Valuing the Tax Shield under Asymmetric Taxation

Models on enterprise valuation show that the effective or marginal tax rate (ETR) increases linearly with the debt ratio, implying that tax benefits from debt are very important. Empirical research has repeatedly emphasized that this result cannot be sustained, and that tax benefits are in reality much less relevant to valuation. It is an open question whether this impression can also be maintained within a theoretical model. All theoretical models so far assume that the tax rate is constant and identical for gains and losses. In this paper, we attempt to analytically determine the value of a tax shield assuming that gains and losses are taxed differently. We want to precisely determine the impact of a non-constant tax rate on the value of the tax shield. Previous research could only integrate this asymmetry by employing empirical methods and simulation studies, as an analytical solution had not yet been presented. Looking at a very popular financing policy we are able to present a closed-form solution for the effective tax rate. Our results reveal that this value, instead of being a linear function of the debt ratio, is rather concave, sustaining repeated empirical observations. However, our results also show that the “power” or “strength” of this concavity is not enough to explain the empirical results concerning the impact of the tax shield. Therefore, adding an asymmetric taxation is not enough to determine the empirically observed puzzle of tax shield valuation.