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Based on the provided data, we will calculate the overhead assigned to Oil using Activity-Based Costing (ABC). Let's go through the steps to solve the problem systematically.
1. Understanding the Total Overhead and Transactions:
The company incurs a total overhead of \$3,600,000 annually across three departments: Processing, Packaging, and Testing.
- Processing:
- Transactions: 800
- Cost: \$1,500,000
- Packaging:
- Transactions: 200,000
- Cost: \$1,500,000
- Testing:
- Transactions: 2,000
- Cost: \$600,000
2. Determine the Overhead Rate per Transaction for Each Department:
We first calculate the overhead rate per transaction by dividing the total cost of each department by the number of transactions in that department.
- Processing Overhead Rate:
[tex]\[ \text{Processing Overhead Rate per Transaction} = \frac{\[tex]$1,500,000}{800} = \$[/tex]1,875.0
\][/tex]
- Packaging Overhead Rate:
[tex]\[ \text{Packaging Overhead Rate per Transaction} = \frac{\[tex]$1,500,000}{200,000} = \$[/tex]7.5
\][/tex]
- Testing Overhead Rate:
[tex]\[ \text{Testing Overhead Rate per Transaction} = \frac{\[tex]$600,000}{2,000} = \$[/tex]300.0
\][/tex]
3. Calculate the Distribution of Transactions between Oil and Sludge:
The total production is 400,000 drums of Oil and 600,000 drums of Sludge, making a total of 1,000,000 drums. The ratio of Oil production to total production is given by:
[tex]\[ \frac{\text{Oil Production}}{\text{Total Production}} = \frac{400,000}{1,000,000} = 0.4 \][/tex]
Therefore, 40% of the transactions in each department are attributable to Oil.
4. Calculate the Transactions Attributable to Oil:
- Processing Transactions for Oil:
[tex]\[ \text{Processing Transactions for Oil} = 0.4 \times 800 = 320 \][/tex]
- Packaging Transactions for Oil:
[tex]\[ \text{Packaging Transactions for Oil} = 0.4 \times 200,000 = 80,000 \][/tex]
- Testing Transactions for Oil:
[tex]\[ \text{Testing Transactions for Oil} = 0.4 \times 2,000 = 800 \][/tex]
5. Calculate the Overhead Assigned to Oil:
The overhead assigned to Oil involves multiplying the transactions attributable to Oil by the overhead rate per transaction in each department and summing these amounts.
- Processing Overhead for Oil:
[tex]\[ 320 \times \[tex]$1,875.0 = \$[/tex]600,000
\][/tex]
- Packaging Overhead for Oil:
[tex]\[ 80,000 \times \[tex]$7.5 = \$[/tex]600,000
\][/tex]
- Testing Overhead for Oil:
[tex]\[ 800 \times \[tex]$300.0 = \$[/tex]240,000
\][/tex]
- Total Overhead Assigned to Oil:
[tex]\[ \[tex]$600,000 + \$[/tex]600,000 + \[tex]$240,000 = \$[/tex]1,440,000
\][/tex]
Thus, the amount of overhead assigned to Oil using Activity-Based Costing is \$1,440,000.
1. Understanding the Total Overhead and Transactions:
The company incurs a total overhead of \$3,600,000 annually across three departments: Processing, Packaging, and Testing.
- Processing:
- Transactions: 800
- Cost: \$1,500,000
- Packaging:
- Transactions: 200,000
- Cost: \$1,500,000
- Testing:
- Transactions: 2,000
- Cost: \$600,000
2. Determine the Overhead Rate per Transaction for Each Department:
We first calculate the overhead rate per transaction by dividing the total cost of each department by the number of transactions in that department.
- Processing Overhead Rate:
[tex]\[ \text{Processing Overhead Rate per Transaction} = \frac{\[tex]$1,500,000}{800} = \$[/tex]1,875.0
\][/tex]
- Packaging Overhead Rate:
[tex]\[ \text{Packaging Overhead Rate per Transaction} = \frac{\[tex]$1,500,000}{200,000} = \$[/tex]7.5
\][/tex]
- Testing Overhead Rate:
[tex]\[ \text{Testing Overhead Rate per Transaction} = \frac{\[tex]$600,000}{2,000} = \$[/tex]300.0
\][/tex]
3. Calculate the Distribution of Transactions between Oil and Sludge:
The total production is 400,000 drums of Oil and 600,000 drums of Sludge, making a total of 1,000,000 drums. The ratio of Oil production to total production is given by:
[tex]\[ \frac{\text{Oil Production}}{\text{Total Production}} = \frac{400,000}{1,000,000} = 0.4 \][/tex]
Therefore, 40% of the transactions in each department are attributable to Oil.
4. Calculate the Transactions Attributable to Oil:
- Processing Transactions for Oil:
[tex]\[ \text{Processing Transactions for Oil} = 0.4 \times 800 = 320 \][/tex]
- Packaging Transactions for Oil:
[tex]\[ \text{Packaging Transactions for Oil} = 0.4 \times 200,000 = 80,000 \][/tex]
- Testing Transactions for Oil:
[tex]\[ \text{Testing Transactions for Oil} = 0.4 \times 2,000 = 800 \][/tex]
5. Calculate the Overhead Assigned to Oil:
The overhead assigned to Oil involves multiplying the transactions attributable to Oil by the overhead rate per transaction in each department and summing these amounts.
- Processing Overhead for Oil:
[tex]\[ 320 \times \[tex]$1,875.0 = \$[/tex]600,000
\][/tex]
- Packaging Overhead for Oil:
[tex]\[ 80,000 \times \[tex]$7.5 = \$[/tex]600,000
\][/tex]
- Testing Overhead for Oil:
[tex]\[ 800 \times \[tex]$300.0 = \$[/tex]240,000
\][/tex]
- Total Overhead Assigned to Oil:
[tex]\[ \[tex]$600,000 + \$[/tex]600,000 + \[tex]$240,000 = \$[/tex]1,440,000
\][/tex]
Thus, the amount of overhead assigned to Oil using Activity-Based Costing is \$1,440,000.
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