Chapter 4, Problem 13E

A.

To determine

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:

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

To compute: The single plant-wide overhead rate using direct machine hours (DLH) as the allocation base, and compute factory overhead or indirect labor cost allocated per unit

Explanation of Solution

Compute single plant-wide overhead rate using DLH as the allocation base.

$\begin{array}{c}\begin{array}{l}\text{Single plant-wide }\\ \text{overhead rate}\end{array}\}\text{ = }\frac{\text{Total budgeted factory overhead}}{\text{Total budgeted plant-wide allocation base}}\\ \text{= }\frac{\text{\$375,000}}{\text{3,750 DLH}}\\ \text{= \$100 per DLH}\end{array}$ (1)

Compute the factory overhead allocated per unit for each product.

Step 1: Compute DLH per unit for cell phones.

$\begin{array}{c}\text{Number of DLH per unit = }\frac{\text{Total DLH for 93,750 units}}{\text{Number of units}}\\ \text{= }\frac{\text{1,875 DLH}}{\text{93,750 units}}\\ \text{= 0}\text{.02 DLH per unit}\end{array}$ (2)

Step 2: Compute DLH per unit for tablets.

$\begin{array}{c}\text{Number of DLH per unit = }\frac{\text{Total DLH for 93,750 units}}{\text{Number of units}}\\ \text{= }\frac{\text{1,875 DLH}}{\text{93,750 units}}\\ \text{= 0}\text{.02 DLH per unit}\end{array}$ (3)

Step 3: Compute indirect labor cost or factory overhead allocated per unit of each product.

Types of Products	Single Plant-Wide Overhead Rate	×	Number of DLH Per Unit of Each Product	=	Factory Overhead Per Unit
Cell phones	$100 per DLH	×	0.2 DLH	=	$2 per unit
Tablets	$100 per DLH	×	0.2 DLH	=	$2 per unit

Table (1)

Note: Refer to Equation (1) for value and computation of single plant-wide overhead rate. Refer to Equations (2) and (3) for value and computation of DLH per unit of each product.

B.

To determine

To compute: The activity-based overhead rate for each of the given activities

Explanation of Solution

Compute activity-based overhead rates for each activity.

Step 1: Compute activity cost for setup activity.

$\begin{array}{c}\text{Activity cost for setup = }\left\{\begin{array}{l}\text{Indirect labor budgeted×}\\ \text{Percentage of setup cost}\end{array}\right\}\\ \text{=\$375,000×40\%}\\ \text{=\$150,000}\end{array}$ (4)

Step 2: Compute activity cost for production support activity.

$\begin{array}{c}\begin{array}{l}\text{Activity cost for }\\ \text{production support}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Indirect labor budgeted×}\\ \text{Percentage of production support cost}\end{array}\right\}\\ \text{=\$375,000×60\%}\\ \text{=\$225,000}\end{array}$ (5)

Step 3: Compute activity-based overhead rates for each activity.

Computation of Activity-Based Overhead Rates
Activity	Activity Cost	÷	Total Activity-Base Usage	=	Activity-Based Overhead Rates
Setup	$150,000	÷	2,000 setups	=	$75 per setup
Production support	225,000	÷	3,750 DLH	=	$60 per DLH

Table (2)

Note: Refer to Equations (4) and (5) for value and computation of activity cost.

C.

To determine

To compute: The activity-cost per unit of the products

Explanation of Solution

Compute activity cost allocated per unit of cell phone.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base (Cost Driver)	=	Activity Cost Allocated
Setup	$75 per setup	×	600 setups	=	$45,000
Production support	$60 per DLH	×	1,875 DLH	=	112,500
Total activity costs allocated to cell phones					$157,500
Number of units of cell phone					÷ 93,750 units
Activity-based overhead cost per unit of cell phone					$1,68

Table (3)

Note: Refer to Table (2) for the value and computation of activity allocation rates.

Compute activity cost allocated per unit of tablet.

Activity	Activity-Based Overhead Rates	×	Actual Use of Activity-Base (Cost Driver)	=	Activity Cost Allocated
Setup	$75 per setup	×	1,400 setups	=	$105,000
Production support	$60 per DLH	×	1,875 DLH	=	112,500
Total activity costs allocated to tablets					$217,500
Number of units of tablet					÷ 93,750 units
Activity-based overhead cost per unit of tablet					$2.32

Table (3)

Note: Refer to Table (2) for the value and computation of activity allocation rates.

D.

To determine

To discuss: The product cost distortion due to single plant-wide overhead rate

Explanation of Solution

The product cost under single plant-wide overhead rate approach and ABC approach are different. The product cost is distorted in single plant-wide overhead rate approach because the time spent for setup production for cell phones and tablets is not in the same ratio as the direct labor hours used in support production for cell phones and tablets.