Incorporating Stochastic Demand into Breakeven Analysis: A Practical Guide

Abstract

The plausibility and usefulness of conventional breakeven analysis is augmented by adding a stochastic linear demand function to the basic breakeven equation. The additional complexity from adding this function is not excessive in a mathematical sense, and the payoff to the additional complexity is considerable. Relatively simple explicit analytical formulas are derived for the determination of the price that maximizes expected value of profits, as well as the price that maximizes breakeven probability. A linear stochastic demand function is utilized if price is taken to be the decision variable, but the analysis is exactly analogous if we take quantity (the “production run”) to be the decision variable and utilize the inverse of the demand function, descriptively termed the “price function.” Similarly simple explicit analytical formulas are derived for the determination of the quantity that maximizes expected value of profits and the quantity that maximizes breakeven probability. These optimal price and quantity formulas are simple enough to be easily implemented in an Excel spreadsheet. Although the addition of a demand function (or a price function) to conventional breakeven analysis incurs a significant cost in terms of increased informational requirements, for some managers the marginal gains from applying a more advanced form of breakeven analysis will exceed the marginal costs.