Chapter 4, Problem 41P

1.

To determine

Calculate the predetermined overhead rate.

Explanation of Solution

Plantwide Overhead Rate: Plantwide overhead rate is the rate a company uses to allocate their manufacturing overhead costs to products and cost centers.

Predetermined factory overhead rate: Predetermined factory overhead cost are applied or allocated to cost of job based on predetermined factory overhead rate.

Calculate budgeted overhead.

$\begin{array}{c}\text{Budgeted overhead}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Variable cost }\\ \text{of department A}\end{array}\right)+\left(\begin{array}{l}\text{Fixed cost }\\ \text{of department A}\end{array}\right)\\ +\left(\begin{array}{l}\text{Variable cost }\\ \text{of department B}\end{array}\right)+\left(\begin{array}{l}\text{Fixed cost }\\ \text{of department B}\end{array}\right)\end{array}\right)\\ =\left(\begin{array}{l}\left(\$150,000+\$94,000\right)\\ +\left(\$80,000+\$163,000\right)\end{array}\right)\\ =\$487,000\end{array}$

Calculate the budgeted direct labor hours.

$\begin{array}{c}\left(\begin{array}{l}\text{Budgeted direct }\\ \text{labor hours}\end{array}\right)=\left(\begin{array}{l}\text{Expected production}\\ \times \left(\begin{array}{l}\left(\begin{array}{l}\text{Direct labor hours per }\\ \text{unit of department A}\end{array}\right)\\ +\left(\begin{array}{l}\text{Direct labor hours per }\\ \text{unit of department B}\end{array}\right)\end{array}\right)\end{array}\right)\\ =1,000\times \left(15+10\right)\\ =25,000\text{ hours}\end{array}$

Calculate the predetermined overhead application rate.

$\begin{array}{c}\left(\begin{array}{l}\text{Predetermined overhead}\\ \text{application rate}\end{array}\right)=\frac{\text{Budgeted overhead}}{\text{Budgeted direct labor hours}}\\ =\frac{\$487,000}{25,000\text{ hours}}\\ =\$19.48\text{ per direct labor hours}\end{array}$

Therefore, the predetermined application rate is $19.48 per direct labor hours.

2.

To determine

Compute plant-wide overhead rate.

Explanation of Solution

Calculate the budgeted machine hours.

$\begin{array}{c}\left(\begin{array}{l}\text{Budgeted machine }\\ \text{hours}\end{array}\right)=\left(\begin{array}{l}\text{Expected production}\\ \times \left(\begin{array}{l}\left(\begin{array}{l}\text{Machine hours per }\\ \text{unit of department A}\end{array}\right)\\ +\left(\begin{array}{l}\text{Machine hours per }\\ \text{unit of department B}\end{array}\right)\end{array}\right)\end{array}\right)\\ =1,000\times \left(5+15\right)\\ =20,000\text{ hours}\end{array}$

Calculate the predetermined overhead application rate.

$\begin{array}{c}\left(\begin{array}{l}\text{Predetermined overhead}\\ \text{application rate}\end{array}\right)=\frac{\text{Budgeted overhead}}{\text{Budgeted machine hours}}\\ =\frac{\$487,000}{20,000}\\ =\$24.35\text{ per machine hours}\end{array}$

Therefore, the predetermined application rate is $24.35 per machine hours.

3.

To determine

Compute the total amount of applied factory overhead.

Explanation of Solution

Compute the total cost allocated.

	Allocated Cost
Method	Department A	Department B	Total
Direct labor hours	$292,200	$194,800	$487,000
Machine hours	$121,750	$365,250	$487,000

Table (1)

Supporting computations:

Particulars	Department A	Department B	Total Hours
Direct labor hours	15,000 (1)	10,000 (2)	25,000
Overhead applied	$292,200 (3)	$194,800 (4)
Machine hours	5,000 (5)	15,000 (6)	20,000
Overhead applied	$121,750 (7)	$365,250 (8)

Table (2)

Working Notes (1): Calculate the direct labor hour of department A.

$\begin{array}{c}\left(\begin{array}{l}\text{Direct labor hour}\\ \text{of department A }\end{array}\right)=\left(\begin{array}{l}\text{Expected production}\\ \times \left(\begin{array}{l}\text{Direct labor hours }\\ \text{per unit department A}\end{array}\right)\end{array}\right)\\ =1,000\times 15\\ =15,000\text{ hours}\end{array}$

(2) Calculate the direct labor hour of department B.

$\begin{array}{c}\left(\begin{array}{l}\text{Direct labor hour}\\ \text{of department B }\end{array}\right)=\left(\begin{array}{l}\text{Expected production}\\ \times \left(\begin{array}{l}\text{Direct labor hours }\\ \text{per unit department B}\end{array}\right)\end{array}\right)\\ =1,000\times 10\\ =10,000\text{ hours}\end{array}$

(3) Calculate the overapplied of department A.

$\begin{array}{c}\left(\begin{array}{l}\text{Overhead applied}\\ \text{of department A }\end{array}\right)=\left(\begin{array}{l}\left(\begin{array}{l}\text{Direct labor hours }\\ \text{of department A}\end{array}\right)\\ \times \text{Predetermined overhead rate}\end{array}\right)\\ =15,000\times \$19.48\\ =\$292,200\end{array}$

(4) Calculate the overapplied of department B.

$\begin{array}{c}\left(\begin{array}{l}\text{Overhead applied}\\ \text{of department A }\end{array}\right)=\left(\begin{array}{l}\left(\begin{array}{l}\text{Direct labor hours }\\ \text{of department B}\end{array}\right)\\ \times \text{Predetermined overhead rate}\end{array}\right)\\ =10,000\times \$19.48\\ =\$194,800\end{array}$

(5) Calculate machine hour of department A.

$\begin{array}{c}\left(\begin{array}{l}\text{Machine hours }\\ \text{of department A}\end{array}\right)=\left(\begin{array}{l}\text{Expected production }\\ \times \left(\begin{array}{l}\text{Machine hour per unit }\\ \text{of department A}\end{array}\right)\end{array}\right)\\ =1,000\times 5\\ =5,000\text{ hours}\end{array}$

(6) Calculate machine hour of department B.

$\begin{array}{c}\left(\begin{array}{l}\text{Machine hours }\\ \text{of department B}\end{array}\right)=\left(\begin{array}{l}\text{Expected production }\\ \times \left(\begin{array}{l}\text{Machine hour per unit }\\ \text{of department B}\end{array}\right)\end{array}\right)\\ =1,000\times 15\\ =15,000\text{ hours}\end{array}$

(7) Calculate the overhead applied.

$\begin{array}{c}\left(\begin{array}{l}\text{Overhead applied}\\ \text{for department A}\end{array}\right)=\left(\begin{array}{l}\text{Machine hours of department A}\\ \times \left(\text{Predetermined overhead rate}\right)\end{array}\right)\\ =5,000\times \$24.35\\ =121,750\end{array}$

(8) Calculate the overhead applied.

$\begin{array}{c}\left(\begin{array}{l}\text{Overhead applied}\\ \text{for department A}\end{array}\right)=\left(\begin{array}{l}\text{Machine hours of department A}\\ \times \left(\text{Predetermined overhead rate}\right)\end{array}\right)\\ =15,000\times \$24.35\\ =365,250\end{array}$

4.

To determine

Explain the type of allocation basis used and give reason.

Explanation of Solution

If factory overhead is applied by the direct labor hours, Department A is allotted more than its total estimated overhead and less is assigned to department B. If departmental rate were used Department A will assign more overhead to products and less is assigned to department B. Department A is undercharged and Department B is overcharged, if machine hours are used because each department has a different cost driver. Department A is labor intensive and Department B is a machine intensive. Hence, one single plantwide overhead rate is not appropriate.

5.

To determine

Calculate the departmental overhead rate and applied overhead amount.

Explanation of Solution

Calculate the predetermined overhead rate using direct labor hours for department A.

$\begin{array}{c}\left(\begin{array}{l}\text{Predetermined overhead}\\ \text{rate for Department A}\end{array}\right)=\frac{\text{Factory overhead}}{\text{Direct labor hour}}\\ =\frac{\$244,000}{15,000}\\ =\$16.267\left(\begin{array}{l}\text{per direct }\\ \text{labor hour}\end{array}\right)\end{array}$

Calculate the applied overhead.

$\begin{array}{c}\text{Applied overhead}=\left(\begin{array}{l}\text{Expected }\\ \text{production}\end{array}\right)\times \left(\begin{array}{l}\text{Direct labor }\\ \text{hour per unit}\end{array}\right)\times \left(\begin{array}{l}\text{Predetermined overhead }\\ \text{rate}\left(\text{Department A}\right)\end{array}\right)\\ =1,000\times 15\times \$16.267\\ =\$244,000\left(\text{rounded off}\right)\end{array}$

Calculate the predetermined overhead rate using machine hours for department B.

$\begin{array}{c}\left(\begin{array}{l}\text{Predetermined overhead }\\ \text{rate}\left(\text{Department B}\right)\end{array}\right)=\frac{\text{Factory overhead cost}}{\left(\text{Machine hour}\right)}\\ =\frac{243,000}{\text{15,000}}\\ =\$16.20\end{array}$

Calculate the applied overhead.

$\begin{array}{c}\text{Applied overhead}=\left(\begin{array}{l}\text{Expected}\\ \text{ production}\end{array}\right)\times \left(\begin{array}{l}\text{Machine hour }\\ \text{per unit}\end{array}\right)\times \left(\begin{array}{l}\text{Predetermined overhead}\\ \text{ rate}\left(\text{Department B}\right)\end{array}\right)\\ =1,000\times 15\times \$16.20\\ =\$243,000\end{array}$