Chapter 17, Problem 25P

1.

To determine

Allocate the company’s service department costs using the direct method combined with dual allocation.

Explanation of Solution

Service department: A service department is a division in an organization which is not involved directly in producing the goods or services of an organization. But, the service department also offers a service that aids the organization to take place the goods or services that are produced.

Allocate the company’s service department costs using the direct method combined with dual allocation as follows:

Variable costs:

Provider of Service	Cost to  be allocated (a)	Production Departments
		Machining		Assembly
		Proportion (b)	Amount ($) $\left(\text{a}\times \text{b}\right)$	Proportion (c)	Amount$\left(\text{a}\times \text{c}\right)$
Human resource	$50,000	$\frac{4}{9}\left(\frac{\$4,000}{\left[\begin{array}{l}\$4,000+\\ \$5,000\end{array}\right]}\right)$	$22,222	$\frac{5}{9}\left(\frac{\$5,000}{\left[\begin{array}{l}\$4,000+\\ \$5,000\end{array}\right]}\right)$	$27,778
Maintenance	80,000	$\frac{35}{75}\left(\frac{\$3,500}{\left[\begin{array}{l}\$3,500+\\ \$4,000\end{array}\right]}\right)$	37,333	$\frac{45}{75}\left(\frac{\$4,500}{\left[\begin{array}{l}\$3,500+\\ \$4,000\end{array}\right]}\right)$	42,667
Computer aided design	50,000	$\frac{45}{60}\left(\frac{\$4,500}{\left[\begin{array}{l}\$4,500+\\ \$1,500\end{array}\right]}\right)$	37,500	$\frac{15}{60}\left(\frac{\$1,500}{\left[\begin{array}{l}\$4,500+\\ \$1,500\end{array}\right]}\right)$	12,500
Total	$180,000		$97,055		$82,945
Grand total			$830,000 $\left(\text{\$480,944}+\text{\$394,056}\right)$

Table (1)

Note:

The proportions are based on short-run usage.

Fixed costs:

Provider of Service	Cost to  be allocated (a)	Production Departments
		Machining		Assembly
		Proportion (b)	Amount ($) $\left(\text{a}\times \text{b}\right)$	Proportion (c)	Amount$\left(\text{a}\times \text{c}\right)$
Human resource	$200,000	$\frac{35}{85}\left(\frac{\$3,500}{\left[\begin{array}{l}\$3,500+\\ \$5,000\end{array}\right]}\right)$	$82,353	$\frac{50}{85}\left(\frac{\$5,000}{\left[\begin{array}{l}\$3,500+\\ \$5,000\end{array}\right]}\right)$	$117,647
Maintenance	150,000	$\frac{48}{72}\left(\frac{\$4,800}{\left[\begin{array}{l}\$4,800+\\ \$2,400\end{array}\right]}\right)$	100,000	$\frac{24}{72}\left(\frac{\$2,400}{\left[\begin{array}{l}\$4,800+\\ \$2,400\end{array}\right]}\right)$	50,000
Computer aided design	300,000	$\frac{48}{60}\left(\frac{\$4,800}{\left[\begin{array}{l}\$4,800+\\ \$1,200\end{array}\right]}\right)$	240,000	$\frac{12}{60}\left(\frac{\$1,200}{\left[\begin{array}{l}\$4,800+\\ \$1,200\end{array}\right]}\right)$	60,000
Total	$650,000		$422,353		$227,647
Grand total			$650,000 $\left(\text{\$422,353}+\text{\$227,647}\right)$

Table (2)

Note:

The proportions are based on long-run usage.

Total cost allocated:

Particulars	Machining	Assembly
Variable costs	$ 97,055	$ 82,945
Fixed costs	422,353	227,647
Total costs	$519,408	$310,592
Grand total	830,000$\left(\text{\$519,408}+\text{\$310,592}\right)$

Table (3)

2.

To determine

Allocate the company’s service department costs using the step-down method combined with dual allocation.

Explanation of Solution

Allocate the company’s service department costs using the step-down method combined with dual allocation:

Variable costs:

Table (4)

Fixed costs:

Table (5)

Total cost allocated:

Particulars	Machining	Assembly
Variable costs	$ 99,336	$80,664
Fixed costs	434,800	215,200
Total costs	$534,136	$295,864
Grand total	830,000$\left(\text{\$534,136}+\text{\$295,864}\right)$

Table (6)