CHAPTER 12
CAPITAL STRUCTURE CONCEPTS
ANSWERS TO QUESTIONS:
1. MM conclude that the value of a firm is independent of its capital structure in perfect capital
markets with no income taxes. However, when MM allow income taxes and bankruptcy costs
to exist, they show a value-maximizing capital structure that is less than 100 percent debt is
obtained. This is shown in Figure 12-4 in the text.
2. Without a corporate income tax (and without bankruptcy or agency costs), the value of the
firm is independent of capital structure. With a corporate income tax (and without bankruptcy
or agency costs), the value of the firm is maximized when its capital structure consists
entirely of debt. This is shown in Figure 12-3 in the text.
3. With a corporate income tax, bankruptcy costs and agency costs, the value of the firm is
maximized at a capital structure consisting of both debt and equity, as illustrated in Figure
12-4 in the text.
4. According to the asymmetric information concept, the officers and managers (i.e., insiders)
have access to information about the expected future earnings and cash flows of the firm that
is not available to outside investors. Given that managers have more information about the
firm than do outside investors, a company’s decisions to change its financial structure or
issue new securities can represent signals to investors concerning management’s assessment
of the expected future returns, and hence the market value, of the company.
5. According to the pecking order theory, if external financing is required, debt (the safest
security) should be issued first. Common equity is issued only as a last resort.
6. According to the pecking order theory, firms prefer internal financing to external financing
for two primary reasons:
• Internal financing is less costly than external financing because of the flotation costs
associated with new security issues.
• Internal financing avoids the discipline and monitoring associated with the issuance of
new securities to the public.
7. Assumptions:
• The firm’s investment policy is held constant, i.e. the level and variability of operating
income is not expected to change as a result of any changes in the firm’s capital structure.
• Perfect capital market conditions exist
• No transactions costs for buying and selling securities;
• Large number of buyers and sellers so that no one investor can have a significant
influence on security prices;
• Relevant information is available and costless to investors;
175
176  CHAPTER 12/CAPITAL STRUCTURE CONCEPTS
•
•
•
All investors can borrow and lend at the same rate;
All investors are rational and have homogeneous expectations about a firm’s earnings;
Firms operating under similar conditions are assumed to face the same degree of business
risk (the homogeneous risk class assumption).
8. Changes in capital structure, such as the issuance of new equity, new debt, or the retirement
of debt, repurchase of common stock, or retirement of preferred stock have been associated
with significant market reactions by investors. These events are thought to signal to investors
changes in the future prospects of the firm. Because of the well-documented market reaction
to capital structure changes, managers need to keep this in mind when they plan a
modification in the firm’s capital structure.
9. Arbitrage is the process of simultaneously buying and selling the same or equivalent
securities in different markets to take advantage of price differences and make a riskless
profit. If the stock price of a levered firm was greater than that of an otherwise equivalent
unlevered firm, investors could use an arbitrage process of selling the overpriced, levered
stock and borrowing and buying the unlevered firm’s stock. This process would have the
effect of decreasing the stock price of the levered firm and increasing the stock price of the
unlevered firm, until the price became equal.
10. Business risk refers to the variability or uncertainty of a firm’s operating income (EBIT).
Financial risk refers to the additional variability of earnings per share and the increased
probability of insolvency that arises when a firm uses fixed-cost sources of funds in its capital
structure.
11. Additional factors affecting business risk include:
• Variability of sales volumes over the business cycle
• Variability of selling prices
• Variability of costs
• Existence of market power
• Growth
CHAPTER 12/CAPITAL STRUCTURE CONCEPTS  177
SOLUTIONS TO PROBLEMS:
1. Value of firm L = D/ke + I/kd
= ($750/.15) + ($250/.05)
= $5,000 + $5,000
= $10,000
2. a
Value of levered firm = Value of unlevered firm
+ Value of tax shield
= $6,000 + ($3,000)(0.40)
= $7,200
b. Net operating income (EBIT)
Less: interest payments to debtholders, I
Income before taxes
Tax @ 40%
Income available to stockholders, D
Value of levered firm = $7,200 (from Part a)
Value of levered firm = D/ke + I/kd
$7,200 = ($510/ke) + $150/.05
ke = 12.1%
$1,000
150
$ 850
340
$ 510
178  CHAPTER 12/CAPITAL STRUCTURE CONCEPTS
3. a.
No Leverage, Inc. High Leverage, Inc.
Net operating income (EBIT)
$100,000
$100,000
---
$35,000
$100,000
$65,000
40,000
26,000
$60,000
$39,000
$60,000
$74,000
Less: interest payments (I)
Earnings before taxes
Income taxes (40%)
Income available to
stockholders (D)
Total income available to
security holders (I + D)
Market value (No Leverage) = $60,000/0.10 = $600,000
b. Market value (High Leverage) = $39,000/0.13 + $35,000/0.07
= $800,000
c. Present value (tax shield) = $500,000 x 0.40 = $200,000
4. a.
Proportion of Debt
Cost of Capital
0.00
ka = 12.0%
0.10
ka = (0.10)(4.7%) + 0.90(12.1%) = 11.36%
0.20
ka = (0.20)(4.9%) + (0.80)(12.5%) = 10.98%
0.30
ka = (0.30)(5.1%) + (0.70)(13.0%) = 10.63%
0.40
ka = (0.40)(5.5%) + (0.60)(13.9%) = 10.54%
0.50
ka = (0.50)(6.1%) + (0.50)(15.0%) = 10.55%
0.60
ka = (0.60)(7.5%) + (0.40)(17.0%) = 11.30%
Therefore, the optimal capital structure is approximately 40% debt and 60% equity.
b. 30% debt and 70% equity: ka = 10.63%
Optimal: ka = 10.54%
Difference: 0.09%
CHAPTER 12/CAPITAL STRUCTURE CONCEPTS  179
5. Piedmont Instrument
a. ka = (fraction of equity) (ke) + (fraction of debt) (ki)
(i) With financial distress costs and without agency costs:
Debt
Fraction
0.00
ka = 12.0%
0.10
ka = (0.9)(12.05) + (0.1)(4.8) = 11.33%
0.30
ka = (0.7)(12.1) + (0.3)(4.9) = 9.94%
0.40
ka = (0.6)(12.2) + (0.4)(5.0) = 9.32%
0.45
ka = (0.55)(12.4) + (0.45)(5.2) = 9.16%
0.50
ka = (0.5)(12.8) + (0.5)(5.7) = 9.25%
0.60
ka = (0.4)(15.0) + (0.6)(7.0) = 10.2%
Therefore, the optimal capital structure is approximately 45%
(ii)
With financial distress and agency costs:
Debt
Fraction
0.00
ka = 12.0%
0.10
ka = (0.9)(12.05) + (0.1)(4.8) = 11.33%
0.30
ka = (0.7)(12.20) + (0.3)(4.9) = 10.01%
0.40
ka = (0.6)(12.60) + (0.4)(5.0) = 9.56%
0.45
ka = (0.55)(13.4) + (0.45)(5.2) = 9.71%
0.50
ka = (0.5)(14.8) + (0.5)(5.7) = 10.25%
0.60
ka = (0.4)(18.0) + (0.6)(7.0) = 11.4%
Therefore, the optimal capital structure is approximately
40% debt + 60% equity.
b. 50% - 50% = 10.25%
optimal = 9.56%
0.69%
debt + 55% equity.
180  CHAPTER 12/CAPITAL STRUCTURE CONCEPTS
c. No, because in practice the optimal portion of the ka curve is saucer-shaped, i.e.,
relatively flat. This problem shows that the ka values at 40% and 45% debt differ only
slightly.
6. a. Leverage Ratio (Debt/Total Assets)
0%
25%
50%
Total assets
$10,000,000
$10,000,000
$10,000,000
Debt (12%)
0
2,500,000
5,000,000
Equity
10,000,000
7,500,000
5,000,000
Total liabilities and equity
$10,000,000
$10,000,000
$10,000,000
Expected operating income (EBIT) $2,500,000
$2,500,000
$2,500,000
Less: Interest (@ 12%)
0
300,000
600,000
Earnings before tax
2,500,000
2,200,000
1,900,000
Less: Income tax @ 40%
1,000,000
880,000
760,000
Earnings after tax
$1,500,000
$1,320,000
$1,140,000
Return on equity
15.0%
17.6%
22.8%
Expected operating income (EBIT) $2,000,000
$2,000,000
$2,000,000
Less: Interest (@ 12%)
0
300,000
600,000
Earnings before tax
2,000,000
1,700,000
1,400,000
Less: Income tax @ 40%
800,000
680,000
560,000
Earnings after tax
$1,200,000
$1,020,000
$840,000
Return on equity
12.0%
13.6%
16.8%
Effect of a 20% Decrease in EBIT to $2,000,000
CHAPTER 12/CAPITAL STRUCTURE CONCEPTS  181
Effect of a 20% Increase in EBIT to $3,000,000
Expected operating income (EBIT) $3,000,000
$3,000,000
$3,000,000
Less: Interest (@ 12%)
0
300,000
600,000
Earnings before tax
3,000,000
2,700,000
2,400,000
Less: Income tax @ 40%
1,200,000
1,080,000
960,000
Earnings after tax
$1,800,000
$1,620,000
1,440,000
Return on equity
18.0%
21.6%
28.8%
b. i. % change = [(12% - 15%)/15%] x 100% = -20%
ii. % change = -22.7%
iii. % change = 26.3%
c. i. % change = [(18% - 15%)/15%] x 100% = +20%
ii. % change = +22.7%
iii. % change = +26.3%
d. A leverage ratio of 50% yields the highest expected rate of return on equity.
e. A leverage ratio of 50% yields the highest variability of expected return on equity.
f. The cost of debt (12%) was assumed to remain constant under the various capital
structures. This may not be realistic since creditors normally require a higher rate of
return to compensate for the additional risk associated with increased leverage.
7. a.
Debt ratio
Pre-tax cost
Cost of equity
Weighted average cost
[B / (B + E)]
of debt (kd)
ke
of capital (ka)
0.00
–
12.0%
12.00%
0.15
7.0%
13.0
11.68
0.30
8.0
14.5
11.59
0.45
10.0
16.5
11.775
0.60
14.0
19.0
12.64
b. 30% debt and 70% equity minimizes the firm’s weighted cost of capital.
182  CHAPTER 12/CAPITAL STRUCTURE CONCEPTS
8. a.
Debt/Total Assets
Total Assets
Debt
Equity
Total Liabilities and
Equity
Expected EBIT
Interest
Earnings before
tax
Income tax
Earnings after tax
Return on equity
0%
$12,000,000
0
12,000,000
12,000,000
20%
$12,000,000
2,400,000
9,600,000
12,000,000
40%
$12,000,000
4,800,000
7,200,000
12,000,000
2,000,000
0
2,000,000
2,000,000
240,000
1,760,000
2,000,000
720,000
1,280,000
800,000
1,200,000
10.0%
704,000
1,056,000
11.0%
512,000
768,000
10.67%
b. 20 percent debt and 80 percent equity.
c. 20 percent decrease in EBIT to $1,600,000
Expected EBIT
Interest
Earnings before
tax
Income tax
Earnings after tax
Return on equity
1,600,000
0
1,600,000
1,600,000
240,000
1,360,000
1,600,000
720,000
880,000
640,000
960,000
8.0%
544,000
816,000
8.5%
352,000
528,000
7.33%
d. 20 percent debt and 80 percent equity
e. 20 percent increase in EBIT to $2,400,000
Expected EBIT
Interest
Earnings before
tax
Income tax
Earnings after tax
Return on equity
2,400,000
0
2,400,000
2,400,000
240,000
2,160,000
2,400,000
720,000
1,680,000
960,000
1,040,000
8.67%
864,000
1,296,000
13.5%
672,000
1,008,000
14.0 %
f. 40 percent debt and 60 percent equity.
9.
Debt Ratio
0.00
Pre-tax cost of debt
--
Cost of equity
14.0%
Weighted Cost of
Capital
14.0%
CHAPTER 12/CAPITAL STRUCTURE CONCEPTS  183
0.10
0.20
0.30
0.40
0.50
0.60
7.0%
7.2
7.6
8.2
9.0
10.0
14.2
14.6
15.4
17.0
20.0
26.0
The optimal capital structure is 30 percent debt and 70 percent equity.
10. No recommended solution.
13.20
12.54
12.15
12.17
12.70
14.00