Question

1. Reciprocal Method of Support Department Cost Allocation

   Valron Company has two support departments, Human Resources and General Factory, and two producing departments, Fabricating and Assembly.

   	Support Departments		Producing Departments
   	Human Resources	General Factory	Fabricating	Assembly
   Direct costs	$150,000	$350,000	$114,200	$94,000
   Normal activity:
   Number of employees	—	60	80	170
   Square footage	1,000	—	5,700	13,300

   The costs of the Human Resources Department are allocated on the basis of number of employees, and the costs of General Factory are allocated on the basis of square footage.

   Now assume that Valron Company uses the reciprocal method to allocate support department costs.

   Required:

   1. Calculate the allocation ratios (rounded to four significant digits) for the four departments using the reciprocal method. If an amount is zero, enter "0". Use the rounded values for subsequent calculations.

   	Proportion of Driver Used by
   	Human Resources	General Factory	Fabricating	Assembly
   Human Resources	0	0.1935	0.2581	0.5484
   General Factory	0.05	0	0.285	0.665

   2. Develop a simultaneous equations system of total costs for the support departments. If required, round your answers to four decimal places. Use these numbers for subsequent calculations. If required, round all other intermediate calculations to six decimal places, except the answers computed in requirement 1.

   Human Resources (HR)	=	$150,000	+ 0.05	(GF)
   General Factory (GF)	=	$350,000	+ 0.1935	(HR)

   Solve for the total reciprocated costs of each support department. (Round reciprocated total costs to the nearest dollar.)

   Human Resources (HR)	$
   General Factory (GF)	$

   3. Using the reciprocal method, allocate the costs of the Human Resources and General Factory departments to the Fabricating and Assembly departments. Round all allocated costs to the nearest dollar. If an amount is zero, enter "0". Note: There may be a "$1" difference due to intermediate rounding.

   	Support Departments			Producing Departments
   	Human Resources	General Factory		Fabricating	Assembly
   Direct costs	$	$		$	$
   Allocate:
   Human Resources
   General Factory
   Total after allocation	$	$		$	$

Answer 1

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Valron Company
Reciprocal Method	Human Resources	General Factory	Fabricating	Assembly	Total
Number of employees		60.00	80.00	170.00	310.00
Number of employees ratio		0.1935	0.2581	0.5484	1.00
Square footage	1,000.00		5,700.00	13,300.00	20,000.00
Square footage ratio	0.05		0.285	0.665	1.00
Department cost	150,000.00	350,000.00	114,200.00	94,000.00	708,200.00
Let Overhead cost of Human Resources is $ X and Overhead cost of General Factory is $ Y
So, X= 150000+ 0.05 of Y	Equation 1
Y= 350000+ 0.1935 of X	Equation 2
Or, X= 150000+ 0.05Y
Y= 350000+ 0.1935X
Substituting the value of X in equation 2:
Y = 350000 + 0.1935(150,000 + 0.05Y)
Y = 350000 + 29,025+0.009675Y
Y – 0.009675Y = 350000 + 29,025
.990325Y= 379025
Y = 379025/.990325
Y = $ 382,727.89
Substituting the value of Y in equation 1:
So, X= 150000+ 0.05 of Y
So, X= 150000+ 0.05 of 382,727.89
So, X= 150000+ 19136.39
So, X= 169136.39
Allocation Summary	Human Resources	General Factory	Fabricating	Assembly	Total
Number of employees		60.00	80.00	170.00	310.00
Number of employees ratio		0.1935	0.2581	0.5484	1.00
Square footage	1,000.00		5,700.00	13,300.00	20,000.00
Square footage ratio	0.05		0.285	0.665	1.00
Department cost	150,000.00	350,000.00	114,200.00	94,000.00	708,200.00
Allocation
Human Resources	(169,136.39)	32,727.89	43,656.10	92,752.39	(0.00)
General Factory	19,136.39	(382,727.89)	109,077.45	254,514.05	-
Total cost after allocation	0.00	0.00	266,933.55	441,266.44	708,200.00