process of allocating service department costs to production departments, where reciprocal services are allowed between service departments; also known as the reciprocal method, the matrix method, the double-distribution method, the cross-allocation method, and simultaneous equation method. The method sets up simultaneous equations to determine the allocatable cost of each service department. The data for an example follows:
The following equations are set up:
GP = $20,000 + 5/85 E
E = $10,000 + 1/6 GP
Substituting M from the second equation into the first:
GP = $20,000 + 5/85 ($10,000 + 1/6 GP)
Solving for GP gives GP = $20,791. Substituting GP = $20,791 into the second equation and solving for E gives E = $13,465.