Chapter 7, Problem 21E

Refer to the data in Exercise 7.20. The company has decided to use the sequential method of allocation instead of the direct method. The support departments are ranked in order of highest cost to lowest cost.

Required:

1. 1. Allocate the overhead costs to the producing departments using the sequential method. (Take allocation ratios out to four significant digits. Round allocated costs to the nearest dollar.)
2. 2. Using machine hours, compute departmental overhead rates. (Round the overhead rates to the nearest cent.)

To determine

Allocate the overhead costs to the producing departments suing the sequential method.

Explanation of Solution

Sequential method of allocation: The sequential method of allocation foresees that the interactions between the supports departments occur; conversely the sequential method considers only partial account of this interaction.

Calculation allocation ratio:

	Power	General Factory	Purchasing	Pesticide	Liquid Fertilizer
Square feet	(1)0.125		(2)0.125	(3)0.35	(4)0.4
Machine hours				(5)0.75	(6)0.25
Purchase orders	(7)0.1			(8)0.6	(9)0.3

Table (1)

Calculate assignment of costs:

Figure (1)

Working notes:

(1)Calculate the allocation of square feet to Power department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of square feet }\\ \text{to Power department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{power}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{power+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{purchasing+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$1,500}}{\text{\$1,500}\text{+}\text{\$1,500+}\text{4,200}\text{+}\text{\$4,800}}\\ \text{=}\frac{\text{\$1,500}}{\text{\$12,000}}\\ \text{=}\text{0}\text{.125}\end{array}$

(2)Calculate the allocation of square feet to Purchasing department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of square feet }\\ \text{to Purchasing department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{Purchasing}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{power+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{purchasing+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$1,500}}{\text{\$1,500}\text{+}\text{\$1,500+}\text{4,200}\text{+}\text{\$4,800}}\\ \text{=}\frac{\text{\$1,500}}{\text{\$12,000}}\\ \text{=}\text{0}\text{.125}\end{array}$

(3)Calculate the allocation of square feet to Pesticide department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of square feet }\\ \text{to Pesticide department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{Pesticide}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{power+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{purchasing+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$4,200}}{\text{\$1,500}\text{+}\text{\$1,500+}\text{4,200}\text{+}\text{\$4,800}}\\ \text{=}\frac{\text{\$4,200}}{\text{\$12,000}}\\ \text{=}\text{0}\text{.35}\end{array}$

(4)Calculate the allocation of square feet to Liquid fertilizer department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of square feet }\\ \text{to Liquid}\text{fertilizer department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{ Liquid}\text{fertilizer}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{power+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{purchasing+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{square}\text{feet}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$4,800}}{\text{\$1,500}\text{+}\text{\$1,500+}\text{4,200}\text{+}\text{\$4,800}}\\ \text{=}\frac{\text{\$4,800}}{\text{\$12,000}}\\ \text{=}\text{0}\text{.4}\end{array}$

(5)Calculate the allocation of machine hours to Pesticide department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of machine}\text{hours }\\ \text{to Pesticide department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{machine}\text{hours}\text{to}\text{pesticide}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{machine}\text{hours}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{machine}\text{hours}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$24,000}}{\text{\$24,000+\$8,000}}\\ \text{=}\frac{\text{\$24,000}}{\text{\$32,000}}\\ \text{=}\text{0}\text{.75}\end{array}$

(6)Calculate the allocation of machine hours to Liquid Fertilizer department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of machine}\text{hours }\\ \text{to Liquid Fertilizer department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{machine}\text{hours}\text{to}\text{ Liquid Fertilizer}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{machine}\text{hours}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{machine}\text{hours}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$8,000}}{\text{\$24,000+\$8,000}}\\ \text{=}\frac{\text{\$8,000}}{\text{\$32,000}}\\ \text{=}\text{0}\text{.25}\end{array}$

(7)Calculate the allocation of purchase orders to power department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of purchase orders }\\ \text{to power department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{purchase orders}\text{to}\text{power}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{purchase orders}\text{to}\text{power}+\\ \text{Allocation}\text{of}\text{purchase orders}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{purchase orders}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$20}}{\text{\$20+120+}\text{\$60}}\\ \text{=}\frac{\text{\$20}}{\text{\$200}}\\ \text{=}\text{0}\text{.1}\end{array}$

(8)Calculate the allocation of purchase orders to pesticide department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of purchase orders }\\ \text{to pesticide department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{purchase orders}\text{to}\text{pesticide}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{purchase orders}\text{to}\text{power}+\\ \text{Allocation}\text{of}\text{purchase orders}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{purchase orders}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$120}}{\text{\$20+120+}\text{\$60}}\\ \text{=}\frac{\text{\$120}}{\text{\$200}}\\ \text{=}\text{0}\text{.6}\end{array}$

(9)Calculate the allocation of purchase orders to liquid fertilizer department:

$\begin{array}{c}\begin{array}{l}\text{Allocation}\text{ratio of purchase orders }\\ \text{to liquid fertilizer department}\end{array}\}\text{=}\frac{\text{Allocation}\text{of}\text{purchase orders}\text{to}\text{liquid fertilizer}}{\left(\begin{array}{l}\text{Allocation}\text{of}\text{purchase orders}\text{to}\text{power}\text{+}\\ \text{Allocation}\text{of}\text{purchase orders}\text{to}\text{pesticide}\text{+}\\ \text{Allocation}\text{of}\text{purchase orders}\text{to}\text{fertilizer}\end{array}\right)}\\ \text{=}\frac{\text{\$60}}{\text{\$20+120+}\text{\$60}}\\ \text{=}\frac{\text{\$60}}{\text{\$200}}\\ \text{=}\text{0}\text{.3}\end{array}$

To determine

Calculate departmental overhead rates using machine hours.

Explanation of Solution

Departmental overhead rates: Departmental overhead rate is calculated by adding the allocated service costs to the overhead costs that are directly noticeable to the producing departments and dividing this total by some measure of activity, such as direct labor hours or machine hours.

Calculate the departmental overhead rate for pesticide department:

$\begin{array}{c}\begin{array}{l}\text{Departmental overhead rate }\\ \text{for pesticide department}\end{array}\}\text{=}\frac{\text{Total}\text{direct}\text{costs}}{\text{Machine}\text{hours}}\\ \text{=}\frac{\text{\$424,956}}{\text{24,000}\text{hours}}\\ \text{=}\text{\$17}\text{.71}\text{per}\text{machine}\text{hour}\end{array}$

Therefore, the departmental overhead rate for pesticide department is $17.71 per machine hour.

Calculate the departmental overhead rate for Liquid fertilizer department:

$\begin{array}{c}\begin{array}{l}\text{Departmental overhead rate }\\ \text{for liquid}\text{fertilizer department}\end{array}\}\text{=}\frac{\text{Total}\text{direct}\text{costs}}{\text{Machine}\text{hours}}\\ \text{=}\frac{\text{\$332,744}}{\text{8,000}\text{hours}}\\ \text{=}\text{\$41}\text{.59per}\text{per}\text{machine}\text{hour}\end{array}$

Therefore, the departmental overhead rate for liquid fertilizer department is $41.59 per machine hour.