Break-even analysis under randomness with heavy-tailed distribution

Abstract

Break-even analysis is a tool suitable for making short-term decisions about the quantity of production. Traditional break-even analysis is based on certain assumptions among which the most important are the following limitations: variable costs are linearly dependent on sales volume; price of the product is stable; fixed costs do not change. Moreover, we assume that all the input variables (variable costs per unit, fixed costs and price of the product) are known with certainty. However, these variables may be random and thus not known in advance. For instance, a firm can be price-taker – the price of the product is a random variable determined by the market, variable costs per unit depend on the price of raw materials, which again cannot be known in advance with certainty. In our paper, we discuss the break-even analysis introducing randomness. We focus on two input variables – the price of the product, which influences the revenues, and the variable costs per unit, which influence the costs. Both random inputs are supposed to follow joint normal distribution and normal inverse Gaussian distributions joined together by copula function.