Valuation effects of taxes on debt cancellation

Standard models on firm valuation regard a simplified default setting, often not revealing relevant implicit assumptions. In this paper, we analyze the impact of risky debt and of taxes on a cancellation of indebtedness (COD) on tax savings. For the case of a taxation of a COD, we explicitly show that the risky components in the pricing equation of tax savings cancel out so that the tax shield pricing is similar to the case of risk-free tax savings. Furthermore, assuming no tax on a COD, we show the standard textbook equations for the tax shield, the tax-adjusted discount rates and WACC subject to risky debt to be generally valid only for a pro-rata loss distribution between interest and principal payments. Using standard equations for the case of no taxes on a COD in case of a non-proportional loss distribution can lead to substantial misvaluations, which we illustrate with an example.