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Value of firm value if all-equity-financed PV1tax shield2

In the special case of permanent debt,

Value of firm value if all-equity-financed TcD

Our imaginary financial surgery on Pfizer provides the perfect illustration of the problems inherent in this “corrected” theory. That $350 million came too easily; it seems to violate the law that there is no such thing as a money machine. And if Pfizer’s stockholders would be richer with $2,123 million of corporate debt, why not $3,123 or $17,199 million?5 Our formula implies that firm value and stockholders’ wealth continue to go up as D increases. The optimal debt policy appears to be embarrassingly extreme. All firms should be 100 percent debtfinanced.

MM were not that fanatical about it. No one would expect the formula to apply at extreme debt ratios. There are several reasons why our calculations overstate the value of interest tax shields. First, it’s wrong to think of debt as fixed and perpetual; a firm’s ability to carry debt changes over time as profits and firm value fluctuate.6 Second, many firms face marginal tax rates less than 35 percent. Third, you can’t use interest tax shields unless there will be future profits to shield—and no firm can be absolutely sure of that.

But none of these qualifications explains why firms like Pfizer not only exist but also thrive with no debt at all. It is hard to believe that the management of Pfizer is simply missing the boat.

Therefore we have argued ourselves into a corner. There are just two ways out:

1.Perhaps a fuller examination of the U.S. system of corporate and personal taxation will uncover a tax disadvantage of corporate borrowing, offsetting the present value of the corporate tax shield.

2.Perhaps firms that borrow incur other costs—bankruptcy costs, for example—offsetting the present value of the tax shield.

We will now explore these two escape routes.

18.2 CORPORATE AND PERSONAL TAXES

When personal taxes are introduced, the firm’s objective is no longer to minimize the corporate tax bill; the firm should try to minimize the present value of all taxes paid on corporate income. “All taxes” include personal taxes paid by bondholders and stockholders.

Figure 18.1 illustrates how corporate and personal taxes are affected by leverage. Depending on the firm’s capital structure, a dollar of operating income will

5The last figure would correspond to a 100 percent book debt ratio. But Pfizer’s market value would be $301,524 million according to our formula for firm value. Pfizer’s common shares would have an aggregate value of $279,995 million.

6The valuation of interest tax shields is discussed again in Section 19.4. Our calculation here adheres to Chapter 19’s “Financing Rule 1,” which assumes that debt is fixed regardless of future performance of the project or the firm.

In this case, we can forget about personal taxes. The tax advantage of corporate borrowing is exactly as MM calculated it.8 They do not have to assume away personal taxes. Their theory of debt and taxes requires only that debt and equity be taxed at the same rate.

The second special case occurs when corporate and personal taxes cancel to make debt policy irrelevant. This requires

1 Tp 11 TpE 2 11 Tc 2

This case can happen only if Tc, the corporate rate, is less than the personal rate Tp and if TpE, the effective rate on equity income, is small. Merton Miller explored this situation at a time when tax rates in the United States were very different from today, but we won’t go into the details of his analysis here.9

In any event we seem to have a simple, practical decision rule. Arrange the firm’s capital structure to shunt operating income down that branch of Figure 18.1 where the tax is least. Unfortunately that is not as simple as it sounds. What’s TpE, for example? The shareholder roster of any large corporation is likely to include tax-exempt investors (such as pension funds or university endowments) as well as millionaires. All possible tax brackets will be mixed together. And it’s the same with Tp, the personal tax rate on interest. The large corporation’s “typical” bondholder might be a taxexempt pension fund, but many taxpaying investors also hold corporate debt.

Some investors may be much happier to buy your debt than others. For example, you should have no problems inducing pension funds to lend; they don’t have to worry about personal tax. But taxpaying investors may be more reluctant to hold debt and will be prepared to do so only if they are compensated by a high rate of interest. Investors paying tax on interest at the top rate of 39.1 percent may be particularly unwilling to hold debt. They will prefer to hold common stock or municipal bonds whose interest is exempt from tax.

To determine the net tax advantage of debt, companies would need to know the tax rates faced by the marginal investor—that is, an investor who is equally happy to hold debt or equity. This makes it hard to put a precise figure on the tax benefit, but we can nevertheless provide a back-of-the-envelope calculation. One way to estimate the tax rate of the marginal debt investor is to see how much yield investors are prepared to give up when they invest in tax-exempt municipal bonds. As we write this in August 2001, short-term municipals yield 2.49 percent, while similar Treasury bonds yield 3.71 percent. An investor with a personal tax rate of 33 percent would receive exactly the same after-tax interest from the two securities and would be equally happy to hold them.10

8Of course, personal taxes reduce the dollar amount of corporate interest tax shields, but the appropriate discount rate for cash flows after personal tax is also lower. If investors are willing to lend at a prospective return before personal taxes of rD , then they must also be willing to accept a return after personal taxes of rD11 Tp 2 , where Tp is the marginal rate of personal tax. Thus we can compute the value after personal taxes of the tax shield on permanent debt:

Tc 1rDD 2 11 Tp 2

This brings us back to our previous formula for firm value:

Value of firm value if all-equity-financed TcD

9See M. H. Miller, “Debt and Taxes,” Journal of Finance 32 (May 1977), pp. 261–276.

10That is, 11 .332 3.71 2.49 percent.

The advantage to debt financing appears to be about $.13 on the dollar.

We should emphasize that our back-of-the-envelope calculation is just that. Economists have come up with differing figures for the tax rate of the marginal debtholder and the effective rate of capital gains tax. These estimates may give higher or lower figures for the tax advantage of debt. Also our calculation of the benefits of debt financing assumed that the firm could be confident that it would have sufficient income to shield. In practice few firms can be sure they will show a taxable profit in the future. If a firm shows a loss and cannot carry the loss back against past taxes, its interest tax shield must be carried forward with the hope of using it later. The firm loses the time value of money while it waits. If its difficulties are deep enough, the wait may be permanent and the interest tax shield may be lost forever.

Notice also that borrowing is not the only way to shield income against tax. Firms have accelerated write-offs for plant and equipment. Investment in many intangible assets can be expensed immediately. So can contributions to the firm’s pension fund. The more that firms shield income in these ways, the lower is the expected shield from corporate borrowing.12 Even if the firm is confident that it will earn a taxable profit with the current level of debt, it is unlikely to be so positive if the amount of debt is increased.13

11For an analysis of the effective rate of capital gains tax, see R. C. Green and B. Hollifield, “The Personal Tax Advantages of Equity,” working paper, Graduate School of Industrial Administration, Carnegie Mellon University, January 2001.

12For a discussion of these and other tax shields on company borrowing, see H. DeAngelo and R. Masulis, “Optimal Capital Structure under Corporate and Personal Taxation,” Journal of Financial Economics 8 (March 1980), pp. 5–29.

13For some evidence on the average marginal tax rate of U.S. firms, see J. R. Graham, “Debt and the Marginal Tax Rate,” Journal of Financial Economics 41 (May 1996), pp. 41–73, and “Proxies for the Corporate Marginal Tax Rate,” Journal of Financial Economics 42 (October 1996), pp. 187–221.

F I G U R E 1 8 . 3

Comparison of limited and unlimited liability for two otherwise identical firms. If the two firms’ asset values are less than $1,000, Ace Limited stockholders default and its bondholders take over the assets. Ace Unlimited stockholders keep the assets, but they must reach into their own pockets to pay off its bondholders. The total payoff to both stockholders and bondholders is the same for the two firms.

ers (creditors and especially shareholders) look at their firm’s present sad state. They think of how valuable their securities used to be and how little is left. Moreover, they think of the lost value as a cost of bankruptcy. That is the mistake. The decline in the value of assets is what the mourning is really about. That has no necessary connection with financing. The bankruptcy is merely a legal mechanism for allowing creditors to take over when the decline in the value of assets triggers a default. Bankruptcy is not the cause of the decline in value. It is the result.

Be careful not to get cause and effect reversed. When a person dies, we do not cite the implementation of his or her will as the cause of death.

We said that bankruptcy is a legal mechanism allowing creditors to take over when a firm defaults. Bankruptcy costs are the costs of using this mechanism.

bankruptcy, it spent $114 million on professional fees.16 Daunting as such numbers may seem, they are not a large fraction of the companies’ asset values. For example, the fees incurred by Eastern amounted to only 3.5 percent of its assets when it entered bankruptcy, or about the equivalent of one jumbo jet.

Lawrence Weiss, who studied 31 firms that went bankrupt between 1980 and 1986, found average costs of about 3 percent of total book assets and 20 percent of the market value of equity in the year prior to bankruptcy. A study by Edward Altman found that costs were similar for retail companies but higher for industrial companies. Also, bankruptcy eats up a larger fraction of asset value for small companies than for large ones. There are significant economies of scale in going bankrupt.17 Finally, a study by Andrade and Kaplan of a sample of troubled and highly leveraged firms estimated costs of financial distress amounting to 10 to 20 percent of predistress market value.18 A breakdown of these costs of corporate bankruptcy is provided in the Finance in the News box.

Direct versus Indirect Costs of Bankruptcy

So far we have discussed the direct (that is, legal and administrative) costs of bankruptcy. There are indirect costs too, which are nearly impossible to measure. But we have circumstantial evidence indicating their importance.

Some of the indirect costs arise from the reluctance to do business with a firm that may not be around for long. Customers worry about the continuity of supplies and the difficulty of obtaining replacement parts if the firm ceases production. Suppliers are disinclined to put effort into servicing the firm’s account and demand cash on the nail for their goods. Potential employees are unwilling to sign on and the existing staff keep slipping away from their desks for job interviews.

Managing a bankrupt firm is not easy. Consent of the bankruptcy court is required for many routine business decisions, such as the sale of assets or investment in new equipment. At best this involves time and effort; at worst the proposals are thwarted by the firm’s creditors, who have little interest in the firm’s long-term prosperity and would prefer the cash to be paid out to them.

Sometimes the problem is reversed: The bankruptcy court is so anxious to maintain the firm as a going concern that it allows the firm to engage in negative-NPV activities. When Eastern Airlines entered the “protection” of the bankruptcy court in 1989, it still had some valuable, profit-making routes and saleable assets such as planes and terminal facilities. The creditors would have been best served by a prompt liquidation, which probably would have generated enough cash to pay off all debt and preferred stockholders. But the bankruptcy judge was keen to keep Eastern’s planes flying at all costs, so he allowed the company to sell many of its assets to fund

16L. Gibbs and A. Boardman, “A Billion Later, Eastern’s Finally Gone,” American Lawyer Newspaper Groups, February 6, 1995.

17The pioneering study of bankruptcy costs is J. B. Warner, “Bankruptcy Costs: Some Evidence,” Journal of Finance 26 (May 1977), pp. 337–348. The Weiss and Altman papers are L. A. Weiss, “Bankruptcy Resolution: Direct Costs and Violation of Priority of Claims,” Journal of Financial Economics 27 (October 1990), pp. 285–314, and E. I. Altman, “A Further Investigation of the Bankruptcy Cost Question,” Journal of Finance 39 (September 1984), pp. 1067–1089.

18G. Andrade and S. N. Kaplan, “How Costly is Financial (not Economic) Distress? Evidence from Highly Leveraged Transactions that Became Distressed,” Journal of Finance 53 (October 1998), pp. 1443–1493.