To prepare a marginal cost statement and estimate the profit of the business when operating at 60% and 80% of capacity, we need to calculate the variable cost per unit and the total contribution at each capacity level.
Given:
- At 50% capacity: Cost per unit = Rs. 180, Selling price per unit = Rs. 200
- Raw material cost = 100, Wages = 30, Factory overheads = 30 (40% fixed), Administrative overheads = 20 (50% fixed)
- Increase in raw material cost at 60% capacity = 2%, Increase in raw material cost at 80% capacity = 5%
- Selling price falls by 2% at 60% capacity and by 5% at 80% capacity
- Current production = 10,000 units
Let’s calculate the variable cost per unit at 50% capacity:
Variable cost per unit = Material cost + Wages + (Factory overheads – Fixed portion) + (Administrative Overheads – Fixed portion)
Variable cost per unit = 100 + 30 + (30 – 0.4 * 30) + (20 – 0.5 * 20)
Variable cost per unit = 100 + 30 + (30 – 12) + (20 – 10)
Variable cost per unit = 100 + 30 + 18 + 10
Variable cost per unit = Rs. 158
Now, let’s calculate the contribution per unit at 50% capacity:
Contribution per unit = Selling price per unit – Variable cost per unit
Contribution per unit = 200 – 158
Contribution per unit = Rs. 42
Now, let’s calculate the total contribution at 60% and 80% capacity:
- At 60% capacity:
- Selling price per unit = Rs. 200 * (1 – 0.02) = Rs. 196
- Variable cost per unit = Rs. 158 * (1 + 0.02) = Rs. 161.16
- Contribution per unit = Rs. 196 – Rs. 161.16 = Rs. 34.84
- Total contribution at 60% capacity = 10,000 units * Rs. 34.84
- At 80% capacity:
- Selling price per unit = Rs. 200 * (1 – 0.05) = Rs. 190
- Variable cost per unit = Rs. 158 * (1 + 0.05) = Rs. 165.9
- Contribution per unit = Rs. 190 – Rs. 165.9 = Rs. 24.1
- Total contribution at 80% capacity = 10,000 units * Rs. 24.1
Finally, let’s prepare the marginal cost statement and calculate the estimated profit:
| Capacity Level | Sales (Rs.) | Variable Cost (Rs.) | Contribution (Rs.) |
|---|---|---|---|
| 50% | 2,000,000 | 1,580,000 | 420,000 |
| 60% | 1,960,000 | 1,611,600 | 348,400 |
| 80% | 1,900,000 | 1,659,000 | 241,000 |
Estimated profit at 60% capacity = Sales – Variable Cost = Rs. 1,960,000 – Rs. 1,611,600 = Rs. 348,400
Estimated profit at 80% capacity = Sales – Variable Cost = Rs. 1,900,000 – Rs. 1,659,000 = Rs. 241,000
Therefore, the estimated profit of the business when operating at 60% capacity is Rs. 348,400, and when operating at 80% capacity is Rs. 241,000.