Comment on 'the Value of Tax Shields is Not Equal to the Present Value of Tax Shields'

Abstract

In a recent paper, Pablo Fernandez (2002) makes the unusual and paradoxical sounding claim that for cash flows in perpetuity with a constant growth rate g, the value of the tax shields VTS is NOT equal to the present value of the tax shields. To be specific, Fernandez purportedly shows that the formula for the present value of the tax shields is as follows.

VTS = TDKu/(Ku - g)

Where Ku is the return to unlevered equity, g is the constant growth rate, T is the tax rate and D is the market value of debt.

Fernandez (2002) asserts that the value of the tax shield, as given in equation, should be properly interpreted as the difference in the taxes paid by the unlevered and levered firms, where the taxes have different risk profiles. Let VTxU be the present value of the taxes paid by the unlevered firm, discounted by KTxU, which is the appropriate risk-adjusted discount, and let VTxL be the present value of the taxes paid by the levered firm, discounted by KTxL, which is the appropriate risk-adjusted discount.

In this note, we assess the validity of the proposed expression for the value of the tax shield. The note is organized is as follows. In Section One, we review and discuss the assumptions underlying the model that Fernandez uses to derive equation 1. In Section Two, we examine critically the derivation of equation 1 and its general relevance and applicability.

Keywords: Present value of tax shield

JEL Classification: G31, H25