How many packets pay for the machine?: Lena's Bakery Ltd sells packets of crackers to cafés for $2.50. The flour, oil and packet for each one cost $0.60. The crackers line also has costs that do not move with output: $140 a week, $7,280 a year.
Lena and Marco want to know one number before anything else. How many packets a year must they sell before the crackers stop losing money?
Start from what you met in 5.5.1. Each packet brings in $2.50 and uses up $0.60, so it leaves $1.90 towards the fixed costs (contribution per unit).
The fixed costs are $7,280. Each packet pays $1.90 of them. So the question is simply: how many lots of $1.90 make $7,280? That number of packets is where total revenue equals total costs (the break-even quantity). It is the same point you read off the chart in 5.5.2.
The formula: Break-even quantity = fixed costs ÷ contribution per unit
Contribution per unit = selling price − variable cost per unit
Worked example: the crackers
Contribution per packet
$2.50 − $0.60 = $1.90 a packet.
Divide the fixed costs by it
$7,280 ÷ $1.90 = 3,831.6 packets.
Round up to a whole packet
3,831 packets bring in 3,831 × $1.90 = $7,278.90, which is $1.10 short. So the answer is 3,832 packets.
Check it
At 3,832 packets, revenue is $9,580 and total costs are $7,280 + $2,299.20 = $9,579.20. Revenue and costs match, give or take 80 cents.
Packets, not dollars: A break-even quantity is a number of things: packets, dresses, litres. Writing "$3,832" turns it into a sum of money, and that answer is wrong.
Round up, never down. At 3,831 packets the crackers are still $1.10 short of covering their costs.
Often the fixed costs arrive in pieces: rent, insurance, a machine lease, a salary. Add every fixed cost together first, then divide once. In the same way, if there are several variable costs per unit (flour, packet, delivery), take all of them off the price before you divide.
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What did the crackers make in 2025?: In 2025 Lena's Bakery Ltd sold 18,000 packets of crackers. Marco wants the profit on the line, not a guess.
There are two ways to get it, and they give the same answer.
| Way 1: revenue minus costs | Way 2: contribution minus fixed costs | |
|---|---|---|
| The rule | Profit = total revenue − total costs | Profit = total contribution − fixed costs |
| First step | Total revenue = 18,000 × $2.50 = $45,000 | Total contribution = 18,000 × $1.90 = $34,200 |
| Second step | Total costs = $7,280 + (18,000 × $0.60) = $7,280 + $10,800 = $18,080 | Fixed costs = $7,280 |
| Profit | $45,000 − $18,080 = $26,920 | $34,200 − $7,280 = $26,920 |
Way 2 is shorter, because it uses the contribution you already have. Way 1 is safer when a table gives you totals rather than per-packet figures. Either is fine; write the rule, then the numbers.
Below break-even: a loss: Suppose the crackers had sold only 3,000 packets, fewer than the 3,832 needed.
Total contribution = 3,000 × $1.90 = $5,700. Take off the fixed costs: $5,700 − $7,280 = −$1,580.
A minus sign means a loss (a loss of $1,580). The contribution was not enough to pay the fixed costs.
When the data gives totals
Total variable costs given
If a table says total variable costs were $10,800 for 18,000 packets, divide: $10,800 ÷ 18,000 = $0.60 a packet.
Then scale it
Variable costs for any other output are that figure times the output: at 20,000 packets, 20,000 × $0.60 = $12,000.
Fixed costs stay put
The $7,280 does not change with output, so never multiply it.
Money answers carry a $ sign: Profit and loss are sums of money: write $26,920, or a loss of $1,580. A bare 26,920 leaves the reader guessing what it counts.
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How bad could 2026 get?: One of the cafés that buys crackers is closing. Marco asks: how far could sales fall before the crackers start losing money?
The answer is the gap between what they sell and what they need to sell.
That gap is the amount by which sales are above the break-even quantity (the margin of safety). It tells the owners how much room they have before a loss.
Margin of safety = actual (or forecast) sales − break-even quantity
Worked example: 2025
Sales
18,000 packets sold in 2025.
Break-even quantity
3,832 packets, worked out in the first section.
Margin of safety
18,000 − 3,832 = 14,168 packets. Sales could fall by 14,168 packets, nearly four-fifths of the total, before the crackers made a loss.
Sales of 18,000
- Margin of safety: 14,168 packets
- A lost café barely matters
- Plenty of room for a bad year
Sales of 4,000
- Margin of safety: 168 packets
- One lost order could tip the line into a loss
- Every café counts
Sales of 3,000
- Margin of safety: −832 packets
- Already below break-even
- The line is making a loss now
Units, and the right way round: The margin of safety is a number of packets, so write the unit: 14,168 packets. Take the break-even quantity away from sales, not sales from break-even.
Sometimes the break-even quantity is not given. Work it out first, then subtract.
Breaking even is not the goal: Covering costs keeps the crackers alive. Lena and Marco want them to pay for something: they want $30,000 of profit from the line in 2026. That figure is their target profit.
Two questions follow. How many packets must they sell at $2.50? And if they cannot sell that many, what price would they need?
Break-even asked how many lots of $1.90 pay the fixed costs. The target question asks how many lots of $1.90 pay the fixed costs and the profit on top. The answer is the target profit output.
Target profit output = (fixed costs + target profit) ÷ contribution per unit
Worked example: output for $30,000 profit
Add the target to the fixed costs
$7,280 + $30,000 = $37,280 of contribution needed.
Divide by contribution per packet
$37,280 ÷ $1.90 = 19,621.05 packets.
Round up
19,622 packets. At 19,621 the profit is $29,999.90, ten cents short.
Another route to the same answer: Start from break-even. The first 3,831.6 packets pay the fixed costs; every packet after that adds $1.90 of profit. $30,000 ÷ $1.90 = 15,789.5 more packets. 3,831.6 + 15,789.5 = 19,621.1, so 19,622 packets. Round only at the end.
Now the other way round. With one café closing, Lena and Marco expect to sell only 16,000 packets. What price would still give $30,000 of profit? That price is the target price.
Target price = (fixed costs + target profit + total variable costs) ÷ number of units
| Step | Working | Result |
|---|---|---|
| Total variable costs | 16,000 × $0.60 | $9,600 |
| Revenue needed | $7,280 + $30,000 + $9,600 | $46,880 |
| Target price | $46,880 ÷ 16,000 | $2.93 a packet |
| Check | 16,000 × $2.93 = $46,880; minus $16,880 of costs | $30,000 profit |
Two different roundings: An output is rounded up to a whole unit, because part of a packet cannot be sold. A price is given to the cent, with a $ sign.
The target price answers "what price?", not "will customers pay it?". Whether cafés would buy crackers at $2.93 is a separate question.
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How this comes up: A short table of costs and prices for one product, then a chain of calculations, each for one or two marks: the break-even quantity, the profit or loss at a forecast output, the margin of safety, the output for a target profit, or the price for one.
Almost every one says "show all your working". Each is marked the same way: one mark for the working, one for the answer with its unit or $ sign.
The answer pattern
- Collect the figures. Add up every fixed cost in the table; take every variable cost per unit off the price.
- Write the rule in words. Break-even quantity = fixed costs ÷ contribution per unit.
- Put the numbers in. $9,600 ÷ ($40 − $16) = $9,600 ÷ $24.
- Give the answer with its unit. 400 cakes. Round a quantity up; give a price or profit to the cent with a $ sign.
The trap: the right number in the wrong unit: "$400" for a break-even quantity is wrong, even when the division is right. So is a profit written as a bare 26,920, or a break-even quantity rounded down.
An answer with no working can lose half the marks even when it is correct.
Calculate the break-even quantity of celebration cakes for the Station Road shop in 2027 (show all your working).
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