Cost Allocation II – Death Spirals Accounting Allocation of Indirect Costs of a Cost Center to Departments ¾ Assume the following: IT Department costs $100,000/month 5 Departments have equal access to IT services Current allocation is $20,000/month to each 1 Allocation of Indirect Costs of a Cost Center to Departments Dept. A B C D E Outside Cost $ 18,000 $ 22,000 $ 30,000 $ 30,000 $ 30,000 $ $ $ $ $ Total $130,000 $100,000 Charge 20,000 20,000 20,000 20,000 20,000 Result Unhappy, wants out Happy Happy Happy Happy Allocation of Indirect Costs of a Cost Center to Departments Dept. A B C D E Outside Charge Charge Charge Charge Cost 1st Iteration 2nd Iteration 3rd Iteration 4th Iteration $ 18,000 $ 20,000 exits 22,000 20,000 25,000 exits 30,000 20,000 25,000 33,333 exits 30,000 20,000 25,000 33,333 exits 30,000 20,000 25,000 33,333 exits Total $130,000 $100,000 $100,000 $100,000 ??? This is a “death spiral” -- a positive feedback loop. Allocation of Indirect Costs of a Cost Center to Departments Dept. A B C D E Total Outside Cost $ 18,000 $ 22,000 $ 30,000 $ 30,000 $ 30,000 $130,000 Charge $ 20,000 $ 20,000 $ 20,000 $ 20,000 $ 20,000 $100,000 ¾ Why might departments C, D, and E have a higher outside cost than department A? Should they pay more for IT services than A? 2 Allocating Costs to Departments - General Points ¾ Charge cost center costs to departments based on % of cost center products they use, so that these departments properly incorporate cost center costs in their decisions. ¾ Under-charging some departments for cost center use implies that these under-charged departments are be “subsidized” by other departments using the cost center ¾ When a cost center is not operating at capacity, allocation of the cost center’s overhead costs may result in allocated costs exceeding the cost of outside alternatives. Thus departments purchase products from external parties. ÎResult in the firm overpaying for products. The Issue of Joint Costs ¾A joint cost is incurred to produce two or more outputs from the same input. ¾Consider a firm that produces fillets, drumsticks and wings from chickens. ¾The chicken and the initial processing of separating it into various parts costs $2.00 Joint costs - Split-Off Point ¾ Split off point: the point beyond which further processing has to take place for fillets, drumsticks and wings before they can be sold. ¾ Assume following data Price Further Processing Cost Fillets 2.40 (0.80) Drumsticks 0.80 (0.04) Wings 0.30 (0.16) NRV* 1.60 0.76 0.14 *Net Realizable Value 3 Joints Costs – How To Allocate? ¾By weight seems appropriate ¾Weight in oz Weight %age weight Allocated Cost Total Fillets 32 16 100% 50% 2.00 Drumsticks Wings 12 4 37.5% 12.5% 1.00 0.75 0.25 Net Profits With Joint Cost Allocation ¾With weight-based allocation, Fillets Drumsticks Wings NRV Joint costs allocated 1.60 (1.00) 0.76 (0.75) 0.14 (0.25) 2.50 (2.00) Net Profit 0.60 0.01 (0.11) ¾ If input/output prices and yields are fixed, then it appears optimal to drop wings Joints Costs – How To Allocate II? ¾Drop wings ¾Redistribute joint costs by weight across fillets and drumsticks ¾Weight in oz Weight %age weight Allocated Cost Total 28 100% Fillets 16 57% 2.00 1.14 Drumsticks 12 43% 0.86 4 Joint Cost Allocation – Death Spiral? ¾ With weight-based allocation, Fillets Drumsticks NRV 1.60 0.76 Joint costs allocated (1.14) (0.86) Net Profit 0.46 (0.10) ¾ If input/output prices and yields are fixed, then it appears optimal to drop drumsticks ¾ With only fillets, joint cost allocation is easy! Fillets NRV 1.60 Joint costs allocated (2.00) Net Profit (0.40) ¾ If input/output prices and yields are fixed, then it now appears optimal to drop fillets! Joints Costs & NRV ¾ Allocate by proportion of NRV NRV %age NRV Allocated Cost Total 2.50 100% Fillets 1.60 64% Drumsticks 0.76 30.4% Wings 0.14 5.6% 2.00 1.28 0.61 0.11 ¾ With above allocation, NRV Joint costs allocated 1.60 (1.28) Fillets 0.76 (0.61) Drumsticks 0.14 (0.11) Wings Net Profit 0.32 0.15 0.03 Joint Costs & NRV ¾ Proportion of NRV (Net Realizable Value) is the only correct way to allocate joint costs ¾ Why? Once the joints costs are incurred, the company is going to have fillets, drumsticks and wings anyway. As long as the profit margins on each of those products are positive, the joint costs are essentially irrelevant in deciding the relative profitability of product lines. 5 Summary ¾ Death Spirals result not just from overhead but from cost-of-raw-material allocations, allocations as well ¾ In most or at least many cases, there are credible alternate allocation methods to avoid death spirals. Eg, joint costs should be allocated using NRVs ¾ But one has to be careful! 6