Question 4 (b)
Break-even analysis and chart; the P/V ratio and its importance
6 marks
- Time to write
- About 12 minutes
Question
Question 4 (b) · 6 marksWhat is your understanding of Break-Even Analysis? Show the Break-Even Chart graphically? (3)
What is P/V ratio? Discuss the importance of it.
Reworded from the university paper; 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…?Show…?Discuss…4 questions in all: answer every one.
- graphicallyDraw the diagram, and label both axes and every curve.
Write it in this order
The parts stand alone: start with the one you are surest of.
- Read; underline the asks; jot your points 1 min
- 1 Break-even analysis and chart 3 marks 5 min
- 2 P/V ratio and its importance 3 marks 5 min
- Check: every ask answered, key terms underlined 1 min
Short on time? A few lines on every part beat a full answer to one: each part is capped at its own marks.
Try it first. About 12 minutes for 6 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.
(i) Break-even analysis and the break-even chart
Break-even analysis studies the relationship between costs, volume and profit to find the level of activity at which total revenue equals total cost, so that there is neither profit nor loss (the break-even point), and the profit or loss at other levels. Break-even point (units) = Fixed costs ÷ Contribution per unit; in sales value = Fixed costs ÷ P/V ratio.
1One early customer at the juice stall—the cost pan still outweighs the coins.
Loss areaThe area below it to the left is the loss area
2A steady line now: the pans hang level, every cost just covered.
Break-even pointThe point where the sales line cuts the total cost line is the break-even point
3The crowd keeps coming—everything past that balance point is the safe margin, and profit.
Margin of safetyThe distance between actual sales and the break-even point is the margin of safety
Graphic presentation: the break-even chart plots output on the horizontal axis and cost and revenue on the vertical axis.
Example (our own) for drawing it: selling price ₹20 a unit, variable cost ₹12 a unit, fixed costs ₹40,000. The break-even point is ₹40,000 ÷ (₹20 − ₹12) = 5,000 units, or ₹1,00,000 of sales. Plot these points:
| Output (units) | Fixed cost line (₹) | Total cost line (₹) | Sales line (₹) | Position |
|---|---|---|---|---|
| 0 | 40,000 | 40,000 | 0 | Loss of ₹40,000 |
| 2,500 | 40,000 | 70,000 | 50,000 | Loss of ₹20,000 |
| 5,000 | 40,000 | 1,00,000 | 1,00,000 | Break-even point |
| 7,500 | 40,000 | 1,30,000 | 1,50,000 | Profit of ₹20,000 |
| 10,000 | 40,000 | 1,60,000 | 2,00,000 | Profit of ₹40,000 |
The break-even chart (drawn from the points above):
Joining the points gives three straight lines: a horizontal fixed cost line at ₹40,000; a total cost line rising from ₹40,000 at nil output; and a sales line rising from the origin, more steeply.
The sales line crosses the total cost line at the break-even point (5,000 units, ₹1,00,000). To the right of it the gap between the two lines is profit; to the left, loss. The distance between actual output and break-even output is the margin of safety: at 7,500 units it is 2,500 units, or ₹50,000 of sales.
(ii) The P/V ratio and its importance
The profit-volume ratio is contribution expressed as a percentage of sales: P/V ratio = Contribution ÷ Sales × 100, or Change in profit ÷ Change in sales × 100.
Example: if sales are ₹2,00,000 and variable costs ₹1,20,000, contribution is ₹80,000 and the P/V ratio is 40%. With fixed costs of ₹60,000, break-even sales are ₹60,000 ÷ 40% = ₹1,50,000.
Importance:
- Gives break-even sales (Fixed cost ÷ P/V ratio) and sales needed for a target profit.
- Shows profit at any level of sales.
- Compares the profitability of products, so that the sales mix can favour products with higher ratios.
- Shows the effect of price changes on profit.
- A higher ratio means each rupee of sales contributes more, so profit grows faster beyond break-even.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Break-even analysis and chart | 3 |
| 2 | P/V ratio and its importance | 3 |
| Total | 6 |
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