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Homework answers / question archive / Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria

Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria

Accounting

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: 
Direct Costs Proportion of Services Used by Maintenance Cafeteria Machining Assembly Department 0254:54 Machining $130,000 Assembly 81,000 Maintenance 52,000 0.1 0.5 0.4 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. 

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

S1(Maintenance) = $52,000 + (0.6 * S2)

S2 (Cafeteria) = $37,000 + (0.1 * S1)

Substituting, the first equation into the second yields,

S2 = $37,000 + [0.1 * ($52,000 + 0.6S2)]

S2 = $37,000 + $5,200 + 0.06S2

S2 - 0.06S2 = $42,200

0.94S2 = $42,200

S2 = $44,893.62

 

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

S1 = $52,000 + (0.6 * $44,893.62)

S1 = $52,000 + $26,936.17

S1 = $78,936.17

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