Final answer:
The manufacturing overhead was underallocated by $30,000 for the year.
Step-by-step explanation:
The manufacturing overhead is calculated using the predetermined manufacturing overhead rate based on direct labor hours. First, we need to calculate the predetermined rate using the estimated manufacturing overhead cost and the estimated direct labor hours:
Predetermined Overhead Rate = Estimated Manufacturing Overhead Cost / Estimated Direct Labor Hours
Predetermined Overhead Rate = $400,000 / 50,000 hours
Predetermined Overhead Rate = $8 per direct labor hour
Next, we can calculate the applied manufacturing overhead by multiplying the predetermined overhead rate by the actual direct labor hours:
Applied Manufacturing Overhead = Predetermined Overhead Rate x Actual Direct Labor Hours
Applied Manufacturing Overhead = $8 x 55,000 hours = $440,000
Finally, we can determine the amount of manufacturing overhead overallocated or underallocated for the year by comparing the applied overhead to the actual overhead:
Manufacturing Overhead Overallocated/Underallocated = Actual Manufacturing Overhead Cost - Applied Manufacturing Overhead
Manufacturing Overhead Overallocated/Underallocated = $410,000 - $440,000 = -$30,000