Chapter 5, Problem 14PSB

a)

To determine

Calculate the predetermined overhead rate used by the company.

Explanation of Solution

Calculation of total labor hours:

$\begin{array}{c}\text{Total labor hour}=\left(\begin{array}{l}\text{Direct labor hour}\times \text{Production time (Product S109)}\\ +\text{Direct labor hour}\times \text{Production time (Product N227)}\end{array}\right)\\ =\left(10,000\times 2+10,000\times 2.8\right)\\ =(20,000+28,000)\\ =\$48,000\end{array}$

Hence, the total labor hours are $48,000.

Calculation of allocation rate:

$\begin{array}{c}\text{Allocation rate}=\frac{\text{Total overhead cost}}{\text{Number of labor hours}}\\ =\frac{\$1,008,000}{48,000\text{ hours}}\\ =\$21\text{ per labor hour}\end{array}$

Hence, the allocation rate per labor hour is $21.

b)

To determine

Calculate the total overhead cost allocated by the company to each product.

Explanation of Solution

Calculation of overhead cost allocated to each type of product:

Table (1)

Hence, the total allocated cost is $1,008,000.

c)

To determine

Determine the cost per unit and total cost of products when direct labor hour is the base of overheads.

Explanation of Solution

Calculation of total cost of each product line and combined cost of the products:

Table (2)

Hence, the total combined cost is $2,088,000.

Calculation of cost per unit using traditional cost method:

Table (3)

Hence, the costs per unit of product S109 and product N227 are $82 and $116.80.

Working notes:

Calculation of direct material cost for product S109:

$\begin{array}{c}\text{Direct material (product S109)}=\text{Direct material cost}\times \text{Number of units}\\ =\$20\times 10,000\text{ units}\\ \text{=\$200,000}\end{array}$

Hence, the direct material cost for product S109 is $200,000.

…… (1)

Calculation of direct material cost for product N227:

$\begin{array}{c}\text{Direct material (product N227)}=\text{Direct material cost}\times \text{Number of units}\\ =\$30\times 10,000\text{ units}\\ \text{=\$300,000}\end{array}$

Hence, the direct material cost for product N227 is $300,000.

…… (2)

Calculation of direct labor cost for product S109:

$\begin{array}{c}\text{Direct labor (product S109)}=\text{Direct labor cost}\times \text{Number of hours}\\ =\$10\times 20,000\text{ hours}\\ \text{=\$200,000}\end{array}$

Hence, the direct labor cost for product S109 is $200,000.

…… (3)

Calculation of direct labor cost for product N227:

$\begin{array}{c}\text{Direct labor (product N227)}=\text{Direct labor cost}\times \text{Number of hours}\\ =\$10\times 28,000\text{ hours}\\ \text{=\$280,000}\end{array}$

Hence, the direct labor cost for product N227 is $280,000.

…… (4)

d)

To determine

Calculate the price of each product using mark-up value.

Explanation of Solution

Calculation of price for each product:

Table (4)

Hence, the prices of each product using markup are $98.4 and 140.16.

Working notes:

Calculation of mark-up value for Product S109:

$\begin{array}{c}\text{Markup value (product S109)}=\text{Cost per unit}\times 20\%\text{(company price)}\\ =\$82\times \text{20\%}\\ =\$16.4\end{array}$

Hence, the mark-up value for Product S109 is 16.4.

…… (5)

Calculation of mark-up value for Product N227:

$\begin{array}{c}\text{Markup value (product N227)}=\text{Cost per unit}\times 20\%\text{(company price)}\\ =\$116.80\times \text{20\%}\\ =\$23.36\end{array}$

Hence, the mark-up value for Product N227 is 23.36.

…… (6)

e)

To determine

Calculate the overhead rate of each product.

Explanation of Solution

Calculation of overhead cost under ABC system:

Table (5)

Working notes:

Calculation of base rate for unit-level cost:

$\begin{array}{c}\text{Base rate (unit-level)}=\text{Use of cost drive (S109)}+\text{Use of cost drive (N227)}\\ =20,000\text{ hour}+60,000\text{ hour}\\ =80,000\text{ hour}\end{array}$

Hence, the base rate for unit-level cost is 80,000 hours.

…… (7)

Calculation of base rate for batch-level cost:

$\begin{array}{c}\text{Base rate (batch-level)}=\text{Use of cost drive (S109)}+\text{Use of cost drive (N227)}\\ =1,500\text{ setups}+3,500\text{ setups}\\ =5,000\text{ setups}\end{array}$

Hence, the base rate for batch-level cost is 5,000 setups.

…… (8)

The calculation of base rate for product-level cost:

$\begin{array}{c}\text{Base rate (product-level)}=\text{Use of cost drive (S109)}+\text{Use of cost drive (N227)}\\ =200\text{ inspectios}+600\text{inspectios}\\ =800\text{inspectios}\end{array}$

Hence, the base rate for product-level cost is 800 inspections.

…… (9)

Calculation of base rate for facility-level cost:

$\begin{array}{c}\text{Base rate (facility-level)}=\text{Use of cost drive (S109)}+\text{Use of cost drive (N227)}\\ \text{=50\%}+50\%\\ =100\%\end{array}$

Hence, the base rate for facility-level cost is 100%.

…… (10)

f)

To determine

Calculate the total and per unit cost of each product using ABC system.

Explanation of Solution

Calculation of total allocated cost for the product S109:

Table (6)

Hence, the total allocated cost for product S109 is $278,000.

Calculation of total allocated cost for the product N227:

Table (7)

Hence, the total allocated cost for product N227 is $729,600.

Calculation of total cost of each product line and combined cost of the products using ABC system:

Table (8)

Hence, the total combined cost is $1,988,000.

Calculation of cost per unit using ABC method:

Table (9)

Hence, the costs per unit of product S109 and product N227 are $67.84 and $130.96.

g)

To determine

Calculate the revised price for the given products.

Explanation of Solution

Calculation of revised price for given products:

Table (10)

Hence, the prices of each product using markup are $81.41 and $157.15.

Working notes:

Calculation of mark-up value for Product S109:

$\begin{array}{c}\text{Markup value (product S109)}=\text{Cost per unit}\times 20\%\text{(company price)}\\ \text{=\$67}\text{.84}\times \text{20\%}\\ \text{=\$13}\text{.57}\end{array}$

Hence, the mark-up value for Product S109 is 13.57.

…… (11)

Calculation of mark-up value for Product N227:

$\begin{array}{c}\text{Markup value (product N227)}=\text{Cost per unit}\times 20\%\text{(company price)}\\ \text{=\$130}\text{.96}\times \text{20\%}\\ \text{=\$26}\text{.19}\end{array}$

Hence, the mark-up value for Product N227 is 26.19.

…… (12)

h

To determine

Based on the results from requirements f and g, discuss the reason product N227 costs more and reason for adjusting sales price.

Explanation of Solution

Manufacturing the product N227 is more costly because it requires more machine setups, inspection cost, and machine hours than Product S109. However, the ABC system reveals the accurate cost of the product. Laboratory I need to adjust its prices in order to sustain in the market for a long term.