Chapter 4, Problem 3PB

Activity-based department rate product costing and product cost distortions

Big Sound Inc. manufactures two products: receivers and loudspeakers. 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:

The activity-base usage quantities and units produced for the two products follow:

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 $420,000 and $294,000 for the Subassembly and Final Assembly 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. 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 rates for subassembly department.

$\begin{array}{c}\begin{array}{l}\text{Multiple production }\\ \text{department overhead rate}\end{array}\}\text{ = }\frac{\text{Budgeted department factory overhead}}{\text{Budgeted department allocation base}}\\ \text{= }\frac{\text{\$420,000}}{\text{1,400 DLH}}\\ \text{= \$300 per DLH}\end{array}$

Compute multiple production department overhead rates for final assembly department.

$\begin{array}{c}\begin{array}{l}\text{Multiple production }\\ \text{department overhead rate}\end{array}\}\text{ = }\frac{\text{Budgeted department factory overhead}}{\text{Budgeted department allocation base}}\\ \text{= }\frac{\text{\$294,000}}{\text{1,400 DLH}}\\ \text{= \$210 per DLH}\end{array}$

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 receivers.

Production Department	Multiple Production Department Overhead Rate	×	Total Number of Budgeted DLH	=	Factory Overhead
Subassembly	$300 per DLH	×	875 DLH	=	$262,500
Final assembly	$210 per DLH	×	525 DLH	=	110,250
Total factory overhead costs allocated for receivers					$372,750
Number of units of receivers					÷ 7,000 units
Factory overhead cost per unit of receivers					$53.25

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 loudspeakers.

Production Department	Multiple Production Department Overhead Rate	×	Total Number of Budgeted DLH	=	Factory Overhead
Subassembly	$300 per DLH	×	525 DLH	=	$157,500
Final assembly	$210 per DLH	×	875 DLH	=	183,750
Total factory overhead costs allocated for loudspeakers					$341,250
Number of units of loudspeakers					÷ 7,000 units
Factory overhead cost per unit of loudspeakers					$48.75

Table (2)

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

To determine

Compute 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
Setup	$138,600	÷	400 setups	=	$346.50 per setup
Quality control	261,800	÷	2,200 inspections	=	$119 per inspection
Subassembly	198,800	÷	1,400 DLH	=	$142 per DLH
Final assembly	114,800	÷	1,400 DLH	=	$82 per DLH

Table (3)

To determine

Compute the activity-cost per unit of the products

Explanation of Solution

Compute activity cost allocated per unit of receivers.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base (Cost Driver)	=	Activity Cost Allocated
Setup	$346.50 per setup	×	80 setups	=	$27,720
Quality control	$119 per inspection	×	450 inspections	=	53,550
Subassembly	$142 per DLH	×	875 DLH	=	124,250
Final assembly	$82 per DLH	×	525 DLH	=	43,050
Total activity costs allocated to receivers					$248,570
Number of units of receivers					÷ 7,000 units
Activity-based overhead cost per unit of receivers					$35.51

Table (4)

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

Compute activity cost allocated per unit of loudspeakers.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base (Cost Driver)	=	Activity Cost Allocated
Setup	$346.50 per setup	×	320 setups	=	$110,880
Quality control	$119 per inspection	×	1,750 inspections	=	208,250
Subassembly	$142 per DLH	×	525 DLH	=	74,550
Final assembly	$82 per DLH	×	875 DLH	=	71,750
Total activity costs allocated to loudspeakers					$465,430
Number of units of loudspeakers					÷ 7,000 units
Activity-based overhead cost per unit of loudspeakers					$66.49

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 subassembly and final assembly departments for loudspeakers and receivers is in the same ratio, but the setup department and quality control department are not accounted for in multiple department overhead rate method.