6. Activity Based Costing (ABC)

Transcription

1 6. Activity Based Costing (ABC) Background Traditional cost accounting is characterized by considerable aggregation a small number of synthetic variables Overhead is allocated neglecting finer details Advances in technology led to increase in overhead as opposed to direct cost Traditional allocation of overhead became subject of criticism ABC The idea of ABC is not substantially different from traditional accounting Ingredients remain the same: aggregation, LLAs, and allocation Difference: less aggregation, more synthetic variables Goal: consider finer details in order to improve quality of unit cost estimation 1

2 Example Two products are produced Product 1: standard product Product 2: advanced product The firm uses an actual costing system and has defined the following cost pools: 2

3 Unit cost determination with traditional accounting Assume an extremely simple costing system A single overhead pool (all four pools are aggregated in one) Direct labor is the only synthetic variable used to allocate overhead Unit costs are displayed in the table below Estimated cost curve: 3

4 Problems with the above procedure Nothing is said about the underlying technology Indirect product costs are a large percentage of total cost Unlikely that all overhead cost change in similar fashion with direct labor Additional information on overhead pools: OV A aggregates primarily labor support services OV B aggregates costs associated with materials such as receiving, handling, and preparing materials for assembly OV C aggregates cost of setup and inspection activities OV D contains miscellaneous costs Managers believe that the resources are roughly associated with resource consumption of the other pools in a ratio of 1:6:3 4

5 Unit cost determination with ABC Using the information about overhead pools synthetic variables are chosen carefully: OV A : direct labor cost OV B : direct material cost OV C : number of setups (2 and 20 setups for product one and two resp.) OV D : allocated to other overhead pools 5

6 Unit cost calculation Estimated cost expression: 6

7 Underlying Structure Definition 18: An activity is a sphere of productive action that is modeled as if it is a separable form of production, with its own output measure and cost structure. Definition 19: An activity based costing (ABC) system partitions the firm s technology into a set of activities, approximates each activity s cost structure with an LLA given by and derives unit costs by allocating activity costs to products via each LLA s synthetic variable, 7

8 Back to the firm s technology Firm produces two products in quantities q 1 and q 2 Labor is the only direct factor 3 overhead pools Single period, no period costs 8 factors z 1...z 6 purchased z 7 and z 8 internally produced Market prices of purchased factors P 1...P 6 Firm s total expenditure: First (second) factor direct labor for first (second) product: assume that z 1 (z 2 ) units of direct labor are required to produce one unit of the first (second) product 8

9 Optimization program (7.3a) total expenditures on purchased factors is minimized (7.3b) and (7.3c) denote how much labor is required (7.3d) and (7.3e): z 3 and z 7 as well as z 4 and z 8 are substitutes; product 1 and 2 need different quantities of factors to be produced (7.3f): z 5 and z 6 are needed to internally produce z 7 and z 8 9

10 Cost pools and marginal cost 10

11 Traditional Answer Assume all indirect product costs are aggregated into a single overhead pool with direct labor cost as the only synthetic variable OV=OV A +OV B +OV C = DL=P 1 z 1 +P 2 z 2 Allocation rate: Unit cost: Cost curve: 11

12 ABC Answer Activities need to be identified ((7.3b)-(7.3f)) Activity consumptions determine allocations (7.3b) and (7.3c) are direct costs - treated as with traditional costing (7.3d)-(7.3f) are indirect costs Constraint (7.3f): Factors z 5 and z 6 are used to produce z 7 and z 8 Costs for z 5 and z 6 are recorded in Overhead pool OV C Let s call the activity provided service Allocation rate: f C =OV C /x C =OV C /(z 7 +z 8 ) LLA accordingly given by: OV C =f C (z 7 +z 8 ) Note: zero intercept, full cost allocated 12

13 ABC Service cost needs to be allocated to overhead pools OV A and OV B Constraint (7.3d): Assume again the activity is some service : x A =A 11 q 1 +A 12 q 2 Allocation rate: LLA: 13

14 ABC Constraint (7.3e): Synthetic Variable: x B =A 21 q 1 +A 22 q 2 Allocation rate: LLA: Unit costs: Implied cost curve: 14

15 Lessons from the examples It is typically impossible to avoid errors Tailoring the accounting we can reduce estimation errors regarding one product s unit cost This occurs at the cost of becoming less precise with regard to another product Errors imply that some products are overcosted and others undercosted Switching to ABC does not necessarily reduce errors in unit cost estimation for each and every product In reality costing art is not tightly connected to technology Linearity and separability are too strong assumptions Cost accounting at best delivers second best 15