Debt valuation with endogenous default and Chapter 11 reorganization

We examine a continuous-time structural model of debt valuation with the possibility of default and Chapter 11 bankruptcy. In doing so, we derive Chapter 11 duration and allocations to the debtor and bondholders in Chapter 1 I as the outcomes of a bargaining game between the debtor and the bondholders. The absolute priority rule (APR) violations arising in equilibrium are then embedded into closed-form solutions for the values of equity, finite-maturity debt, and credit spreads. It has been recently documented that existing credit risk models explain only a fraction of the observed yield spreads when confronted with the data on default rate and recovery rate at default (e.g., Collin-Dufresne et al. (2001) and Elton et al. (2001)). Taking the exclusivity period as an approximation to a legal environment of the bargaining process, we model Chapter 11 as the debtor's ultimatum offers to the bondholders and calibrate the model using an approach similar to that of Huang and Huang (2002). We obtain credit spreads that are twice to three times as large as those produced by the model in Leland and Toft (1996). The reason why this result holds in our model is that when the debtor obtains a non-zero allocation in bankruptcy, her option to default is worth more and exercised sooner than in Leland and Toft's model. Therefore, the debt value is smaller, and consequently, credit spreads are higher. Calibrated credit spreads are high for firms expected to be more solvent at default and those with large absolute priority rule violations. Finally, our model predicts a significant cross-sectional variation in Chapter 11 duration. Indeed, such heterogeneity is seen in actual bankruptcy experiences. We discuss several new empirical implications of the model with regards to the expected time in bankruptcy as a function of different firm characteristics. The model predicts that firms with a higher fraction of intangible assets, lower pre-bankruptcy volatility of asset value, and lower average maturity of debt in their capital structure spend less time in Chapter 11