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	$	120,000
Assembly		84,000
Maintenance		55,000		—		0.2		0.5		0.3
Cafeteria		42,000		0.7		—		0.2		0.1

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.)

	Maintenance	Personnel	Printing	Developing
Service department costs
Maintenance
Personnel
Total	$0	$0	$0	$0

Answer 1

Reciprocal method

The separate expense maintenance is 55,000. But it gets the allocation from cafeteria expense to the extent of 70%. Suppose the total expense of maintenance is X and total expense of the cafeteria is Y. hence, the total expense of X will be

X's total expense = 55,000 + 70/100(Y)

X = 55,000 + 0.7 (Y) ........... (1)

similarly, the separate expense of Y is 42,000 but to this will be added 20% of the expense of X, hence, total expense of Y will be

Y's total expense = 42,000 + 20/100 (X)

Y = 42,000 + 0.2(X) ........(2)

if we put value of X = X = 55,000 + 0.7 (Y) in this equation we get

Y = 42,000 + 0.2 (55,000 + 0.7 (Y))

Y = 42,000 +11,000 + 0.14Y

0.86Y = 53,000

Y = 61,628, hence cafeteria expense (including maintenance) = 61,628…put in equation 1 X = 55,000 +0.7 (61,628) X = 55,000 + 43,140 X = 98,140, hence maintenance expense (including maintenance cafeteria) = 61,628 Maintenance Cafeteria Machining Assembly Service department cost 98,140 61,628 - - Maintenance -98,140 - 49,070 29,442 Cafeteria - -61,628 12,326 6,163 total 0 0 61,396 35,605