The Valuation of Corporate Debt with Default Risk

This article values equity and corporate debt by taking into account the fact that in practice the default point differs from the liquidation point and that it might be in the creditors’ interest to delay liquidation. The article develops a continuous time asset pricing model of debt restructuring which explicitly considers the inalienability of human capital. The study finds that even though in general the creditors will not liquidate the firm on the incidence of default, but nevertheless would liquidate the firm prematurely relative to the first best threshold. This agency problem leads to the breakdown of the capital structure irrelevance result. 1. Theoretical Foundation The literature on the pricing of defaultable bonds started with Merton (1974) who applied the contingent claims valuation insight of Black and Scholes (1973) to the pricing of corporate bonds. He obtained closed form valuation expressions for (zero-coupon) risky bonds, by taking the lower reorganization boundary as given. Thus in his model, default occurred at maturity if the value of the firm was less than the payment promised to the bondholders. Furthermore, at maturity the compensation received by the creditors is fixed and they receive the minimum of the value of the firm or the contracted payment. In the event of a default, the control of the firm is transferred to the creditors and this default point can also be interpreted as a liquidation point with zero bankruptcy costs. Thus, in Merton’s model, both the lower reorganization boundary and the compensation received by the bondholders is taken to be exogenous. In practice, however, the compensation received by the creditors may vary continuously with the value of the firm if the firm is in financial distress. Furthermore, Merton does not make the distinction between default and liquidation. There have been a number of extensions of the Merton model. Black and Cox (1976) incorporate bond indenture provisions. Jones, Mason and Rosenfeld (1984) consider multiple issue of callable coupon debt. In both of these models however the induced lower boundary at which the firm is liquidated is taken to be exogenous. Further, default is again tantamount to bankruptcy in these models. Leland (1993) and Leland and Toft (1996) extend Merton’s analysis by endogenising the lower reorganization boundary. By assuming that the equityholders will always issue equity to prevent a default, they obtain expressions for the values of risky debt via the smooth-pasting condition. Thus in their models, the equityholders keep on issuing equity (when necessary) to avoid a default until the value of equity falls to zero. Thus default occurs when the value of equity falls to zero and this default point is again synonymous ∗I would like to thank Ronald Anderson for his support and encouragement. I would also like to thank Hyun Song Shin and Abhijeet Singh for valuable comments. Comments from the participants of FMG doctoral seminar are also appreciated. Any errors remain my responsibility. Correspondence to be addressed to Hassan Naqvi, Room R4z17A, Financial Markets Group, London School of Economics, Houghton Street, London, WC2A 2AE, or email: [email protected]