Abstract
Cost–volume–profit (CVP) analysis is a widely used decision tool across many business disciplines. The current literature on stochastic applications of the CVP model is limited in that the model is studied under the restrictive forms of the Gaussian and Lognormal distributions. In this paper we introduce the Mellin Transform as a methodology to generalize stochastic modeling of the CVP problem. We demonstrate the versatility of using the Mellin transform to model the CVP problem, and present a generalization of the CVP model when the contribution margin and sales volume are both defined by continuous random distributions.
Highlights
As a part of overall long-term business strategy, organizations are continually faced with the task of deciding between competing alternatives
The Mellin transform may be defined for −∞ < x < ∞, but for application purposes we focus only on the positive part
Cost–volume–profit (CVP analysis) is a decision tool that is used in many facets of managerial decision making
Summary
As a part of overall long-term business strategy, organizations are continually faced with the task of deciding between competing alternatives. The research bridges the aforementioned gaps of the stochastic CVP model and contributes to supporting an expanded scope of application for the model, as the model’s resulting profitability distribution (which would no longer have to be restricted to being normally or lognormally distributed) and multiple stochastic input parameters can be used. This extended scope of modeling flexibility enhances the attractiveness and application of the model in decision-making environments where uncertainty exists.
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