Multiproduct Cost-Volume-Profit Analysis: Mathematical Representation Of Classical Linear Models

The subject of research in the paper is classical multiproduct Cost-Volume-Profit (MCVP) analysis models. Methods of mathematical representation and proof, as well as empirical verification on a selected specific case from practice, were used. It has been mathematically shown that the known linear relational MCVP model, which starts from the equation of operating income, and the model that considers the average unit margin, results in identical solutions that can be substituted with one general solution. This way, the determined general solution can be used also for the financial calculation of the multiproduct break-even point. Regarding the use of contribution coefficients of individual products, the derived general MCVP models can cover absolute or relative relations in such a way that a defined structure (historical or target) of the production volume relations of individual products is maintained, that no product is declared as the base or that any product is declared as the base product. Also, the obtained general MCVP models provide solutions in one step, so they are simpler to understand and implement compared to classical approaches, which can improve the efficiency of their use.