Question

Shiva, owner of Automated fabric, Inc., is interested in using the reciprocal allocation method to allocate service department costs to operating (i.e. production) departments. Automated Fabric has two operating departments: Weaving and Colorizing. Automated Fabric has two service departments: Maintenance and Personnel. The following data is available:                                                                                      

                                             Maintenance Dept.                        Personnel Dept.                                                               

Budgeted costs                               $300,000                           $160,000                                                                        

The quantity of service provided by maintenance dept to other departments is measured by the budgeted maintenance hours. The quantity of service provided by personnel department is measured by the number of employees in the department receiving service. The following data has been provided to you.                                                                                                                                                                     

	Maintenance	Personnel	Weaving	Colorizing
Budgeted maintenance hours for the user department	-	1000	7000	4000
# of employees in the user department	10	-	30	20

                   

a) Write down the linear equations for calculating the modified costs for the service departments for the purpose of reciprocal method of allocation.

b) Calculate the modified costs for the maintenance and personnel departments after solving the system of equations in (a)                          

c) Find the costs allocated from Maintenance and Personnel to Weaving and Colorizing departments

Answer 1

Please give positive ratings so I can keep answering. It would help me a lot. Please comment if you have any query. Thanks!

Shiva, Automated fabric
Reciprocal Method	Maintenance	Personnel	Weaving	Colorizing	Total
Maintenance Hours		1,000.00	7,000.00	4,000.00	12,000.00
Number of Users	10.00		30.00	20.00	60.00
Maintenance Hours %		8.33%	58.33%	33.33%	100.00%
Number of Users %	16.67%		50.00%	33.33%	100.00%
Budgeted costs	300,000.00	160,000.00			460,000.00

Answer a

Let cost of Maintenance is $ X and Personnel is $ Y

So, X= 300000+ 16.67% of Y

So, X= 300000+ 0.1667Y

Y= 160000+ 8.33% of X

Y= 160000+ 0.0833X

Answer b

Substituting the value of X in equation 2:

Y = 160000 + 0.0833(300000 + 0.1667Y)

Y = 160000 + 25000+.013889Y

Y – 0.013889 = 160000+25000

0.98611Y = 185,000

Y = 185,000/0.98611

Y = $ 187,606

Substituting the value of Y in equation 1:

So, X= 300000+ 0.1667Y

So, X= 300000+ 0.1667*187,606

So, X= 300000+ 31,268

X= $ 331,268

Answer c	Maintenance	Personnel	Weaving	Colorizing	Total
Maintenance Hours %	-	8.33%	58.33%	33.33%	100.00%
Number of Users %	16.67%	-	50.00%	33.33%	100.00%
Department cost	300,000.00	160,000.00	-	-	460,000.00
Total costs
Maintenance	(331,268.00)	27,606.00	193,240.00	110,422.00	-
Personnel	31,268.00	(187,606.00)	93,803.00	62,535.00	-
Cost after allocation	-	-	287,043.00	172,957.00	460,000.00