Chapter 7, Problem 4CE

Refer to Cornerstone Exercise 7.3. Now assume that Valron Company uses the sequential method to allocate support department costs. The support departments are ranked in order of highest cost to lowest cost.

Required:

1. 1. Calculate the allocation ratios (rounded to four significant digits) for the four departments using the sequential method.
2. 2. Using the sequential 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.)
3. 3. What if the allocation ratios in Requirement 1 were rounded to six significant digits rather than four? How would that affect any rounding error in the allocation of costs?

To determine

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

Explanation of Solution

Sequential method of allocation: Sequential method of allocation identifies interactions between the support departments; conversely, the sequential method considers only partial account of this interaction.

Compute the allocation ratios for the four departments:

	Proportion of driver used
	Human resources	General factory	Fabricating	Assembly
Human resources			(1)0.32	(2)0.68
General factory	(3)0.05		(4)0.285	(5)0.665

Table (1)

Working notes:

(1)Calculate the proportion of employees in fabricating:

$\begin{array}{c}\begin{array}{l}\text{Proportion of employees }\\ \text{in fabricating}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{employees}\text{in}\text{fabricating}}{\left(\begin{array}{l}\text{Number}\text{of}\text{employees}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{employees}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{\text{80}}{\left(\text{80+}\text{170}\right)}\\ \text{=}\text{0}\text{.32}\end{array}$

(2)Calculate the proportion of employees in assembly:

$\begin{array}{c}\begin{array}{l}\text{Proportion of employees }\\ \text{in}\text{assembly}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{employees}\text{in}\text{assembly}}{\left(\begin{array}{l}\text{Number}\text{of}\text{employees}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{employees}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{170}{\left(\text{80+}\text{170}\right)}\\ \text{=}\text{0}\text{.68}\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Proportion of square}\text{feet }\\ \text{in human}\text{resource}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resource}}{\left(\begin{array}{l}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resource}+\\ \text{Number}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{1,000}{\left(\text{1,000+5,700+}13,300\right)}\\ \text{=}\text{0}\text{.05}\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Proportion of square}\text{feet }\\ \text{in}\text{fabricating}\end{array}\}\text{=}\frac{\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}}{\left(\begin{array}{l}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resource+}\\ \text{Number}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}\\ \text{+}\text{Number}\text{of}\text{square}\text{feet}\text{in}\text{assembly}\end{array}\right)}\\ \text{=}\frac{\text{5,700}}{\left(\text{1,000+5,700+}\text{13,300}\right)}\\ \text{=}\text{0}\text{.285}\end{array}$

(5)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

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

	Support Departments		Producing departments
Direct costs	Human resources	General factory	Fabricating department	Assembly department
Allocate	$160,000	$340,000	$114,600	$93,000
General factory	$17,000	($340,000)	$96,900	$226,100
Human resources	($177,000)		$56,640	$120,360
Total after allocation	$0	$0	$268,140	$439,460

Table (2)

Working notes:

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

$\begin{array}{c}\begin{array}{l}\text{Amount of general}\text{factory allocated}\\ \text{ to human resources}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{square}\text{feet}\text{in}\text{human}\text{resources}\text{×}\\ \text{Direct}\text{costs}\text{for}\text{general}\text{factory}\end{array}\right)\\ \text{=}\text{0}\text{.05}\text{(3)}\text{×}\text{\$340,000}\\ \text{=\$17,000}\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Amount of general factory }\\ \text{allocated to fabricating department}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{square}\text{feet}\text{in}\text{fabricating}\text{×}\\ \text{Direct}\text{cost}\text{for}\text{general}\text{factory}\end{array}\right)\\ \text{=}\text{0}\text{.285}(4)\text{×}\text{\$340,000}\\ \text{=\$96,900}\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Amount of general}\text{factory }\\ \text{allocated to assembly department}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{square}\text{feet}\text{in}\text{assembly}\text{×}\\ \text{Direct}\text{costs}\text{for}\text{general}\text{factory}\end{array}\right)\\ \text{=}\text{0}\text{.665}(5)\text{×}\text{\$340,000}\\ \text{=\$226,100}\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Amount of human}\text{resource }\\ \text{allocated to fabricating department}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{employees}\text{in}\text{fabricating}\text{×}\\ \text{Direct}\text{cost}\text{for}\text{human}\text{resource}\end{array}\right)\\ \text{=}\text{0}\text{.32}(1)\text{×}\text{\$177,000}\\ \text{=\$56,640}\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Amount of human}\text{resource }\\ \text{allocated to assembly department}\end{array}\}\text{=}\left(\begin{array}{l}\text{Proportion}\text{of}\text{employees}\text{in}\text{assembly}\text{×}\\ \text{Direct}\text{cost}\text{for}\text{human}\text{resource}\end{array}\right)\\ \text{=}\text{0}\text{.68}\text{(2)×}\text{\$177,000}\\ \text{=\$120,360}\end{array}$

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

Usually, “rounding the allocation ratios to six significant digits” will produce exact allocation of costs and will “decrease” rounding error. In this situation, all allocation ratios came out efficiently to three significant digits, so rounding to six will not make much difference.