Answer :
To calculate the total job cost for Job M242 at Alsobrooks Corporation, we need to go through several steps: determining the predetermined overhead rate, calculating the manufacturing overhead specific to Job M242, and then using this information to compute the total job cost. Here’s a step-by-step breakdown:
### Step 1: Calculation of the Predetermined Overhead Rate
The predetermined overhead rate is calculated using the following formula:
[tex]\[ \text{Predetermined Overhead Rate} = \frac{\text{Total Fixed Manufacturing Overhead Cost} + (\text{Variable Manufacturing Overhead per Machine-Hour} \times \text{Total Machine-Hours})}{\text{Total Machine-Hours}} \][/tex]
Given data:
- Total fixed manufacturing overhead cost (\[tex]$): \( \text{ Fixed MOH } = 125,000 \) - Variable manufacturing overhead per machine-hour (\$[/tex]): [tex]\( \text{ Variable MOH rate per MH } = 4.00 \)[/tex]
- Total machine-hours: [tex]\( \text{ Total MH } = 42,000 \)[/tex]
Substituting these values into the formula gives:
[tex]\[ \text{Predetermined Overhead Rate} = \frac{125,000 + (4.00 \times 42,000)}{42,000} \][/tex]
[tex]\[ = \frac{125,000 + 168,000}{42,000} \][/tex]
[tex]\[ = \frac{293,000}{42,000} \][/tex]
[tex]\[ \approx 6.9762 \text{ per machine-hour} \][/tex]
### Step 2: Calculation of Manufacturing Overhead for Job M242
To find the manufacturing overhead allocated to Job M242, we multiply the predetermined overhead rate by the number of machine hours used by the job:
[tex]\[ \text{Manufacturing Overhead for Job M242} = \text{Predetermined Overhead Rate} \times \text{Total Machine-Hours for Job M242} \][/tex]
Given:
- Total machine-hours for Job M242: [tex]\( \text{ Job M242 MH } = 50 \)[/tex]
Using the predetermined overhead rate already calculated:
[tex]\[ \text{Manufacturing Overhead for Job M242} = 6.9762 \times 50 \][/tex]
[tex]\[ = 348.81 \][/tex]
### Step 3: Calculation of the Total Job Cost for Job M242
The total job cost is the sum of direct materials, direct labor, and manufacturing overhead allocated to the job:
[tex]\[ \text{Total Job Cost for Job M242} = \text{Direct Materials} + \text{Direct Labor Cost} + \text{Manufacturing Overhead} \][/tex]
Given:
- Direct materials (\[tex]$): \( \text{DM} = 750 \) - Direct labor cost (\$[/tex]): [tex]\( \text{DL} = 1,700 \)[/tex]
- Manufacturing overhead for Job M242 (\[tex]$): \( \text{MOH for Job M242} = 348.81 \) Substituting these values into the formula gives: \[ \text{Total Job Cost for Job M242} = 750 + 1,700 + 348.81 \] \[ = 2,798.81 \] ### Summary of Results - Predetermined Overhead Rate: \( 6.9762 \) per machine-hour - Manufacturing Overhead for Job M242: \( 348.81 \) - Total Job Cost for Job M242: \( 2,798.81 \) Hence, the total job cost for Job M242 comes out to \( \$[/tex]2,798.81 \).
### Step 1: Calculation of the Predetermined Overhead Rate
The predetermined overhead rate is calculated using the following formula:
[tex]\[ \text{Predetermined Overhead Rate} = \frac{\text{Total Fixed Manufacturing Overhead Cost} + (\text{Variable Manufacturing Overhead per Machine-Hour} \times \text{Total Machine-Hours})}{\text{Total Machine-Hours}} \][/tex]
Given data:
- Total fixed manufacturing overhead cost (\[tex]$): \( \text{ Fixed MOH } = 125,000 \) - Variable manufacturing overhead per machine-hour (\$[/tex]): [tex]\( \text{ Variable MOH rate per MH } = 4.00 \)[/tex]
- Total machine-hours: [tex]\( \text{ Total MH } = 42,000 \)[/tex]
Substituting these values into the formula gives:
[tex]\[ \text{Predetermined Overhead Rate} = \frac{125,000 + (4.00 \times 42,000)}{42,000} \][/tex]
[tex]\[ = \frac{125,000 + 168,000}{42,000} \][/tex]
[tex]\[ = \frac{293,000}{42,000} \][/tex]
[tex]\[ \approx 6.9762 \text{ per machine-hour} \][/tex]
### Step 2: Calculation of Manufacturing Overhead for Job M242
To find the manufacturing overhead allocated to Job M242, we multiply the predetermined overhead rate by the number of machine hours used by the job:
[tex]\[ \text{Manufacturing Overhead for Job M242} = \text{Predetermined Overhead Rate} \times \text{Total Machine-Hours for Job M242} \][/tex]
Given:
- Total machine-hours for Job M242: [tex]\( \text{ Job M242 MH } = 50 \)[/tex]
Using the predetermined overhead rate already calculated:
[tex]\[ \text{Manufacturing Overhead for Job M242} = 6.9762 \times 50 \][/tex]
[tex]\[ = 348.81 \][/tex]
### Step 3: Calculation of the Total Job Cost for Job M242
The total job cost is the sum of direct materials, direct labor, and manufacturing overhead allocated to the job:
[tex]\[ \text{Total Job Cost for Job M242} = \text{Direct Materials} + \text{Direct Labor Cost} + \text{Manufacturing Overhead} \][/tex]
Given:
- Direct materials (\[tex]$): \( \text{DM} = 750 \) - Direct labor cost (\$[/tex]): [tex]\( \text{DL} = 1,700 \)[/tex]
- Manufacturing overhead for Job M242 (\[tex]$): \( \text{MOH for Job M242} = 348.81 \) Substituting these values into the formula gives: \[ \text{Total Job Cost for Job M242} = 750 + 1,700 + 348.81 \] \[ = 2,798.81 \] ### Summary of Results - Predetermined Overhead Rate: \( 6.9762 \) per machine-hour - Manufacturing Overhead for Job M242: \( 348.81 \) - Total Job Cost for Job M242: \( 2,798.81 \) Hence, the total job cost for Job M242 comes out to \( \$[/tex]2,798.81 \).
