dividend payment times the number of shares you still own, so the Year 2 cash flow is:
Year 2 cash flow = $40(1,000 – 525.52) = $18,979.07
15. If you only want $200 in Year 1, you will buy:
($700 – 200)/$34.78 = 14.38 shares
at time 1. Your dividend payment in Year 2 will be:
Year 2 dividend = (1,000 + 14.38)($40) = $40,575
Note, the present value of each cash flow stream is the same. Below we show this by finding the present values as:
PV = $200/1.15 + $40,575/1.152 = $30,854.44
PV = 1,000($0.70)/1.15 + 1,000($40)/1.152 = $30,854.44
16. a. If the company makes a dividend payment, we can calculate the wealth of a shareholder as:
Dividend per share = $5,000/200 shares = $25.00
The stock price after the dividend payment will be:
PX = $40 – 25 = $15 per share
The shareholder will have a stock worth $15 and a $25 dividend for a total wealth of $40. If the company makes a repurchase, the company will repurchase:
Shares repurchased = $5,000/$40 = 125 shares
If the shareholder lets their shares be repurchased, they will have $40 in cash. If the shareholder keeps their shares, they’re still worth $40.
b. If the company pays dividends, the current EPS is $0.95, and the P/E ratio is:
P/E = $15/$0.95 = 15.79
If the company repurchases stock, the number of shares will decrease. The total net income is the EPS times the current number of shares outstanding. Dividing net income by the new number of shares outstanding, we find the EPS under the repurchase is:
EPS = $0.95(200)/(200 – 125) = $2.53
The stock price will remain at $40 per share, so the P/E ratio is:
P/E = $40/$2.53 = 15.79
- A share repurchase would seem to be the preferred course of action. Only those shareholders who wish to sell will do so, giving the shareholder a tax timing option that he or she doesn’t get with a dividend payment.
Challenge
17. Assuming no capital gains tax, the aftertax return for the Gordon Company is the capital gains growth rate, plus the dividend yield times one minus the tax rate. Using the constant growth dividend model, we get:
Aftertax return = g + D(1 – t) = .15
Solving for g, we get:
.15 = g + .06(1 – .35)
g = .1110
The equivalent pretax return for Gecko Company, which pays no dividend, is:
Pretax return = g + D = .1110 + .06 = 17.10%
18. Using the equation for the decline in the stock price ex-dividend for each of the tax rate policies, we get:
(P0 – PX)/D = (1 – TP)/(1 – TG)
a. P0 – PX = D(1 – 0)/(1 – 0)
P0 – PX = D
b. P0 – PX = D(1 – .15)/(1 – 0)
P0 – PX = .85D
c. P0 – PX = D(1 – .15)/(1 – .20)
P0 – PX = 1.0625D
d. With this tax policy, we simply need to multiply the personal tax rate times one minus the dividend exemption percentage, so:
P0 – PX = D[1 – (.35)(.30)]/(1 – .65)
P0 – PX = 1.377D
e. Since different investors have widely varying tax rates on ordinary income and capital gains, dividend payments have different after-tax implications for different investors. This differential taxation among investors is one aspect of what we have called the clientele effect.
