Break-even point, target profit and margin of safety
Work out the P/V ratio, break-even point in units and rupees, the units needed for a target profit, and the margin of safety.
Marks
8 marks
Exam time
12 min
Difficulty
Moderate
The question
A company sells a single product at ₹200 per unit. Variable cost is ₹120 per unit and annual fixed costs are ₹4,00,000. Current annual sales are 10,000 units. Compute (i) the P/V ratio, (ii) the break-even point in units and in rupees, (iii) the number of units required to earn a profit of ₹2,00,000, and (iv) the margin of safety in units and as a percentage.
- Given
- Selling price = ₹200 per unitVariable cost = ₹120 per unitFixed cost = ₹4,00,000 per yearCurrent sales = 10,000 units
Formulas used
- Contribution per unit = Selling price − Variable cost
- P/V ratio = Contribution ÷ Sales × 100
- BEP (units) = Fixed cost ÷ Contribution per unit
- Units for target profit = (Fixed cost + Target profit) ÷ Contribution per unit
- Margin of safety = Actual sales − Break-even sales
Step-by-step working
01Compute contribution and the P/V ratio
2Contribution per unit = ₹200 − ₹120 = ₹80 P/V ratio = ₹80 ÷ ₹200 × 100 = 40%
Contribution per unit is the number every later part depends on. Compute it once, at the top, and label it clearly.
02Compute the break-even point
2BEP (units) = ₹4,00,000 ÷ ₹80 = 5,000 units BEP (₹) = 5,000 units × ₹200 = ₹10,00,000 Check: BEP (₹) = ₹4,00,000 ÷ 40% = ₹10,00,000 ✓
Two routes to BEP in rupees. Showing the cross-check costs one line and protects the mark if you slip elsewhere.
03Compute units for the target profit
2Required units = (₹4,00,000 + ₹2,00,000) ÷ ₹80 = ₹6,00,000 ÷ ₹80 = 7,500 unitsTarget profit is added to fixed cost, never subtracted and never netted against contribution.
04Compute the margin of safety
2MOS (units) = 10,000 − 5,000 = 5,000 units MOS (%) = 5,000 ÷ 10,000 × 100 = 50% MOS (₹) = 5,000 × ₹200 = ₹10,00,000
Margin of safety is measured against actual sales, not against the target-profit level you computed in the previous part.
P/V · BEP · Target units · MOS
40% · 5,000 units (₹10,00,000) · 7,500 units · 50%
Where marks are lost
- Computing the margin of safety from the 7,500 target units instead of the 10,000 actual units.
- Subtracting target profit from fixed cost rather than adding it.
- Reporting the P/V ratio as a fraction of contribution to variable cost instead of to sales.
- Treating fixed cost per unit as constant when output changes — it is not, and that assumption breaks every part of this question.
In the exam
Marginal costing is among the most reliably examined chapters in Intermediate Costing. The step that separates full marks from partial marks is presentation: a clean contribution statement at the top makes every subsequent part traceable for the examiner.
Practise next
Have questions?
Find answers.
Still unsure about something? We're happy to help you figure it out.
Talk to usWhat happens to the break-even point if fixed costs rise?
It rises proportionately, because BEP is fixed cost divided by contribution per unit. A rise in fixed cost from ₹4,00,000 to ₹4,80,000 in this question would push BEP from 5,000 to 6,000 units, with contribution per unit unchanged at ₹80.
Is margin of safety better expressed in units, rupees or percentage?
Give whichever the question asks for, and the percentage if it does not specify. The percentage is the most useful for comparison because it is independent of scale.
Reading a solution is not practice. Writing one is.
Generate fresh numericals on this exact chapter, attempt them under time, and have your written working evaluated step by step.
Start practising free- Free to start
- Step-wise marking
- All 3 CA levels