Company Valuation: A Comparison of Three DCF Models (MM (1958), Fernandez (2007), Hamada (1972)) and Why MM's Corrected Equation for Cost of Equity is Wrong

Abstract

In a correction paper (MM, 1963), MM argued that because of financial risk due to leverage, firms with different capital structure will have different distribution of returns – due to the inclusion of certain stream of tax shields as compared to unlevered firms. Based on this premise, they derived a different equation for cost of equity for firms with financial leverage. This derivation is based on the assumption that the tax shields, being certain stream, can be discounted at cost of debt which is a WRONG conclusion. This paper contends that MM’s original propositions are valid and sufficient even in the presence of taxes and that the corrected equation for cost of equity is WRONG. The Valuation Model presented in this paper ignores MM’s correction paper and provides valid results in different scenarios based on MM’s original equation for cost of equity. The paper also explains why the derivation of corrected equation is wrong (with or without CAPM) and shows that the corrected equation anyway does not take care of financial risk due to leverage as the value of levered firm as per corrected equation will always be more than that arrived at using MM’s original propositions. Moreover, MM’s correction paper itself however correctly states that variance of returns of leveraged firms will be lower than that of unlevered firms. Using Hamada’s approach, the paper shows the MM’s original propositions are valid and sufficient and derives an equation for levered beta using CAPM. This also shows that unlike what is generally assumed, Hamada’s equation does not take care of any additional financial risk due to leverage. The paper also lists the problems associated with the usage of corrected equation for valuation and compares the three possible valuation models. A review of currently available methods for Unlevering beta shows that none of them anyway considers financial risk and most are based on the incorrect assumption of cost of debt being discount rate for tax shields.