Question 4 (b)
Units needed to raise profit after a price cut and extra sales promotion
9 marks
- Time to write
- About 18 minutes
Question
Question 4 (b) · 9 marksThe following data relate to a manufacturing company:
Plant Capacity = 4,00,000 units a year. Present Utilization = 45%
Actual for the year 2023-24 were:
Selling price = Rs.60 per unit, Material cost = Rs.24 per unit,
Variable Manufacturing costs = Rs.18 per unit and Fixed cost = Rs. 34,00,000.
To improve the utilization of capacity, the following proposal is under consideration:
Reduce the Selling price by 10% and spend an additional Rs.2,00,000 on Sales Promotion.
To increase profit by Rs. 7,60,000 per year, how many units should be produced and sold?
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
- how manyFormula 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 Present contribution and profit 3 marks 5 min
- 2 Revised contribution, fixed cost and target profit 3 marks 5 min
- 3 Units required and verification 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.
- Present output = 45% of 4,00,000 = 1,80,000 units.
- Variable cost per unit = Material ₹24 + Variable manufacturing ₹18 = ₹42.
- Contribution per unit = ₹60 − ₹42 = ₹18.
| Particulars | ₹ |
|---|---|
| Contribution (1,80,000 × ₹18) | 32,40,000 |
| Less: Fixed cost | 34,00,000 |
| Present profit (loss) | (1,60,000) |
The company is at present making a loss of ₹1,60,000.
- New selling price = ₹60 − 10% = ₹54; variable cost stays ₹42; new contribution per unit = ₹12.
- Fixed cost = ₹34,00,000 + ₹2,00,000 (additional sales promotion) = ₹36,00,000.
- Required profit = present result + ₹7,60,000 = −₹1,60,000 + ₹7,60,000 = ₹6,00,000.
Units = (Fixed cost + Required profit) ÷ Contribution per unit = (₹36,00,000 + ₹6,00,000) ÷ ₹12 = 3,50,000 units, that is, 87.5% of the plant capacity of 4,00,000 units, so the plan is feasible.
Verification: 3,50,000 × ₹12 = ₹42,00,000 contribution − ₹36,00,000 fixed cost = ₹6,00,000 profit, which is ₹7,60,000 more than the present loss of ₹1,60,000.
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present contribution and profit | 3 |
| 2 | Revised contribution, fixed cost and target profit | 3 |
| 3 | Units required and verification | 3 |
| Total | 9 |
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