Pricing training and development programs using stochastic CVP analysis

Abstract

This paper sets forth, analyzes and applies a stochastic cost-volume-profit (CVP) model specifically geared toward the determination of enrollment fees for training and development (T+D) programs. It is a simpler model than many of those developed in the research literature, but it does incorporate one advanced component: an 'economic' demand function relating the expected sales level to price. Price is neither a constant nor a random variable in this model but rather the decision-maker's basic control variable. The simplicity of the model permits analytical solutions for five 'special prices': (1) the highest price which sets breakeven probability equal to a minimum acceptable level; (2) the price which maximizes expected profits; (3) the price which maximizes a Cobb-Douglas utility function based on expected profits and breakeven probability; (4) the price which maximizes breakeven probability; and (5) the lowest price which sets breakeven probability equal to a minimum acceptable level. The model is applied to data provided by the Center for Management and Professional Development at the authors' university. The results suggest that there could be a significant payoff to fine-tuning a T+D provider's pricing strategy using formal analysis. Copyright © 2005 John Wiley & Sons, Ltd.

Research on Pricing Strategy and Profit-Distribution Mechanism of Green and Low-Carbon Agricultural Products’ Traceability Supply Chain

“…In 1922, Williams first proposed the words "break-even" and "balance point" to describe the key points [52]. Yunker [53] proposed that CVP analysis can solve how product income and cost affect sales and can provide clear and understandable results to managers through simple calculations. DISKIN [54] and Kikuta [55] found that the Raiffa value method is a cooperative-game income-distribution method that considers the upper and lower limits of income distribution to protect the weak to a certain extent.…”

Fluctuations of company yearly profits vs. scaled revenue: Fat-tail distribution of Lévy type

“…Several attempts have been made in order to incorporate a stochastic be-havior of profits into the analysis (see e.g. [5][6][7][8][9][10]), in which fluctuations are assumed to be normally distributed.…”

“…( 9) and Eq. (10), can be accurately performed in order that ∆π = 0. This is achieved for γ g ≃ 0.052, the value used in the discussions above.…”

“…Clearly, the question arises of how to estimate in a more realistic fashion profit fluctuations, and therefore attempting to improve the accuracy of earnings predictions, the latter being closely related to the issue of profitability or break-even point [4]. Several (a) E-mail: eduardo.roman@mib.infn.it attempts have been made in order to incorporate a stochastic behavior of profits into the analysis (see, e.g., [5][6][7][8][9][10]), in which fluctuations are assumed to be normally distributed.…”

“…Therefore, we postulate that the expected mean profit p is a function of r and obeying p = γ g r, with γ g ∼ = 0.052. (10) We will explain below the reason for choosing the above value for γ g . Thus, in the present context, company mean profit is a function of solely the actual company revenue r, times a global market parameter γ g , which is taken the same for all companies.…”