Product-line selection, production decisions and allocation of common fixed costs

Abstract

Product costs are determined in practice for the purpose of pricing, make-buy and product-line decisions. While many costs are directly assignable to individual products, common costs have historically presented a difficult conundrum. A variety of cost allocation methods are used in practice, or have been suggested in the literature, to attach these costs to individual products. While such procedures are theoretically unsupported, they may be able to mimic the “correct” decisions adequately. In this paper, we investigate the efficacy of certain cost allocation schemes in a competitive environment. The schemes are evaluated with reference to a scenario in which there is a single fixed cost incurred in manufacturing any subset of a set of products. Under idealized conditions, a Cournot-Nash model is developed that describes the number of entering firms and the equilibrium price and production levels. Using this as a point of reference, it is shown that by using gross contribution as an allocation basis, optimal product-line decisions are achieved, without distorting the selection of production levels. Moreover, competitive pressure sufficient to drive total net profits close to zero is sufficient to require that any allocation rule supporting optimal product-line decisions yields allocations nearly proportional to gross contributions. An analogy is drawn with the allocation of joint costs to coproducts in a competitive environment, and the corresponding allocation in proportion to net realizable value.