U-Shaped Cost of Equity Function? Digging Into Modigliani-Miller (1958) Mistake

Abstract

Modigliani and Miller (1958, The cost of capital, corporation finance and the theory of investment, The American Economic Review, Vol. 48, No 3) assert that, beyond some high level of leverage, the cost of equity curve may be decreasing. Despite the lack of rigour of their argument, this proposition received a small amount of criticism. However, it is wrong: in an MM world, the cost of equity function must be increasing, because under the dynamics of MM Proposition II, the marginal cost of debt must be lower than the cost of equity. Should, by any chance, the marginal cost of debt be higher than the cost of equity, arbitrage opportunities, incompatible with market equilibrium, would emerge. In this way, the intuitive idea that the cost of equity may increase unboundedly is recovered. Nevertheless, the cost of equity function will tend to infinity only if the first derivative of the interest cost function also tends to infinity. Otherwise, in the limit, the cost of equity will tend to a finite number. These findings reinforce the theoretical validity of MM propositions.