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An industry adopting activity-based costing is producing two products. The overhead costs incurred by the industry along with their cost drivers are as follows:

[tex]\[
\begin{aligned}
&\text{Production set-up cost:} & \text{Rs. 30,000} & \quad \text{(Production run)} \\
&\text{Machine department cost:} & \text{Rs. 40,000} & \quad \text{(Machine hour)} \\
&\text{Selling and distribution cost:} & \text{Rs. 20,000} & \quad \text{(Order execution)} \\
&\text{Indirect labour cost:} & \text{Rs. 50,000} & \quad \text{(DLH)}
\end{aligned}
\][/tex]

The output and other details of the products are as follows:

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\text{Products} & \text{Output in units} & \text{DLH per unit} & \text{Machine hour per unit} & \text{Production run} & \text{Sales per order} & \text{Price cost per unit} \\
\hline
\text{X} & 20,000 & 3 & \frac{3}{4} & 40 & 400 \, \text{units} & \text{Rs. 8} \\
\hline
\text{Y} & 10,000 & 4 & \frac{1}{2} & 20 & 200 \, \text{units} & \text{Rs. 5} \\
\hline
\end{tabular}
\][/tex]

Required: Calculate the total cost per unit of each product.

[tex]\[
\text{Answer: Rs. 12.50 and Rs. 10}
\][/tex]

Sagot :

GinnyAnswer
Sure, let's go through a detailed step-by-step solution to calculate the total cost per unit for products X and Y using the Activity-Based Costing (ABC) method.

### Step 1: Identify and Collect Data

#### Overhead Costs and Cost Drivers

1. Production setup cost: Rs. 30,000 (cost driver: Production run)
2. Machine department cost: Rs. 40,000 (cost driver: Machine hour)
3. Selling and distribution cost: Rs. 20,000 (cost driver: Order execution)
4. Indirect labor cost: Rs. 50,000 (cost driver: Direct labor hours, DLH)

#### Product Details
- Product X
- Output: 20,000 units
- DLH per unit: 3
- Machine hour per unit: 0.75
- Production runs: 40
- Sales per order: 400 units
- Price cost per unit: Rs. 8

- Product Y
- Output: 10,000 units
- DLH per unit: 4
- Machine hour per unit: 0.5
- Production runs: 20
- Sales per order: 200 units
- Price cost per unit: Rs. 5

### Step 2: Calculate the Total for Each Cost Driver

1. Total DLH (Direct Labor Hours)
- For product X: [tex]\( 20,000 \text{ units} \times 3 \text{ DLH} = 60,000 \text{ DLH} \)[/tex]
- For product Y: [tex]\( 10,000 \text{ units} \times 4 \text{ DLH} = 40,000 \text{ DLH} \)[/tex]

2. Total Machine Hours
- For product X: [tex]\( 20,000 \text{ units} \times 0.75 \text{ hrs/unit} = 15,000 \text{ machine hours} \)[/tex]
- For product Y: [tex]\( 10,000 \text{ units} \times 0.5 \text{ hrs/unit} = 5,000 \text{ machine hours} \)[/tex]

3. Total Production Runs
- For product X: 40 runs
- For product Y: 20 runs

4. Total Order Executions
- For product X: [tex]\( \frac{20,000 \text{ units}}{400 \text{ units/order}} = 50 \text{ orders} \)[/tex]
- For product Y: [tex]\( \frac{10,000 \text{ units}}{200 \text{ units/order}} = 50 \text{ orders} \)[/tex]

### Step 3: Allocate Overhead Costs to Products

1. Cost per DLH
- Total DLH: [tex]\( 60,000 + 40,000 = 100,000 \)[/tex]
- For product X: [tex]\( \frac{60,000}{100,000} \times 50,000 = 30,000 \)[/tex]
- For product Y: [tex]\( \frac{40,000}{100,000} \times 50,000 = 20,000 \)[/tex]

2. Cost per Machine Hour
- Total Machine Hours: [tex]\( 15,000 + 5,000 = 20,000 \)[/tex]
- For product X: [tex]\( \frac{15,000}{20,000} \times 40,000 = 30,000 \)[/tex]
- For product Y: [tex]\( \frac{5,000}{20,000} \times 40,000 = 10,000 \)[/tex]

3. Cost per Production Run
- Total Production Runs: [tex]\( 40 + 20 = 60 \)[/tex]
- For product X: [tex]\( \frac{40}{60} \times 30,000 = 20,000 \)[/tex]
- For product Y: [tex]\( \frac{20}{60} \times 30,000 = 10,000 \)[/tex]

4. Cost per Order Execution
- Total Orders: [tex]\( 50 + 50 = 100 \)[/tex]
- For product X: [tex]\( \frac{50}{100} \times 20,000 = 10,000 \)[/tex]
- For product Y: [tex]\( \frac{50}{100} \times 20,000 = 10,000 \)[/tex]

### Step 4: Summarize the Overhead Costs per Product
1. Total overhead cost for Product X
- DLH cost: [tex]\( 30,000 \)[/tex]
- Machine hour cost: [tex]\( 30,000 \)[/tex]
- Production setup cost: [tex]\( 20,000 \)[/tex]
- Order execution cost: [tex]\( 10,000 \)[/tex]

Total: [tex]\( 30,000 + 30,000 + 20,000 + 10,000 = 90,000 \)[/tex]

2. Total overhead cost for Product Y
- DLH cost: [tex]\( 20,000 \)[/tex]
- Machine hour cost: [tex]\( 10,000 \)[/tex]
- Production setup cost: [tex]\( 10,000 \)[/tex]
- Order execution cost: [tex]\( 10,000 \)[/tex]

Total: [tex]\( 20,000 + 10,000 + 10,000 + 10,000 = 50,000 \)[/tex]

### Step 5: Calculate the Total Cost per Unit
1. Total cost per unit for Product X
- Overhead cost per unit: [tex]\( \frac{90,000}{20,000} = 4.5 \)[/tex]
- Price cost per unit: [tex]\( 8 \)[/tex]

Total: [tex]\( 8 + 4.5 = 12.5 \)[/tex]

2. Total cost per unit for Product Y
- Overhead cost per unit: [tex]\( \frac{50,000}{10,000} = 5 \)[/tex]
- Price cost per unit: [tex]\( 5 \)[/tex]

Total: [tex]\( 5 + 5 = 10 \)[/tex]

### Conclusion

The total cost per unit of Product X is [tex]\( Rs. 12.50 \)[/tex] and the total cost per unit of Product Y is [tex]\( Rs. 10 \)[/tex].
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