Key Idea: Every product must cover its fixed costs before it makes a profit. This topic is how many units that takes, how far sales are above it, and what happens when the price or a cost changes.
Contribution
- Contribution per unit = price − variable cost per unit.
- Crackers: $2.50 − $0.60 = $1.90 a packet.
- Total contribution − fixed costs = profit.
Break-even
- Break-even quantity = fixed costs ÷ contribution per unit.
- Crackers: $7,280 ÷ $1.90 = 3,832 packets (round up).
- Margin of safety = sales − break-even quantity.
Changes and limits
- A higher price or lower cost lowers break-even; the opposite raises it.
- Target profit output = (fixed costs + target profit) ÷ contribution.
- It assumes every unit sells, at one price, with straight-line costs.
The words to know
| Word | Means | Do not confuse with |
|---|---|---|
| Contribution per unit | price minus variable cost per unit: what each unit adds towards fixed costs | profit per unit |
| Break-even quantity | the output at which total revenue equals total costs | the break-even revenue in $ |
| Margin of safety | how far actual sales are above break-even, in units | profit |
| Target profit output | the output needed to make a chosen profit | break-even quantity, which aims at zero profit |
| Target price | the price needed to reach a chosen profit at a planned output | the price customers are paying now |
Write the formula, put the case's numbers in, and give the answer with its unit: packets, not dollars. Round a break-even quantity up: 3,831 packets would still leave a loss.
Exam-style question
Lena's Bakery Ltd sells its crackers to cafés at $2.50 a packet. Each packet has a variable cost of $0.60, and the crackers carry fixed costs of $7,280 a year. In 2025 the cafés bought 18,000 packets. Calculate the margin of safety for the crackers in 2025 (show all your working).
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Important: Break-even is fixed costs ÷ contribution, not ÷ price. $7,280 ÷ $2.50 = 2,912 packets forgets that every packet also costs $0.60 to make.
Tap each card to check yourself.
What profit do the crackers make on 18,000 packets? 18,000 × $1.90 − $7,280 = $26,920.
Where does the total costs line start on a break-even chart? At fixed costs on the vertical axis, because they are paid even when nothing is made.
Why round a break-even quantity up? At 3,831 packets the crackers still make a small loss; the 3,832nd packet covers it.
What happens to break-even if flour costs rise? Variable cost rises, contribution falls, so more packets are needed: break-even rises.
How many packets for a $30,000 profit? ($7,280 + $30,000) ÷ $1.90 = 19,621.1, so 19,622 packets.
Name one limitation of break-even. Any one: it assumes every unit is sold, at one price, with costs that rise in a straight line; it suits one product, not a mix.
Exam tips
- Start every calculation with contribution per unit.
- Write the formula, then the numbers, then the answer with its unit.
- Round a break-even quantity up to a whole unit.
- For a change, say which way break-even moves and why.
- A limitation needs the case: say what the assumption hides for this product.