A Model of Optimal Capital Structure with Stochastic Interest Rates

Abstract

This paper develops a model of optimal capital structure with stochastic interest rate which is assumed to follow a mean-reverting process. Closed-form solutions are obtained for both the value of the firm and the value of its risky debt. The paper finds that the current level and the long-run mean of the interest rate process play distinctive roles in our integrated model. The current level of the interest rate is critical in the pricing of risky bonds, while the long-run mean plays a key role in the determination of a firm’s optimal capital structure such as the optimal coupon rate and leverage ratio. Our findings demonstrate that a model of optimal capital structure with a constant interest rate cannot price risky bonds and determine the optimal capital structure simultaneously in a satisfactory manner. Furthermore, our numerical results indicate that the correlation between the stochastic interest rate and the asset return of a firm has little impact on the firm’s optimal capital structure.