# 102 10.4 The Reciprocal Method

## The Reciprocal Method:

The reciprocal method is the most accurate of the three methods for allocating service department costs, because it recognizes reciprocal services among service departments. It is also the most complicated method, because it requires solving a set of simultaneous linear equations.

Using the data from the step-down method example, the simultaneous equations are:

H.R. = \$ 80,000 + (0.08 x D.P.)
D.P. = \$120,000 + (0.20 x H.R.)
R.M. = \$ 40,000 + (0.10 x H.R.) + (0.07 x D.P.)

Where the variables H.R., D.P. and R.M. represent the total costs to allocate from each of these service departments. For example, Human Resources receives services from Data Processing, but not from Risk Management. 8% of the services that Data Processing provides, it provides to Human Resources. Therefore, the total costs allocated from Human Resources should include not only the \$80,000 incurred in that department, but also 8% of the costs incurred by Data Processing. Solving for the three unknowns (which can be performed using spreadsheet software):

H.R. = \$ 91,057
D.P. = \$138,211
R.M. = \$ 58,781
Hence, costs are allocated as follows:

 H.R D.P R.M Machining Assembly Total Dept.’s own costs \$80,000 \$120,000 \$40,000 — — Allocation of H.R. (\$91, 057) 18,211 9,106 \$36,423 \$27,317 Allocation of D.P. 11,057 (138.211) 9,675 41,463 76,016 Allocation of R.M. (58,781) 29,390 29,390 Total \$       0 \$       0 \$      0 \$107,276 \$132,723 \$240,000*

* rounding error of \$ 1.

Summary of Service Department Cost Allocation Methods:

1) The point of allocating service department costs to operating (product departments) is to recognize the full costs of the operating departments. The full costs have to be recovered through pricing.
2) The direct method and step-down method have no advantages over the reciprocal method except for their simplicity, and the step-down method is sometimes not very simple. In this case, the cost allocations are not very different under each method.

 Machining Department Assembly Department Direct method, costs allocated \$107,600 \$132,400 Step-Down method, costs allocated 105,522 134,478 Reciprocal method, costs allocated 107,276 132,723

The situation would be different if one service department consumed a lot of a second service department, and that first service department primarily served a single operating department. Failure to allocate service department costs in a way that recognizes this consumption pattern between service departments,  could distort a correct understanding of cost behaviour and lead to poor decision making.

Nevertheless, the reciprocal method is not widely used. Given advances in computing power, the reciprocal method would seem to be accessible to many companies that are not using it. Presumably, these companies believe that the benefits obtained from more accurate service department cost allocations do not justify the costs required to implement the reciprocal method. In fact, many companies do not allocate service department costs at all, either because they do not think these allocations are beneficial, or because they do not believe that the benefits justify the costs.