Default Risk, Asset Pricing and Debt Control

The pricing and control of firms’ debt has become a major issue since Merton’s (1974) seminal paper. Yet, Merton as well as other recent theories presume that the asset value of the firm is independent of the debt of the firm. However, when using debt finance firms may have to pay a premium for an idiosyncratic default risk and may face debt constraints. We demonstrate that firm specific debt constraints and endogenous risk premia, based on collateralized borrowing, affect the asset value of the firm and, in turn, the collateral value of the firm. In order to explore the interdependence of debt finance and asset pricing of firms we endogenize default premia and borrowing constraints in a production based asset pricing model. In this context then the dynamic decision problem of maximizing the present value of the firm faces an additional constraint giving rise to the debt dependent firm value. We solve for the asset value of the firm with debt finance by the use of numerical dynamic programming. This allows us to solve the debt control problem and to compute sustainable debt as well as firm’s debt value. We want to thank John Donaldson, Martin Lettau and Buz Brock for helpful suggestions and discussions. We also want to thank participants in a workshop at the University of Technology, Vienna, the Macroeconomic Workshop at Columbia University, and the SCE conferences at Yale University, June 2001 and Aix-en-Provence, July 2002, and participants of the workshop on Economic Dynamics in Leiden, June 2002 and the CFS workshop on New Directions in Financial Risk Management, November 2003. ∗Department of Mathematics, University of Frankfurt, Robert–Mayer–Str. 8-10, 60054 Frankfurt, Germany, e-mail:[email protected] †Center for Empirical Macroeconomics, Bielefeld and New School University, New York, e-mail:[email protected]