Review of Quantitative Finance and Accounting, 12 (1999): 159–170
© 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.
CVP under Uncertainty and the Manager’s Utility
DEREK K. CHAN
Department of Accounting, School of Business and Management, Hong Kong University of Science and
Technology, Clear Water Bay, Hong Kong, e-mail: email@example.com.
KIT PONG WONG
School of Economics and Finance, University of Hong Kong, Pokfulam Road, Hong Kong
Abstract. This paper re-examines the model of Kim, Abdolmohammada, and Klein (KAK, 1996) in which
owners of a ﬁrm delegate the production decision to a risk-averse manager. Conﬂict of interest between the
owners and the manager emerges as the latter maximizes the expected utility of his/her own wealth rather than
that of the ﬁrm’s proﬁts. This paper shows that the results of KAK on the expected contribution margin and the
excess return on the risky asset are ﬂawed. Furthermore, while KAK study the effects of delegating the
production decision to the manager on the ﬁrm’s optimal output based on the mean-variance analysis, this paper
derives parallel results within utility functions exhibiting constant absolute risk aversion and any arbitrary
probability distribution functions.
Key words: Cost-volume-proﬁt analysis, conﬂict of interest, risk aversion, multiple sources of uncertainty
Traditional approach of the cost-volume-proﬁt (CVP) analysis under uncertainty postu-
lates that the objective of the CVP analysis is either maximization of expected proﬁts (see,
e.g., Morrison and Kaczka (1969), Johnson and Simik (1971), Dickinson (1974), and
Hilliard and Leitch (1975)) or maximization of expected utility of proﬁts (see, e.g., Magee
(1975) and Adar, Barnea, and Lev (1977)). In the real world, corporations are typically
characterized by the separation of ownership and management. Managers are paid salaries
and given other beneﬁts by the ﬁrm to make decisions on behalf of the ﬁrm’s shareholders.
When managers hold little equity in the ﬁrm and shareholders are too dispersed to enforce
proﬁt maximization, Berle and Means (1932) point out that managers may make decisions
that are in their best own self-interest rather than in the shareholders’ best interest. As
such, Simon (1964), Williamson (1964), and Jensen and Meckling (1976) argue that the
analysis of manager/shareholder relationships should be used for an analysis of the ﬁrm’s
Kim, Abdolmohammada, and Klein (1996) (henceforth KAK) have recently presented
an interesting model which departs from the traditional CVP analysis under uncertainty.
Taking the separation of ownership and management as a fact of life, KAK consider a ﬁrm
which delegates the production decision to a risk-averse manager. To motivate the man-
ager to work, the ﬁrm’s owners offer the manager a linear proﬁt-sharing incentive scheme.
The production decision is complicated by the manager’s access to many investment
instruments, including stocks of other companies which may have direct competition with
@ats-ss2/data11/kluwer/journals/requ/v12n2art4 COMPOSED: 01/13/99 1:34 pm. PG.POS. 1 SESSION: 35