Stochastic Demand and the Equity Capitalization Rate

Abstract

While the relationship between capital cost and financing mix has long been of interest to those interested in exploring firm decisions, detailed study of the relationship between capital cost and the firm's output and investment decisions has awaited development of a theory of the firm which formally incorporates uncertainty. Though only partially developed, such a theory is now available.Sandmo (23), Leland (1 l), Lintner (16), and others in their pioneering works developed the implications of stochastic demand for enterprise optimization. They focused on the effects of uncertainty on a risk averse firm maximizing its utility. Their development implicitly ruled out the firm's participation in external capital markets as Hite (7) points out. These works lead to the models of Long and Racette (17) and Hite (6) which incorporate both capital markets and stochastic demand into the firms operating and investment decisions. The Sharpe (24), Lintner (1 S), Mossin (21) Capital Asset Pricing Model (CAPM) is used to model the capital markets. Though the CAPM imposes rather restrictive assumptions on the capital market structure, this framework allows detailed investigation into the impact of output and investment decisions on risk, equilibrium rates of return, and firm value. This paper focuses on the behaviour of equilibrium rates of return. Since, in the context of the model, it is generally accepted that an optimizing firm should maximize value, this focus requires some justification.That is, one can relate firm decisions directly to the value maximization criterion without stopping to discuss equilibrium rates of return. We feel that our focus serves two important purposes. On a theoretical level, relating the required rate of investment and output allows direct assessment of the impact of managerial decisions on the risk of the firm as specified by the CAPM. On a more pragmatic level, we recognize that required rates of return are of more than passing interest to finance practitioners. The value of an asset is most often assessed by computing the present value of expected future cash flows using some risk-adjusted discount rate as an essential element of the calculation. Our analysis shows that it is not only financing policy which should be considered when establishing the appropriate discount rate. The level of output and the size of investment may be equally important.