Reciprocal Algebraic Method Of Cost Allocation

The allocation of service department costs is incomplete if the method used for cost allocation ignores or does not give full recognition to interdepartmental services. Interdepartmental services are services that two or more service departments provide to each other. For example, consider a case where service department A provides service to service department B, and in turn, department B provides service to department A.

If you have already studieddirect method and step method of cost allocation you may have noticed that the direct method completely ignores the interdepartmental services and step method gives them only a partial recognition because it allocates costs forward – never backward. To overcome this problem, a method known asreciprocal methodis used which fully recognizes interdepartmental services and provides greater exactness in allocating the cost of a service departments to other departments. The reciprocal method uses the simultaneous equations technique and is therefore also referred to as simultaneous equations method and algebraic method of departmental cost allocation.

Example
A company has two service departments and two producing departments. The two service departments provide service not only to two producing departments but also one another. The costs of four departments and relationship among them is shown below:

Required: Allocate the cost of service departments to producing departments using reciprocal/algebraic method.

Solution
Let:

Y = \$7,260 + 0.3Z —— Eq.1
Z = \$4,000 + 0.2Y —— Eq.2

Substituting the value of Z in equation 1:

Y = \$7,260 + 0.3(\$4,000 + 0.2Y)
Y = \$7,260 + \$1,200 + 0.06Y
Y – 0.06Y = \$7,260 + \$1,200
0.94Y = \$8,460
Y = \$8,460/0.94
Y = \$9,000

Substituting the value of Y in equation 2:

Z = \$4,000 + 0.2(9,000)
Z = \$4,000 + \$1,800
Z = \$5,800

Distribution summary: