Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads




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    • Leland is from the Haas School of Business, University of California at Berkeley. Toft is from the Department of Finance, University of Texas at Austin. The authors thank Edward Altman, David Babbel, Robert Dammon, William Keirstead, Eric Reiner, Ehud Ronn, Michael Ross, Mark Rubinstein, Stephen Schaefer, Eduardo Schwartz, Richard Stanton, and Matt Spiegel for helpful comments. Research support from the Institute for Quantitative Research in Finance is gratefully acknowledged. Partial and preliminary results are reported in an earlier paper by the first author. (Finance Working paper No. 240, IBER, Haas School of Business, November 1994).


This article examines the optimal capital structure of a firm that can choose both the amount and maturity of its debt. Bankruptcy is determined endogenously rather than by the imposition of a positive net worth condition or by a cash flow constraint. The results extend Leland's (1994a) closed-form results to a much richer class of possible debt structures and permit study of the optimal maturity of debt as well as the optimal amount of debt. The model predicts leverage, credit spreads, default rates, and writedowns, which accord quite closely with historical averages. While short term debt does not exploit tax benefits as completely as long term debt, it is more likely to provide incentive compatibility between debt holders and equity holders. Short term debt reduces or eliminates “asset substitution” agency costs. The tax advantage of debt must be balanced against bankruptcy and agency costs in determining the optimal maturity of the capital structure. The model predicts differently shaped term structures of credit spreads for different levels of risk. These term structures are similar to those found empirically by Sarig and Warga (1989). Our results have important implications for bond portfolio management. In general, Macaulay duration dramatically overstates true duration of risky debt, which may be negative for “junk” bonds. Furthermore, the “convexity” of bond prices can become “concavity.”