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 $110,000 67,000 51,000 38,000 0.2 0.7 0.5 0.1 0.3 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. Round your final answers to the nearest whole dollar amounts.)

Answer 1

Answer)

From:	Cost Allocation To:
	Maintenance	Cafeteria	Machining	Assembly
Maintenance (0.2, 0.5, 0.3)	-	$ 18,046.51	$ 45,116.28	$ 27,069.77
Cafeteria (0.7, 0.1, 0.2)	$ 39,232.56	-	$ 5,604.65	$ 11,209.30
Total	$ 39,232.56	$ 18,046.51	$ 50,720.93	$ 38,279.07
Total (rounded off)	$ 39,233	$ 18,047	$ 50,721	$ 38,279

Working Notes:

Department	Departmental overheads before allocation	Proportion of Service used by
		Maintenance	Cafeteria
Machining	$ 110,000	0.50	0.10
Assembly	$ 67,000	0.30	0.20
Maintenance	$ 51,000	-	0.70
Cafeteria	$ 38,000	0.20	-
Total	$ 266,000	1.00	1.00

Let the total overhead cost of maintenance department be “x” and that of Cafeteria department be “y”

Therefore total overhead cost of the two service departments is represented by following equation:

x = $ 51,000 + 0.70 y    ........Equation 1

y = $ 38,000 + 0.20 x     ......... Equation 2

By putting the value of “y” in equation 1 we get,

x = $ 51,000 + 0.70 ($ 38,000 + 0.20x)

x = $ 51,000 + (0.70 X $ 38,000) + (0.70 X 0.20x)

x = $ 51,000 + $ 26,600 + 0.14x

x – 0.14x = $ 77,600

0.86x = $ 77,600

x = $ 90,232.56

Therefore total overheads of Machining Department are $ 90,232.56

By putting the value of “x” in equation 2 we get,

y = $ 38,000 + 0.20 X $ 90,232.56

y = $ 38,000 + $ 18046.51

y = $ 56,046.51

Therefore total overheads of Cafeteria Department are $ 56,046.51

Allocation of Maintenance Department overheads:

Overheads Allocated = (Total Overheads of respective service department X proportion of service of that department used by other departments)

Cafeteria Department = $ 90,232.56 X 0.20

                                          = $ 18,046.51  

Machining Department = $ 90,232.56 X 0.50

                                            = $ 45,116.28

Assembly Department = $ 90,232.56 X 0.30

                                          = $ 27,069.77

Allocation of Cafeteria Department overheads:

Overheads Allocated = (Total Overheads of respective service department X proportion of service of that department used by other departments)

Maintenance Department = $ 56,046.51 X 0.70

                                          = $ 39,232.56  

Machining Department = $ 56,046.51 X 0.10

                                            = $ 5,604.65

Assembly Department = $ 56,046.51 X 0.2

                                          = $ 11,209.30