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17.2 HOW LEVERAGE AFFECTS RETURNS

Implications of Proposition I

Consider now the implications of proposition I for the expected returns on Macbeth stock:

Leverage increases the expected stream of earnings per share but not the share price. The reason is that the change in the expected earnings stream is exactly offset by a change in the rate at which the earnings are capitalized. The expected return on the share (which for a perpetuity is equal to the earnings–price ratio) increases from 15 to 20 percent. We now show how this comes about.

The expected return on Macbeth’s assets rA is equal to the expected operating income divided by the total market value of the firm’s securities:

expected operating income Expected return on assets rA market value of all securities

We have seen that in perfect capital markets the company’s borrowing decision does not affect either the firm’s operating income or the total market value of its securities. Therefore the borrowing decision also does not affect the expected return on the firm’s assets rA.

Suppose that an investor holds all of a company’s debt and all of its equity. This investor would be entitled to all the firm’s operating income; therefore, the expected return on the portfolio would be equal to rA.

The expected return on a portfolio is equal to a weighted average of the expected returns on the individual holdings. Therefore the expected return on a portfolio consisting of all the firm’s securities is6

D E

rA aD E rD b aD E rE b

We can rearrange this equation to obtain an expression for rE, the expected return on the equity of a levered firm:

6This equation should look familiar. We introduced it in Chapter 9 when we showed that the company cost of capital is a weighted average of the expected returns on the debt and equity. (Company cost of capital is simply another term for the expected return on assets, rA.) We also stated in Chapter 9 that changing the capital structure does not change the company cost of capital. In other words, we implicitly assumed MM’s proposition I.

Look at what happens to the risk of Macbeth shares if it moves to equal debt– equity proportions. Table 17.4 shows how a shortfall in operating income affects the payoff to the shareholders.

The debt–equity proportion does not affect the dollar risk borne by equityholders. Suppose operating income drops from $1,500 to $500. Under all-equity financing, equity earnings drop by $1 per share. There are 1,000 outstanding shares, and so total equity earnings fall by $1 1,000 $1,000. With 50 percent debt, the same drop in operating income reduces earnings per share by $2. But there are only 500 shares outstanding, and so total equity income drops by $2 500 $1,000, just as in the all-equity case.

However, the debt–equity choice does amplify the spread of percentage returns. If the firm is all-equity-financed, a decline of $1,000 in the operating income reduces the return on the shares by 10 percent. If the firm issues risk-free debt with a fixed interest payment of $500 a year, then a decline of $1,000 in the operating income reduces the return on the shares by 20 percent. In other words,

the effect of leverage is to double the amplitude of the swings in Macbeth’s shares. Whatever the beta of the firm’s shares before the refinancing, it would be twice as high afterward.

Just as the expected return on the firm’s assets is a weighted average of the expected return on the individual securities, so likewise is the beta of the firm’s assets a weighted average of the betas of the individual securities:7

We can rearrange this equation also to give an expression for E, the beta of the equity of a levered firm:

Now you can see why investors require higher returns on levered equity. The required return simply rises to match the increased risk.

In Figure 17.3, we have plotted the expected returns and the risk of Macbeth’s securities, assuming that the interest on the debt is risk-free.8

7This equation should also look old-hat. We used it in Section 9.3 when we stated that changes in the capital structure change the beta of stock but not the asset beta.

8In this case D 0 and E A 1D/E 2 A.

Anything that increases the value of the firm reduces the weighted-average cost of capital if operating income is constant. But if operating income is varying too, all bets are off.

In Chapter 18 we will show that financial leverage can affect operating income in several ways. Therefore maximizing the value of the firm is not always equivalent to minimizing the weighted-average cost of capital.

Warning 1 Shareholders want management to increase the firm’s value. They are more interested in being rich than in owning a firm with a low weighted-average cost of capital.

Warning 2 Trying to minimize the weighted-average cost of capital seems to encourage logical short circuits like the following. Suppose that someone says, “Shareholders demand—and deserve—higher expected rates of return than bondholders do. Therefore debt is the cheaper capital source. We can reduce the weighted-average cost of capital by borrowing more.” But this doesn’t follow if the extra borrowing leads stockholders to demand a still higher expected rate of return. According to MM’s proposition II the cost of equity capital rE increases by just enough to keep the weighted-average cost of capital constant.

This is not the only logical short circuit you are likely to encounter. We have cited two more in practice question 5 at the end of this chapter.

Rates of Return on Levered Equity—The Traditional Position

You may ask why we have even mentioned the aim of minimizing the weightedaverage cost of capital if it is often wrong or confusing. We had to because the traditionalists accept this objective and argue their case in terms of it.

The logical short circuit we just described rested on the assumption that rE, the expected rate of return demanded by stockholders, does not rise as the firm borrows more. Suppose, just for the sake of argument, that this is true. Then rA, the weighted-average cost of capital, must decline as the debt–equity ratio rises.

Take Figure 17.4, for example, which is drawn on the assumption that shareholders demand 12 percent no matter how much debt the firm has and that bondholders always want 8 percent. The weighted-average cost of capital starts at 12 percent and ends up at 8. Suppose that this firm’s operating income is a level, perpetual stream of $100,000 a year. Then firm value starts at

V 100,000 $833,333

.12

and ends up at

V 100,000 $1,250,000

.08

The gain of $416,667 falls into the stockholders’ pockets.11

Of course this is absurd: A firm that reaches 100 percent debt has to be bankrupt. If there is any chance that the firm could remain solvent, then the equity retains

11Note that Figure 17.4 relates rE and rD to D/V, the ratio of debt to firm value, rather than to the debt– equity ratio D/E. In this figure we wanted to show what happens when the firm is 100 percent debtfinanced. At that point E 0 and D/E is infinite.

some value, and the firm cannot be 100 percent debt-financed. (Remember that we are working with the market values of debt and equity.)

But if the firm is bankrupt and its original shares are worthless pieces of paper, then its lenders are its new shareholders. The firm is back to all-equity financing! We assumed that the original stockholders demanded 12 percent—why should the new ones demand any less? They have to bear all of the firm’s business risk.12

The situation described in Figure 17.4 is just impossible.13 However, it is possible to stake out a position somewhere between Figures 17.3 and 17.4. That is exactly what the traditionalists have done. Their hypothesis is shown in Figure 17.5. They hold that a moderate degree of financial leverage may increase the expected equity return rE, although not to the degree predicted by MM’s proposition II. But irresponsible firms that borrow excessively find rE shooting up faster than MM predict. Consequently, the weighted-average cost of capital rA declines at first, then rises. Its minimum point is the point of optimal capital structure. Remember that minimizing rA is equivalent to maximizing overall firm value if, as the traditionalists assume, operating income is unaffected by borrowing.

Two arguments might be advanced in support of the traditional position. First, it could be that investors don’t notice or appreciate the financial risk created by “moderate” borrowing, although they wake up when debt is “excessive.” If so, investors in moderately leveraged firms may accept a lower rate of return than they really should.

12We ignore the costs, delays, and other complications of bankruptcy. They are discussed in Chapter 18.

13This case is often termed the net-income (NI) approach because investors are assumed to capitalize income after interest at the same rate regardless of financial leverage. In contrast, MM’s approach is a net- operating-income (NOI) approach because the value of the firm is fundamentally determined by operating income, the total dollar return to both bondholders and stockholders. This distinction was emphasized by D. Durand in his important, pre-MM paper, “Cost of Debt and Equity Funds for Business: Trends and Problems of Measurement,” in Conference on Research in Business Finance, National Bureau of Economic Research, New York, 1952.

That seems naive.14 The second argument is better. It accepts MM’s reasoning as applied to perfect capital markets but holds that actual markets are imperfect. Imperfections may allow firms that borrow to provide a valuable service for investors. If so, levered shares might trade at premium prices compared to their theoretical values in perfect markets.

Suppose that corporations can borrow more cheaply than individuals. Then it would pay investors who want to borrow to do so indirectly by holding the stock of levered firms. They would be willing to live with expected rates of return that do not fully compensate them for the business and financial risk they bear.

Is corporate borrowing really cheaper? It’s hard to say. Interest rates on home mortgages are not too different from rates on high-grade corporate bonds.15 Rates on margin debt (borrowing from a stockbroker with the investor’s shares tendered as security) are not too different from the rates firms pay banks for short-term loans.

There are some individuals who face relatively high interest rates, largely because of the costs lenders incur in making and servicing small loans. There are economies of scale in borrowing. A group of small investors could do better by borrowing via a corporation, in effect pooling their loans and saving transaction costs.16

14This first argument may reflect a confusion between financial risk and the risk of default. Default is not a serious threat when borrowing is moderate; stockholders worry about it only when the firm goes “too far.” But stockholders bear financial risk—in the form of increased volatility of rate of return and higher beta—even when the chance of default is nil. We demonstrated this in Figure 17.3.

15One of the authors once obtained a home mortgage at a rate 1⁄2 percentage point less than the contemporaneous yield on long-term AAA bonds.

16Even here there are alternatives to borrowing on personal account. Investors can draw down their savings accounts or sell a portion of their investment in bonds. The impact of reductions in lending on the investor’s balance sheet and risk position is exactly the same as increases in borrowing.

But suppose that this class of investors is large, both in number and in the aggregate wealth it brings to capital markets. Shouldn’t the investors’ needs be fully satisfied by the thousands of levered firms already existing? Is there really an unsatisfied clientele of small investors standing ready to pay a premium for one more firm that borrows?

Maybe the market for corporate leverage is like the market for automobiles. Americans need millions of automobiles and are willing to pay thousands of dollars apiece for them. But that doesn’t mean that you could strike it rich by going into the automobile business. You’re at least 50 years too late.

Where to Look for Violations of MM’s Propositions

MM’s propositions depend on perfect capital markets. We believe capital markets are generally well-functioning, but they are not 100 percent perfect 100 percent of the time. Therefore, MM must be wrong some times in some places. The financial manager’s problem is to figure out when and where.

That is not easy. Just finding market imperfections is insufficient.

Consider the traditionalists’ claim that imperfections make borrowing costly and inconvenient for many individuals. That creates a clientele for whom corporate borrowing is better than personal borrowing. That clientele would, in principle, be willing to pay a premium for the shares of a levered firm.

But maybe it doesn’t have to pay a premium. Perhaps smart financial managers long ago recognized this clientele and shifted the capital structures of their firms to meet its needs. The shifts would not have been difficult or costly to make. But if the clientele is now satisfied, it is no longer willing to pay a premium for levered shares. Only the financial managers who first recognized the clientele extracted any advantage from it.

Today’s Unsatisfied Clienteles Are Probably Interested in Exotic Securities

So far we have made little progress in identifying cases where firm value might plausibly depend on financing. But our examples illustrate what smart financial managers look for. They look for an unsatisfied clientele, investors who want a particular kind of financial instrument but because of market imperfections can’t get it or can’t get it cheaply.

MM’s proposition I is violated when the firm, by imaginative design of its capital structure, can offer some financial service that meets the needs of such a clientele. Either the service must be new and unique or the firm must find a way to provide some old service more cheaply than other firms or financial intermediaries can.

Now, is there an unsatisfied clientele for garden-variety debt or levered equity? We doubt it. But perhaps you can invent an exotic security and uncover a latent demand for it.

In the next several chapters we will encounter a number of new securities that have been invented by companies and advisers. These securities take the company’s basic cash flows and repackage them in ways that are thought to be more attractive to investors. However, while inventing these new securities is easy, it is more difficult to find investors who will rush to buy them.17

Imperfections and Opportunities

The most serious capital market imperfections are often those created by government. An imperfection which supports a violation of MM’s proposition I also cre-

17We return to the topic of security innovation in Section 25.8.