Question

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	$170,500	$360,000	$114,250	$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
General Factory

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)	=	$	+	(GF)
General Factory (GF)	=	$	+	(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

1)

	Human resource	General factory	Fabricating	Assembly	Total employees /square footage
Human resource	0	60/310= .1935	80/310= .2581	170/310= .5484	310
General factory	1000/20000= .05	0	5700/20000= .285	13300/20000= .665	20000

2)Equation :

Human Resources (HR) = 170500+ [.05 *GF]                                   [Equation 1]

General factory (GF) = 360000+ [.1935 HR]                                      [Equation 2]

Now,

putting the value of HR from equation 1 to equation 2

General factory (GF) = 360000+ [.1935 HR]          

                                 = 360000+ [.1935* (170500+ .05 GF)]

                                = 360000 + [32991.75+.05 GF]

                                = 392991.75 + .009675 GF

GF - .009675 GF = 392991.75

.990325 GF = 392991.75

     GF= 392991.75/.990325

           = 396831 Rounded

Putting value of GF in equation 1

   Human Resources (HR) = 170500+ [.05 *GF]                

                                  = 170500+ [.05 *396831]

                                   = 170500 + 19842

                                    = 190342

3)

	SUPPORT DEPARTMENT		PRODUCING DEPARTMENT
	Human resources	General factory	Fabricating	Assembly
Direct cost	170500	360000	114250	94000
Allocate
Human resource	-190342	190342*.1935=36831	190342*.2581=49127	190342*.5484= 104384
General factory	396831*.05= 19842	-396831	396831*.285= 113097	396831*.665= 263893
Total	0	0	276474	462277