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		−			640			520			2,840
Labor-hours		399			−			357			1,344
Department direct costs	$	11,000		$	22,000		$	30,000		$	18,000

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. Round your final answers to the nearest whole dollar amounts.)

	Cost Allocation To: From: Maintenance Personnel Printing Developing Service department costs Maintenance Personnel Total $0 $0 $0 $0

Answer 1

Allocation of service department cost using the reciprocal method :

Particular	Printing	Developing	Total
Departmental direct costs	30000	18000	48000
Allocation of costs of maintenace department (13% & 71%)	1673	9138	10811
( see working)	(12871 * 13%)	(12871 * 71%)
Allocation of cost of personnel department	4090	15398	19488
( see working )	( 24059 * 17%)	(24059 * 64%)
Total	35763	42536
Hence ,
From	Maintenance	Personnel	Printing	Developing
Service department Costs	11000	22000	30000	18000
Mainteneance	-12871	2059	1673	9138
Personnel	1871	-24059	4090	15398
Total	0	0	35763	42536
Computation of allocation basis
	Maintenance	Personnel	Printing	Developing	Total
Machine hours	0	640	520	2840	4000
(%)		16%	13%	71%	100%
Labor hours	399	0	357	1344	2100
(%)	19%		17%	64%	100%
Departmental Direct costs	11000	22000	30000	18000	81000

Working :

Let M = Maintenance department

P = Personnel Department

M = 11000 + 0.19 P

P = 22000 + 0.16M

Solving the above equation

M = 11000 + 0.19 ( 22000 + 0.16 M)

M = 11000 + 4180 + 0.0304 M

0.9696 M = 12480

M = 12871

P = 22000 + 0.16 ( 12871 )

P = 24059