The Miles & Ezzell (M & E) WACC Reconsidered

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In a recent paper, Loeffler (2001) showed that the Miles & Ezzell (M & E) WACC allows arbitrage if the cash flow process does not have a certain growth To be specific, for a particular period, the set of up and down coefficients must be the same at all the nodes in a binomial cash flow process. In this teaching note, we use simple three period numerical examples to illustrate the calculations of the WACC for cash flow processes that satisfy and violate the growth rate assumption. The note is organized as follows. In Section One, we present a simple three period binomial cash flow process S with multiplicative coefficients that satisfy the growth rate assumption. We calculate the unlevered value with two equivalent methods. One approach uses the risk-neutral probabilities and the risk-free rate. The other approach uses the objective probabilities that are consistent with the risk-neutral probabilities and the return to unlevered equity. In Section Two, we introduce debt and calculate the levered values with the same two methods. Since process S satisfies the growth rate assumption, we verify that the WACCME does not allow arbitrage. In Section Three, with a simple modification, we create a new binomial cash flow process that violates the growth rate assumption and show that the WACCME allows arbitrage.