Reconciling the Two Definitions of the Present Value of the Tax Shield (PVTS)

Abstract:     
There are two ways to define the present value of the tax shield (PVTS). First, the (present) value of the tax shield VTS is simply the tax shield, discounted by y, which is the appropriate discount rate for the tax shield. Second, the (present) value of the tax shield VTS is the difference in the present values of the tax payments for the unlevered firm and the levered firm, where the risk profiles of the two tax payments are different. Happily, in this note, we show that both definitions of the present value of the tax shield are equivalent.

To reconcile the two definitions of VTS, it is important to specify the risk profile of the free cash flow (FCF) and estimate the appropriate discount rates for the different cash flow profiles. We use a simple binomial model to specify the risk profile of the FCF and present simple numerical examples to illustrate the equivalence between the two definitions of the present value of the tax shield. The growth rate of the FCF and the leverage cost are zero.

We assume that the reader is familiar with risk-neutral valuation. In Section One, we present a numerical example with risk-free debt. In Section Two, we present a numerical example with risky debt.

Number of Pages in PDF File: 43

Keywords: Tax shield, risk of tax shield, WACC, Cost of Capital

JEL Classification: D61, G31, H43

working papers series