Support Department Cost Allocation Using the Algebraic or Reciprocal Method

The algebraic or reciprocal method takes full account of support department reciprocity. This method requires the solution of a system of simultaneous equations to determine the total support department costs to be allocated. In practice, relatively few companies use the reciprocal method.

Let's use Anders Company, as an example. Anders has two producing departments - Cutting and Sewing - and two support departments - Maintenance and General Factory (GF). Anders provided the following information on the four departments:

		Maintenance			GF			Cutting			Sewing
Direct overhead cost		$10,000			$270,000			$56,400			$75,000
Machine hours		459			2,000			9,000			9,000
Square footage		2,500			3,418			5,000			8,500

Anders uses the algebraic method of support department cost allocation. Maintenance is allocated based on machine hours, and GF on the basis of square footage.

Calculate the allocation ratios to five significant digits and fill them into the following table (Leave cells blank that do not require an entry.):

Maintenance

GF

Cutting

Sewing

General Factory

Maintenance

Using the allocation ratios, solve a system of simultaneous equations for support department cost as follows.

Maintenance = $100,000 + 0.15625 GF

GF = $270,000 + 0.1 Maintenance

Substituting Maintenance into the equation for GF and solving for GF:

GF = $270,000 + 0.1 ($100,000 + 0.15625 GF)

GF = $270,000 + $10,000 + 0.015625 GF

0.984375 GF = $280,000

GF = $284,444

Then,

Maintenance = $100,000 + 0.15625 ($284,444) = $144,444

Using the newly calculated amounts for GF and Maintenance and the allocation ratios, fill in the following table to allocate support department costs to the producing departments. (Round all allocated amounts to the nearest dollar. Leave cells blank that do not require an entry.)

Maintenance

GF

Cutting

Sewing

Direct overhead cost

$100,000

$270,000

$56,400

$75,000

Allocate:

General Factory

Maintenance

Total after allocation

Notice that after allocation, zero dollars remain in the support departments and all overhead cost has been allocated to the producing departments. As a check on your work, add all direct overhead costs from the first line - it equals $501,400. Then add the totals after allocation - again, it equals $501,400.