Break-even concept and break-even point
The break-even point is where sales just cover total cost: no profit, no loss. Break-even meals = fixed cost ÷ contribution per meal.
Meaning, uses and limits
The break-even point (BEP) is the volume of sales at which total sales equal total cost, so there is no profit and no loss. Each meal sold brings a contribution (selling price minus variable cost). Contributions first pay off the fixed costs; after the BEP, every contribution is profit. Sales above the BEP are the margin of safety. Uses: find the minimum meals to sell, test the effect of a price or cost change, plan a new outlet, judge how much subsidy a canteen needs. Limits: it assumes price and variable cost per meal stay constant, fixed costs do not change, and everything prepared is sold.
Break-even formulas
| Term | Formula |
|---|---|
| Contribution per unit | Selling price per unit − variable cost per unit |
| Break-even point (units) | Fixed cost ÷ contribution per unit |
| P/V (profit-volume) ratio | Contribution ÷ sales × 100 |
| Break-even point (₹ sales) | Fixed cost ÷ P/V ratio, or BEP units × selling price |
| Margin of safety | Actual sales − break-even sales |
| Units for a target profit | (Fixed cost + target profit) ÷ contribution per unit |
Break-even for a college canteen thali
A college canteen sells a thali at ₹80. Variable cost (food, gas, disposables) is ₹50 per thali. Fixed costs are ₹90,000 a month. Find (a) the break-even point in thalis and in rupees, (b) the profit and margin of safety if it sells 4,000 thalis, (c) the thalis needed for a profit of ₹45,000.
- Contribution = 80 − 50 = ₹30 per thali
- (a) BEP = 90,000 ÷ 30 = 3,000 thalis a month (about 100 a day over 30 days)
- BEP sales = 3,000 × 80 = ₹2,40,000. Check by P/V ratio: 30 ÷ 80 × 100 = 37.5%; 90,000 ÷ 0.375 = ₹2,40,000
- (b) Profit = (4,000 − 3,000) × 30 = ₹30,000. Check: sales 3,20,000 − variable 2,00,000 − fixed 90,000 = ₹30,000
- Margin of safety = 1,000 thalis = 1,000 × 80 = ₹80,000 (25% of sales of ₹3,20,000)
- (c) Thalis needed = (90,000 + 45,000) ÷ 30 = 4,500
BEP 3,000 thalis (₹2,40,000); profit ₹30,000 and margin of safety ₹80,000 at 4,000 thalis; 4,500 thalis for ₹45,000 profit.
Effect of a price rise, and rounding up
The same canteen raises the thali price to ₹85, with variable cost still ₹50 and fixed costs ₹90,000. Find the new break-even point.
- New contribution = 85 − 50 = ₹35
- BEP = 90,000 ÷ 35 = 2,571.4 thalis
- Round up, because a part-thali cannot be sold: 2,571 × 35 = ₹89,985 (still ₹15 short); 2,572 × 35 = ₹90,020 (covers fixed cost)
2,572 thalis a month, about 428 fewer than at ₹80. Always round the BEP up to the next whole unit.
Drawing a break-even chart
- 1Draw the x-axis for number of meals and the y-axis for rupees.
- 2Draw the fixed cost line flat at ₹90,000.
- 3Draw the total cost line starting at ₹90,000 and rising by ₹50 per meal.
- 4Draw the sales line from zero, rising by ₹80 per meal.
- 5★Mark the BEP where the sales line crosses the total cost line (3,000 meals, ₹2,40,000).
- 6Label the loss area below the BEP and the profit area above it; mark the margin of safety.
★ one-way, controls the pace
A school or hospital canteen that knows its BEP can tell how many meals it must sell, or how much subsidy it needs, to keep quality food at a fair price instead of cutting portions.
2 marks: “What is the break-even point?” The level of sales at which total sales equal total cost, giving neither profit nor loss. BEP (units) = fixed cost ÷ contribution per unit.
5 marks: “A canteen sells a meal at ₹60. Variable cost is ₹35 per meal and fixed costs are ₹50,000 a month. Find the break-even point.” Contribution = 60 − 35 = ₹25; BEP = 50,000 ÷ 25 = 2,000 meals; BEP sales = 2,000 × 60 = ₹1,20,000.
10 marks: “Explain the concept of break-even with a chart and a worked example. State its uses and limitations.” Define BEP, contribution, P/V ratio, margin of safety; formulas; draw and label the chart; worked example; uses and limitations; conclude.
BEP = Fixed ÷ (Price − Variable): 'Fix the gap'.