Does Debt Policy Matter?
1. a. The two firms have equal value; let V represent the total value of the firm. Rosencrantz could buy one percent of Company B’s equity and borrow an amount equal to:
0.01 ´ (D_{A}  D_{B}) = 0.002V
This investment requires a net cash outlay of (0.007V) and provides a net cash return of:
(0.01 ´ Profits) – (0.003 ´ r_{f} ´ V)
where r_{f} is the riskfree rate of interest on debt. Thus, the two investments are identical.
b. Guildenstern could buy two percent of Company A’s equity and lend an amount equal to:
0.02 ´ (D_{A}  D_{B}) = 0.004V
This investment requires a net cash outlay of (0.018V) and provides a net cash return of:
(0.02 ´ Profits) – (0.002 ´ r_{f} ´ V)
Thus the two investments are identical.
c. The expected dollar return to Rosencrantz’ original investment in A is:
(0.01 ´ C) – (0.003 ´ r_{f} ´ V_{A})
where C is the expected profit (cash flow) generated by the firm’s assets. Since the firms are the same except for capital structure, C must also be the expected cash flow for Firm B. The dollar return to Rosencrantz’ alternative strategy is:
(0.01 ´ C) – (0.003 ´ r_{f} ´ V_{B})
Also, the cost of the original strategy is (0.007V_{A}) while the cost of the alternative strategy is (0.007V_{B}).
If V_{A} is less than V_{B}, then the original strategy of investing in Company A would provide a larger dollar return at the same time that it would cost less than the alternative. Thus, no rational investor would invest in Company B if the value of Company A were less than that of Company B.
2. When a firm issues debt, it shifts its cash flow into two streams. MM’s Proposition I states that this does not affect firm value if the investor can reconstitute a firm’s cash flow stream by creating personal leverage or by undoing the effect of the firm’s leverage by investing in both debt and equity.
It is similar with Carruther’s cows. If the cream and skim milk go into the same pail, the cows have no special value. (If an investor holds both the debt and equity, the firm does not add value by splitting the cash flows into the two streams.) In the same vein, the cows have no special value if a dairy can costlessly split up whole milk into cream and skim milk. (Firm borrowing does not add value if investors can borrow on their own account.) Carruther’s cows will have extra value if consumers want cream and skim milk and if the dairy cannot split up whole milk, or if it is costly to do so.
3. The company cost of capital is:
r_{A} = (0.8 ´ 0.12) + (0.2´ 0.06) = 0.108 = 10.8%
Under Proposition I, this is unaffected by capital structure changes. With the bonds remaining at the 6 percent defaultrisk free rate, we have:
DebtEquity Ratio 

r_{E} 

r_{A} 
0.00 

0.108 

0.108 
0.10 

0.113 

0.108 
0.50 

0.132 

0.108 
1.00 

0.156 

0.108 
2.00 

0.204 

0.108 
3.00 

0.252 

0.108 
See figure on next page.
4. This is not a valid objection. MM’s Proposition II explicitly allows for the rates of return for both debt and equity to increase as the proportion of debt in the capital structure increases. The rate for debt increases because the debtholders are taking on more of the risk of the firm; the rate for common stock increases because of increasing financial leverage. See Figure 17.2 and the accompanying discussion.
_{ }
5. a. Under Proposition I, the firm’s cost of capital (r_{A}) is not affected by the choice of capital structure. The reason the quoted statement seems to be true is that it does not account for the changing proportions of the firm financed by debt and equity. As the debtequity ratio increases, it is true that both the cost of equity and the cost of debt increase, but a smaller proportion of the firm is financed by equity. The overall effect is to leave the firm’s cost of capital unchanged.
b. Moderate borrowing does not significantly affect the probability of financial distress, but it does increase the variability (and market risk) borne by stockholders. This additional risk must be offset by a higher average return to stockholders.
6. a. If the opportunity were the firm’s only asset, this would be a good deal. Stockholders would put up no money and, therefore, would have nothing to lose. However, rational lenders will not advance 100 percent of the asset’s value for an 8 percent promised return unless other assets are put up as collateral.
Sometimes firms find it convenient to borrow all the cash required for a particular investment. Such investments do not support all of the additional debt; lenders are protected by the firm’s other assets too.
In any case, if firm value is independent of leverage, then any asset’s contribution to firm value must be independent of how it is financed. Note also that the statement ignores the effect on the stockholders of an increase in financial leverage.
b. This is not an important reason for conservative debt levels. So long as MM’s Proposition I holds, the company’s overall cost of capital is unchanged despite increasing interest rates paid as the firm borrows more. (However, the increasing interest rates may signal an increasing probability of financial distress—and that can be important.
7. Examples of such securities are given in the text and include unbundled stock units, preferred equity redemption cumulative stock and floatingrate notes. Note that, in order to succeed, such securities must both meet regulatory requirements and appeal to an unsatisfied clientele.
8. Why does share price drop during a recession? Because forecasted cash flows to stockholders decline. (Stockholders may also perceive higher risks and demand a higher expected rate of return.) The stock price will decline to the point where the expected return to the stock, given the amount of debt, is a ‘fair’ return.
Suppose that a recession hits and stock price declines. Would the cost of capital for new investment be less if the firm had used more debt in the past? No, the firm’s past financing decisions are bygones. Moreover, MM’s Proposition I holds in recessions as well as booms. The firm’s overall cost of capital is independent of its debt ratio.
Incidentally, the more debt a firm has, the greater the percentage decline in the value of its shares as a result of a recession or any other unfortunate event.
9. a. As the debt/equity ratio increases, both the cost of debt capital and the cost of equity capital increase. The cost of debt capital increases because increasing the debt/equity ratio increases the risk of default so that bondholders require a higher rate of return to compensate for the increase in risk. The cost of equity capital increases because increasing the debt/equity ratio increases the financial risk borne by the stockholders; a higher rate of return is required to compensate for this increase in risk.
b. For higher levels of the debt/equity ratio, we have the cost of debt capital increasing and approaching (but never being equal to, or greater than) the cost of capital for the firm. Similarly, the cost of equity capital will also continue to rise; in particular, it can not decrease beyond a certain point.
10. a. As leverage is increased, the cost of equity capital rises. This is the same as saying that, as leverage is increased, the ratio of the income after interest (which is the cash flow stockholders are entitled to) to the value of equity increases. Thus, as leverage increases, the ratio of the market value of the equity to income after interest decreases.
b. (i) Assume MM are correct. The market value of the firm is determined by the income of the firm, not how it is divided among the firm’s security holders. Also, the firm’s income before interest is independent of the firm’s financing. Thus, both the value of the firm and the value of the firm’s income before interest remain constant as leverage is increased. Hence, the ratio is a constant.
(ii) Assume the traditionalists are correct. The firm’s income before interest is independent of leverage. As leverage increases, the firm’s cost of capital first decreases and then increases; as a result, the market value of the firm first increases and then decreases. Thus, the ratio of the market value of the firm to firm income before interest first increases and then decreases, as leverage increases.
11. We begin with r_{E} and the capital asset pricing model:
r_{E} = r_{f} + b_{E} (r_{m}  r_{f})
r_{E} = 0.10 + 1.5 (0.18  0.10) = 0.22 = 22.0%
Similarly for debt:
r_{D} = r_{f} + b_{D} (r_{m}  r_{f})
0.12 = 0.10 + b_{D} (0.18 – 0.10)
b_{D} = 0.25
Also, we know that:
_{}
To solve for b_{A}, use the following:
_{}
12. We know from Proposition I that the value of the firm will not change. Also, because the expected operating income is unaffected by changes in leverage, the firm’s overall cost of capital will not change. In other words, r_{A} remains equal to 17% and b_{A} remains equal to 0.875. However, risk and, hence, the expected return for equity and for debt, will change. We know that r_{D} is 11%, so that, for debt:
r_{D} = r_{f} + b_{D} (r_{m}  r_{f})
0.11 = 0.10 + b_{D} (0.18  0.10)
b_{D} = 0.125
For equity:
_{}
0.17 = (0.3 ´ 0.11) + (0.7 ´ r_{E})
r_{E} = 0.196 = 19.6%
Also:
r_{E} = r_{f} + b_{E} (r_{m}  r_{f})
0.196 = 0.10 + b_{E} (0.18  0.10)
b_{E} = 1.20
13. Before the refinancing, Schuldenfrei is all equity financed. The equity beta is 0.8 and the expected return on equity is 8%. Thus, the firm’s asset beta is 0.8 and the firm’s cost of capital is 8%. We know that these overall firm values will not change after the refinancing and that the debt is riskfree.
a. _{}
0.8 = (0.5 ´ 0) + (0.5 ´ b_{E})
b_{E} = 1.60
b. Before the refinancing, the stock’s required return is 8% and the riskfree rate is 5%; thus, the risk premium for the stock is 3%.
c. After the refinancing:
_{}
0.08 = (0.5 ´ 0.05) + (0.5 ´ r_{E})
r_{E} = 0.11 = 11.0%
After the refinancing, the risk premium for the stock is 6%.
d. The required return for the debt is 5%, the riskfree rate.
e. The required return for the company remains at 8%.
f. Let E be the operating profit of the company and N the number of shares outstanding before the refinancing. Also, we know that E is (0.08V). Thus, the earnings per share before the refinancing is:
EPS_{B} = 0.08V/N
After the refinancing the operating profit is still E and the number of shares is (0.5 ´ N). Interest on the debt is 5% of the value of the debt, which is (0.5 ´ V). Thus, the earnings per share after the refinancing is:
EPS_{A} = [0.08V – (0.05 ´ 0.5 ´ V)]/(0.5 ´ N) = 0.11V/N
It follows that earnings per share has increased by 37.5%.
g. Before the refinancing, the P/E ratio is 12.5. The price of the common stock is the same before and after the refinancing, but the earnings per share has increased from (0.08V/N) to (0.11V/N). (See Part (f) above.) Thus, the new P/E ratio is 9.09.
14. We make use of the basic relationship:
_{}
If the company is allequityfinanced and the cost of equity capital (r_{E}) is 18%, then the company cost of capital (r_{A}) is 18%, which will not change as the capital structure changes. In addition, we know that the riskfree rate (r_{f}) is 10% and that Gamma’s debt is riskfree. Thus:
D/E 

r_{A} 

r_{D} 

r_{E} 
0 

0.18 

0.10 

0.18 
1 

0.18 

0.10 

0.26 
2 

0.18 

0.10 

0.34 
3 

0.18 

0.10 

0.42 
D/V 

r_{A} 

r_{D} 

r_{E} 
0 

0.18 

0.10 

0.180 
0.25 

0.18 

0.10 

0.207 
0.50 

0.18 

0.10 

0.260 
0.75 

0.18 

0.10 

0.420 
15. a. Because the firms are identical except for capital structure, and there are no taxes or other market imperfections, the total values of these companies must be the same. Thus, L’s stock is worth:
($500  $400) = $100.
b. If you own $20 of U’s common stock, you own 4% of the outstanding shares and, thus, are entitled to (0.04 ´ $150) = $6 if there is a boom and (0.04 ´ $50) = $2 if there is a slump.
The equivalent investment is to purchase 4% of L’s outstanding stock, which will cost (0.04 ´ $100) = $4, and to invest $16 at the riskfree rate. The total amount invested is the same ($20). In a boom, you are entitled to: [(0.10 ´ $16) + (0.04) ´ ($150  $40)] = $6, and in a slump you are entitled to: [(0.10 ´ $16) + (0.04) ´ ($50  $40)] = $2.
c. If you own $20 of L’s common stock, you own 20% of the outstanding shares and, thus, are entitled to [0.20 ´ ($150  $40)] = $22 if there is a boom, and [0.20 ´ ($50  $40) = $2 if there is a slump.
The equivalent investment is to purchase 20% of U’s outstanding stock, which costs: (0.20 ´ $500) = $100 and to borrow $80 at the riskfree rate. The total invested is the same ($20). In a boom you are entitled to:
[(0.10) ´ ($80) + (0.20 ´ $150)] = $22 and in a slump you are entitled to: [(0.10) ´ ($80) + (0.20 ´ $50)] = $2.
d. Proposition II can be stated as follows:
_{}
_{ }For U, the expected return on assets is:
_{}
Thus, for both companies, r_{A} is 20%. For L, the expected return on equity is:
_{}
This is the same result we derive from the Proposition II formula:
r_{E} = 0.20 + [4 ´ (0.20  0.10) = 0.60 = 60%
Challenge Questions
1. Assume the election is near so that we can safely ignore the time value of money.
Because one, and only one, of three events will occur, the guaranteed payoff from holding all three tickets is $10. Thus, the three tickets, taken together, could never sell for less than $10. This is true whether they are bundled into one composite security or unbundled into three separate securities.
However, unbundled they may sell for more than $10. This will occur if the separate tickets fill a need for some currently unsatisfied clientele. If this is indeed the case, Proposition I fails. The sum of the parts is worth more than the whole.
2. Some shoppers may want only the chicken drumstick. They could buy a whole chicken, cut it up, and sell off the other parts in the supermarket parking lot. This is costly. It is far more efficient for the store to cut up the chicken and sell the pieces separately. But this also has some cost, hence the observation that supermarkets charge more for chickens after they have been cut.
The same considerations affect financial products, but:
a. The proportionate costs to companies of repackaging the cash flow stream are generally small.
b. Investors can also repackage cash flows cheaply for themselves. In fact, specialist financial institutions can often do so more cheaply than the companies can do it themselves.