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SUMMARY At the start of this chapter we characterized the firm’s financing decision as a mar- keting problem. Think of the financial manager as taking all of the firm’s real as-

sets and selling them to investors as a package of securities. Some financial managers choose the simplest package possible: all-equity financing. Some end up issuing dozens of debt and equity securities. The problem is to find the particular combination that maximizes the market value of the firm.

Modigliani and Miller’s (MM’s) famous proposition I states that no combination is better than any other—that the firm’s overall market value (the value of all its securities) is independent of capital structure. Firms that borrow do offer investors a more complex menu of securities, but investors yawn in response. The menu is redundant. Any shift in capital structure can be duplicated or “undone” by investors. Why should they pay extra for borrowing indirectly (by holding shares in a levered firm) when they can borrow just as easily and cheaply on their own accounts?

MM agree that borrowing increases the expected rate of return on shareholders’ investments. But it also increases the risk of the firm’s shares. MM show that the risk increase exactly offsets the increase in expected return, leaving stockholders no better or worse off.

Proposition I is an extremely general result. It applies not just to the debt–equity trade-off but to any choice of financing instruments. For example, MM would say that the choice between long-term and short-term debt has no effect on firm value.

The formal proofs of proposition I all depend on the assumption of perfect capital markets.19 MM’s opponents, the “traditionalists,” argue that market imperfections make personal borrowing excessively costly, risky, and inconvenient for some investors. This creates a natural clientele willing to pay a premium for shares of levered firms. The traditionalists say that firms should borrow to realize the premium.

But this argument is incomplete. There may be a clientele for levered equity, but that is not enough; the clientele has to be unsatisfied. There are already thousands of levered firms available for investment. Is there still an unsatiated clientele for garden-variety debt and equity? We doubt it.

Proposition I is violated when financial managers find an untapped demand and satisfy it by issuing something new and different. The argument between MM and the traditionalists finally boils down to whether this is difficult or easy. We lean toward MM’s view: Finding unsatisfied clienteles and designing exotic securities to meet their needs is a game that’s fun to play but hard to win.

19Proposition I can be proved umpteen different ways. The references at the end of this chapter include several more abstract and general proofs. Our formal proofs have been limited to MM’s own arguments.

MM provided a shorter and clearer proof of capital structure irrelevance in:

F.Modigliani and M. H. Miller: “Reply to Heins and Sprenkle,” American Economic Review, 59:592–595 (September 1969).

A somewhat difficult article which analyzes capital structure in the context of capital asset pricing theory is:

R. S. Hamada: “Portfolio Analysis, Market Equilibrium and Corporation Finance,” Journal of Finance, 24:13–31 (March 1969).

More abstract and general theoretical treatments can be found in:

J.E. Stiglitz: “On the Irrelevance of Corporate Financial Policy,” American Economic Review, 64:851–866 (December 1974).

E.F. Fama: “The Effects of a Firm’s Investment and Financing Decisions,” American Economic Review, 68:272–284 (June 1978).

The fall 1988 issue of the Journal of Economic Perspectives contains an anniversary collection of articles, including one by Modigliani and Miller, which review and assess the MM propositions. The summer 1989 issue of Financial Management contains three more articles under the heading “Reflections on the MM Propositions 30 Years Later.”

1. Assume a perfectly competitive market with no corporate or personal taxes. Compa- QUIZ nies A and B each earn gross profits of P and differ only in their capital structure—A is

wholly equity-financed and B has debt outstanding on which it pays a certain $100 of interest each year. Investor X purchases 10 percent of the equity of A.

a.What profits does X obtain?

b.What alternative strategy would provide the same result?

c.Suppose investor Y purchases 10 percent of the equity of B. What profits does Y obtain?

d.What alternative strategy would provide the same result?

2.Ms. Kraft owns 50,000 shares of the common stock of Copperhead Corporation with a market value of $2 per share, or $100,000 overall. The company is currently financed as follows:

Copperhead now announces that it is replacing $1 million of short-term debt with an issue of common stock. What action can Ms. Kraft take to ensure that she is entitled to exactly the same proportion of profits as before? (Ignore taxes.)

3.The common stock and debt of Northern Sludge are valued at $50 million and $30 million, respectively. Investors currently require a 16 percent return on the common stock and an 8 percent return on the debt. If Northern Sludge issues an additional $10 million of common stock and uses this money to retire debt, what happens to the expected return on the stock? Assume that the change in capital structure does not affect the risk of the debt and that there are no taxes. If the risk of the debt did increase, would your answer underestimate or overestimate the expected return on the stock?

4.Company C is financed entirely by common stock and has a of 1.0. The stock has a price–earnings multiple of 10 and is priced to offer a 10 percent expected return. The company decides to repurchase half the common stock and substitute an equal value of debt. Assume that the debt yields a risk-free 5 percent.

a. Give

i. The beta of the common stock after the refinancing.

ii.The beta of the debt.

iii.The beta of the company (i.e., stock and debt combined).

F I G U R E 1 7 . 6

See quiz question 7.

10.Executive Chalk is financed solely by common stock and has outstanding 25 million shares with a market price of $10 a share. It now announces that it intends to issue $160 million of debt and to use the proceeds to buy back common stock.

a.How is the market price of the stock affected by the announcement?

b.How many shares can the company buy back with the $160 million of new debt that it issues?

c.What is the market value of the firm (equity plus debt) after the change in capital structure?

d.What is the debt ratio after the change in structure?

e.Who (if anyone) gains or loses?

Now try the next question.

11.Executive Cheese has issued debt with a market value of $100 million and has outstanding 15 million shares with a market price of $10 a share. It now announces that it intends to issue a further $60 million of debt and to use the proceeds to buy back common stock. Debtholders, seeing the extra risk, mark the value of the existing debt down to $70 million.

a.How is the market price of the stock affected by the announcement?

b.How many shares can the company buy back with the $60 million of new debt that it issues?

c.What is the market value of the firm (equity plus debt) after the change in capital structure?

d.What is the debt ratio after the change in structure?

e.Who (if anyone) gains or loses?

There once was a man named Carruthers, Who kept cows with miraculous udders.

13.Schuldenfrei a.g. pays no taxes and is financed entirely by common stock. The stock has a beta of .8, a price–earnings ratio of 12.5, and is priced to offer an 8 percent expected return. Schuldenfrei now decides to repurchase half the common stock and substitute an equal value of debt. If the debt yields a risk-free 5 percent, calculate

a.The beta of the common stock after the refinancing.

b.The required return and risk premium on the stock before the refinancing.

c.The required return and risk premium on the stock after the refinancing.

d.The required return on the debt.

e.The required return on the company (i.e., stock and debt combined) after the

refinancing.

Assume that the operating profit of the firm is expected to remain constant in perpetuity. Give

f.The percentage increase in expected earnings per share.

g.The new price–earnings multiple.

14.Gamma Airlines is currently all-equity-financed, and its shares offer an expected return of 18 percent. The risk-free interest rate is 10 percent. Draw a graph with return on the vertical axis and debt–equity ratio (D/E) on the horizontal axis, and plot for different

levels of leverage the expected return on assets (rA), the expected return on equity (rE), and the return on debt (rD). Assume that the debt is risk-free. Now draw a similar graph with the debt ratio (D/V) on the horizontal axis.

15.Two firms, U and L, are identical except for their capital structure. Both will earn $150 in a boom and $50 in a slump. There is a 50 percent chance of each event. U is entirely equity-financed, and therefore shareholders receive the entire income. Its shares are valued at $500. L has issued $400 of risk-free debt at an interest rate of 10 percent, and therefore $40 of L’s income is paid out as interest. There are no taxes or other market imperfections. Investors can borrow and lend at the risk-free rate of interest.

a.What is the value of L’s stock?

b.Suppose that you invest $20 in U’s stock. Is there an alternative investment in L that would give identical payoffs in boom and slump? What is the expected payoff from such a strategy?

c.Now suppose that you invest $20 in L’s stock. Design an alternative strategy with identical payoffs.

d.Now show that MM’s proposition II holds.

C H A P T E R E I G H T E E N

HOW MUCH SHOULD

A FIRM BORROW?

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IN CHAPTER 17 we found that debt policy rarely matters in well-functioning capital markets. Few financial managers would accept that conclusion as a practical guideline. If debt policy doesn’t matter, then they shouldn’t worry about it—financing decisions should be delegated to underlings. Yet financial managers do worry about debt policy. This chapter explains why.

If debt policy were completely irrelevant, then actual debt ratios should vary randomly from firm to firm and industry to industry. Yet almost all airlines, utilities, banks, and real estate development companies rely heavily on debt. And so do many firms in capital-intensive industries like steel, aluminum, chemicals, petroleum, and mining. On the other hand, it is rare to find a drug company or advertising agency that is not predominantly equity-financed. Glamorous growth companies rarely use much debt despite rapid expansion and often heavy requirements for capital.

The explanation of these patterns lies partly in the things we left out of the last chapter. We ignored taxes. We assumed bankruptcy was cheap, quick, and painless. It isn’t, and there are costs associated with financial distress even if legal bankruptcy is ultimately avoided. We ignored potential conflicts of interest between the firm’s security holders. For example, we did not consider what happens to the firm’s “old” creditors when new debt is issued or when a shift in investment strategy takes the firm into a riskier business. We ignored the information problems that favor debt over equity when cash must be raised from new security issues. We ignored the incentive effects of financial leverage on management’s investment and payout decisions.

Now we will put all these things back in: taxes first, then the costs of bankruptcy and financial distress. This will lead us to conflicts of interest and to information and incentive problems. In the end we will have to admit that debt policy does matter.

However, we will not throw away the MM theory we developed so carefully in Chapter 17. We’re shooting for a theory combining MM’s insights plus the effects of taxes, costs of bankruptcy and financial distress, and various other complications. We’re not dropping back to the traditional view based on inefficiencies in the capital market. Instead, we want to see how well-functioning capital markets respond to taxes and the other things covered in this chapter.

18.1 CORPORATE TAXES

Debt financing has one important advantage under the corporate income tax system in the United States. The interest that the company pays is a tax-deductible expense. Dividends and retained earnings are not. Thus the return to bondholders escapes taxation at the corporate level.

Table 18.1 shows simple income statements for firm U, which has no debt, and firm L, which has borrowed $1,000 at 8 percent. The tax bill of L is $28 less than that of U. This is the tax shield provided by the debt of L. In effect the government pays 35 percent of the interest expense of L. The total income that L can pay out to its bondholders and stockholders increases by that amount.

Tax shields can be valuable assets. Suppose that the debt of L is fixed and permanent. (That is, the company commits to refinance its present debt obligations when they mature and to keep rolling over its debt obligations indefinitely.) It looks forward to a permanent stream of cash flows of $28 per year. The risk of these flows is likely to be less than the risk of the operating assets of L. The tax shields

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depend only on the corporate tax rate1 and on the ability of L to earn enough to cover interest payments. The corporate tax rate has been pretty stable. (It did fall from 46 to 34 percent after the Tax Reform Act of 1986, but that was the first material change since the 1950s.) And the ability of L to earn its interest payments must be reasonably sure; otherwise it could not have borrowed at 8 percent.2 Therefore we should discount the interest tax shields at a relatively low rate.

But what rate? One common assumption is that the risk of the tax shields is the same as that of the interest payments generating them. Thus we discount at 8 percent, the expected rate of return demanded by investors who are holding the firm’s debt:

PV1tax shield2 .2808 $350

In effect the government itself assumes 35 percent of the $1,000 debt obligation of L. Under these assumptions, the present value of the tax shield is independent of the return on the debt rD. It equals the corporate tax rate Tc times the amount borrowed D:

Interest payment return on debt amount borrowed

rD D

corporate tax rate expected interest payment

PV1tax shield2

expected return on debt

Tc1rDD 2

rD TcD

Of course, PV(tax shield) is less if the firm does not plan to borrow permanently, or if it may not be able to use the tax shields in the future.

1Always use the marginal corporate tax rate, not the average rate. Average rates are often much lower than marginal rates because of accelerated depreciation and other tax adjustments. For large corporations, the marginal rate is usually taken as the statutory rate, which was 35 percent when this chapter was written (2001). However, effective marginal rates can be less than the statutory rate, especially for smaller, riskier companies which cannot be sure that they will earn taxable income in the future.

2If the income of L does not cover interest in some future year, the tax shield is not necessarily lost. L can carry back the loss and receive a tax refund up to the amount of taxes paid in the previous three years. If L has a string of losses, and thus no prior tax payments that can be refunded, then losses can be carried forward and used to shield income in subsequent years.

How Do Interest Tax Shields Contribute to the Value of Stockholders’ Equity?

MM’s proposition I amounts to saying that the value of a pie does not depend on how it is sliced. The pie is the firm’s assets, and the slices are the debt and equity claims. If we hold the pie constant, then a dollar more of debt means a dollar less of equity value.

But there is really a third slice, the government’s. Look at Table 18.2. It shows an expanded balance sheet with pretax asset value on the left and the value of the government’s tax claim recognized as a liability on the right. MM would still say that the value of the pie—in this case pretax asset value—is not changed by slicing. But anything the firm can do to reduce the size of the government’s slice obviously makes stockholders better off. One thing it can do is borrow money, which reduces its tax bill and, as we saw in Table 18.1, increases the cash flows to debt and equity investors. The after-tax value of the firm (the sum of its debt and equity values as shown in a normal market value balance sheet) goes up by PV(tax shield).

Recasting Pfizer’s Capital Structure

Pfizer, Inc., is a large successful firm that uses essentially no long-term debt. Table 18.3(a) shows simplified book and market value balance sheets for Pfizer as of year-end 2000.

Suppose that you were Pfizer’s financial manager in 2001 with complete responsibility for its capital structure. You decide to borrow $1 billion on a permanent basis and use the proceeds to repurchase shares.

Table 18.3(b) shows the new balance sheets. The book version simply has $1,000 million more long-term debt and $1,000 million less equity. But we know that Pfizer’s assets must be worth more, for its tax bill has been reduced by 35 percent of the interest on the new debt. In other words, Pfizer has an increase in PV(tax shield), which is worth TcD .35 $1,000 million $350 million. If the MM theory holds except for taxes, firm value must increase by $350 million to $296,247 million. Pfizer’s equity ends up worth $289,794 million.