Question

Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow:

				Proportion of Services Used by
Department	Direct Costs			Maintenance		Cafeteria		Machining		Assembly
Machining	$	130,000
Assembly		76,000
Maintenance		55,000		—		0.3		0.4		0.3
Cafeteria		37,000		0.6		—		0.2		0.2

Required:

Use the reciprocal method to allocate the service costs. (Matrix algebra is not required.) (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

	Cost Allocation To:
From:	Maintenance	Cafeteria	Machining	Assembly
Service department costs	$55,000	$37,000
Maintenance
Cafeteria
Total	$55,000	$37,000	$0	$0

Answer 1

Let Y be the cost of Maintenance department and Z be the cost of Cafeteria department.

Y = 55,000 + 0.6Z (equ i)

Z = 37,000 + 0.3Y (equ. ii)

Substituting the value of Z in equ. i

Y = 55,000 + 0.6(37,000 + 0.3Y)

Y = 55,000 + 22,200 + 0.18Y

Y - 0.18Y = 77,200

0.82Y = 77,200

Y = 77,200/0.82

= $94,146

Z = 37,000 + 0.3Y

= 37,000 + 0.3 x 94,146

= 37,000 + 28,244

= $65,244

	Cost allocation to
	Maintenance	Cafeteria	Machining	Assembly
Service department cost	55,000	37,000
Maintenance (0.3:0.4:0.3)	(94,146)	28,244	37,658	28,244
Cafeteria (0.6:0.2:0.2)	39,146	(65,244)	13,049	13,049
	0	0	50,707	41,293