WEALTH, WELFARE, AND THE PRICE OF RISK

Abstract

IN THE THEORY of business finance, the most commonly advocated criterion for corporate investment is that such investment (and its associated financing) should be undertaken if and only if it serves to increase the price of the firm's common shares. This rule is often justified on the basis that an increase in the price of shares results in increased stockholder wealth which in turn results in increased stockholder welfare. In this paper, conditions are discussed under which maximum wealth does not correspond to maximum welfare. As one might suspect, these conditions involve situations in which capital investment on the part of the individual firm influences not only the wealth of its stockholders but also the prices and/or characteristics of existing assets available to stockholders in the market. In these situations changes in nominal stockholder wealth due to corporate investment may not correspond in direction to the concomitant changes in the size of stockholders' real opportunity sets. The discussion of conditions under which changes in wealth do not measure changes in welfare naturally leads to consideration of (a) conditions under which the price maximization rule is equivalent to maximization of stockholder welfare, and (b) alternative investment criteria which avoid the problems associated with price maximization. With respect to the optimality of the price maximization rule it is argued that rather stringent conditions on capital market structure are required. This is particularly true of, though not limited to, the case of uncertainty. As for alternative investment criteria, a simple and operational welfare maximizing rule is given of which price maximization is a special case under appropriate conditions. The welfare rule, however, applies to all capital market structures. The motivation for this paper stems largely from the recent development of detailed mathematical valuation models. These models provide, in effect, a formula relating changes in the equilibrium price of a firm's shares to the variables which specify the nature and scale of new investment and its associated financing. This, in turn, offers the opportunity for a rather literal and exact application of the price maximization rule in that mathematical conditions can be derived for maximization of the pricing formula with respect to the investment and financing variables. The capital asset pricing model of Sharpe [14], Lintner [7, 8], and Mossin [13], for example, has been used in this manner by several authors, including Lintner [8] and Mossin [12]. In this paper it is argued that, because of the potential divergence of wealth