The Use of Probability Inequalities in Multiproduct C-V-P Analysis Under Uncertainty

Abstract

Traditional cost-volume-profit analysis is based on a certainty-assuming model in which price (p), variable cost per unit (v), sales volume (x), and total fixed cost (F) of; a single-product firm, or one product of a multiproduct firm, are assumed to be known. With given p, v, and F, total profit (P) can be determined based on a point estimate of x, and the effect on profits of different sales volume levels (i.e., picked constants) over the relevant operating range can be analyzed. The traditional C-V-P model is extended to the multiproduct firm by the additional assumption of a given sales miix to determine total profits, as well as by analyzing the effect on total profits and break-even sales of different sales mixes. Formulations of the C-V-P model under conditions of uncertainty have generally taken the form of treating sales volume as a random variable, with the other variables held constant, and determining the probabilities of achieving various target profit levels, break-even sales, and possible loss levels.! Multiproduct C-V-P analysis under uncertainty has been further extended by using multivariate analysis in which the interdependency of product demand is accounted for.2 However, all of these C-V-P analyses