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Single plantwide and multiple production department factory overhead rate methods and product cost distortion

Eclipse Motor Company manufactures two types of specialty electric motors, a commercial motor and a residential motor, through two production departments, Assembly and Testing. Presently, the company uses a single plantwide factory overhead rate for allocating factory overhead to the two products. However, management is considering using the multiple production department factory overhead rate method. The following factory overhead was budgeted for Eclipse:

Department Amount
Assembly Department $280,000
Testing Department 800,000
Total $1,080,000
Direct machine hours were estimated as follows:

Department Amount
Assembly Department 4,000 hours
Testing Department 5,000
Total 9,000 hours
In addition, the direct machine hours (dmh) used to produce a unit of each product in each department were determined from engineering records, as follows:

Departments Commercial Residential
Assembly Department 2.0 dmh 3.0 dmh
Testing Department 6.0 1.5
Total machine hours per unit 8.0 dmh 4.5 dmh
a. Determine the per-unit factory overhead allocated to the commercial and residential motors under the single plantwide factory overhead rate method, using direct machine hours as the allocation base.
Commercial fill in the blank 1 of 2$
per unit
Residential fill in the blank 2 of 2$
per unit

b. Determine the per-unit factory overhead allocated to the commercial and residential motors under the multiple production department factory overhead rate method, using direct machine hours as the allocation base for each department.
Commercial fill in the blank 1 of 2$
per unit
Residential fill in the blank 2 of 2$
per unit

c. Recommend to management a product costing approach, based on your analyses in (a) and (b).
1. The management should consider multiple production department factory overhead rate methods, because this method calculates the cost more accurately and considers the fact that commercial products use more costly overheads than residential products.
2. The management should consider single plantwide factory overhead rate methods, because this method calculates the cost more accurately and considers the fact that the overheads are applied evenly based on the direct labor hours.
3. The management could consider either multiple production department factory overhead rate method or the single plantwide rate, as both these methods have the same effect on the final costs.
fill in the blank 1 of 1

Answer 1

To answer this question, we will go through the calculations step by step.

### Part a: Single Plantwide Factory Overhead Rate Method

1. **Calculate the Total Plantwide Overhead Rate**:
- Total Estimated Factory Overhead = $1,080,000
- Total Estimated Direct Machine Hours (dmh) = 9,000 hours
- Plantwide Overhead Rate = Total Overhead / Total Machine Hours
\[
\text{Plantwide Overhead Rate} = \frac{1,080,000}{9,000} = 120 \text{ per hour}
\]

2. **Calculate the Factory Overhead Allocated for Each Product**:
- **Commercial Motor**:
- Total dmh per unit = 8.0 dmh (2.0 + 6.0)
- Overhead Allocated = 8.0 dmh * $120 = $960 per unit
- **Residential Motor**:
- Total dmh per unit = 4.5 dmh (3.0 + 1.5)
- Overhead Allocated = 4.5 dmh * $120 = $540 per unit

**Answers**:
- **Commercial**: $960 per unit
- **Residential**: $540 per unit

### Part b: Multiple Production Department Factory Overhead Rate Method

1. **Calculate Overhead Rate for Each Department**:
- **Assembly Department**:
\[
\text{Overhead Rate (Assembly)} = \frac{280,000}{4,000} = 70 \text{ per hour}
\]
- **Testing Department**:
\[
\text{Overhead Rate (Testing)} = \frac{800,000}{5,000} = 160 \text{ per hour}
\]

2. **Calculate Overhead Allocated for Each Product in Each Department**:
- **Commercial Motor**:
- Assembly: 2.0 dmh * $70 = $140
- Testing: 6.0 dmh * $160 = $960
- Total Overhead for Commercial = $140 + $960 = $1,100 per unit
- **Residential Motor**:
- Assembly: 3.0 dmh * $70 = $210
- Testing: 1.5 dmh * $160 = $240
- Total Overhead for Residential = $210 + $240 = $450 per unit

**Answers**:
- **Commercial**: $1,100 per unit
- **Residential**: $450 per unit

### Part c: Recommendation

Given the calculated overhead allocations using both methods, the analysis shows that the multiple production department factory overhead rate method provides more accurate cost allocations for each product based on their specific usage of resources in different departments. The commercial product incurs higher overhead costs in both the assembly and testing departments, reflecting a more precise costing approach.

**Recommendation**:
The correct recommendation is:
1. The management should consider multiple production department factory overhead rate methods, because this method calculates the cost more accurately and considers the fact that commercial products use more costly overheads than residential products.