Fundamentals of Cost Accounting 3rd Edition by William N. Lanen, Shannon W. Anderson, Michael Maher

Exercise 50

Reciprocal Cost Allocation—Outsourcing a Service Department

Refer to the facts in Problem 11-42. GB estimates that the cost structure in the their operations is

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as follows:

	Administration	Accounting	East	West
Variable costs	$25,000	$6,000	$113,000	$427,000
Fixed costs	35,000	18,000	43,000	173,000
Total costs	$60,000	$24,000	$156,000	$600,000
Avoidable fixed costs	$10,000	$3,000	$20,000	$112,500

Required

a.If GB outsources the Administration Department, what is the maximum they can pay an outside vendor without increasing total costs?

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b.If GB outsources the Accounting Department, what is the maximum they can pay an outside vendor without increasing total costs?

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c.If GB outsources both the Administration and the Accounting Departments, what is the maximum they can pay an outside vendor without increasing total costs? (Hint: Stop and think before solving any equations.)

Step 1 of 3

a.??To determine the avoidable cost, first determine the variable cost (including the variable cost of reciprocal services for the maintenance department). This is done by using the reciprocal method using only variable costs.

Set up the equations:

Total service department costs	=	Direct costs of the service department	+	Cost Allocated to the Service Department
S1 (Administration)	=	$25,000	+	0.50 S2
S2 (Accounting)	=	6,000	+	0.25 S1

Substituting, the first equation into the second yields,

S2	=	$6,000 + 0.25 ($25,000 + 0.50 S2)
S2	=	$6,000 + $6,250 + 0.125 S2
0.875 S2	=	$12,250
S2	=	$14,000

Substituting the value of S2 back into the first equation gives,

S1	=	$25,000 + 0.50 ($14,000)
S1	=	$32,000

The avoidable costs from outsourcing Administration is $42,000 (= $10,000 avoidable fixed costs + $32,000 avoidable variable costs).