Optimal Debt and Profitability in the Tradeoff Theory∗

This paper develops and analyzes a dynamic model of leverage, taking account of tax deductibility of interest payments and the endogenous expected cost of default. The interest rate on debt includes a premium to compensate lenders for expected losses in default. Lenders are unwilling to lend an amount that would trigger immediate default, which places a borrowing constraint on the firm. When the borrowing constraint is not binding and the firm faces a positive probability of default, the tradeoff theory of debt holds–that is, optimal debt is determined by the equality of the marginal tax shield and the marginal cost of default associated with an additional dollar of debt. When the tradeoff theory of debt holds, an increase in current or expected future profitability reduces optimal leverage, a finding that is opposite of the conventional interpretation of the tradeoff theory, but is consistent with empirical findings. ∗I thank Jeff Campbell, Vincent Glode, Joao Gomes, Christian Goulding, Richard Kihlstrom, Bob McDonald, Adriano Rampini, Scott Richard, Michael Roberts, Ali Shourideh and seminar participants at the Federal Reserve Bank of Chicago, Kellogg Finance, and Wharton Finance for helpful comments and discussion. The tradeoff theory of capital structure is the longest standing theory of capital structure1 and underlies much of the large body of empirical work that studies capital structure. In the tradeoff theory, the optimal amount of debt equates the marginal benefit of a dollar of debt arising from the tax deductibility of interest payments with the marginal cost of a dollar of debt arising from increased exposure to default. This framework implies that changes in leverage over time, or variation in leverage across firms, can be attributed to differences in the interest tax shield and/or differences in the (marginal) cost of default. The tradeoff theory has been interpreted2 to imply that more profitable firms should have higher leverage ratios–a prediction that is contrary to the empirical fact3 that more profitable firms tend to have lower leverage ratios. In this paper, I develop and analyze a model of capital structure that incorporates an interest tax shield associated with debt as well as the possibility of default. In some situations, the optimal amount of debt will be determined by the equality of the marginal benefit of debt arising from the interest tax shield and the marginal cost of debt associated with increased risk of default–that is, optimal debt will be characterized by the tradeoff theory in these situations. However, in other situations within the model, optimal debt will not be characterized by the equality of marginal benefit and marginal cost that epitomizes the tradeoff theory. Because the model allows for situations in which the tradeoff theory holds and situations in which it does not hold, the model has the potential to guide empirical tests by including both a null hypothesis in terms of the tradeoff theory and an alternative hypothesis that offers an explanation of leverage other than the tradeoff theory. In particular, I show that the model developed here accommodates situations in which higher profitability (either current profitability or expected future profitability) is associated with lower leverage. Furthermore, if the probability of default is nonzero, these situations arise when and only when the tradeoff theory is operative. That is, the empirical finding that more profitable firms tend to have lower leverage ratios, which has been viewed by others as evidence against the tradeoff theory, is viewed as evidence in favor of the tradeoff theory when viewed through the lens of the model presented here. As the tradeoff theory has developed over the past half century, it has become increasingly complex, especially in empirical structural models of the firm that are designed to capture realistic features of a firm’s environment.4 The model I develop here will be stripped of these complexities so that I can focus on its new features and implications in a framework that admits analytic results without relying on numerical solution. The model’s biggest departure from standard models of debt concerns the maturity of the debt. Many standard models of debt5 assume that debt has infinite maturity and pays a fixed coupon over the infinite future, or until the firm defaults. Clearly, the assumption of infinite 1Robichek and Myers (1966), Kraus and Litzenberger (1973), and Scott (1976). 2 Scott (1976), Fama and French (1992), Frank and Goyal (2007), and Strebulaev (2007). 3Fama and French (1992). 4Hennessy and Whited (2007). 5Modigliani and Miller (1958) and Leland (1994).