Cost allocation can be carried out using three methods: the direct method, the sequential method and the reciprocal method. The three methods differ in the manner by which costs are split among the producing departments. There is absolutely no doubt that no matter which method is used, total overhead costs remain unchanged. The reciprocal method recognizes the reciprocal services provided by support departments to other support departments; in other words, it gives full recognition to interdepartmental services. The method is also known as the simultaneous equation method, or the algebraic method.

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Determine the total cost of support departments so that the total cost reflects interaction with other support departments. In the example, the human resources (HR) department receives 20 percent of data processing (DP) services, and data processing receives 10 percent of human resources output. In the consecutive period, the HR costs were $160,000 and DP costs were $250,000.

Form a simultaneous linear equation system. Each equation would be a cost equation for a support department. This will be the total of the departmentâ€™s direct cost and the proportion of service received from the other department. In other words:

Total Cost = Direct Cost + Allocated Cost.

Substitute the data from the example into the equation. Thus ...

DP = $250000 + 0.1HR and HR = $160000 + 0.2DP.

Solve the above mentioned simultaneous equations. Hence,

HR = $160000 + 0.2DP HR = $160000 + 0.2 ($250000 + 0.1HR) HR =$160000 + $50000 + 0.02HR 0.98HR = $210000 HR = $214286

DP = $250000 + 0.1HR DP = $250000 + 0.1 ($214286) DP = $250000 + $21429 DP = $271429

Analyze your findings. The total cost for the data processing department is $271,429 and for the human resources department it's $214,286. Both costs aptly reflect all interactions between the two support departments.

#### Warning

The method is rarely used, as the math and computation can become complex.