University Printers has two service departments (Maintenance and Personnel) and two operating departments (Printing and Developing). Management has decided to allocate maintenance costs on the basis of machine-hours in each department and personnel costs on the basis of labor-hours worked by the employees in each. The following data appear in the company records for the current period: Maintenance Personnel Printing Developing Machine-hours — 1,000 1,000 3,000 Labor-hours 500 — 500 2,000 Department direct costs $ 13,000 $ 38,250 $ 47,000 $ 31,500 University Printers estimates that the variable costs in the Personnel Department total $15,000 and in the Maintenance Department variable costs total $7,600. Avoidable fixed costs in the Personnel Department are $5,700. Required: If University Printers outsources the Personnel Department functions, what is the maximum it can pay an outside vendor without increasing total costs? (Do not round intermediate calculations.)

First calculate total machine hours

1500 + 1500 + 4500 = 7500 total machine hours

personnel   = 1500/7500 x 4,800

printing   = 1500/7500 x 4,800

developing = 4500/7500 x 4,800

for personnel:

500 printing + 3,500 developing = 4,000

For Departments:

printing        = 500/4,000   x  15,760

developing   = 3,500/4,000x 15,760

23880.00

Explanation:

To determine the avoidable cost, first determine the variable cost (including the variable cost of reciprocal services for the maintenance department). This can be done by setting up the equations for the reciprocal method using only variable costs.

Set up the equations:

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

S1 (Maintenance)=$9,400+(1/6) S2

S2 (Personnel)=  16,000+(1/5) S1

Substituting, the first equation into the second yields,

S2 = $16,000 + (1/5) [$9,400 + (1/6) S2]

S2 = $16,000 + $1,880 + (1/30) S2

The variable cost savings are the first two terms and equal $17,880 (= $16,000 + $1,880). The avoidable cost from outsourcing Personnel is $23,880 (= $6,000 avoidable fixed costs + $17,880 avoidable variable costs).

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