The effect of cross sectional cost allocations on the statistical variance of accounting earnings

Cross sectional cost-allocations (COSAC) (allocation of costs to different products or objects at the same time intervals) are routine accounting procedures for most organisations. However, the purpose and decision making usefulness of COSAC remains controversial. Does COSAC have meaningful statistical purposes? If so, is there an optimal or better COSAC? Prior literature have discussed the criteria of judging different cost allocation methods under the concept of estimation of long term profitability - a concept defined as income smoothing measured by statistical variance. This allows an objective comparison between different COSAC, a central concept to this thesis. This thesis discusses the examinations of COSAC on statistical variance of earnings in both semi-theoretical and theoretical contexts. These analyses showed that some COSAC do have meaningful statistical purpose, allowing greater income smoothing effect, as opposed to not allocating any costs. From simulation analysis of commonly used COSAC such as quantity based, equal apportionment, ABC and sales to production ratio, cost allocation under perfect information (perfect) and ABC with consistently high accuracy (abc) gives the best income smoothing effect. Further, theoretical analyses on the optimal income smoothing showed that while abc and perfect do not always give the best estimation of the long term profit, it tends to reduce the statistical variance of earnings in many cases. Interestingly, for profitable firms, optimal income smoothing effect firms often occurs when one over-allocates costs, a phenomenon consistent with the accounting conservatism principle. Additionally, this thesis examines the use of generalised lambda distribution to model the cost and physical parameters of real life accounting numbers into the Statistical Activity Cost Theory framework. The development of this technique provides the basic tools to extend this research, by incorporating real world accounting data.