Support Department Cost Allocations with a Matrix-Based Reciprocal Approach

The reciprocal method for allocating support department costs is preferred over the direct and step-down methods because it captures all support services provided to other departments. However, even as business organizations increase the number of support departments and their costs, the adoption of the reciprocal method has been hindered by mathematical difficulties in solving simultaneous equations. This paper illustrates spreadsheet matrix functions that remove the difficulties associated with the reciprocal method. The algebraic expressions for reciprocated costs commonly presented in accounting textbooks are used to form an equivalent matrix relationship. Then spreadsheet matrix functions easily compute reciprocated costs for support departments from the matrix relationship, and also allocate the reciprocated costs to other departments.