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Capital Structure Determination
When you have eliminated the impossible, whatever
remains, however improbable, must be the truth.
SHERLOCK HOLMES
IN THE SIGN OF THE FOUR
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ANSWERS TO QUESTIONS
1. The net operating income (NOI) approach and the Modigliani-Miller (M&M) approach, in
the absence of taxes, are identical in form. The only difference is that M&M specify the
2. The optimal capital structure would differ from one industry to another because each
industry has a different level of business risk. The higher the level of business risk, the
3. Many factors influence the interest rate a firm must pay for debt funds. Some factors are
external to the firm. For example, the expected inflation rate, the Federal Reserve’s activity
4. The
total-value principle states that a corporation is valued on the basis of its earnings’
potential and its business risk. The total “pie” of value stays the same regardless of how it is
5. Arbitrage implies that an identical product cannot sell for different prices in different
markets. If it does, arbitragers will buy in one market and sell in another to earn an arbitrage
profit with no risk to them. These actions will cause the price of one asset to rise and the
6. Without financial-market imperfections, variation in capital structure would have no impact
on share price. Capital structure decisions would be irrelevant, as suggested by Modigliani-
Miller. Market imperfections take us away from a frictionless world and reduce the
7. Bankruptcy costs include out-of-pocket expenses to lawyers, accountants, appraisers,
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8. For reasons of prudence as well as legal reasons, institutional investors will not lend money
to a company that has excessive financial leverage. Both the investors, under state
9. Without the payment of taxes, the corporate tax-shield due to debt, disappears and so too
10. Debt financing would decrease on a relative basis, all other things being the same. The tax
11. The tax effect associated with debt and equity financing would be the same, as opposed to
12. If there is asymmetric information between management and investors, the former might
signal via capital structure. The implication is that management would not bind itself to the
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SOLUTIONS TO PROBLEMS
1. a.
O Net operating income $10,000,000
I Interest on debt 1,400,000
b.
O Net operating income $10,000,000
k
o Overall capitalization rate ÷ 0.1126126
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2. a. (i) Sell your Gottahave stock for $22,500.
Your net dollar return, $3,600, is the same as it was for your investment in
b. When there is no further opportunity for employing fewer funds and achieving the same
3. a. $400,000 in debt. The market price per share of common stock is highest at this amount
of financial leverage.
b. (000s omitted)
# shares B EBIT I EBT EAT
100 $ 0 $250 $ 0.0 $250.0 $125.00
ki EPS P ke = EPS/P S = (# shares) × P V = B + S
— $1.25 $10.00 12.5% $1,000.0 $1000.0
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ki(B/V) + ke(S/V) = ko
(12.5%)($1,000/$1,000.0) = 12.50%
(5.00%)($100/$1,000.0) + (13.3%)($900.0/$1,000.0) = 12.47
c. Yes. The optimal capital structure – the one possessing the lowest overall cost of capital
– involves $400,000 in debt.
4. a.
All-equity Debt and Equity
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5.
(in millions)
(1)
Debt
(2)
Value of Unlevered
Firm
(3)
PV of tax- shield
benefits
(1) × 0.22
(4)
PV of
Bankruptcy
Costs
(5)
Value of
Levered Firm
(2) + (3) – (4)
$0 $10 $0.00 $0.00 $10.00
1 10 0.22 0.00 10.22
*The optimal amount of debt would be $5 million.
6. a. without bankruptcy costs
[ki × (B/V)] + [ke × (S/V)] = ko
(10.00%) (1.00) = 10.000%
(4.00%) (0.10) + (10.50%) (0.90) = 9.850%
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b. with bankruptcy costs
[ki × (B/V)] + [ke × (S/V)] = ko
(10.00%)(1.00) = 10.000%
(4.00%)(0.10) + (10.50%)(0.90) = 9.850%
With bankruptcy costs, the optimal capital structure is 40 percent debt in contrast to 60
percent bankruptcy costs.
7. According to the notion of asymmetric information between management and investors, the
company should issue the overvalued security, or at least the one that is not undervalued in
In contrast, if the common stock were believed to be overvalued, management would want
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SOLUTIONS TO SELF-CORRECTION PROBLEMS
1. a. Qwert Typewriter Company:
O Net operating income $ 360,000
k
o Overall capitalization rate ÷ 0.18
b. Yuiop Typewriters, Inc.:
O Net operating income $ 360,000
k
o Overall capitalization rate ÷ 0.18
Yuiop has a lower equity capitalization rate than Qwert, because Yuiop uses less debt in
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2. Value of firm if unlevered:
Earnings before interest and taxes $ 3,000,000
Value with $4 million in debt:
Value of
levered firm = Value of firm
if unlevered + Present value of
tax-shield benefits of debt
Value with $7 million in debt:
Due to the tax subsidy, the firm is able to increase its value in a linear manner with more
debt.
3. (In millions):
(1)
Level
of
Debt
(2)
Firm
Value
Unlevered
(3)
PV of Tax-Shield
Benefits Of Debt
(1) × 0.20
(4)
PV of Bankruptcy,
Agency & Increased
Interest Costs
Value of Firm
(2)+(3)–(4)
$ 0 $15 $0 $0.0 $15.0
5 15 1 0.0 16.0
*The market value of the firm is maximized with $20 million in debt.