Math Problem Statement

Crich Corporation uses direct labor-hours in its predetermined overhead rate. At the beginning of the year, the estimated direct labor-hours were 21,960 hours and the total estimated manufacturing overhead was $535,824. At the end of the year, actual direct labor-hours for the year were 21,900 hours and the actual manufacturing overhead for the year was $535,824. Overhead at the end of the year was:

Note: Do not round intermediate calculations.

Multiple Choice $1,514 overapplied $1,514 underapplied $1,464 underapplied $1,464 overapplied

Solution

To determine whether the overhead is overapplied or underapplied, we first need to calculate the predetermined overhead rate and then compare the applied overhead to the actual overhead.

Step 1: Calculate the Predetermined Overhead Rate

The formula for the predetermined overhead rate is: Predetermined Overhead Rate=Estimated Total Manufacturing OverheadEstimated Direct Labor-Hours\text{Predetermined Overhead Rate} = \frac{\text{Estimated Total Manufacturing Overhead}}{\text{Estimated Direct Labor-Hours}} Using the given information:

  • Estimated Total Manufacturing Overhead = $535,824
  • Estimated Direct Labor-Hours = 21,960 hours

Predetermined Overhead Rate=535,82421,960=24.4per direct labor-hour\text{Predetermined Overhead Rate} = \frac{535,824}{21,960} = 24.4 \, \text{per direct labor-hour}

Step 2: Apply Overhead to Actual Direct Labor-Hours

The formula for applied overhead is: Applied Overhead=Predetermined Overhead Rate×Actual Direct Labor-Hours\text{Applied Overhead} = \text{Predetermined Overhead Rate} \times \text{Actual Direct Labor-Hours} Using the given actual labor-hours:

  • Actual Direct Labor-Hours = 21,900 hours

Applied Overhead=24.4×21,900=534,360\text{Applied Overhead} = 24.4 \times 21,900 = 534,360

Step 3: Compare Applied Overhead to Actual Overhead

The actual manufacturing overhead is given as $535,824. Now, we compare the applied overhead to the actual overhead: Difference=Actual OverheadApplied Overhead\text{Difference} = \text{Actual Overhead} - \text{Applied Overhead} Difference=535,824534,360=1,464\text{Difference} = 535,824 - 534,360 = 1,464

Since the actual overhead is greater than the applied overhead, the overhead is underapplied.

Final Answer:

The overhead at the end of the year was $1,464 underapplied.

The correct choice is:

  • $1,464 underapplied

Would you like further details or have any questions? Here are some related questions:

  1. How is overapplied overhead different from underapplied overhead?
  2. What are some consequences of underapplied overhead in managerial decision-making?
  3. How can a company correct underapplied or overapplied overhead?
  4. What is the significance of using direct labor-hours for overhead allocation?
  5. How would a change in estimated labor-hours affect the predetermined overhead rate?

Tip: Always ensure the estimated costs and labor hours are accurate to avoid significant discrepancies in overhead allocation.

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Math Problem Analysis

Mathematical Concepts

Cost Accounting
Manufacturing Overhead
Direct Labor-Hours
Overhead Allocation

Formulas

Predetermined Overhead Rate = Estimated Total Manufacturing Overhead / Estimated Direct Labor-Hours
Applied Overhead = Predetermined Overhead Rate × Actual Direct Labor-Hours
Overhead Difference = Actual Overhead - Applied Overhead

Theorems

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Suitable Grade Level

College-level (Accounting/Finance)