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Business · Putting a business idea into practice

Break-even analysis

A business breaks even when its revenue exactly covers its costs. Break-even analysis tells an owner how much they must sell before making a profit, how safe their sales are, and what happens when prices or costs change.

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Last Lesson

Answer from memory before the answers appear.

How do you calculate revenue?
Price × quantity sold.
How do you calculate total costs?
Fixed costs + (variable cost per unit × quantity).
How do you calculate profit?
Total revenue - total costs.
Give one example each of a fixed and a variable cost.
Fixed: rent, salaries, insurance. Variable: raw materials, packaging, stock.

Learning Objectives

1Explain what is meant by break-even.
2Calculate the break-even level of output.
3Calculate and explain the margin of safety.
4Read profit, loss and break-even from a break-even diagram.
5Explain the impact of changes in revenue and costs on break-even.

What Is Break-Even?

Break-even is the point where total revenue equals total costs - no profit and no loss.

Break-even output
The number of units a business must sell to cover all its costs.
Below break-even
Every unit short of break-even means the business makes a loss.
Above break-even
Every unit sold beyond break-even adds to profit.
Why it matters
It tells a new business how much it must sell before it makes any money, and helps owners and banks judge whether an idea is realistic.

Calculating Break-Even

Break-even output = fixed costs ÷ (sales price - variable cost per unit).

Sales price - variable cost
The amount each unit contributes towards paying the fixed costs.
Fixed costs
The costs that must be covered before any profit is made.
The answer
Is always in units, not pounds. Round up to a whole unit if needed - you cannot sell part of a product.

The Café's Break-Even Point

Write the formula first, then put in the numbers.

The café sells coffee at £4. Each cup costs £1.50 to make, and fixed costs are £6,000 a month. Calculate how many cups it must sell to break even.

1 Write the formula Break-even = fixed costs ÷ (sales price - variable cost per unit)
2 Price - variable cost £4.00 - £1.50 = £2.50 per cup
3 Divide fixed costs £6,000 ÷ £2.50 = 2,400

AnswerBreak-even = 2,400 cups a month

The Margin of Safety

Margin of safety = actual (or budgeted) sales - break-even output.

What it means
How far sales could fall before the business starts to make a loss.
A big margin
Is safer: sales can drop a long way before the business is in trouble.
A small margin
Is risky: a small fall in sales could push the business into a loss.
Example
The café sells 3,000 cups and breaks even at 2,400, so its margin of safety = 3,000 - 2,400 = 600 cups.

Reading a Break-Even Diagram

On a break-even diagram, fixed costs are a flat line because they do not change with output. Total costs start at the fixed costs and rise with every cup made. Total revenue starts at zero and rises faster. Where revenue crosses total costs, the business breaks even.

A break-even diagram with fixed costs, total costs and total revenue lines, crossing at 2,400 cups, with loss and profit areas and the margin of safety marked.

What Each Part of the Diagram Shows

Fixed costs line
What it shows: Costs that do not change with output. Where to find it: Flat, horizontal line
Total costs line
What it shows: Fixed costs + variable costs. Where to find it: Starts at the fixed costs line, slopes up
Total revenue line
What it shows: Money from sales. Where to find it: Starts at zero, slopes up more steeply
Break-even point
What it shows: Revenue = total costs. Where to find it: Where the revenue and total costs lines cross
Loss
What it shows: Costs are greater than revenue. Where to find it: Gap between the lines, left of break-even
Profit
What it shows: Revenue is greater than costs. Where to find it: Gap between the lines, right of break-even
Margin of safety
What it shows: How far sales can fall before a loss. Where to find it: Gap between actual sales and break-even output

How Changes Affect the Café's Break-Even

Nothing changes
New calculation: £6,000 ÷ (£4.00 - £1.50). New break-even: 2,400 cups. Effect: The starting point
Price rises to £4.50
New calculation: £6,000 ÷ (£4.50 - £1.50). New break-even: 2,000 cups. Effect: Falls: better
Fixed costs rise to £7,500
New calculation: £7,500 ÷ (£4.00 - £1.50). New break-even: 3,000 cups. Effect: Rises: worse
Variable cost rises to £2.00
New calculation: £6,000 ÷ (£4.00 - £2.00). New break-even: 3,000 cups. Effect: Rises: worse

What Moves the Break-Even Point?

Break-even FALLS (good)

Selling price rises.
Fixed costs fall.
Variable cost per unit falls.
The business needs to sell fewer units to cover its costs.
The margin of safety grows.

Break-even RISES (bad)

Selling price falls.
Fixed costs rise.
Variable cost per unit rises.
The business needs to sell more units to cover its costs.
The margin of safety shrinks.

Limitations of Break-Even Analysis

Break-even is useful, but it rests on assumptions.

Assumes everything is sold
In reality some stock may be left unsold or wasted.
Assumes prices and costs stay the same
Suppliers raise prices, and businesses offer discounts.
Only as good as its figures
If the estimates of sales or costs are wrong, so is the break-even point.
Does not show cash
A business can be above break-even and still run out of cash.

Break-Even Challenge

A candle maker sells candles at £12. Each candle costs £4 in wax, wicks and jars, and fixed costs are £1,600 a month. Calculate the break-even output. She sells 300 candles a month - calculate her margin of safety. Then work out the new break-even output if she raises her price to £14.

1. Calculate price - variable cost.

2. Calculate break-even output.

3. Calculate the margin of safety.

4. Recalculate at the new price.

A good answer shows: Break-even 200 candles; margin of safety 100 candles; new break-even 160 candles at £14.

Can I...?

1Explain what break-even means.
2Calculate break-even output.
3Calculate the margin of safety.
4Label a break-even diagram.
5Read break-even, profit and loss from a diagram.
6Explain the effect of a price change.
7Explain the effect of a change in costs.
8Explain the limitations of break-even.

Summary & Exam Focus

Break-even output = fixed costs ÷ (sales price - variable cost per unit).
Margin of safety = actual sales - break-even output.
On a diagram, break-even is where total revenue crosses total costs.
Higher prices or lower costs lower the break-even point; lower prices or higher costs raise it.

Exam focus

Calculate the break-even output for a business with fixed costs of £12,000, a selling price of £20 and variable costs of £8 per unit. (2 marks) (2 marks)

Always subtract the variable cost from the price before dividing. Your answer is in units, not pounds.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Break-even: The point where total revenue equals total costs, so there is no profit and no loss.
Break-even output: The number of units a business must sell to cover its costs.
Margin of safety: The difference between actual sales and break-even output.
Break-even diagram: A graph showing fixed costs, total costs and total revenue, and where they cross.

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