--- title: "Explain break-even analysis and its significance" subject: "Engineering Economics" chapter: 1 key: "semester_6/engineering_economics:breakeven-significance" source: https://www.bctengineer.com/q/semester_6/engineering_economics/breakeven-significance site: BCT Engineering --- # Explain break-even analysis and its significance Engineering Economics · Chapter 1: Introduction - Asked in: 2076 Shrawan, 2 marks; 2066 Magh, 4 marks; 2065 Chaitra, 6 marks (asked 3 times) - Video: [Break Even Analysis - Fundamentals of Engineering Economics](https://www.youtube.com/watch?v=kla5dJVCCDc) — Prepineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/engineering_economics/breakeven-significance - Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-1 ## Question Explain break-even analysis. What is the breakeven value and its significance in the selection of a project? Explain with a suitable example. ## Short answer Break-even analysis finds the output where total revenue equals total cost, yielding zero profit. The break-even quantity is fixed cost divided by (price − variable cost per unit); a lower break-even point means lower risk and higher margin of safety. Example: with fixed cost Rs 100,000, price Rs 50, and variable cost Rs 30, break-even is 5,000 units. ## Answer Break-even analysis finds the level of output (or sales) at which total revenue equals total cost, so that there is neither profit nor loss. #### Basic relations - Total cost TC = Fixed cost (FC) + Variable cost per unit (v) × Q - Revenue TR = Selling price per unit (p) × Q - Break-even quantity: **Q* = FC / (p − v)**, where (p − v) is the contribution per unit - Break-even sales value = FC / (1 − v/p) - Below Q* the project makes a loss; above Q* it makes a profit. ```text Rs | TR | / | / ...... TC | /...... | ... * | ....... / | |----------/---|--------------------- FC | / | | / | * = break-even point | / | | / | |/_____________|_________________________ Q Q* ``` #### Break-even value and its significance The break-even value (Q* or break-even sales) is the minimum volume the project must reach to recover all its costs. Its significance in project selection: - A lower break-even point means lower risk, since the project becomes profitable sooner. - It gives the margin of safety = (expected sales − break-even sales) / expected sales. - For two alternatives with different cost structures (e.g. machine A: high FC, low v; machine B: low FC, high v), the volume at which their total costs are equal shows which one to choose: below that volume pick the option with the lower fixed cost, above it pick the option with the lower variable cost. - It helps in pricing and cost-control decisions. #### Example A factory has FC = Rs 100,000 per year, v = Rs 30 per unit and p = Rs 50 per unit. - Q* = 100,000 / (50 − 30) = **5,000 units** - Break-even sales = 5,000 × 50 = Rs 250,000 - If expected sales are 8,000 units, margin of safety = (8,000 − 5,000)/8,000 = 37.5%, and profit = 8,000 × 20 − 100,000 = Rs 60,000. Since the expected output exceeds the break-even output, the project is acceptable. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. At the break-even point: A. Total revenue equals total cost, giving neither profit nor loss B. Fixed cost equals variable cost C. Profit is at its maximum D. Variable cost equals revenue Answer: A. Break-even is the output where TR = TC. (Key point: Break-even definition) 2. The break-even quantity is given by: A. Q* = (p - v) / FC B. Q* = FC / (p - v) C. Q* = FC x (p - v) D. Q* = FC / (p + v) Answer: B. Fixed cost is recovered by the contribution (p - v) per unit. (Key point: Formula) 3. A factory has Q* = 5,000 units and expected sales of 8,000 units. The margin of safety is: A. 3,000% B. 62.5% C. 37.5% D. 60% Answer: C. (8,000 - 5,000)/8,000 = 37.5%. (Key point: Safety margin) 4. Machine A has high fixed cost and low variable cost; machine B the reverse. Above the volume where their total costs are equal, which is chosen? A. Machine B, the lower fixed cost option B. Either, they cost the same C. Neither; the project is rejected D. Machine A, the lower variable cost option Answer: D. At high volume variable cost dominates, so the lower variable cost machine wins. 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