Financial cost allocations: a game-theoretic approach

Arthur L. Thomas has argued that financial cost allocations in general and depreciation allocations in particular are arbitrary and incorrigible whenever the firm's revenues are generated by interacting assets. The game-theoretic Shapley technique is applied to the net-revenue-contributions approach to depreciation allocations. The resulting allocations, it is maintained, are non-arbitrary and corrigible if statement users and the accounting profession are willing to accept a constitution of three "reasonable" allocation axioms. IN two research studies published by the American Accounting Association, Arthur L. Thomas [1969, 1974] concludes that financial cost allocations are not only arbitrary but also incorrigible, i.e., incapable of verification or refutation by reference to external "real world" phenomena. While maintaining that the logic can be generalized to all financial cost allocations, Thomas particularizes his argument to depreciation allocations. He contends that either depreciation allocations are essentially arbitrary because they have no theoretical justification, or they are predicated on a net-revenue-contributions (NRC) approach. The latter appears to be justifiable since the resulting allocation pattern follows the expected net revenue contributions of the asset or project to the firm-entity. However, even NRC allocations cannot be justified if the inputs to the revenue generating process interact to produce the revenues of the firm. Unless the inputs operate independently of each other, the allocation of depreciation over time must result in the arbitrary allocation of a joint cost to a specific asset. Since there is no unique and identifiable causeand-effect relationship between a specific asset and the revenues generated by interacting assets, any and all allocations are equally justifiable and, therefore, incorrigible.' In this paper I hope to demonstrate that, time-dependent financial cost allocations, such as depreciation, need not be arbitrary or incorrigible even though asset interactions are prevalent. In what follows, the first section illustrates Thomas's argument in a simple depreciation allocation example. The next section briefly reviews the Shapley technique for allocating joint costs and applies it to my example. The final section concludes that Shapley values represent a defensible and corrigible cost allocation mechanism. THE COST ALLOCATION PROBLEM,