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 Maintenance Cafeteria Machining Assembly Department Machining Assembly Maintenance Cafeteria Direct Costs $ 100,000 75,000 52, eee 42,000 - 0.3 0.2 0.5 2.2 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. Round your final answers to the nearest whole dollar amounts.) Cost Allocation To: Cafeteria Machining Maintenance Assembly From: Service department costs Maintenance Cafeteria Total

Answer 1

	Cost Allocated To:
From:	Maintenance	Cafeteria	Machining	Assembly
Service department costs	52000	42000
Maintenance	-103038	30911	51519	20608
Cafeteria	51038	-72911	14582	7291
Total	0	0	66101	27899

Total service department costs = Direct costs of the service department + Cost allocated to the service department

S1 (Maintenance) = 52000+0.7 S2

S2 (Cafeteria) = 42000 + 0.3 S1

Substituting, the first equation into the second yields,
	S2	=	$42,000 + 0.30 ($52000 + 0.70 S2)
	S2	=	$42000 + $15600 + 0.21 S2
0.79	S2	=	$57600
	S2	=	$72911

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

S1 = $52000 + 0.70 ($72911)

S1 = $103038

Maintenance: 103038*0.3 = 30911 103038*0.5 = 51519 103038*0.2 = 20608 Cafeteria: 72911*0.7=51038 72911*0.2 = 14582 72911*0.1 = 7291