Equivalence of the different discounted cash flow valuation methods. Different alternatives for determining the discounted value of tax shields and their implications for the valuation

This paper addresses the valuation of firms by cash flow discounting. The first part shows that the four most commonly used discounted cash flow valuation methods (free cash flow discounted at the WACC; cash flow available for equity holders discounted at the required return on the equity flows; capital cash flow discounted at the WACC before taxes; and Adjusted Present Value) always give the same value. This result is logical because all the methods analyse the same reality under the same hypotheses; they differ only in the flows used as the starting point for the valuation. The disagreements in the various theories on the valuation of the firm arise from the calculation of the discounted value of tax shields (DVTS). The paper shows and analyses 7 different theories on the calculation of the DVTS: Modigliani and Miller (1963), Myers (1974), Miller (1977), Miles and Ezzell (1980), Harris and Pringle (1985), Ruback (1995), Damodaran (1994), and Practitioners method. It is shown that Myers' method (1974) gives inconsistent results. When analysing the results given by the different theories, it should be remembered that the DVTS is not actually the present value of the tax saving due to the payment of interested discounted at a certain rate but the difference between two present values: the present value of the taxes paid by the firm with no debt minus the present value of the taxes paid by the company with debt. The risk of the taxes paid by the company with no debt is less than the risk of the taxes paid by the company with debt. The paper also shows the changes that take place in the valuation formulas when the debt's market value does not match its book value.