The Value of Tax Shields is the Difference of Two Present Values with Different Risk

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. For any company, 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 it does not mean that the appropriate discount for the tax shields is the unlevered cost of equity. We discount D T Ku, which is not the tax shield. This expression arises as the difference of two present values each with different risk.