The value of tax shields is not equal to the present value of tax shields

We show that the 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. For perpetuities without costs of leverage, the value of tax shields is equal to the tax rate times the value of debt. Since the existence of leverage costs is independent of taxes, the value of tax shields when there are no taxes should be negative. We later on look at the case of constant growth and derive similar implications. We then identify 9 valuation theories proposed in the literature to estimate the present value of tax shields and show that only one valuation method is consistent when we look at the case of constant growth and no leverage costs. Three theories provide consistent valuations once leverage costs and growth are allowed for. For constant growth companies, we claim that the value of the tax shield in a world with no leverage cost is the present value of the debt (D) times the tax rate (T) times the required return to the unlevered equity (Ku), discounted at the unlevered cost of equity (Ku): VTS = PV[Ku; D T Ku]. Please note that this does not mean that the appropriate discount for the tax shields is the unlevered cost of equity. We discount D T Ku, which is higher than the shield. This expression arises as the difference of two present values, each with different risk