Chapter 18, Problem 16E

Single plantwide rate and activity-based costing

Whirlpool Corporation conducted an activity-based costing study of its Evansville, Indiana, plant in order to identify its most profitable products. Assume that we select three representative refrigerators (out of 333): one low-, one medium-, and one high-volume refrigerator. Additionally, we assume the following activity-base information for each of the three refrigerators:

Prior to conducting the study, the factory overhead allocation was based on a single machine hour rate. The machine hour rate was $200 per hour. After conducting the activity-based costing study, assume that three activities were used to allocate the factory overhead. The new activity rate information is assumed to be as follows:

Complete the following table, using the single machine hour rate to determine the per-unit factory overhead for each refrigerator (Column A) and the three activity-based rates to determine the activity-based factory overhead per unit (Column B). Finally, compute the percent change in per-unit allocation from the single to activity-based rate methods (Column C). (Round per-unit overhead to two decimal places and percents to one decimal place.)

Why is the traditional overhead rate per machine hour greater under the single-rate method than under the activity-based method?

Interpret Column C in your table from part (A).

To determine

Compute the single plant-wide overhead, ABC overhead for all the three products, and the percentage change in the allocation, and complete the Columns A, B, and C in the given table.

Explanation of Solution

Single plant-wide factory overhead rate: The rate at which the factory or manufacturing overheads are allocated to products is referred to as single plant-wide factory overhead rate.

Formula to compute single plant-wide overhead rate:

  $\begin{array}{l}\text{Single plant-wide }\\ \text{overhead rate}\end{array}\}\text{ = }\frac{\text{Total budgeted factory overhead}}{\text{Total budgeted plant-wide allocation base}}$

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:

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

Complete the blanks for Column A, B, and C.

Product Volume Class	Column A (Single Rate Overhead Allocation Per Unit) (1)	Column B (ABC Overhead Allocation Per Unit) (2)	Column C (Percent Change in Allocation) (3)
Low	$30.00	$58.06
Medium	30.00	29.31
High	30.00	25.46

Table (1)

Working Note (1):

Compute factory overhead allocated per unit of each product, using single machine rate of $200 per machine hour (MH) (Column A).

Product Volume Class	Single Plant-Wide Overhead Rate	×	Total Number of MH	=	Total Factory Overhead	÷	Number of  Units	=	Factory Overhead Per Unit
Low	$200	×	24 MH	=	$4,800	÷	160	=	$30.00
Medium	$200	×	225 MH	=	45,000	÷	1,500	=	$30.00
High	$200	×	900 MH	=	180,000	÷	6,000	=	$30 .00

Table (2)

Working Note (2):

Compute ABC factory overhead allocated per unit of each product (Column B).

Step 1: Compute activity cost allocated per unit of low volume refrigerators.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base	=	Activity Cost
Machining	$160 per MH	×	24 MH	=	$3,840
Setup	$240 per setup	×	14 setups	=	3,360
Sales order processing	$55 per sales order	×	38 orders	=	2,090
Total activity costs allocated to low volume refrigerators					$9,290
Number of units of low volume refrigerators					÷160 units
Activity-based overhead cost per unit of low volume refrigerator					$58.06

Table (3)

Step 2: Compute activity cost allocated per unit of medium volume refrigerators.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base	=	Activity Cost Allocated
Machining	$160 per MH	×	225 MH	=	$36,000
Setup	$240 per setup	×	13 setups	=	3,120
Sales order processing	$55 per sales order	×	88 orders	=	4,840
Total activity costs allocated to medium volume refrigerators					$43,960
Number of units of medium volume refrigerators					÷1,500 units
Activity-based overhead cost per unit of refrigerator					$29.31

Table (4)

Step 3: Compute activity cost allocated per unit of high volume refrigerators.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base	=	Activity Cost Allocated
Machining	$160 per MH	×	900 MH	=	$144,000
Setup	$240 per setup	×	9 setups	=	2,160
Sales order processing	$55 per sales order	×	120 orders	=	6,600
Total activity costs allocated to high volume refrigerators					$152,760
Number of units of high volume refrigerators					÷6,000 units
Activity-based overhead cost per unit of refrigerator					$25.46

Table (5)

Working Note (3):

Compute the percent change in the allocation (Column C).

Product Volume Class	Column B (ABC Overhead Allocation Per Unit)	˗	Column A (Single Rate Overhead Allocation Per Unit)	÷	Column A (Single Rate Overhead Allocation Per Unit)	=	Percent Change in Allocation
Low	$58.06	˗	$30.00	÷	$30.00	=	93.53%
Medium	29.31	˗	30.00	÷	30.00	=	(2.3)%
High	25.46	˗	30.00	÷	30.00	=	(15.1)%

Table (6)

Note: refer to Tables (2), (3), (4), and (5) for value and computation of Column A and Column B values.

To determine

Discuss the reasons for the difference in machine rate under single plant-wide approach and ABC approach.

Explanation of Solution

The machine hour rate under ABC, $160 per machine hour, as computed in Part (1), is different from the $200 single machine rate under single plant-wide approach. This is because the ABC method allocates all the overheads based on the activities under production. So, setup and sales order processing activities are allocated their share in factory overheads.

To determine

Discuss the percent change in allocation (Column C).

Explanation of Solution

As per the ABC method, low volume refrigerator has high activity cost per unit comparatively. This is because this product consumes high overheads for the setup activity with highest cost. The company could reduce the cost of setup activity.