The Reciprocal Method of Cost Accounting
In a manufacturing business, one or more service departments often provide services to one or more production departments and also to other service departments. These costs, which are included in indirect overhead, must be allocated to the departments that use those services. Examples of service departments are human resources, accounting, information technology and custodial services.
There are a few generally used methods to allocate service costs among the various departments that use the services. Of these methods, the reciprocal method is the most complex, but it is also the most accurate. Other names for the reciprocal method are simultaneous solution method, cross allocation method, matrix allocation method and double distribution method.
Because indirect overhead costs cannot be easily traced to cost objects -- products, processes, employees, departments, facilities, etc. -- an allocation base must be determined. Commonly used criteria for determining an allocation base include cause and effect and benefits received. An allocation base for custodial services could be square footage of each department. An allocation base for human resources could be the number of employees in each department.
For this example, the two service departments of human resources and custodial services provide services to each other as well as to the production departments of assembly and painting.
The human resources department allocates its costs based on the number of employees. Total human resources costs for the year are $150,000. Assembly has 10 employees, accounting for 67 percent of the employees used to allocate costs. Painting has three employees, accounting for 20 percent of the employees used to allocate costs. Custodial services has two employees accounting, for 13 percent of the employees used to allocate costs.
The custodial services department allocates its costs based on square footage. Total custodial services costs for the year are $70,000. Assembly occupies 3,000 square feet, accounting for 71 percent of the square footage used to allocate costs. Painting occupies 800 square feet, accounting for 19 percent of the square footage used to allocate costs. Human resources occupies 400 square feet, accounting for 10 percent of the square footage used to allocate costs.
Since 13 percent of human resources service costs are allocated to custodial services, another service department, those costs will have to be re-allocated to the production departments. The same applies to the 10 percent of custodial services costs that are allocated to human resources. Therefore, it is necessary to calculate fully reciprocated costs for each service department.
Using the data above, fully reciprocated human resources costs equal $150,000 + (fully reciprocated custodial services costs x 10 percent). Fully reciprocated custodial services costs equal $70,000 + (fully reciprocated human resources costs x 13 percent). Using this information, FRHRC and FRCSC can be calculated algebraically.
FRHRC = $150,000 + [($70,000 + FRHRC x 13%) x 10%].
FRHRC = $150,000 + [($70,000 + 0.13 x FRHRC) x 0.1] FRHRC = $150,000 + $7,000 + .013 x FRHRC 0.987 x FRHRC = $157,000 FRHRC = $159,068
FRCSC = $70,000 + (FRHRC x 13%). FRCSC = $70,000 + ($159,068 x 13%) FRCSC = $70,000 + $20,679 FRCSC = $90,679
Now that the fully reciprocated costs of each service department have been calculated, the allocation for each production department can be completed.
Fully reciprocated human resources costs to be allocated to production departments, as calculated above, equal $159,068. The assembly department allocation equals 67 percent of $159,068, which is $106,575. The painting department allocation equals 20 percent of $159,068, which is $31,814.
Fully reciprocated custodial services costs to be allocated to production departments, as calculated above, equal $90,679. The assembly department allocation equals 71 percent of $90,679, which is $64,382. The painting department allocation equals 19 percent of $90,679, which is $17,229.
Total service costs allocated to assembly of $170,957 plus total service costs allocated to painting of $49,043 equal $220,000, which is the total of actual service department costs given in the example data above.