ارزیابی هزینه یابی بر مبنای فعالیت و هزینه یابی بر مبنای عملکرد : رویکرد تئوری-بازی

This study develops a theoretical product cost framework independent of cost assignment concepts. The framework is used in conjunction with cooperative game-theory concepts to develop constructs for evaluating the accuracy of competing cost systems. Cooperative game theory provides rational, non-arbitrary criteria for assigning joint benefits and defines two possible constructs; the set of imputations and the core. Using these two constructs to define accuracy, along with an operational measure of product diversity developed in the study, formal conditions are identified where activity-based costing (ABC) is theoretically closer to the true product cost than functional-based costing (FBC). Our results, therefore, provide a theoretical foundation for ABC.

Many factors influence the decision maker. Essential to many cost-based decisions, such as cost-plus pricing, is information related to product cost. Different product costing methods exist that can provide very different product cost assignments, which could lead to very different decisions. Activity-based costing (ABC) and functional-based costing (FBC) represent two competing product costing methods. FBC is a traditional approach using only unit-level drivers to assign costs to products. ABC differs from FBC in that it uses more cost pools, more cost drivers, and both unit-level and non-unit-level cost drivers. Decision makers, assuming information is relevant, prefer more accurate product cost information to less. Therefore, a desirable characteristic of a product costing system is the ability to provide accurate product cost assignments. Few studies have addressed the comparative accuracy of ABC and FBC. Kee and Schmidt (2000) compared ABC and the theory of constraints in product mix decisions and Brierley et al. (2006) compared product costing practices in different types of manufacturing environments. Pierce and Brown (2006) examined the usage and perceived success of activity-based and traditional costing systems and found no major differences between the two types of systems. However, none of these studies address the issue of relative accuracy of ABC and FBC. When ABC and FBC assignments differ, there are few methods by which to examine and evaluate the relative accuracy of each system. Prior studies (Datar et al., 1993; Banker and Johnston, 1993) seek to obtain a better understanding of underlying cost functions with the objective of obtaining materially different estimates of activity and product costs. When ABC produces numbers that are materially different from the numbers generated by FBC, it is believed that the new numbers will lead to desirable changes in cost-based decisions. However, Dopuch (1993, p. 618) states “no materiality study can demonstrate that one set of cost estimates is more accurate than another unless the researcher knows the true cost function.” Identifying the nature of the true cost function has significant appeal because it would allow an independent evaluation of competing cost systems. Of course, all other things being equal, if the true cost function were known in practice, then the true product cost would be used, the optimal cost system would be revealed, and there would be no need to evaluate the relative accuracy of competing cost systems. However, knowing the true product cost in practice is virtually impossible, which implies representations of the true cost function must be identified to assess the relative accuracy of ABC and FBC. When evaluating product cost assignments, ABC proponents assume that the true product cost is identified under an idealized ABC structure when all cause-and-effect relationships are identified and used in assigning costs. This implies that the relative accuracy of a cost assignment increases as the number of cause-and-effect relationships identified and used increases. Thus, it is assumed that since ABC uses more cause-and-effect relationships in assigning costs than FBC, it provides better numbers for decisions. However, Datar and Gupta (1994) show that increasing the number of cost drivers and cost pools will not necessarily move product costs closer to the “true” product cost. Based on their examination, they also show that cases do exist where improving driver specification or degree of aggregation may not increase product-costing accuracy. Additionally, Homburg (2001) concludes that the accuracy of an ABC system is not dependent upon the number of cost drivers and finds that reducing the number of cost drivers in a system does not impair accuracy. An idealized ABC structure has been used to evaluate loss of accuracy from misspecification of cost pools and/or cost drivers (Babad and Balachandran, 1993; Datar and Gupta, 1996). These studies calculate product-costing errors for ABC systems that vary based on the level of correctness in the specification of drivers and degree of aggregation, but do not explicitly compare ABC with FBC systems. Using an idealized ABC structure to represent the true cost function must be regarded with some suspicion. While an idealized ABC structure may be useful to evaluate and improve less-than-ideal ABC systems, it says nothing about the relative accuracy of ABC if the true cost function does not correspond to the idealized ABC structure. Nor does it provide a fair evaluation of FBC systems. Thus, an independent representation of the true product cost is needed for evaluating competing cost systems. One possibility, developed in this paper, is to use criteria based on cooperative game-theory concepts. Cooperative game theory provides defensible criteria that define how rational agents will share a cost in a non-arbitrary manner. Game-theoretic concepts, such as the core (Hamlen et al., 1977; Balachandran and Ramakrishnan, 1981), and the nucleolus (Hamlen et al., 1977; Barton, 1992) have been used to assess different joint cost allocation schemes. Joint costs, arising from the production of two or more products simultaneously, must be shared on the divisional level in a manner that prevents unprofitable suboptimal decisions by either independent divisions or any potential subcoalitions of divisions (Hamlen et al., 1977). This implies that joint cost allocations must be rational and stable allocations to meet this definition. In cooperative game-theory terms, rational allocations are referred to as imputations and stable allocations belong to the core. The product-costing problem, where multiple products are produced independently in a single plant, is merely an example of the joint cost allocation problem. When a multiple product plant is observed, shared (common) costs are created that take on the same characteristics as joint costs. For example, in a multiple product setting, the cost of the common resources must be assigned to independent products in a manner that would prevent any of the managers of the products to leave the multiple product plant and operate independently. This implies a necessity for rational and stable cost assignments. It is assumed that the true underlying product cost exhibits rationality and stability and would, therefore, be a member of the set of imputations and the core. Based on this representation of the underlying true product cost, alternative product-costing systems can be evaluation according to their membership in these two cooperative game-theory sets. Our analysis begins by producing a theoretical framework that yields constructs that serve as hypothetical benchmarks so that the relative merits of actual cost systems can be evaluated—even if the theoretical cost is not observable or known in practice. Essentially, microeconomic theory is used to identify the theoretical product cost in a single-product setting. We then show that ABC and FBC cost assignments are the same in the single-product setting, assuming no productive or allocative inefficiencies. Next, the microeconomic framework is expanded to include multiple-product settings. Microeconomic theory, using the concept of economies of scope, suggests that multiple-product plants exist because sharing productive inputs can lower production costs (relative to the single-product setting). Our analysis then identifies an infinite set of potential product costs, which depends on the assignment of the shared cost savings to each product. Although it is logical that the true product cost is a member of this set, microeconomic theory offers no further insights about how to identify the correct cost assignment system. However, cooperative game theory does specifically deal with the theoretical division of jointly created savings and helps to reduce the infinite set of potential product costs to facilitate evaluations of competing cost systems. In terms of assessing relative accuracy, a cost assignment system that provides assignments that are members of the sets defined by cooperative game theory will share the same characteristics of the true product cost than a cost system that does not. Using these two game-theory constructs (imputations and the core) to assess accuracy, we prove that ABC product costs belong to the set of imputations and the core, whereas FBC product costs do not give a sufficient amount of product diversity.

Accurate product-cost information is critical for decision makers. To facilitate an evaluation of the accuracy of competing cost assignments, a theoretical product-cost framework was developed independent of cost assignment concepts. This framework represents an infinite set of cost systems, of which the true product cost is expected to be a member. Cooperative game theory provides reasonable restrictions that can be placed on the infinite set of cost systems to reduce the set and provide a definition of accuracy that can be used to evaluate existing cost systems. Two possible constructs offered by cooperative game theory include the set of imputations and the core. An analytical evaluation of ABC and FBC based on these constructs revealed that ABC assignments are always imputations and members of the core and thus, always qualify as potential true product-cost assignments. The analysis further reveals that FBC assignments do not always conform to these criteria. A threshold value of product diversity, PDi, identifies when FBC fails to satisfy the conditions defined by the set of imputations and the core, and therefore, PDi also indicates when ABC is theoretically more accurate than FBC when sufficient product diversity exists. Our results show that, under certain conditions, ABC qualifies as a more accurate product-costing system than FBC. Decision makers rely on information provided by a cost system to make cost-based decisions such as pricing, product mix and make or buy decisions. Therefore, using more accurate product-cost information may impact decision quality, where more accurate information may lead to an increase in the quality of decisions. In addition, the identification of an aggregate ABC assignment ratio, View the MathML sourceεi¯, and PDi in this study has significant implications for research and practice in the area of product costing. For example, the aggregate ABC assignment ratio reduces the apparent complexity of ABC and may provide other practical implications related to implementation decisions or the design of future cost systems. PDi provides researchers with the ability to quantify the source of difference between ABC, FBC, or any other cost systems. PDi also represents a tool that can be used in the future to empirically test for an association between product diversity and cost system choice.