Kingsley Products estimated that direct labor for the year would be 64,000 hoursThe company also estimated that the fixed overhead cost for the year would be $160,000. They further estimated the variable overhead cost to be $4.00 per direct labor-hourAll overhead at Kingsley Products is applied on the basis of direct labor-hours. During the yearfixed overhead costs were exactly as planned ( 160,000)Variable overhead was incurred at $4.50 per direct labor-hour Underapplied overhead for the year was calculated as $18,000 Required: How many direct labor-hours were worked during the period? Note: Do not round intermediate calculations

Let's break this down and solve the problem step by step.

### Step 1: Formula for Total Overhead Applied
The total overhead is the sum of the fixed and variable overheads, and overhead is applied based on direct labor-hours (DLH).

- **Fixed Overhead (FOH):** $160,000 (as given)
- **Variable Overhead (VOH) per direct labor-hour (DLH):** $4.00 (as estimated)
  
The total estimated overhead per DLH would be:
\[
\text{Estimated overhead rate} = \text{FOH} + \text{VOH per DLH} = 160,000 + (4.00 \times \text{DLH})
\]

### Step 2: Underapplied Overhead
We know that the underapplied overhead was calculated as $18,000, which means that the actual overhead incurred exceeded the applied overhead by $18,000.

\[
\text{Underapplied overhead} = \text{Actual Overhead} - \text{Applied Overhead}
\]

### Step 3: Actual Overhead
The actual overhead is the sum of actual fixed overhead and actual variable overhead:

- **Actual Fixed Overhead (AFOH):** $160,000 (as planned)
- **Actual Variable Overhead (AVOH):** $4.50 per DLH

So, the total actual overhead is:
\[
\text{Actual Overhead} = 160,000 + (4.50 \times \text{DLH})
\]

### Step 4: Applied Overhead
The applied overhead is based on the estimated rate of $4.00 per DLH for variable overhead and $160,000 for fixed overhead:
\[
\text{Applied Overhead} = 160,000 + (4.00 \times \text{DLH})
\]

### Step 5: Underapplied Overhead Equation
Since we know the underapplied overhead is $18,000, we can set up the equation:
\[
18,000 = \left( 160,000 + (4.50 \times \text{DLH}) \right) - \left( 160,000 + (4.00 \times \text{DLH}) \right)
\]

Simplifying the equation:
\[
18,000 = (4.50 \times \text{DLH}) - (4.00 \times \text{DLH})
\]
\[
18,000 = 0.50 \times \text{DLH}
\]

### Step

Kingsley Products estimated that direct labor for the year would be 64,000 hours. The company also estimated that the fixed overhead cost for the year would be $160,000. They further estimated the variable overhead cost to be $4.00 per direct labor-hour. All overhead at Kingsley Products is applied on the basis of direct labor-hours. During the year, fixed overhead costs were exactly as planned ($160,000). Variable overhead was incurred at $4.50 per direct labor-hour. Underapplied overhead for the year was calculated as $18,000. Required: How many direct labor-hours were worked during the period? Note: Do not round intermediate calculations.

This problem explores how Kingsley Products applied overhead based on direct labor-hours, and includes a step-by-step solution to calculate the total number of direct labor-hours worked during the year. Concepts include cost accounting, linear equations, and overhead allocation methods.

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