Question 4 (a)
Break-even point and profit at 75% capacity from two years' cost data
9 marks
- Time to write
- About 18 minutes
Question
Question 4 (a) · 9 marksNavya Limited began operations in 2022-23 with a total production capacity of 2,00,000 units. Data for two years are given below:
| 2022-23 | 2023-24 | |
|---|---|---|
| Sales units | 90,000 | 1,30,000 |
| Total cost ( Rs.) | 37,70,000 | 48,10,000 |
The cost structure and selling price have not changed, and they are expected to remain the same in 2024-25.
The selling price is Rs.39 per unit. Find:
Break-Even Point (in units)
Profit at 75% of total capacity
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- FindFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Variable cost per unit and fixed cost 3 marks 5 min
- 2 Break-even point 3 marks 5 min
- 3 Profit at 75% of capacity 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 18 minutes for 9 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Working: variable and fixed cost
The cost structure and selling price did not change, so the increase in total cost between the two years is due only to the increase in units (high-low method):
- Variable cost per unit = (₹48,10,000 − ₹37,70,000) ÷ (1,30,000 − 90,000) = ₹10,40,000 ÷ 40,000 = ₹26.
- Fixed cost = ₹37,70,000 − 90,000 × ₹26 = ₹37,70,000 − ₹23,40,000 = ₹14,30,000. Check with 2023-24: 1,30,000 × ₹26 + ₹14,30,000 = ₹33,80,000 + ₹14,30,000 = ₹48,10,000.
- Contribution per unit = ₹39 − ₹26 = ₹13; P/V ratio = 13 ÷ 39 = 33.33%.
Break-even point = Fixed cost ÷ Contribution per unit = ₹14,30,000 ÷ ₹13 = 1,10,000 units (₹42,90,000 of sales at ₹39). Sales of 90,000 units in 2022-23 were below this level, and 1,30,000 units in 2023-24 above it.
(ii) Profit at 75% of capacity
75% of 2,00,000 units = 1,50,000 units.
| Particulars | ₹ |
|---|---|
| Sales (1,50,000 × ₹39) | 58,50,000 |
| Less: Variable cost (1,50,000 × ₹26) | 39,00,000 |
| Contribution (1,50,000 × ₹13) | 19,50,000 |
| Less: Fixed cost | 14,30,000 |
| Profit | 5,20,000 |
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Variable cost per unit and fixed cost | 3 |
| 2 | Break-even point | 3 |
| 3 | Profit at 75% of capacity | 3 |
| Total | 9 |
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