courses › Business Math

Break-Even

level 15 course

How many sales cover the fixed costs, and how much room you have above that.

In your head, jot if needed · no calculator why?

Opens at level 15.

Builds on: Contribution Margin (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

Break-even is where total contribution exactly covers the fixed costs: no profit, no loss. Break-even units are the fixed costs ÷ the contribution per unit, rounded up, since one unit fewer still leaves a loss.

In sales dollars, divide the fixed costs by the contribution margin ratio. The margin of safety is how far sales could fall before break-even, as a share of current sales: with 40 customers and break-even at 30, it is 10 out of 40, or 25%.

Techniques

Fixed costs ÷ contribution

Break-even units, from a contribution or from a price.

Find the contribution per unit: price minus variable cost.
Divide the fixed costs by it.
Round up to a whole unit, even for a small remainder.

worked example

Example: A product sells for $60 and has $35 of variable cost per unit. Fixed costs are $2,030 a month. How many whole units must it sell each month to break even?

Contribution: $60 − $35 = $25 a unit.
$2,030 ÷ $25 = 81.2.
Round up: 81 units would leave $5 uncovered.

Answer: 82

Break-even in sales dollars

You know the fixed costs and the contribution margin ratio.

Write the ratio as a decimal: 40% is 0.4.
Divide the fixed costs by it.
Check: the ratio times your answer gives back the fixed costs.

worked example

Example: Fixed costs are $9,000 a month and the contribution margin ratio is 40%. What monthly sales revenue breaks even?

$9,000 ÷ 0.4 = $22,500.
Check: 40% of $22,500 is $9,000.

Answer: $22,500

Bundle the sales mix

Two products sell in a fixed ratio.

Make one bundle in the stated mix, like 3 coffees and 1 sandwich.
Add up the bundle's contribution, and divide the fixed costs by it.
Multiply the bundles by the items in each bundle.

worked example

Example: A food truck sells 2 tacos for every 1 drink. Each taco contributes $3 and each drink $2. Fixed costs are $4,000 a month. How many total items must it sell to break even if the mix holds?

One bundle: 2 × $3 + 1 × $2 = $8 for 3 items.
$4,000 ÷ $8 = 500 bundles.
500 × 3 = 1,500 items.

Answer: 1,500

Tips by skill

TipBreak-even units: Divide the fixed costs by the contribution per sale, then round up to the next whole sale.
TipBreak-even from price and cost: Find the contribution first: price minus variable cost. Divide the fixed costs by it, then round up.
TipBreak-even sales dollars: Divide the fixed costs by the ratio written as a decimal. The answer should be bigger than the fixed costs.
TipMargin of safety: Subtract break-even from current sales, then divide by current sales, not by break-even.
TipBreak-even with a sales mix: Build one bundle in the stated mix and add its contribution. Divide the fixed costs by it, then count the items.

Watch out for

Rounding break-even down. 81.2 units means 82, because at 81 the business is still short.
Dividing the fixed costs by the price. Part of the price pays the variable costs, so divide by the contribution.
Averaging two contributions without weighting them by the mix.
Dividing the margin of safety by break-even instead of by current sales.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

Break-even units par 15 s not tried yet
worked example
Fixed costs are $15,100 a month and each service contributes $385. How many whole services are needed to break even?

Answer: 40
1. Break-even = fixed ÷ contribution = $15,100 ÷ $385 ≈ 39.22; round up to 40.
2. At 39, contribution is $15,015, $85 short of fixed costs.
Break-even from price and cost par 20 s not tried yet
worked example
A product sells for $365 and has $215 of variable cost per unit. Fixed costs are $9,070 a month. How many whole units must it sell each month to break even?

Answer: 61
1. Contribution = $365 − $215 = $150 per unit.
2. Break-even = $9,070 ÷ $150 ≈ 60.47; round up to 61 units.
Break-even sales dollars par 17 s not tried yet
worked example
Fixed costs are $38,500 a month and the contribution margin ratio is 25%. What monthly sales revenue breaks even?

Answer: $154,000.00
1. Each sales dollar contributes $0.25, so revenue needed = $38,500 ÷ 0.25 = $154,000.
2. Check: 25% of $154,000 is $38,500.
Margin of safety par 16 s not tried yet
worked example
A business has 200 customers and breaks even at 116 customers. What percentage of its current customers could it lose before it reaches break-even?

Answer: 42%
1. Headroom ÷ current = (200 − 116) ÷ 200 = 84 ÷ 200 = 42%.
2. Divide by current sales, not by the break-even point.
Break-even with a sales mix par 30 s not tried yet
worked example
A bakery sells 3 loaves of bread for every 4 cakes. Each loaf of bread contributes $9 and each cake $2. Fixed costs are $10,500 a month. How many total items must it sell to break even if the mix holds?

Answer: 2,100
1. Group the mix into a bundle: 3 × $9 + 4 × $2 = $35 per 7 items.
2. $10,500 ÷ $35 = 300 bundles = 300 × 7 = 2,100 items.

rest ladder

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