Unconventional Wisdom on Psi, the Appropriate Discount Rate for the Tax Shield

Abstract

The conventional wisdom about psi, the appropriate discount rate for the tax shield, is as follows. If the tax shield is risk-free, that is, the revenue is sufficient to ensure that the interest deduction will be used with full certainty in the relevant period, then the appropriate discount rate for the tax shield is d, which is the cost of the risk-free debt. On the other hand, if the revenue is stochastic, there may be a finite probability that the revenue will be insufficient to allow for the use of the tax shield. In such a case, whether the debt is risk-free or not, the tax shield is no longer risk-free. In the single period case, some authors suggest that if the tax shield is risky, then the risk of the tax shield is the same as the risk of the free cash flow (FCF) and consequently, the appropriate discount rate is rho, which is the return to unlevered equity. In this teaching note, using a single period binomial example, we show that the conventional wisdom on the appropriate discount rate for the tax shield is incorrect when the tax shield is risky. The appropriate discount rate for the tax shield depends on the risk of the tax shield and the value of psi may be higher than e, the return to levered equity. If the tax shield is correlated with the cash flow to equity, that is, the payoff structure for the tax shield is similar to the payoff structure for the cash flow to equity, then the value of psi is equal to e, which is higher than rho.

Keywords: Discount Rate for Tax Shield

JEL Classification: D61, G12, G31, H43