Chapter 5, Problem 14PSA

a

To determine

Calculate the total cost and cost per unit for each product line and calculate the combined cost of the products.

Explanation of Solution

Calculation of total overhead cost:

$\begin{array}{c}\text{Total overhead cost}=\text{Unit cost}+\text{Batch cost}+\text{Product cost}+\text{Facility cost}\\ =\$360,000+\$194,400+\$105,600+\$300,000\\ =\$960,000\end{array}$

Hence, the total overhead cost is $960,000.

Calculation of allocation rate:

$\begin{array}{c}\text{Allocation rate}=\frac{\text{Total overhead cost}}{\text{Number of labor hours}}\\ =\frac{\$960,000}{20,000\text{ hours}}\\ =\$48\text{ per labor hour}\end{array}$

Hence, the allocation rate per labor hour is $48.

Calculation of overhead cost allocated to each type of product:

Table (1)

Hence, the total allocated cost is $960,000.

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

Table (2)

Hence, the total combined cost is $2,127,600.

Calculation of cost per unit using traditional cost method:

Table (3)

Hence, the costs per unit for Products C, H, and M are $40.08, 26.72, and 23.14.

Working notes:

Calculation of direct material cost for Product C:

$\begin{array}{c}\text{Direct material (Product C)}=\text{Direct material cost}\times \text{Number of units}\\ =\$18\times 15,000\text{ units}\\ \text{=\$270,000}\end{array}$

Hence, the direct material cost for Product C is $270,000.

….. (1)

Calculation of direct material cost for Product H:

$\begin{array}{c}\text{Direct material (Product H)}=\text{Direct material cost}\times \text{Number of units}\\ =\$12\times 45,000\text{ units}\\ \text{=\$540,000}\end{array}$

Hence, the direct material cost for Product H is $540,000.

….. (2)

Calculation of direct material cost for Product M:

$\begin{array}{c}\text{Direct material (Product M)}=\text{Direct material cost}\times \text{Number of units}\\ =\$15\times 14,000\text{ units}\\ \text{=\$210,000}\end{array}$

Hence, the direct material cost for Product M is $210,000.

….. (3)

Calculation of direct labor cost for Product C:

$\begin{array}{c}\text{Direct labor (Product C)}=\text{Direct labor cost}\times \text{Number of units}\\ =\$7.20\times 6,000\text{ units}\\ \text{=\$43,200}\end{array}$

Hence, the direct labor cost for Product is $43,200.

….. (4)

Calculation of direct labor cost for Product H:

$\begin{array}{c}\text{Direct labor (Product H)}=\text{Direct labor cost}\times \text{Number of units}\\ =\$7.2\times 12,000\text{ units}\\ \text{=\$86,400}\end{array}$

Hence, the direct labor cost for home products is $86,400.

….. (5)

Calculation of direct labor cost for miniature products:

$\begin{array}{c}\text{Direct labor (Product M)}=\text{Direct labor cost}\times \text{Number of units}\\ =\$9\times 2,000\text{ units}\\ \text{=\$18,000}\end{array}$

Hence, the direct labor cost for Product M is $18,000.

….. (6)

b

To determine

Calculate the total cost and cost per unit for each product line and calculate the combined cost of the products using ABC analysis.

Explanation of Solution

Calculation of allocation rate:

Table (4)

Hence, the total allocated cost is $960,000.

Calculation of allocated cost for Product C:

Table (5)

Hence, the total allocated cost for Product C is $128,520.

Calculation of allocated cost for Product H:

Table (6)

Hence, the total allocated cost for Product H is $503,220.

Calculation of allocated cost for Product M:

Table (7)

Hence, the total allocated cost for Product M is $328,260.

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

Table (8)

Hence, the total combined cost is $2,127,600.

Calculation of cost per unit using ABC system:

Table (9)

Hence, the costs per unit for products C, H, and M are $29.45, $25.10, and $39.72.

c

To determine

Explain the reason why the combined total cost is the same in both the requirements and is the ABC system more accurate than the traditional system.

Explanation of Solution

The ABC system or traditional system does not affect the total amount of allocated cost. Consequently, the total cost will remain the same under all the systems.

ABC system accurately traces the cost of the product than the traditional costing system. There is a difference in cost per unit under traditional system and ABC system. ABC system helps to improve pricing and in making other decisions.