In retrospect, writing about “risk and valuation” is somewhat akin to killing Hydra, the mythical, many-headed creature which would grow two heads whenever one was cut off. It is only fair to admit at the outset that I cannot lay claim to have slain the beast. As a matter of fact, by the time the reader finishes the article, he may have concluded that the beast has more heads than ever!

In “Valuation Under Uncertainty, ” which recently appeared in this Journal (September 1967), Houng-Yhi Chen argues [1, pp. 313–314] that “Robichek and Myers' criticism [2, 3] of the use of the risk-adjusted discount rate is unfounded, ” and suggests that our “conclusions must be based in part on a misunderstanding of the risk-adjusted discount rate method.” These charges are without foundation, as we will show here.

This paper considers several related problems in the theory of optimal capital structure for corporations. It is divided into four sections, which may be briefly summarized as follows.1. Modigliani and Miller (MM) proposed that under the assumption of perfect markets and in the absence of taxes on corporate income, the total market value of the firm is unaffected by leverage. They showed that the leverage irrelevance proposition holds for “non-growth” firms when all investors agree in their estimates of the expected amount and the risk of each firm's future earnings. In section I, we show that this conclusion is not affected by growth trends or heterogeneous investor expectations. However, our analysis uncovers several additional assumptions which must be made explicitly for MM's Proposition I to hold. These additional assumptions pertain to the effects of leverage on the firm's future financing needs and future investment decisions. The generalized state-preference framework used for this demonstration is retained for subsequent discussion.