Cost Allocation in Multiagent Settings.

Abstract Cost allocation is a pervasive practice in accounting. Horngren and Foster (1987, 411) define it as "the assignment and reassignment of a cost or group of costs to one or more cost objectives." An important form of cost allocation is the apportionment of corporate-level costs to various decentralized profit centers. The reason usually given for this procedure is that it is "a major means of getting subordinates to behave as desired by top managers" (1987, 422). Although such allocations have been criticized in the agency literature (Demski 1981) as being irrelevant for motivating managers in the presence of compensation contracts, this article identifies a precise role for indirect cost allocations, in conjunction with other instruments such as participative budgets, in settings with multiple divisions. A survey by Fremgen and Liao (1981) showed that 84 percent of firms allocated at least part of their indirect costs to their profit centers, and 80 percent did so for the purpose of evaluating the performance of profit center managers. The major aim was to remind managers that indirect costs exist and that at least a portion of these costs had to be covered by profit center earnings. Further, Atkinson's (1987) poll reported that the primary objectives of allocating indirect costs were the motivation of employees and the provision of signals for resource allocation. There has been little analytical work, however, on the economic role played by cost allocation systems. Demski (1981) claims that allocation mechanisms are useful only if they provide additional information that can be contracted upon. Similarly, Baiman and Noel (1985) show that in certain multiperiod settings, it is optimal to compensate an agent on the basis of prior periods' realizations of costs that were not in the agent's control, provided these costs affect the principal's capacity decisions. Magee (1988) identifies conditions under which an agent is compensated according to the usage of some resource, in addition to output. The agency studies described above cannot address cost allocations across operating units since they do not model multiple productive divisions among which common costs are to be allocated. Further, because they model single-agent settings, the second-best incentive schemes they derive suffice to motivate managers efficiently; thus, there is no role for allocations unless they provide additional information to the owner. With multiple divisions, however, simple compensation contracts do not provide adequate incentives to guarantee the owner's desired outcome. The role for allocations, over and above that of second-best contracts, in providing assurance to the owner is demonstrated here with a one-period model of an entrepreneur who incurs fixed costs in the production of different products by two workers. When the workers have correlated private information about the productivity 01: a common, central resource, the entrepreneur may fail to recover the fixed costs because the optimal payment schedules encourage the workers to misreport the productivity of the resource. By asking each worker to submit a budget to determine overhead rates, and by evaluating managers on their divisional profit after allocation of overhead costs, the entrepreneur can obtain the second-best return on the fixed investment. This mechanism is then compared to allocation systems observed empirically and to those recommended in the accounting literature. The mechanism design approach pursued in this paper, with the game itself a variable, enables the study of procedures by which accounting numbers are derived for purposes of performance evaluation. The accounting system is not imposed as a monitor or source of information; its value arises from its procedures, which enable the owner to play off the managers' private information against each other to guarantee a second-best return on investment. In the absence of such a system, the division managers would gain from implicitly colluding in their use of the central resource. The allocation scheme coordinates their actions and induces them to act in the manner desired by the owner. This positive role for the allocation of indirect costs in conjunction with the budgetary process emphasizes the value of a cost allocation system as a set of linked motivational devices.