Break-even analysis answers a question every business owner needs to know: how much do we have to sell just to cover our costs? It ties together pricing, costs, and profit, and it's one of the most testable calculations in Unit 3B.
What Break-Even Means
The break-even point is the level of sales where total revenue exactly equals total costs — no profit, no loss. Sell below it and you lose money; sell above it and every additional sale contributes to profit. Knowing this number turns a vague hope into a concrete sales target.
The Pieces You Need
Break-even uses three inputs: fixed costs (costs that don't change with sales, like rent), the selling price per unit, and the variable cost per unit (the cost of making one more, like materials). From these you get the contribution margin — the price minus the variable cost — which is how much each sale contributes toward covering fixed costs.
The Formula
Break-even (in units) = Fixed Costs ÷ Contribution Margin. In other words, take your fixed costs and divide by how much each sale contributes, and you get the number of units you must sell to break even.
A Worked Example
A pizza food truck sells pizzas for $12 each. The ingredients and box cost $4 per pizza, so the contribution margin is $12 − $4 = $8. If fixed costs are $8,000 a month, then break-even = $8,000 ÷ $8 = 1,000 pizzas per month. Below 1,000 the truck loses money; above it, each pizza adds $8 of profit.
Why It Matters
Break-even analysis guides real decisions: it shows whether a price is high enough, how many customers you need, and how risky a business is. A high break-even point means you need lots of sales just to survive — useful to know before you launch.
Key Takeaways
- Break-even is where total revenue equals total costs — no profit, no loss.
- Contribution margin = price per unit − variable cost per unit.
- Break-even units = fixed costs ÷ contribution margin.
- It sets a concrete sales target and reveals how risky a business is.
Check Your Understanding: Break-Even Analysis
Five practice questions on Break-Even Analysis. Tap an answer to see whether you're right and why each choice is right or wrong.
1. Sofia sells custom phone cases online for $20 each. Each case costs $5 in materials and $1 for a shipping mailer. Her fixed costs, including design software and website fees, are $4,200 a month. How many cases must she sell each month to break even?
Answer: C. Contribution margin = $20 − ($5 + $1) = $14. Break-even = $4,200 ÷ $14 = 300 cases.
Why the other choices are wrong:
- A. 210 divides fixed costs by the $20 price ($4,200 ÷ $20) and ignores the variable costs of each case.
- B. 280 leaves out the $1 mailer and uses a contribution margin of $15 ($4,200 ÷ $15). Shipping supplies for each case are a variable cost too.
- D. 700 divides fixed costs by the $6 variable cost ($4,200 ÷ $6) instead of by the contribution margin.
2. Corner Dog Cart sells hot dogs for $6 each. Each hot dog has $2 in variable costs, and fixed costs are $4,000 a month. In February, the cart sold only 750 hot dogs. What was its result for February?
Answer: B. Contribution = 750 × ($6 − $2) = $3,000, which is $1,000 short of the $4,000 in fixed costs. The cart sold 250 hot dogs fewer than its break-even point of 1,000.
Why the other choices are wrong:
- A. This multiplies the 250 hot dogs below break-even by the $6 price. Each missing sale costs the cart only its $4 contribution margin, not the full price.
- C. $500 subtracts fixed costs from revenue ($4,500 − $4,000) but leaves out the $2 variable cost of each hot dog ($1,500 in total).
- D. $3,000 is the total contribution margin (750 × $4). The $4,000 in fixed costs still has to be paid out of it.
3. Bubble Bay Car Wash currently breaks even at 2,000 washes a month. Which change would lower the number of washes it needs to sell to break even?
Answer: D. A higher price raises the contribution margin per wash, so fewer washes are needed to cover the same fixed costs.
Why the other choices are wrong:
- A. A higher cost per wash shrinks the contribution margin, so each wash covers less of the fixed costs and the break-even point rises.
- B. Higher rent increases fixed costs, so more washes are needed to cover them and the break-even point rises.
- C. Selling more washes helps the business get past its break-even point, but it doesn't move that point. Break-even depends on fixed costs, price, and variable cost.
4. Rohan sells handmade soap for $9 a bar. Each bar costs $3 to make, and his fixed costs are $1,200 a month. What does the $6 difference between price and variable cost mean for Rohan?
Answer: A. The contribution margin is $9 − $3 = $6. Until the $1,200 in fixed costs is covered, each bar's $6 goes toward those costs; after that, each bar adds $6 of profit.
Why the other choices are wrong:
- B. The $6 isn't profit yet. The first bars' contributions go toward the $1,200 in fixed costs, and profit starts only after break-even.
- C. Each bar still brings in $6 more than it costs to make. Rohan has a loss below break-even because fixed costs aren't fully covered yet, not because each bar loses money.
- D. Each extra bar adds only its $3 variable cost to total costs. The $6 is what's left of the price after that cost.
5. Keisha is comparing two business plans for her first year:
Plan A: break-even point of 2,000 units a month; expected sales of 2,200 units a month
Plan B: break-even point of 800 units a month; expected sales of 1,500 units a month
Which plan is less risky, and why?
Answer: C. Plan B could lose almost half its expected sales (from 1,500 down to 800) and still break even, while Plan A has only a 200-unit cushion.
Why the other choices are wrong:
- A. Selling more units doesn't make a plan safer by itself. Plan A must sell 2,000 units just to break even, so a 10% drop in sales would push it into a loss.
- B. A high break-even point means more sales are needed just to cover costs, which makes a business riskier, not more profitable.
- D. Both expect to beat break-even, but the size of the cushion matters. Plan A is only 200 units above its break-even point, while Plan B is 700 above.
Keep Studying
Related: Fixed vs. Variable Costs, Income Statement.
These guides are educational explanations written for the AP Business with Personal Finance course.