Reconsidering the appropriate discount rate for tax shield valuation

Abstract

This paper aims at identifying the appropriate discount rate for tax shield valuation in a setting where a partial default is possible and either principal or interest payments are prioritized in default. As a general valuation framework we use the stochastic discount factor. We assume a tax framework with corporate taxes, tax-deductible interest payments of the firm, no taxes on the cancellation of debt and no personal taxes. We strictly decompose the payments owed to the debtholders into interest and principal payments and analyze discount rates of those claims for the different priorities. As a result of the single-period analysis we find that the discount rate for tax savings, i.e., the conditional expected return on tax savings, is always equal to the discount rate of debt only for a proportional loss distribution on interest and principal payments. If losses are distributed according to one of the priority assumptions, the discount rate of tax savings behaves different from the discount rate of debt and both discount rates are equal only in very special cases. Furthermore, we derive qualitative statements for the relation between the discount rate of debt and the discount rate of tax savings assuming certain correlations between the stochastic discount factor and the debt repayments. Finally, we show how the prioritization assumptions can be implemented in a multi-period setting. We obtain for the presented set of assumptions a pricing equation equivalent to the one by Miles and Ezzell (J Finance 40:1485–1492, 1985).