SIMPLER THAN ABC
New Ideas for Using Microsoft
Excel for Allocating Costs
Reciprocal Costing
IMA Hands-on: Simpler than ABC
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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
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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
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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
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Example
Service Departments
Production Departments
Maintenance
Product A
Personnel
Product B
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Budgeted Costs & Allocation
Maintenance
Personnel
$1,000,000
$1.800,000
Allocation Basis
Allocation Basis
Value of Assets
Number of Workers
IMA Hands-on: Simpler than ABC
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Table 1: Allocation Amounts
Maintenance (M)
Personnel (P)
A
B
Total
$
$
$
$
Assets
Employees
2,000,000
8
1,000,000
2
8,000,000
20
24,000,000
15
$ 35,000,000
Costs
$ 1,000,000
$ 1,800,000
45
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Solution Methods
 Direct allocation
 Sequential Allocation
 Reciprocal Allocation
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DIRECT ALLOCATION
Products
A
$1,000,000  8
 MA
32
$1,000,000  24
 MB
32
$250,000
$1,800,000  20
$1,028,571
$1,800,000  15
35
35
 PA
B
$750,000
$771,429
 PB
$1,278.571
IMA Hands-on: Simpler than ABC
$1,521,4299
Sequential Method
Maintenance First
A
P
1,000,000  1
1,000,000  8
1,000,000  24
33
33
33
1,830,303  20
1,830,303  15
 MP
35
30,303
242,424
 MA
727,273
 MB
35
B
 PA
1,045,887
784,416
 PB
$1,288,311 $1,511,689
IMA Hands-on: Simpler than ABC
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Sequential Method
Personnel First A
M
1,800,000  8
 PM
43
1,800,000  20  PA
43
1,800,000  15  PB
43
1,334,884  8
1,334,884  24
32
32
B
334,884
837.209
627,907
 MA
333,721
 MB
1,001,163
1,170,930 1,629,070
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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.
Maintenance first
A
1,288,311
B
1,511,689
Personnel first
1,170,930
1,629,070
IMA Hands-on: Simpler than ABC
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Reciprocal Allocation
Textbook Algebraic Method
8
M  1,000,000  P 
43
1
P  1,800,000  M 
33
IMA Hands-on: Simpler than ABC
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Reciprocal Allocation
Textbook Algebraic Method(2)
8 
1 
M  1,000,000  1,800,000  M 
43 
33 
8
M 
M  1,334,884 
1419
1411

M   1,334,884
1419
M  1,342,452
IMA Hands-on: Simpler than ABC
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Reciprocal Allocation
Algebraic Method(3)
1
P  1,800,000  1,342,452
33
P  1,840,680
M  P  3,183,132
BudgetedM  P  2,800,000
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Reciprocal Method
Final Allocations to A & B
A
1,342,452 x 8/33
1,342,452 x 24/33
325,443
1,840,680 x 20/43
1,840,680 x 15/43
856,130
B
976,329
1,181,573
IMA Hands-on: Simpler than ABC
642,098
1,618,427
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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.
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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.
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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.
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Same example: new method.
8
1
M  1,000,000  P   M 
45
35
1
8
P  1,800,000  M   P 
35
45
IMA Hands-on: Simpler than ABC
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Reciprocal Cost New Method (2)
1
8
1 M   P   1,000,000
35
45
1
8
 M   1 P   1,800,000
35
45
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Constructing the Matrix
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