The Correct Value of Tax Shields. An Analysis of 23 Theories

Abstract

Although Copeland et al. (2000) claim that "the finance literature does not provide a clear answer about which discount rate for the tax benefit of interest is theoretically correct," we show that we can provide some clear answers on that topic.

This paper provides clear, theoretically sound, guidelines to evaluate the appropriateness of different valuation methods to estimate the present value of tax shields.

We first show that the discounted value of tax shields is the difference between the present values of two different cash flows with their own risk: the present value of taxes for the unlevered company and the present value of taxes for the levered company. This implies as a first guideline that, for the particular case of a perpetuity and a world without costs of leverage, the discounted value of tax shields is equal to the tax rate times the value of debt (i.e. Modigliani-Miller). The discounted value of tax shields can be lower, when costs of leverage exist. In that case, we show that, since the existence of leverage costs is independent of taxes, a second guideline for the appropriateness of the valuation method should be that the discounted value of tax shields when there are no taxes is negative. We then look at the case of constant growth and derive similar implications.

Second, we identify 23 valuation theories proposed in the literature to estimate the present discounted value of tax shields and show their performance relative to the proposed guidelines. Eight of these theories do not satisfy the two proposed guidelines for the case of perpetuities. Only one of the valuation methods is consistent with these restrictions when we look at the case of constant growth and no leverage costs. Three theories provide consistent valuations when we allow for leverage costs and growth. Finally, we use the 23 theories to value a hypothetical firm and show remarkable differences in the obtained values suggesting the importance of using a method consistent with the proposed guidelines.

Keywords: Value of the tax shield; Tax shield valuation; APV; Present value of taxes; Required return to taxes; Taxes; Debt value; Creation

JEL Classification: G12, G31, M21