Question

Laval produces lamps and home lighting fixtures. Its most popular product is a brushed aluminum desk lamp. This lamp is made from components shaped in the fabricating department and assembled in the assembly department. Information related to the 35,000 desk lamps produced annually follows.

Direct materials	\(280,000
Direct labor
Fabricating department (7,000 DLH × \)20 per DLH)	\(140,000
Assembly department (16,000 DLH × \)29 per DLH)	\(464,000
Machine hours
Fabricating department.	15,040 MH
Assembly department	21,000 MH

Expected overhead cost and related data for the two production departments follow.

	Fabricating	Assembly
Direct labor hours	75,000 DLH	125,000 DLH
Machine hours	80,000 MH	62,500 MH
Overhead cost	\)300,000	$200,000

Required

1. Determine the plantwide overhead rate for Laval using direct labor hours as a base.
2. Determine the total manufacturing cost per unit for the aluminum desk lamp using the plantwide overhead rate.
3. Compute departmental overhead rates based on machine hours in the fabricating department and direct labor hours in the assembly department.
4. Use departmental overhead rates from requirement 3 to determine the total manufacturing cost per unit for the aluminum desk lamps.

Short answer

1. The plant-wide overhead rate is$2.50 DLH
2. The manufacturing cost per unit is$26.90
3. Departmental overhead rates are$3.75 and$1.60
4. The manufacturing cost per unit is$27.60

Step-by-step solution

Meaning of Overhead Cost

Overhead is a study of the expenses incurred to maintain healthy functioning on the monthly revenue statement. The labor, materials, or services cost is not economically linked to an actual saleable cost of products or services per business unit.

(a) Determining plantwide overhead rate

Computing the plantwide overheads rate

$$\begin{gathered} \text{Plantwide}\text{overhead}\text{rate}=\frac{\text{Total}\text{overhead}\text{cost}}{\text{Total}\text{Direct}\text{labour}\text{hours}} \\ =\frac{\$300,000+\$200,000}{75,000+125,000} \\ =\frac{\$500,0000}{200,000} \\ =\$2.50\text{per}\text{DLH} \end{gathered}$$

(b) Determining the total manufacturing cost per unit

Computation of manufacturing cost per unit

Particulars	Amount ($)
Total manufacturing cost
Direct materials	$280,000
Direct Labor:
Fabricating department	$140,000
Assembly department	$464,000
Applied overhead	$57,500
Total manufacturing cost	$941,500
Total desk lamp produced	$35,000
Manufacturing cost per unit	$26.90

Working notes:

Calculation of manufacturing cost per unit

$$\begin{gathered} \text{Manufacturing}\text{cost}\text{per}\text{unit}=\frac{\text{Total}\text{manufacturing}\text{cost}}{\text{Total}\text{desk}\text{lamp}\text{produced}} \\ =\frac{\$941,500}{\$35,000} \\ =\$26.90 \end{gathered}$$

(c) Computing departmental overhead rates

Particulars	Fabricating	Assembly
The overhead cost of the department	$300,000	$200,000
Allocation base	MH	DLH
Total machine hours	80,000	-
Total direct labor hours	-	125,000
Overhead rate of department	$3.75	$1.60

Working notes:

Calculation of Overhead rate of the department of fabricating

$$\begin{gathered} \text{Overhead} \text{rate}\text{of}\text{department}=\frac{\text{Overhead}\text{cost}}{\text{Total}\text{machine}\text{hours}} \\ =\frac{\$300,000}{80,000} \\ =\$3.75 \end{gathered}$$

Calculation of Overhead rate of the department of assembly

$$\begin{gathered} \text{Overhead} \text{rate}\text{of}\text{department}=\frac{\text{Overhead}\text{cost}}{\text{Total}\text{machine}\text{hours}} \\ =\frac{\$200,000}{125,000} \\ =\$1.60 \end{gathered}$$

(d) Determining the total manufacturing cost per unit

Calculation of manufacturing cost per unit

Particulars	Amount ($)
Total manufacturing cost
Direct materials	$280,000
Direct labor:
Fabricating departments	$140,000
Assembly department	$464,000
Applied overhead:
Fabricating department	$56,400
Assembly department	$25,600
Total manufacturing cost	$966,000
Total desk lamp produced	$35,000
Manufacturing cost per unit	$27.60

Working notes:

$$\begin{gathered} \text{Manufacturing}\text{cost}\text{per}\text{unit}=\frac{\text{Total}\text{manufacturing}\text{cost}}{\text{Total}\text{desk}\text{lamp}\text{produced}} \\ =\frac{\$966,000}{\$35,000} \\ =\$27.60 \end{gathered}$$