The Present Value of the Tax Shield (Pvts) for Fcf in Perpetuity with Growth

The discount rate for the tax shield depends on the risk of the tax shield. If the tax shield is risk-free, then the appropriate discount rate for the tax shield is the risk-free rate rf. If the debt is risky, then we must make the distinction between the contractual return and the expected return on the debt.In this paper, using a simple numerical example, we illustrate the calculation of the present value of the tax shield (PVTS) for a free cash flow (FCF) in perpetuity with a constant growth rate g. We assume that the tax shield is risk-free and the debt is risky. Most importantly, we model explicitly the risk of the tax shield and the debt with a stochastic process.In addition, the net incomes for the unlevered and levered firms are not equal to the corresponding cash flows for the unlevered and levered firms. Consequently, the discount rates for the taxes paid by the unlevered and levered firms are not equal to the return to unlevered equity Ku and the return to levered equity Ke, respectively. Without a specific stochastic process, it would not be possible to calculate the discount rates for the taxes paid by the unlevered and levered firms