This paper examines the value of debt subject to default risk in a continuous time framework. By considering debt with regular principal repayments (e.g. through a sinking fund), we are able to examine bonds with arbitrary maturity while retaining a time-homogeneous environment. This extends Leland's [1994] earlier closed-form results to a much richer class of possible debt structures. We examine the term structure of yield spreads and find that a rise in interest rates will reduce yield spreads of current debt issues. It may tilt the term structure as well. Duration is also affected by default risk. The traditional Macaulay duration measure overstates effective duration, which for junk bonds may even be negative. While short term debt does not exploit tax benefits as completely as does long term debt, it is more likely to provide incentive compatibility between debt holders and equity holders. The agency costs of asset substitution are minimized when firms use shorter term debt. Optimal capital structure depends upon debt maturity. Optimal leverage ratios are smaller, and maximal firm values are less, when short term debt is used. The yield spread at the optimal leverage ratio increases with debt maturity.
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