# The Effects of Inaccurate Parameter Estimates in Cost Variance Investigation Decisions

## Article excerpt

INTRODUCTION

Formulating a cost variance investigation decision (CVID) as a cost minimization problem for a multiperiod two state process (Kaplan, 1969, 1975, 1982) is accepted as theoretically sound; well-defined solution procedures are available (Kaplan, 1969; Dittman and Prakash, 1978, 1979). This model, however, uses several parameters that are often difficult and expensive to estimate accurately. The purpose of this study is to investigate how inaccuracies in these parameters affect the quality of the CVID made with Dittman-Prakash's procedure. Our results are useful for estimating the appropriate expenses warranted for obtaining each cost parameter and in evaluating the robustness and superiority of the two state cost minimization CVID models relative to the earlier and simpler alternatives.

Many managerial accounting researchers have been concerned about the mathematical and/or computational complexity of the more sophisticated models; therefore, some researchers considered the use of simpler models. (See, e.g., Magee's (1976) study in the case of CVID models.) Given today's proliferation of computers and software, however, the computation cost of even the most complex managerial accounting models (e.g., Kaplan's (1969) CVID model) is almost always trivial compared to the cost of determining the values of the model's parameters. Rejecting a managerial accounting model may be justified by the high cost of parameter estimation or the sensitivity of the solutions' quality to parameter errors, but seldom by mathematical/computational considerations.

BRIEF REVIEW OF THE CVID PROBLEM

Reviews of CVID models are found in Kaplan (1975, 1982), Magee (1976), and Greenberg (1986). We consider only the following formulation:

* At the end of each period the cost generation process can be either in control or out of control;

* One decides whether an investigation (at a cost) is warranted on the basis of a reported cost (or cost variance) x for the period;

* If an investigation reveals that the process is out of control, it is corrected (at a cost) so that the next period begins in control;

* One has to determine a policy R to be used in all periods as follows: investigate if x [greater than] R, otherwise do not investigate.

Among procedures for solving this formulation, Kaplan's (1969) dynamic programming solution gives the multiperiod theoretical optimum, but Dittman-Prakash's procedure (1978, 1979) is accepted more widely because it is much simpler and yet gives solutions close to the optima.

SUMMARY OF DITTMAN-PRAKASH'S APPROACH

Dittman and Prakash state their model in terms of cost distributions; the following modification uses the cost-variance distributions, which matches our needs better.

Dittman and Prakash show that C'(R), the expected system cost (including operating, investigation, and correcting costs) per period for any policy R, is:

(1) C'(R) = [M.sub.i] + C(R)

where:

(2) C(R) = [Delta] - [gI.[F.sub.i](r) - I - (1-g)K + g[Delta]] [center dot] 1-[F.sub.o](r)/1-g[F.sub.o](r).

The parameters are:

[M.sub.i] = Mean operating cost/period when the process is in control;

g = Transition probability, the probability that the cost process remains in control at the end of a period given that it was in control at the beginning of the period;

[F.sub.i](.) = Distribution function of the in control cost-variance distribution, with mean = 0;

Fo(.) = Distribution function of the out-of-control cost-variance distribution, with mean = [Delta];

I = Investigation cost; and

K = Cost to correct an out-of-control process.

The objective is to find [R.sup.*] that minimizes C'(R) in equation (1), which is equivalent to finding [R.sup.*] that minimizes C(R) in equation. (2) because [M.sub.i] is fixed and does not vary with R for a given process. This paper considers only C(R). …

Search by...
Show...

### Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.