Chapter 4, Problem 3PA

Activity-based and department rate product costing and product cost distortions

Black and Blue Sports Inc. manufactures two products: snowboards and skis. The factory overhead incurred is as follows:

The activity base associated with the two production departments is direct labor hours. The indirect labor can be assigned to two different activities as follows:

Instructions

Determine the factory overhead rates under the multiple production department rate method. Assume that indirect labor is associated with the production departments, so that the total factory overhead is $315,000 and $540,000 for the Cutting and Finishing departments, respectively.

Determine the total and per-unit factory overhead costs allocated to each product, using the multiple production department overhead rates in (1).

Determine the activity rates, assuming that the indirect labor is associated with activities rather than with the production departments.

Determine the total and per-unit cost assigned to each product under activity-based costing.

Explain the difference in the per-unit overhead allocated to each product under the multiple production department factory overhead rate and activity-based costing methods.

To determine

Compute the multiple production department overhead rates for both departments.

Explanation of Solution

Multiple production department factory overhead rates: This allocation method identifies different departments in the process of production. The factory overheads are allocated to products based on the overhead rate for each of the production departments.

Formula to compute multiple production department overhead rates:

  $\begin{array}{l}\text{Multiple production }\\ \text{department overhead rate}\end{array}\}\text{ = }\frac{\text{Budgeted department factory overhead}}{\text{Budgeted Department allocation base}}$

Activity-based costing (ABC) method: The costing method which allocates overheads to the products based on factory overhead rate for each activity or cost object, according to the cost pooled for the cost drivers (allocation base).

Formula to compute activity-based overhead rate:

$\begin{array}{l}\text{Activity-based}\\ \text{overhead rate}\end{array}\}\text{ = }\frac{\text{Budgeted activity cost}}{\text{Total activity-base usage}}$

Compute multiple production department overhead rate for cutting department.

$\begin{array}{c}\begin{array}{l}\text{Multiple production }\\ \text{department overhead rate}\end{array}\}\text{ = }\frac{\text{Budgeted department factory overhead}}{\text{Budgeted department allocation base}}\\ \text{= }\frac{\text{\$315,000}}{\text{6,000 DLH}}\\ \text{= \$52}\text{.50 per DLH}\end{array}$

Compute multiple production department overhead rate for finishing department.

$\begin{array}{c}\begin{array}{l}\text{Multiple production }\\ \text{department overhead rate}\end{array}\}\text{ = }\frac{\text{Budgeted department factory overhead}}{\text{Budgeted department allocation base}}\\ \text{= }\frac{\text{\$540,000}}{\text{6,000 DLH}}\\ \text{= \$90 per DLH}\end{array}$

To determine

Compute the factory overhead allocated to total and per unit of each product.

Explanation of Solution

Compute total factory overhead and per unit overhead allocated for snowboards.

Production Department	Multiple Production Department Overhead Rate	×	Total Number of Budgeted DLH	=	Factory Overhead
Cutting	$52.50 per DLH	×	4,000 DLH	=	$210,000
Finishing	$90 per DLH	×	2,000 DLH	=	180,000
Total factory overhead costs allocated for snowboards					$390,000
Number of units of snowboards					÷ 6,000 units
Factory overhead cost per unit of snowboard					$65.00

Table (1)

Note: Refer to part (A) for value and computation of multiple production department overhead rate.

Compute total factory overhead and per unit overhead allocated for skis.

Production Department	Multiple Production Department Overhead Rate	×	Total Number of Budgeted DLH	=	Factory Overhead
Cutting	$52.50 per DLH	×	2,000 DLH	=	$105,000
Finishing	$90 per DLH	×	4,000 DLH	=	360,000
Total factory overhead costs allocated for skis					$465,000
Number of units of skis					÷ 6,000 units
Factory overhead cost per unit of ski					$77.50

Table (2)

Note: Refer to part (A) for value and computation of multiple production department overhead rate.

To determine

Calculate the activity-based overhead rate for each of the given activities

Explanation of Solution

Compute activity-based overhead rates.

Computation of Activity-Based Overhead Rates
Activity	Activity Cost	÷	Total Activity-Base Usage	=	Activity-Based Overhead Rates
Production control	$237,000	÷	500 production runs	=	$474 per run
Materials handling	270,000	÷	7,500 moves	=	$36 per move
Cutting	156,000	÷	6,000 DLH	=	$26 per DLH
Finishing	192,000	÷	6,000 DLH	=	$32 per DLH

Table (3)

To determine

Calculate the activity-cost per unit of the products

Explanation of Solution

Compute activity cost allocated per unit of snowboards.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base (Cost Driver)	=	Activity Cost Allocated
Production control	$474 per run	×	430 runs	=	$203,820
Materials handling	36 per move	×	5,000 moves	=	180,000
Cutting	26 per DLH	×	4,000 DLH	=	104,000
Finishing	32 per DLH	×	2,000 DLH	=	64,000
Total activity costs allocated to snowboards					$551,820
Number of units of snowboard					÷ 6,000 units
Activity-based overhead cost per unit of snowboards					$91.97

Table (4)

Note: Refer to Table (3) for the value and computation of activity allocation rates.

Compute activity cost allocated per unit of snowboards.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base (Cost Driver)	=	Activity Cost Allocated
Production control	$474 per run	×	70 runs	=	$33,180
Materials handling	36 per move	×	2,500 moves	=	90,000
Cutting	26 per DLH	×	2,000 DLH	=	52,000
Finishing	32 per DLH	×	4,000 DLH	=	128,000
Total activity costs allocated to skis					$303,180
Number of units of skis					÷ 6,000 units
Activity-based overhead cost per unit of ski					$50.53

Table (5)

Note: Refer to Table (3) for the value and computation of activity allocation rates.

To determine

Discuss the product cost distortion due to multiple production department overhead rate

Explanation of Solution

The product cost under multiple production department overhead rate approach and ABC approach are different. The product cost is distorted in multiple production department overhead rate approach. Although the time spent for cutting and finishing for snowboards and skis is in the same ratio, but the production control department and materials handling department are not accounted for in multiple department overhead rate method.