The Non-Conventional WACC with Risky Debt and Risky Tax Shield

Abstract

In the traditional formulation of the WACC, the debt and the tax shield are risk-free. However, even though the debt is risk-free, the tax shield can be risky. Furthermore, both the debt and the tax shield can be risky. In this paper, we present the non-conventional weighted average cost of capital (WACC) for the single period binomial process with risky debt and risky tax shield, and derive the relevant formulas for the returns to the levered equity holder and the debt holder. Risk-free debt does not imply that the tax shield is risk-free. Unlike the traditional formulation, with the non-conventional WACC, the discount rate for the tax shield is not be restricted to two values, the risk-free rate rf and the return to unlevered equity rho. We make no prior assumption about the value of the discount rate for the tax shield psi. The value of psi depends on the riskiness of the tax shield. If the tax shield is risk-free, then the value of psi is equal to the risk-free rate rf. If the tax shield is risky, then the value of psi is simply higher than the risk-free rate rf. In particular, if the payoff structure of the tax shield is the same as the payoff structure for the levered equity holder, the value of psi is equal to the return to the levered equity holder. In Section One, we present the non-conventional WACC for the single period with the capital cash flow (CCF) rather than the free cash flow (FCF) and examine the traditional position, where both the debt and the tax shield are risk-free. In Section Two, we assume that both the debt and the tax shield are risky.