Cost-Volume-Profit Analysis and Break-Even Point
The core equations
Contribution = Sales − Variable Cost = Fixed Cost + Profit. P/V ratio = Contribution ÷ Sales = (Sales − Variable Cost) ÷ Sales. BEP in units = Fixed Cost ÷ Contribution per unit. BEP in value = Fixed Cost ÷ P/V ratio. Margin of safety = Actual Sales − BEP Sales = Profit ÷ P/V ratio. Sales needed for a target profit = (Fixed Cost + Desired Profit) ÷ P/V ratio.
Assumptions to state
Selling price constant; variable cost per unit constant; fixed cost constant over the relevant range; constant sales mix; no change in stock; revenue and cost behave linearly.
Worked example
Selling price ₹50, variable cost ₹30, fixed cost ₹2,00,000. Contribution per unit = ₹20; P/V ratio = 20 ÷ 50 = 40%; BEP units = 2,00,000 ÷ 20 = 10,000 units; BEP sales = ₹5,00,000. At actual sales of 15,000 units, margin of safety = 5,000 units or ₹2,50,000. Profit = 5,000 × ₹20 = ₹1,00,000. Cross-check: Profit ÷ P/V ratio = 1,00,000 ÷ 0.40 = ₹2,50,000, matching the margin of safety. Reasoning: every unit above 10,000 adds ₹20 of contribution straight to profit, because fixed costs are already covered.
Traps that cost marks
Confusing the P/V ratio with contribution per unit (one is a percentage, the other is rupees); reporting BEP in units when the question asks for value; forgetting that depreciation is a fixed cost even though non-cash; recomputing BEP when the sales mix changes without noting the assumption fails; getting a negative margin of safety and not interpreting it as a loss position.