Chapter 7, Problem 5CE

Refer to Cornerstone Exercise 7.3. Now assume that Valron Company uses the reciprocal method to allocate support department costs.

Required:

1. 1. Calculate the allocation ratios (rounded to four significant digits) for the four departments using the reciprocal method.
2. 2. Develop a simultaneous equations system of total costs for the support departments. Solve for the total reciprocated costs of each support department. (Round reciprocated total costs to the nearest dollar.)
3. 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.)
4. 4. What if the square footage in Fabricating were 13,300 and the square footage in Assembly were 5,700. How would that affect the allocation of support department costs?

To determine

Calculate the allocation ratios for the four departments using the reciprocal method.

Explanation of Solution

Reciprocal method of allocation: Reciprocal method of allocation identifies all interactions of support department. The usage of one support department by another is used to identify the total cost of each support department.

Calculate the allocation ratios:

	Proportion of drivers used
	Human resources	General factory	Fabricating	Assembly
Human resources		(1)0.1935	(2)0.2581	(3)0.5484
General factory	(4)0.0500		(5)0.2850	(6)0.6650

Table (1)

Working notes:

(1)Calculate the proportion of employees in general factory:

$\begin{array}{c}\begin{array}{l}\text{Proportion of employees }\\ \text{in}\text{general}\text{factory}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{employees}\text{in}\text{general}\text{factory}}{\left(\begin{array}{l}\text{Number}\text{of}\text{employees}\text{in}\text{fabricating}\\ \text{+Number}\text{of}\text{employees}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{employees}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{\text{60}}{\left(\text{60+80+}\text{170}\right)}\\ \text{=}\text{0}\text{.1935}\end{array}$

(2)Calculate the proportion of employees in fabricating:

$\begin{array}{c}\begin{array}{l}\text{Proportion of employees }\\ \text{in}\text{fabricating}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{employees}\text{in}\text{fabricating}}{\left(\begin{array}{l}\text{Number}\text{of}\text{employees}\text{in}\text{general}\text{factory}\\ \text{+Number}\text{of}\text{employees}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{employees}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{\text{80}}{\left(\text{60+80+}\text{170}\right)}\\ \text{=}\text{0}\text{.2581}\end{array}$

(3)Calculate the proportion of employees in assembly:

$\begin{array}{c}\begin{array}{l}\text{Proportion of employees }\\ \text{in}\text{assembly}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{employees}\text{in}\text{assembly}}{\left(\begin{array}{l}\text{Number}\text{of}\text{employees}\text{in}\text{general}\text{factory}\\ \text{+Number}\text{of}\text{employees}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{employees}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{\text{170}}{\left(\text{60+80+}\text{170}\right)}\\ \text{=}\text{0}\text{.5484}\end{array}$

(4)Calculate the proportion of square feet in human resources:

$\begin{array}{c}\begin{array}{l}\text{Proportion of square}\text{feet }\\ \text{in human}\text{resource}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resource}}{\left(\begin{array}{l}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resource}+\\ \text{Number}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{1,000}{\left(\text{1,000+5,700+}13,300\right)}\\ \text{=}\text{0}\text{.0500}\end{array}$

(5)Calculate the proportion of square feet in fabricating:

$\begin{array}{c}\begin{array}{l}\text{Proportion of square}\text{feet }\\ \text{in}\text{fabricating}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}}{\left(\begin{array}{l}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resource+}\\ \text{Number}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{\text{5,700}}{\left(\text{1,000+5,700+}\text{13,300}\right)}\\ \text{=}\text{0}\text{.2850}\end{array}$

(6)Calculate the proportion of square feet in assembly:

$\begin{array}{c}\begin{array}{l}\text{Proportion of square}\text{feet }\\ \text{in assembly}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{assembly}}{\left(\begin{array}{l}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resource}\\ \text{Number}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{13,300}{\left(\text{1,000+5,700+}13,300\right)}\\ \text{=}\text{0}\text{.665}\end{array}$

To determine

Allocate the costs of the human resources and general factory departments to the fabricating and assembly departments.

Explanation of Solution

Let HR be “Human Resources” and GF be “General Factory”.

$\begin{array}{l}\text{HR=}\text{\$160,000}\text{+}(4)\text{0}\text{.0500GF}\\ \text{GF=}\text{\$340,000}\text{+(1)}\text{0}\text{.1935HR}\end{array}$

Calculation for human resources:

$\begin{array}{c}\text{HR=}\text{\$160,000}\text{+}\text{0}\text{.05}\text{GF}\\ \text{=}\text{\$160,000}\text{+}\text{0}\text{.05}\times \text{(\$340,000+0}\text{.1935HR)}\\ \text{=\$160,000}\text{+}\text{\$17,000+0}\text{.009675HR}\\ \text{0}\text{.990325HR=}\text{\$177,000}\\ \text{HR=}\text{\$178,729}\end{array}$

Calculation for general factory:

$\begin{array}{c}\text{GF=}\text{\$340,000}\text{+}\text{0}\text{.1935HR}\\ \text{=}\text{\$340,000+0}\text{.1935}\times \text{(\$178,729)}\\ \text{=}\text{\$374,584}\end{array}$

To determine

Explain the situation if the allocation ratios in requirement 1 is rounded to six significant digits rather than four and explain the manner in which rounding error is affected in the allocation of cost.

Explanation of Solution

	Support Departments		Producing departments
Direct costs	Human resources	General factory	Fabricating department	Assembly department
Allocate	$160,000	$340,000	$114,600	$93,000
Human resources	($178,729)	(7)$34,584	(8)$46,130	(9)$98,015
General factory	(10)$18,729	($374,584)	(11)$106,756	(12)$249,098
Total after allocation	$0	$0	$267,486	$440,113

Table (2)

(7)Calculate the amount of human resources allocated to general factory:

$\begin{array}{c}\begin{array}{l}\text{Amount of human}\text{resource }\\ \text{allocated to general}\text{factory}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{employees}\text{in}\text{general}\text{factory}\text{×}\\ \text{Direct}\text{cost}\text{for}\text{human}\text{resource}\end{array}\right)\\ \text{=(1)}\text{0}\text{.1935×}\text{\$178,729}\\ \text{=\$34,584}\end{array}$

(8)Calculate the amount of human resources allocated to fabricating department:

$\begin{array}{c}\begin{array}{l}\text{Amount of human}\text{resource }\\ \text{allocated to fabricating department}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{employees}\text{in}\text{fabricating}\text{×}\\ \text{Direct}\text{cost}\text{for}\text{human}\text{resource}\end{array}\right)\\ \text{=}\text{0}\text{.2581}\text{(2)×}\text{\$178,729}\\ \text{=\$46,130}\end{array}$

(9) Calculate the amount of human resources allocated to assembly department:

$\begin{array}{c}\begin{array}{l}\text{Amount of human}\text{resource }\\ \text{allocated to assembly department}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{employees}\text{in}\text{assembly}\text{×}\\ \text{Direct}\text{cost}\text{for}\text{human}\text{resource}\end{array}\right)\\ \text{=}\text{0}\text{.5484}\text{(3)×}\text{\$178,729}\\ \text{=\$98,015}\end{array}$

(10)Calculate the amount of general factory allocated to human resources:

$\begin{array}{c}\begin{array}{l}\text{Amount of general}\text{factory allocated}\\ \text{ to human}\text{resources}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resources}\text{×}\\ \text{Direct}\text{costs}\text{for}\text{general}\text{factory}\end{array}\right)\\ \text{=}\text{0}\text{.0500}\text{(4)}\text{×}\text{\$374,584}\\ \text{=\$18,729}\end{array}$

(11)Calculate the amount of general factory allocated to fabricating department:

$\begin{array}{c}\begin{array}{l}\text{Amount of general factory }\\ \text{allocated to fabricating department}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}\text{×}\\ \text{Direct}\text{cost}\text{for}\text{general}\text{factory}\end{array}\right)\\ \text{=}\text{0}\text{.2850}(5)\text{×}\text{\$374,584}\\ \text{=\$106,756}\end{array}$

(12)Calculate the amount of general factory allocated to assembly department:

$\begin{array}{c}\begin{array}{l}\text{Amount of general}\text{factory }\\ \text{allocated to assembly department}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{square}\text{feet}\text{in}\text{assembly}\text{×}\\ \text{Direct}\text{costs}\text{for}\text{general}\text{factory}\end{array}\right)\\ \text{=}\text{0}\text{.6650}(6)\text{×}\text{\$374584}\\ \text{=\$249,098}\end{array}$

To determine

State the manner in which the allocation of support department costs are affected if the square footage in fabricating is $13,300 and the square footage in assembly is $5,700.

Explanation of Solution

Fabricating department will get the largest allocation of General Factory costs, if Fabricating had the bulk of the square footage. Thus, Fabricating would have the majority of support department costs, instead of Assembly.