Optimization Approach to Constrained Break Even Points with Respect to Price

Abstract

Break even and profitability analysis is a classical and widely used topic in business analysis. Break-Even Point or point of equilibrium is the point of sales volume making neither a profit nor a loss. It is a valuable number to know. Traditional break-even analysis is used to determine how much sales volume your business needs to start making a profit. In this paper, we extend the classical break-even point concept by introducing a new notion of constrained break-even points with respect to prices. In this case, a traditional method of calculating break even point may fail. For this purpose, for finding constrained break-even points, we propose an optimization approach based on solving convex and nonconvex optimization problems. Convex minimization and convex maximization algorithms are used. We show that global minimum, local maximum, and stationary points of both problems are the constrained break-even points with respect to price. The proposed approaches illustrated on some fictitious business examples providing numerical results.