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Answer :
To calculate the cost per unit of each product A and B using both the traditional method and the Activity-Based Costing (ABC) method, we need to follow a structured approach:
1. Traditional Method of Charging Overhead:
In the traditional method, the total overhead is allocated based on machine hours. Here’s how it can be done:
Calculate the total machine hours for products A and B:
[tex]\text{Total Machine Hours} = 20,000 + 120,000 = 140,000 \text{ hours}[/tex]Calculate the overhead rate per machine hour:
[tex]\text{Overhead Rate per Machine Hour} = \frac{\text{Total Overhead Cost}}{\text{Total Machine Hours}} \\
\text{Total Overhead Cost} = 550,000 + 820,000 + 618,000 = 1,988,000 \\
\text{Overhead Rate per Machine Hour} = \frac{1,988,000}{140,000} = 14.20 \, \text{per hour}[/tex]Allocate overhead to each product based on machine hours:
Product A:
[tex]\text{Overhead for A} = 20,000 \times 14.20 = 284,000[/tex]Product B:
[tex]\text{Overhead for B} = 120,000 \times 14.20 = 1,704,000[/tex]Calculate the cost per unit of product A and B:
Cost per Unit for Product A:
[tex]\text{Cost per Unit A} = \frac{284,000}{5,000} = 56.80[/tex]Cost per Unit for Product B:
[tex]\text{Cost per Unit B} = \frac{1,704,000}{60,000} = 28.40[/tex]
2. Activity-Based Costing (ABC) Method:
The ABC method allocates costs based on activities such as value, setup, and purchase order-related activities.
Calculate the cost drivers for each activity:
Value-related activities:
[tex]\text{Allocation rate} = \frac{550,000}{140,000} = 3.93 \, \text{per machine hour}[/tex]Setup-related activities:
[tex]\text{Allocation rate} = \frac{820,000}{(90+44)} = 5,962.96 \, \text{per setup}[/tex]Purchase-related activities:
[tex]\text{Allocation rate} = \frac{618,000}{(160+384)} = 1,057.89 \, \text{per purchase order}[/tex]
Allocate costs to each product based on activities:
Product A:
- Value-related:
[tex]20,000 \times 3.93 = 78,600[/tex] - Setup-related:
[tex]90 \times 5,962.96 = 536,666.40[/tex] - Purchase-related:
[tex]160 \times 1,057.89 = 169,262.40[/tex] - Total for A:
[tex]78,600 + 536,666.40 + 169,262.40 = 784,528.80[/tex]
Cost per Unit for Product A:
[tex]\frac{784,528.80}{5,000} = 156.91[/tex]Product B:
- Value-related:
[tex]120,000 \times 3.93 = 471,600[/tex] - Setup-related:
[tex]44 \times 5,962.96 = 262,370.24[/tex] - Purchase-related:
[tex]384 \times 1,057.89 = 406,229.76[/tex] - Total for B:
[tex]471,600 + 262,370.24 + 406,229.76 = 1,140,200[/tex]
Cost per Unit for Product B:
[tex]\frac{1,140,200}{60,000} = 19.00[/tex]- Value-related:
The ABC method provides a more accurate cost per unit by taking into account the specific activities that drive overhead costs for each product, while the traditional method spreads the cost uniformly based on machine hours.
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