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Sure, let's walk through the computing of the required values for the Chocolate ice cream step by step for both the Activity-Based Costing (ABC) system and the traditional costing system.
### a. Using ABC (Activity-Based Costing) System
#### 1. Compute the Activity-Cost-Driver Rate
- Fridge Overhead Rate: The overhead costs for the fridge are divided by the total fridge hours.
[tex]\[ \text{Fridge Overhead Rate} = \frac{\text{Total Fridge Overhead Costs}}{\text{Total Fridge Hours}} = \frac{₹ 21,000,000}{1,900 \text{ hours}} = ₹ 11,052.63 \text{ per hour} \][/tex]
- Packaging Overhead Rate: The overhead costs for packaging are divided by the total packaging hours.
[tex]\[ \text{Packaging Overhead Rate} = \frac{\text{Total Packaging Overhead Costs}}{\text{Total Packaging Hours}} = \frac{₹ 15,000,000}{950 \text{ hours}} = ₹ 15,789.47 \text{ per hour} \][/tex]
#### 2. Compute the Estimated Overhead Costs per Thousand Ice Cream
- Fridge Overhead Cost per Batch: Multiply the fridge hours required per batch by the fridge overhead rate.
[tex]\[ \text{Fridge Overhead Cost per Batch} = 1 \text{ hour} \times ₹ 11,052.63 \text{ per hour} = ₹ 11,052.63 \][/tex]
- Packaging Overhead Cost per Batch: Multiply the packaging hours required per batch by the packaging overhead rate.
[tex]\[ \text{Packaging Overhead Cost per Batch} = 0.5 \text{ hours} \times ₹ 15,789.47 \text{ per hour} = ₹ 7,894.74 \][/tex]
- Total Overhead Costs per Batch (ABC): Sum the fridge and packaging overhead costs.
[tex]\[ \text{Total Overhead Costs per Batch} = ₹ 11,052.63 + ₹ 7,894.74 = ₹ 18,947.37 \][/tex]
#### 3. Compute the Estimated Operating Profit per Thousand Ice Cream
- Revenue per Batch: Multiply the selling price per unit by the number of units per batch.
[tex]\[ \text{Revenue per Batch} = ₹ 75 \text{ per unit} \times 1,000 \text{ units} = ₹ 75,000 \][/tex]
- Variable Costs per Batch: Sum the direct materials and direct labor costs per unit, and then multiply by the number of units per batch.
[tex]\[ \text{Variable Costs per Batch} = (₹ 15 + ₹ 2) \times 1,000 \text{ units} = ₹ 17,000 \][/tex]
- Operating Profit per Batch (ABC): Subtract the variable costs and overhead costs from the revenue.
[tex]\[ \text{Operating Profit (ABC)} = ₹ 75,000 - ₹ 17,000 - ₹ 18,947.37 = ₹ 39,052.63 \][/tex]
### b. Using Traditional Costing System
#### 1. Compute Total Overhead Costs
- Total Overhead Costs: Sum the overhead costs for fridge and packaging.
[tex]\[ \text{Total Overhead Costs} = ₹ 21,000,000 + ₹ 15,000,000 = ₹ 36,000,000 \][/tex]
#### 2. Compute Overhead Cost Rate per Direct Labor Hour
- Overhead Rate per Direct Labor Hour: Divide the total overhead costs by the total direct labor hours.
[tex]\[ \text{Overhead Rate} = \frac{₹ 36,000,000}{2,400 \text{ hours}} = ₹ 15,000 \text{ per hour} \][/tex]
#### 3. Compute Overhead Costs per Thousand Ice Cream Using Direct Labor Hours
- Overhead Costs per Batch (Traditional): Multiply the direct labor hours required per batch by the overhead rate.
[tex]\[ \text{Overhead Costs per Batch (Traditional)} = 10 \text{ hours} \times ₹ 15,000 \text{ per hour} = ₹ 150,000 \][/tex]
#### 4. Compute the Estimated Operating Profit per Thousand Ice Cream
- Revenue per Batch: Already calculated above as ₹ 75,000.
- Variable Costs per Batch: Already calculated above as ₹ 17,000.
- Operating Profit per Batch (Traditional): Subtract the variable costs and overhead costs from the revenue.
[tex]\[ \text{Operating Profit (Traditional)} = ₹ 75,000 - ₹ 17,000 - ₹ 150,000 = -₹ 92,000 \][/tex]
### Final Results
Summary of the results:
#### ABC System
- Fridge Rate: ₹ 11,052.63 per hour
- Packaging Rate: ₹ 15,789.47 per hour
- Overhead Costs per Batch: ₹ 18,947.37
- Operating Profit per Batch (ABC): ₹ 39,052.63
#### Traditional System
- Overhead Costs per Batch (Traditional): ₹ 150,000
- Operating Profit per Batch (Traditional): -₹ 92,000
### a. Using ABC (Activity-Based Costing) System
#### 1. Compute the Activity-Cost-Driver Rate
- Fridge Overhead Rate: The overhead costs for the fridge are divided by the total fridge hours.
[tex]\[ \text{Fridge Overhead Rate} = \frac{\text{Total Fridge Overhead Costs}}{\text{Total Fridge Hours}} = \frac{₹ 21,000,000}{1,900 \text{ hours}} = ₹ 11,052.63 \text{ per hour} \][/tex]
- Packaging Overhead Rate: The overhead costs for packaging are divided by the total packaging hours.
[tex]\[ \text{Packaging Overhead Rate} = \frac{\text{Total Packaging Overhead Costs}}{\text{Total Packaging Hours}} = \frac{₹ 15,000,000}{950 \text{ hours}} = ₹ 15,789.47 \text{ per hour} \][/tex]
#### 2. Compute the Estimated Overhead Costs per Thousand Ice Cream
- Fridge Overhead Cost per Batch: Multiply the fridge hours required per batch by the fridge overhead rate.
[tex]\[ \text{Fridge Overhead Cost per Batch} = 1 \text{ hour} \times ₹ 11,052.63 \text{ per hour} = ₹ 11,052.63 \][/tex]
- Packaging Overhead Cost per Batch: Multiply the packaging hours required per batch by the packaging overhead rate.
[tex]\[ \text{Packaging Overhead Cost per Batch} = 0.5 \text{ hours} \times ₹ 15,789.47 \text{ per hour} = ₹ 7,894.74 \][/tex]
- Total Overhead Costs per Batch (ABC): Sum the fridge and packaging overhead costs.
[tex]\[ \text{Total Overhead Costs per Batch} = ₹ 11,052.63 + ₹ 7,894.74 = ₹ 18,947.37 \][/tex]
#### 3. Compute the Estimated Operating Profit per Thousand Ice Cream
- Revenue per Batch: Multiply the selling price per unit by the number of units per batch.
[tex]\[ \text{Revenue per Batch} = ₹ 75 \text{ per unit} \times 1,000 \text{ units} = ₹ 75,000 \][/tex]
- Variable Costs per Batch: Sum the direct materials and direct labor costs per unit, and then multiply by the number of units per batch.
[tex]\[ \text{Variable Costs per Batch} = (₹ 15 + ₹ 2) \times 1,000 \text{ units} = ₹ 17,000 \][/tex]
- Operating Profit per Batch (ABC): Subtract the variable costs and overhead costs from the revenue.
[tex]\[ \text{Operating Profit (ABC)} = ₹ 75,000 - ₹ 17,000 - ₹ 18,947.37 = ₹ 39,052.63 \][/tex]
### b. Using Traditional Costing System
#### 1. Compute Total Overhead Costs
- Total Overhead Costs: Sum the overhead costs for fridge and packaging.
[tex]\[ \text{Total Overhead Costs} = ₹ 21,000,000 + ₹ 15,000,000 = ₹ 36,000,000 \][/tex]
#### 2. Compute Overhead Cost Rate per Direct Labor Hour
- Overhead Rate per Direct Labor Hour: Divide the total overhead costs by the total direct labor hours.
[tex]\[ \text{Overhead Rate} = \frac{₹ 36,000,000}{2,400 \text{ hours}} = ₹ 15,000 \text{ per hour} \][/tex]
#### 3. Compute Overhead Costs per Thousand Ice Cream Using Direct Labor Hours
- Overhead Costs per Batch (Traditional): Multiply the direct labor hours required per batch by the overhead rate.
[tex]\[ \text{Overhead Costs per Batch (Traditional)} = 10 \text{ hours} \times ₹ 15,000 \text{ per hour} = ₹ 150,000 \][/tex]
#### 4. Compute the Estimated Operating Profit per Thousand Ice Cream
- Revenue per Batch: Already calculated above as ₹ 75,000.
- Variable Costs per Batch: Already calculated above as ₹ 17,000.
- Operating Profit per Batch (Traditional): Subtract the variable costs and overhead costs from the revenue.
[tex]\[ \text{Operating Profit (Traditional)} = ₹ 75,000 - ₹ 17,000 - ₹ 150,000 = -₹ 92,000 \][/tex]
### Final Results
Summary of the results:
#### ABC System
- Fridge Rate: ₹ 11,052.63 per hour
- Packaging Rate: ₹ 15,789.47 per hour
- Overhead Costs per Batch: ₹ 18,947.37
- Operating Profit per Batch (ABC): ₹ 39,052.63
#### Traditional System
- Overhead Costs per Batch (Traditional): ₹ 150,000
- Operating Profit per Batch (Traditional): -₹ 92,000
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