Question

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	$	5,000		$	12,000		$	15,000		$	10,000

Required:

Allocate the service department costs using the reciprocal method. (Matrix algebra is not required because there are only two service departments.) (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

Answer 1

Let the total cost of Maintenance and Personnel Departments be x and y, respectively.
x	=	$ 5000 + 0.16y		(i)
y	=	$ 12000 + 0.20x		(ii)
Putting the value of x in equation (ii), we get
y	=	$ 12000 + 0.20($ 5000 + 0.16y)
y	=	$ 12000 + $ 1000 + 0.033y
0.97y	=	$ 13000
y	=	$ 13448
Therefore,
x	=	$ 5000 + 0.16($ 13448)
	=	$ 7241

Particulars			Maintenance	Personnel	Printing	Developing
Direct costs			$        5,000	$        12,000	$      15,000	$      10,000
Allocating cost of:
Maintenance			$      -7,241	$          1,448	$         1,448	$         4,345
Personnel			$        2,241	$      -13,448	$         2,241	$         8,965
Total costs			$                0	$                  0	$      18,690	$      23,310

Note: There might be some differences because of decimals