Question 4 (c)
Merger of two factories: break-even capacity, capacity for a target profit, profit at 80%
15 marks
- Time to write
- About 30 minutes
Question
Question 4 (c) · 15 marksThe same management runs two factories and wishes to merge the two plants. These particulars are available:
| Factory I | Factory II | |
|---|---|---|
| Capacity operation | 100% | 50% |
| Sales | Rs 320 lakhs | Rs 110 lakhs |
| Variable cost | Rs 240 lakhs | Rs 80 lakhs |
| Fixed cost | Rs 45 lakhs | Rs 25 lakhs |
You are required to calculate:
At what capacity would the merged plant have to be operated for breaking even?
At what capacity would the merged plant earn a profit of Rs. 56 lakhs?
If the merged plant works at 80% of its capacity, what would the profit be?
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
- What…?3 questions in all: answer every one.
- 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 Merged plant at 100% capacity 5 marks 9 min
- 2 Break-even capacity 3 marks 5 min
- 3 Capacity for the target profit 3 marks 5 min
- 4 Profit at 80% capacity 4 marks 7 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 30 minutes for 15 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: the merged plant at 100% capacity (₹ lakhs)
Factory II works at 50% of its capacity; its sales and variable cost are doubled to bring it to 100%. Fixed cost does not change with capacity.
| Particulars | Factory I (100%) | Factory II at 50% | Factory II at 100% | Merged plant (100%) |
|---|---|---|---|---|
| Sales | 320 | 110 | 220 | 540 |
| Variable cost | 240 | 80 | 160 | 400 |
| Contribution | 80 | 30 | 60 | 140 |
| Fixed cost | 45 | 25 | 25 | 70 |
P/V ratio of the merged plant = 140 ÷ 540 = 25.93%.
Break-even capacity = Fixed cost ÷ Contribution at 100% = 70 ÷ 140 = 50% of the merged capacity (break-even sales = 540 × 50% = ₹270 lakhs).
(ii) Capacity for a profit of ₹56 lakhs
Required capacity = (Fixed cost + Profit) ÷ Contribution at 100% = (70 + 56) ÷ 140 = 126 ÷ 140 = 90% (sales of ₹486 lakhs).
| Particulars | ₹ lakhs |
|---|---|
| Sales (80% of 540) | 432 |
| Less: Variable cost (80% of 400) | 320 |
| Contribution (80% of 140) | 112 |
| Less: Fixed cost | 70 |
| Profit | 42 |
Where the 15 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Merged plant at 100% capacity | 5 |
| 2 | Break-even capacity | 3 |
| 3 | Capacity for the target profit | 3 |
| 4 | Profit at 80% capacity | 4 |
| Total | 15 |
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