Optimization of the break-even point for non-homogeneous products sales

Abstract

Break-even point analysis is a classic management accounting tool. In the case of the sale of one product, the notion of the break-even point is well described in the literature, conceptually simple, and relatively easy to apply in business practice. However, when it comes to heterogeneous sales, consisting of various products, this problem is presented less frequently, and the methods used in this case exploit rather arbitrary and often ambiguous criteria. The aim of the article is to present and analyze alternative ways of determining break-even points for non-homogeneous sales based on econometric modeling methods. Production levels determined by the proposed methods meet the classical condition set for the break-even point, and in addition are optimal from the point of view of criteria used in the economic analysis. Three methods were presented: first – based on the classic criterion of profit maximization and linear programming, second – minimizing variable production costs and taking into account the scale effects on the production costs, and third – taking into account the random aspect of the business operations and maximizing the probability of profitability. According to the authors' knowledge, the proposed methods are original and are not known in the existing literature on the subject.