In simple terms
A friendly intro before the formal notes — no formulas yet.
Finding the point where you stop losing money
Break-even analysis finds the exact number of units a business must sell just to cover all its costs — no profit, no loss. Every unit sold after that point starts building profit, and every unit short of it means a loss. It is the first survival target any new product or venture has to clear.
Imagine renting a stall at a market for $100 for the day (a fixed cost you pay whether you sell nothing or sell out). Each smoothie you make costs you $2 in fruit and cups (a variable cost) and you sell it for $6. Every smoothie therefore puts $4 towards paying off that $100 stall fee - that $4 is the contribution. You need 25 smoothies just to cover the stall (100 divided by 4), so 25 is your break-even quantity. Smoothie number 26 onwards is where the profit finally begins, and how far your real sales sit above 25 is your safety cushion.
- 1
Split every cost into fixed costs (the stall fee, rent, salaries) and variable cost per unit (fruit, materials, direct labour).
- 2
Work out the contribution per unit: selling price per unit minus variable cost per unit.
- 3
Find the break-even quantity by dividing total fixed costs by the contribution per unit.
- 4
Use the same figures to find the margin of safety (how far current sales sit above break-even) or the output needed to hit a target profit.
Explore the concept
Use the live diagram and synced steps — play it or tap a step card to walk through.
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
Contribution: the engine of break-even analysis
Everything in this topic rests on one idea: contribution. The contribution per unit is the selling price of one unit minus its variable cost. It is the slice of each sale left over once the direct cost of making that unit has been paid — money that is free to 'contribute' first towards the fixed costs and, once those are covered, towards profit. Total contribution is simply the contribution per unit multiplied by the number of units sold, and it also equals total revenue minus total variable costs. The single most important warning in this whole topic is that contribution is not profit: below break-even a firm can have healthy positive contribution on every unit and still be making an overall loss, because the fixed costs have not yet been paid off.
Contribution per unit = selling price per unit − variable cost per unit.
Total contribution = contribution per unit × quantity sold (also total revenue − total variable costs).
At the break-even point, total contribution exactly equals total fixed costs, so profit is zero.
Beyond break-even, Profit = total contribution − total fixed costs; contribution is NOT the same as profit.
The break-even quantity and break-even revenue
The break-even quantity is the number of units a business must sell so that total contribution exactly covers total fixed costs. Because each unit sold delivers one lot of contribution, and fixed costs are paid off one contribution at a time, you find the break-even quantity by dividing total fixed costs by the contribution per unit. The break-even revenue is then the sales income earned at that quantity — the break-even quantity multiplied by the selling price. Notice that the denominator is contribution per unit, not total cost and not price: using the wrong denominator is the classic way to throw away the method mark.
The margin of safety
The margin of safety measures the cushion between a firm's actual (or budgeted) output and its break-even output. It answers a manager's key risk question: how far can sales fall before we start losing money? A large margin of safety signals a lower-risk position, because demand can drop a long way before the firm slips below break-even; a small margin is a warning that even a modest fall in sales would tip the business into loss. It is found by subtracting the break-even output from the actual output, and it can also be expressed as a percentage of actual sales.
A question may ask for the margin of safety in units, as a revenue figure, or as a percentage of current sales — the percentage is . Read the command carefully and always attach the correct unit ($, units or %) to your answer, because in our marking engine the accuracy (A) mark requires the correct value WITH its unit.
Using break-even to hit a target profit
Break-even analysis does more than find the survival point — it can also tell a business how much it must sell to earn a specific amount of profit. The logic is a small extension of the break-even formula: now each unit's contribution must cover the fixed costs AND build up the desired profit, so you treat the target profit as an extra block of cost to be paid off. Add the target profit to the fixed costs and divide by contribution per unit.
The break-even chart
A break-even chart shows the same information graphically. Output in units runs along the horizontal (x) axis and costs and revenues in currency run up the vertical (y) axis. Three lines are plotted: the fixed-cost line, the total-cost line and the total-revenue line. The point where total revenue and total cost cross is the break-even point; to its left the total-cost line lies above total revenue, showing a loss, and to its right total revenue lies above total cost, showing a profit. The horizontal gap between the break-even output and the firm's actual output is the margin of safety.
X-axis: level of output (units). Y-axis: costs and revenues (currency).
Fixed-cost line: horizontal, because fixed costs do not change with output.
Total-cost line: starts at the fixed-cost level on the y-axis (output zero still incurs fixed costs) and slopes upward as variable costs are added.
Total-revenue line: starts at the origin (0,0) — zero output earns zero revenue — and slopes upward more steeply than total cost.
Break-even point: where the total-revenue and total-cost lines intersect.
Loss area lies to the left of the break-even point (total cost above total revenue); the profit area lies to the right (total revenue above total cost).
Margin of safety: the horizontal distance from the break-even output to the actual output.
Benefits and limitations of break-even analysis
Break-even analysis is popular because it is quick, cheap and easy to understand, and it converts a jumble of cost and price data into a single clear target. But it rests on simplifying assumptions, and strong evaluation answers weigh its usefulness against those limits rather than simply listing one side.
Benefit — planning and targets: gives a precise output and revenue target for survival, useful when writing a business plan or seeking a loan.
Benefit — decision support: lets managers test how changes in price, costs or fixed overheads would move the break-even point before committing.
Benefit — risk assessment: the margin of safety shows how much sales can fall before losses begin.
Limitation — static model: it assumes price and costs are constant at every output, ignoring discounts, price changes and economies of scale that lower unit costs.
Limitation — assumes all output is sold: it treats every unit produced as sold, ignoring unsold inventory.
Limitation — single product: simple break-even is hard to apply to firms selling many products with different prices and costs.
Limitation — data quality: the answer is only as reliable as the cost and price estimates fed in; poor estimates give a misleading break-even point.
Common mistakes examiners penalise
Using the wrong denominator — the break-even formula divides fixed costs by CONTRIBUTION per unit (price − variable cost), never by total cost and never by price alone. Wrong denominator loses the method mark.
Confusing contribution with profit — contribution per unit is price minus variable cost; it still has to pay off fixed costs first. Only total contribution minus fixed costs is profit.
Subtracting fixed cost instead of variable cost — contribution is selling price minus VARIABLE cost per unit; using fixed cost per unit here is a classic error.
Forgetting the target profit in the target-output formula — output for a target profit is (fixed costs + target profit) ÷ contribution, not fixed costs ÷ contribution.
Reversing the margin of safety — it is ACTUAL output minus BREAK-EVEN output; doing it the other way round or adding the two is wrong.
Dropping the units — a bare number with no $, units or % attached forfeits the accuracy mark even when the arithmetic is right.
Rounding the break-even quantity down — round UP to the next whole unit, because rounding down still leaves the firm below break-even.
Model answer — marked the way our engine marks it
Business Management quantitative questions are marked with method (M) and accuracy (A) marks. An M mark rewards showing the correct method — the right formula, with the right figures substituted in — even if the final number is wrong. An A mark rewards the correct final value WITH its unit. Crucially, our engine applies the own-figure rule (follow-through): if you make an error early but then use YOUR figure correctly in the next step, the later method marks are still awarded. Watch how the marks below attach to each formula and each accurate value, and how a slip in one step need not cost the marks in the steps that follow.
Where this leads
Break-even analysis connects directly to the rest of the finance and operations material. The split between fixed and variable costs comes straight from cost and revenue analysis; contribution and break-even feed into production planning, pricing decisions and investment appraisal, where managers test whether a new product or capacity change can clear its break-even point. Master the discipline built here — identify the contribution, apply the right formula, follow through your own figures and always label the units — and you have the method that earns full marks on every quantitative question in Business Management.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
'Artisan Mugs Ltd' has fixed costs of $20,000 per month. Each mug costs $3 in materials and labour (variable cost) and sells for $8. Calculate (a) the monthly break-even quantity and (b) the break-even revenue.
- 1
Contribution per unit = selling price − variable cost per unit = 3 = $5 per mug.
A bakery has fixed costs of $5,000 per month. The variable cost per loaf is $1.50 and the selling price is $4.00. It currently sells 3,000 loaves per month. Calculate (a) the break-even quantity, (b) the profit at the current sales level and (c) the margin of safety in units.
- 1
Contribution per loaf = 1.50 =
A furniture maker has fixed costs of $60,000. Each table sells for $250 and has a variable cost of $150. The owner wants to make a profit of $30,000. Calculate (a) the break-even quantity and (b) the output needed to achieve the target profit.
- 1
Contribution per table = 150 =
A business sells a product for $20. Variable cost per unit is $12 and fixed costs are $40,000. Calculate the contribution per unit, the break-even quantity, and the margin of safety if the business currently sells 6,000 units. [6]
- 1
Model answer.
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Try to recall each definition before you reveal it.
Quick check
Answer in your head first — then tap to check. No pressure.
Revision flashcards
Flip the card. Test yourself before the exam.
Break-even point (BEP)
The level of output or sales at which total revenue exactly equals total cost. At this point the business makes neither a profit nor a loss.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
- ✓
Contribution per unit = selling price per unit − variable cost per unit.
- ✓
Total contribution = contribution per unit × quantity sold (also total revenue − total variable costs).
- ✓
At the break-even point, total contribution exactly equals total fixed costs, so profit is zero.
- ✓
Beyond break-even, Profit = total contribution − total fixed costs; contribution is NOT the same as profit.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Get a Paper 2 question marked: calculate contribution, break-even, margin of safety or target-profit output and show your method the way the engine credits it
Get a Paper 2 question marked: calculate contribution, break-even, margin of safety or target-profit output and show your method the way the engine credits it
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do Get a Paper 2 question marked: calculate contribution, break-even, margin of safety or target-profit output and show your method the way the engine credits it on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.