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### SIMPLERTHAN ABC

New Ideas for Using Microsoft Excel for Allocating Costs

Reciprocal Costing

IMA Hands-on: Simpler than ABC

OUTLINE

- The purpose of the presentation is to introduce a new method of solving an old problem
- The old problem is service cost allocation using reciprocal costing.
- The new method uses Excel to determine the reciprocal allocations using matrix algebra and a mathematics technique known as Cramer’s Rule.

IMA Hands-on: Simpler than ABC

Benefits

- By understanding this technique Decision Support Specialists can have at their fingertips what is considered the most accurate method of cost allocation between service departments while overcoming some of the problems which have kept reciprocal costing from being more widely used in practice.

IMA Hands-on: Simpler than ABC

Benefits

- Traceability of costs
- Doesn’t require specialized software
- Doesn’t require extensive mathematical training to solve systems of equations.
- More accurate than earlier methods of reciprocal costing

IMA Hands-on: Simpler than ABC

Service Departments

Maintenance

Personnel

Production Departments

Product A

Product B

ExampleIMA Hands-on: Simpler than ABC

Maintenance

$1,000,000

Allocation Basis

Value of Assets

Personnel

$1.800,000

Allocation Basis

Number of Workers

Budgeted Costs & AllocationIMA Hands-on: Simpler than ABC

Solution Methods

- Direct allocation
- Sequential Allocation
- Reciprocal Allocation

IMA Hands-on: Simpler than ABC

DIRECT ALLOCATION

Products

A

B

$250,000

$750,000

$1,028,571

$771,429

$1,278.571 $1,521,429

IMA Hands-on: Simpler than ABC

Sequential MethodMaintenance First

IMA Hands-on: Simpler than ABC

Sequential MethodPersonnel First

IMA Hands-on: Simpler than ABC

Direct & Sequential Methods

- Direct method is simple but less accurate
- Traceability of costs are easy with sequential method but
- Results are dependent on the order of allocation so sequencing needs to be justified.

A B

Maintenance first 1,288,311 1,511,689

Personnel first 1,170,930 1,629,070

IMA Hands-on: Simpler than ABC

Reciprocal AllocationTextbook Algebraic Method

IMA Hands-on: Simpler than ABC

Reciprocal AllocationTextbook Algebraic Method(2)

IMA Hands-on: Simpler than ABC

Reciprocal AllocationAlgebraic Method(3)

IMA Hands-on: Simpler than ABC

Reciprocal MethodFinal Allocations to A & B

IMA Hands-on: Simpler than ABC

Problems with Textbook Reciprocal Allocation Method

In the preceding method the sums attributed to each service department include added amounts which defy easy explanation and leave the reciprocal costs useful only for allocation to final product.

These reciprocal costs include only inward flows of resources so cannot be used to provide useful information to service department managers.

IMA Hands-on: Simpler than ABC

Problems with Textbook Reciprocal Allocation Method

- Traceability of cost flows between service departments is limited.
- Solution of problems becomes cumbersome when service departments become numerous.

IMA Hands-on: Simpler than ABC

Alternative Solution: The Math

Rewriting the equations for each service department to include both outflows and inflows allows the full specification of a matrix that can be used with a common Excel function to provide reciprocal costs that do not include double counted amounts and provide for traceability of cost flows between service departments.

IMA Hands-on: Simpler than ABC

Same example: new method.

IMA Hands-on: Simpler than ABC

Reciprocal Cost New Method (2)

IMA Hands-on: Simpler than ABC

Constructing the Matrix

IMA Hands-on: Simpler than ABC

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