Question 4 (c)
P/V ratio, break-even point, profit, required sales and margin of safety from two years' results
12 marks
- Time to write
- About 24 minutes
Question
Question 4 (c) · 12 marksThe following data are given:
| Sales | Profit | |
|---|---|---|
| Year 2023 | Rs. 1,30,000 | Rs. 8000 |
| Year 2024 | Rs. 1,50,000 | Rs13000 |
Calculate:
P/v Ratio
Break Even Point
The Profit when sales are Rs. 1, 80,000
The Sales required for earning a profit of Rs. 11,000
Margin of Safety for Year 2023
Margin of Safety for Year 2024
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
- CalculateFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 P/V ratio 2 marks 4 min
- 2 Fixed cost and break-even point 2 marks 3 min
- 3 Profit 2 marks 3 min
- 4 Sales for the target profit 2 marks 3 min
- 5 Margin of safety, both years 4 marks 7 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 24 minutes for 12 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.
P/V ratio = Change in profit ÷ Change in sales × 100 = (₹13,000 − ₹8,000) ÷ (₹1,50,000 − ₹1,30,000) × 100 = ₹5,000 ÷ ₹20,000 × 100 = 25%
Contribution in 2023 = ₹1,30,000 × 25% = ₹32,500. Fixed cost = Contribution − Profit = ₹32,500 − ₹8,000 = ₹24,500. (Check, 2024: ₹1,50,000 × 25% − ₹13,000 = ₹37,500 − ₹13,000 = ₹24,500.)
BEP (sales) = Fixed cost ÷ P/V ratio = ₹24,500 ÷ 25% = ₹98,000
(iii) Profit when sales are ₹1,80,000
Profit = Sales × P/V ratio − Fixed cost = ₹1,80,000 × 25% − ₹24,500 = ₹45,000 − ₹24,500 = ₹20,500
(iv) Sales required for a profit of ₹11,000
Sales = (Fixed cost + Desired profit) ÷ P/V ratio = (₹24,500 + ₹11,000) ÷ 25% = ₹35,500 ÷ 25% = ₹1,42,000
Margin of safety = Actual sales − Break-even sales (check: Profit ÷ P/V ratio).
| Year | Actual sales (₹) | Break-even sales (₹) | Margin of safety (₹) | Check: Profit ÷ P/V ratio (₹) |
|---|---|---|---|---|
| (v) 2023 | 1,30,000 | 98,000 | 32,000 | 8,000 ÷ 25% = 32,000 |
| (vi) 2024 | 1,50,000 | 98,000 | 52,000 | 13,000 ÷ 25% = 52,000 |
| Item | Answer |
|---|---|
| P/V ratio | 25% |
| Break-even point | ₹98,000 |
| Profit at sales of ₹1,80,000 | ₹20,500 |
| Sales for a profit of ₹11,000 | ₹1,42,000 |
| Margin of safety, 2023 | ₹32,000 |
| Margin of safety, 2024 | ₹52,000 |
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | P/V ratio | 2 |
| 2 | Fixed cost and break-even point | 2 |
| 3 | Profit at ₹1,80,000 | 2 |
| 4 | Sales for the target profit | 2 |
| 5 | Margin of safety, both years | 4 |
| Total | 12 |
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