Red Raider Company uses a plantwide overhead rate with direct labor hours as the allocation base. Next year, 400,000 units are expected to be produced, taking 0.90 direct labor hours each. How much overhead will be assigned to each unit produced given the following estimated amounts?

\begin{tabular}{|l|r|r|}
\hline
Estimated: & Department 1 & Department 2 \\
\hline
Manufacturing overhead costs & \[tex]$2,530,000 & \$[/tex]900,000 \\
\hline
Direct labor hours & 168,000 DLH & 110,000 DLH \\
\hline
Machine hours & 30,000 MH & 8,000 MH \\
\hline
\end{tabular}

A. \[tex]$15.06 per unit
B. \$[/tex]12.34 per unit
C. \[tex]$63.95 per unit
D. \$[/tex]7.32 per unit
E. \$11.11 per unit



Answer :

Let's solve this step-by-step.

1. Calculate total manufacturing overhead costs:
The estimated manufacturing overhead costs for Department 1 are \[tex]$2,530,000 and for Department 2 are \$[/tex]900,000.
[tex]\[ \text{Total manufacturing overhead costs} = \$2,530,000 + \$900,000 = \$3,430,000 \][/tex]

2. Calculate total direct labor hours (DLH):
The estimated direct labor hours for Department 1 are 168,000 hours and for Department 2 are 110,000 hours.
[tex]\[ \text{Total direct labor hours} = 168,000 \text{ DLH} + 110,000 \text{ DLH} = 278,000 \text{ DLH} \][/tex]

3. Calculate the plantwide overhead rate:
The plantwide overhead rate is calculated by dividing the total manufacturing overhead costs by the total direct labor hours.
[tex]\[ \text{Plantwide overhead rate} = \frac{\text{Total manufacturing overhead costs}}{\text{Total direct labor hours}} = \frac{\$3,430,000}{278,000 \text{ DLH}} = \$12.34 \text{ per DLH} \][/tex]

4. Calculate total direct labor hours needed for the expected production:
The company expects to produce 400,000 units, with each unit requiring 0.90 direct labor hours.
[tex]\[ \text{Total direct labor hours needed} = 400,000 \text{ units} \times 0.90 \text{ DLH/unit} = 360,000 \text{ DLH} \][/tex]

5. Calculate overhead assigned to each unit:
First, we find the overhead per unit based on the labor hours each unit requires and the plantwide overhead rate.
[tex]\[ \text{Overhead assigned to each unit} = 0.90 \text{ DLH/unit} \times \$12.34 \text{ per DLH} = \$11.11 \text{ per unit} \][/tex]

Therefore, the amount of overhead assigned to each unit produced is \[tex]$11.11 per unit. The correct answer from the options is: \[ \$[/tex]11.11 \text{ per unit}
\]