cost allocation, mean absolute relative error, service departments


There are several methods (direct, step, reciprocal) to allocate the cost of service departments to operating departments. Most cost accounting textbooks describe the direct and step methods in detail, but only briefly refer to the reciprocal method. Although the reciprocal method is generally regarded as the most accurate, it is also the most complicated and often requires the use of simultaneous equations and matrix algebra. Kaplan and Atkinson (1998) report that the reciprocal method was initially recommended by the Cost Accounting Standards Board (CASB), but based on industry concerns regarding the complexity of the method, the CASB modified the proposed standard to allow either the reciprocal or step methods, or the direct method if its results approximated the results of the other two methods.

Electronic spreadsheet software has greatly facilitated the reciprocal method by providing matrix algebra functions. This paper illustrates the use of Excel to perform the reciprocal method on simplified textbook problems. As such, the value of this paper is largely pedagogical. However, the paper also makes an original empirical contribution by comparing the relative accuracy of the direct and step methods. Using simulation, allocation error data are computed for the direct method and two popular versions of the step method. The results show that the mean absolute relative error (MARE) of the step method is significantly less than the MARE of the direct method.

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