This paper considers CVP analysis in a situation where: (i) a stochastic price‐demand relationship exists for the product, (ii) production quantity fixed at the beginning of the period may not be equal to the actual demand realized in the period, (iii) the difference between production quantity and realized demand results in either shortage or surplus cost. Procedures for determining optimal price level and production quantity are developed for the managerial objectives of maximizing either (i) expected profit, (ii) expected utility, or (iii) probability of achieving a profit target. Résumé. Cet article examine l'analyse des interactions coût‐volume‐profit dans un contexte où: (i) une relation stochastique entre le prix et la demande existe pour le produit, (ii) la quantité de production établie en début de période peut ne pas être égale à la demande réelle atteinte au cours de la période, (iii) la différence entre la quantité fabriquée et la demande atteinte donne lieu à un coût soit de pénurie ou d'excédent. Des procédés de détermination du niveau optimal de prix et de la quantité fabriquée sont élaborés dans le cadre d'objectifs de la direction visant à maximiser soit (i) le bénéfice espéré, (ii) l'utilité espérée, ou (iii) la probabilité d'atteindre un bénéfice cible.

By analyzing the performance of various alternative approaches under a set of reasonable criteria, this paper demonstrates that, contrary to popular implications, direct simulation is the superior approach for stochastic CVP analysis. Also presented are simple formulas for controlling and determining the accuracy of simulation results. Besides being relevant to practitioners seeking an efficient approach for stochastic CVP analysis and other similar problems, this study should also affect the future direction of stochastic CVP research.

The often substantial amount of uncertainty associated with unit volume, unit variable cost, fixed cost, or even unit price in cost-volume-profit (CVP) analysis has made apparent the need for an easy-to-use and accurate means of making probabilistic statements about profit. Over the last dozen years, three main approaches to stochastic CVP analysis have evolved. They are Chebyshev-type inequalities approach, direct simulation approach and theoretical distribution approach. The study of Ferrara-Hayya-Nachman (FHN) considers an important aspect of the third approach. However, the purpose of this paper is to show that the study of FHN is based on inappropriate statistical methodology and their recommendation is, therefore, invalid. Thus, at the current stage of development, it appears that a practitioner should seriously consider using the direct simulation approach. This approach, is easily implemented on even a small computer and provides reasonable levels of accuracy. On the other hand, the facility of application of the theoretical distribution approach to CVP analysis continues to be attractive.

Human Capital, Human resource accounting, Depreciation, Markovian personnel system

Shih [1979] recently proposed a general decision model for CVP-analysis under uncertainty, and he presented three major results for the model: (1) derivation of profit's probability distribution, (2) formulas for computing profit's mean and variance, and (3) formulas for determining the production quantity to maximize the probability of achieving a target profit. The purpose of this Comment is to present simpler and more general formulas for Shih's problems (2) and (3). These formulas considerably enhance the practicality of Shih's model.

The article focuses on cost-volume-profit (CPV) analysis. Professors J.E. Hilliard and R.A. Leitch have recently proposed recently that the primary variables in the standard CVP equation be assumed lognormally distributed. They claim two major advantages for using this distribution form. Using lognormal distributions solves the problem associated with the multiplicative operation. The distribution form is more appropriate for describing the behavior of the primary variables. Authors feel that these claims warrant careful scrutiny. The basic CVP equation is presented in the article. It is described that to study functions of several random variable samples analytically is generally difficulty. Authors emphasize that although using lognormal distributions will simplify the multiplicative operation; the subtractions become problematic, since subtracting one lognormally distributed from another produces complicated distribution forms. Using the lognormal distribution necessitates grouping two of the primary variables together and fixing a third one constant; as a result, the richness of the model is reduced considerably.

This article presents the authors' views on the criticism of their article which evaluated human resource valuation models and presented a new model based on the actuarial concept of homogeneous group and Markov analysis, published in an earlier issue of the journal "The Accounting Review." It is important to note that there are two kinds of products for two K-element column vectors, namely, the scalar product and the vector product. According to the authors, it should also be noted that the scalar product of two column vectors is a column vector, but the vector product of two column vectors results in a scalar. The authors feel that a scalar product is more appropriate, and their equation is preferable to the one suggested in the criticism of their article. The accuracy of a solution depends on two components, namely, the accuracy of the model's parameters and the accuracy of the computational procedures. In the human resource valuation model, two groups of parameters used are, the rank transitional probabilities and the economic values of unit period of service. All these have to be estimated statistically.

The article informs that human resources is of importance to management as well as to outside users. Accountants are faced with the challenge of designing systems which are capable of providing accurate and reliable information about human resources. The model in this article provides a framework for determining the value of these resources. This model is based on valuation of groups rather than individuals; the term "group" refers to a homogeneous group of employees working in a firm. This group approach represents a major difference over the prior models. In this model, a Markov chain representation is used to consider the career movements of the employees within the firm and the chances of their leaving the firm before their retirement or death. The probabilities of career movement and of exit from the firm can be estimated on the basis of historical data and the Markovian chain technique. Since the pattern of movements is considered to be constant, the probabilities determined for one period are extended to future periods.

This article presents a general framework for handling a large class of stochastic management models that includes the stochastic CVP problem and stochastic present value analysis. After demonstrating the need of more flexibility and realism in risk analysis modeling, the authors consider the "four-moments" approach in describing diverse probability forms. Next, a set of easy-to-use formulas are presented for computing the exact values of the first four moments of the model's objective variable. Finally, methods. are discussed for achieving the two most important purposes of stochastic management modeling: estimating the probability of realizing various objective variable levels and determining the expected utility of a risky project. The entire framework blends several original formulas with some well-established techniques previously little known in the accounting/management literature. Compared to other recently published approaches, this framework permits more realistic modeling, requires less computations and provides more accurate and meaningful managerial information.