Managerial accountants are often called upon to provide measures of performance efficiency. Such a task is essentially trivial if there is a single input measure and a single output measure. One could simply divide the output measure by the input measure and use the resulting performance efficiency measure to either: (1) compare the unit's performance over time, or (2) compare the unit's performance with other comparable units.
While there are numerous purposes for performance efficiency measures (i.e., performance evaluation, managerial compensation, benchmarking, and cost control, to name a few), the specific purpose of this research is to explain and illustrate how a proposed estimation principle can be used with activity-based costing for determining performance efficiency measures for the purpose of cost control. Activity-based costing is one approach that could be used to develop a performance measure for such purposes. Activity-based costing consists of disaggregating costs into specific cost pools that can be linked causally with their respective activities. Cooper and Kaplan (1992) illustrate how such an approach can be used with purchase order data. The approach consists of dividing the monthly cost of processing purchase orders by the number of purchase orders processed per month. This purchase order cost can then be used as a benchmark for comparison purposes. This approach is very simple and easy to use if there is only one cost pool and one activity with a single cost driver. But there are many realistic scenarios in which there are multiple cost drivers for a single cost pool. For example, faculty salaries for an academic unit (department or college) appear to be driven by at least two cost drivers. Both student credit hours generated and the level of academic degrees offered (bachelor's, master's, and doctorate) appears to drive the amount of faculty salaries for an academic unit. The dilemma is that faculty salaries are in a single cost pool, and there is no simple and objective method for disaggregating faculty salaries. The task of attributing the faculty salary pool to separate activities and cost drivers is essentially impossible. There is no easy way for determining how much of the faculty salary pool is due to: (1) the generation of student credit hours, and (2) the level of academic degrees offered by academic unit.
The methodology explained and illustrated in this chapter allows for the inclusion of multiple cost drivers in determining performance efficiency measures. The allocation of the combined cost pool to individual activities might be regarded as not objectively possible, impractical, expensive, or of insufficient additional value for the costing system. We first consider the problem of estimating average costs per unit of cost driver in such situations when cross-sectional data are available for a set of what we call comparable business units. We also consider application of the same techniques to basic cost models having marginal cost assessment capability, and briefly discuss the setting in which a single business unit is observed over several time periods.
We define benchmark or best practice average costs per unit of cost driver as the average cost rates associated with the most efficient unit(s). A principle of maximum performance efficiency (MPE) is proposed and estimation criteria based on efficiency measures are derived from this principle. This is a generalization of the maximum decisional efficiency (MDE) principle introduced in Troutt (1995) and also discussed in Troutt (1997) and Troutt, Zhang, Tadisina, and Rai (1997). The efficiency measure used may be considered analogous to the cost of unused capacity concept proposed by Cooper and Kaplan (1992). These models also provide a different view on the lack of proportionality of costs to driver levels documented in Noreen and Soderstrom (1994).
A basic assumption underlying the estimation principle employed here is that all business units under comparison seek to maximize their efficiencies in performing their services. The data we study are from public service entities that are presumed to have this goal on behalf of the public interest. However, this assumption needs verification as a kind of model aptness or validation issue similar to the requirement of normally distributed errors in OLS regression. As an estimation model aptness test, we propose what may be called a normal-like-or-better performance effectiveness measure. The estimation models proposed here are linear programming (LP) models. Use of such models in cost accounting is not new. See for example, Demski (1967), Itami and Kaplan (1980), Kaplan and Thompson (1971), and Onsi (1970). These previous works have generally utilized LP models assuming that data are known. That is, they assume that technological coefficients and resource levels are given. Then the dual optimal solution (especially the shadow prices) of these fully specified LP models has been employed for (1) overhead allocation (Kaplan & Thompson, 1971), (2) transfer pricing (Onsi, 1970), and (3) reallocation of costs to multiple products (Itami & Kaplan, 1980). However, the use of LP models enters in a different way in this chapter. Namely, the estimation models are themselves LP problems in which the decision variables are the unknown best practice cost rates. The next section distinguishes between basic cost models and the models used to estimate the parameters of the basic cost models. The MPE principle is also presented here.