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 $ 125,000 Assembly 84,000 Maintenance 52,000 — 0.2 0.5 0.3 Cafeteria 33,000 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.)

Answer 1

The answer is:

From:	Maintenance	Cafetria	Machining	Assembly
Service department costs	52,000.00	33,000.00
Maintenance	-         81,591.00	16,318.00	40,796.00	24,477.00
Cafetria	29,591.00	-   49,318.00	9,864.00	9,864.00
Total	-	-	50,660.00	34,341.00

Calculations and explanations:

We will first set up the equations:

Total service department service costs	=	Direct costs of the service department	+	Cost allocated to the service department
S1 (maintenance)	=	52,000.00	+	0.60S2
S2 (cafeteria)	=	33,000.00	+	0.20S1

Thus S2 = 33,000+0.2*(52,000+0.60S2)

or S2 = 33,000+10,400+0.12S2

or S2 = 49,318

Thus S1 = 52,000+(0.6*49,318) = 81,591

Thus maintenance = 0.2*81,591 = 16318. 40,796 = 0.5*81591 and 24477 = 0.3*81591

Cafeteria: 29591 = 0.6*49318.

9864 = 0.2*49318