EDEXCEL GCSE BUSINESS · PAPER 1
Break-even analysis
Putting a business idea into practice · Lesson 3 of 5
Teacher copy - includes the notes for whoever is teaching from it.
Last Lesson
Answer from memory before the answers appear.
1. How do you calculate revenue?
Price × quantity sold.
2. How do you calculate total costs?
Fixed costs + (variable cost per unit × quantity).
3. How do you calculate profit?
Total revenue - total costs.
4. Give one example each of a fixed and a variable cost.
Fixed: rent, salaries, insurance. Variable: raw materials, packaging, stock.
Learning Objectives
1. Explain what is meant by break-even.
2. Calculate the break-even level of output.
3. Calculate and explain the margin of safety.
4. Read profit, loss and break-even from a break-even diagram.
5. Explain 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
Answer: Break-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.
PART TWO
The Break-Even Diagram
The same numbers, drawn as a graph.
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. |
The café breaks even at 2,400 cups. At 3,000 cups its margin of safety is 600 cups. |
What Each Part of the Diagram Shows
|
Part |
What it shows |
Where to find it |
|---|---|---|
|
Fixed costs line |
Costs that do not change with output |
Flat, horizontal line |
|
Total costs line |
Fixed costs + variable costs |
Starts at the fixed costs line, slopes up |
|
Total revenue line |
Money from sales |
Starts at zero, slopes up more steeply |
|
Break-even point |
Revenue = total costs |
Where the revenue and total costs lines cross |
|
Loss |
Costs are greater than revenue |
Gap between the lines, left of break-even |
|
Profit |
Revenue is greater than costs |
Gap between the lines, right of break-even |
|
Margin of safety |
How far sales can fall before a loss |
Gap between actual sales and break-even output |
PART THREE
When Things Change
A change in price or costs moves the break-even point.
How Changes Affect the Café's Break-Even
|
Change |
New calculation |
New break-even |
Effect |
|---|---|---|---|
|
Nothing changes |
£6,000 ÷ (£4.00 - £1.50) |
2,400 cups |
The starting point |
|
Price rises to £4.50 |
£6,000 ÷ (£4.50 - £1.50) |
2,000 cups |
Falls: better |
|
Fixed costs rise to £7,500 |
£7,500 ÷ (£4.00 - £1.50) |
3,000 cups |
Rises: worse |
|
Variable cost rises to £2.00 |
£6,000 ÷ (£4.00 - £2.00) |
3,000 cups |
Rises: worse |
What Moves the Break-Even Point?
|
BREAK-EVEN FALLS (GOOD) |
BREAK-EVEN RISES (BAD) |
|
▸ 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. |
▸ 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.
Key Terms
|
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. |
Your Task: Break-Even Challenge
15 minutes
|
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.
Note: Check they subtract the variable cost before dividing - the most common mistake is £1,600 ÷ £12.
Can I...?
☐ Explain what break-even means.
☐ Calculate break-even output.
☐ Calculate the margin of safety.
☐ Label a break-even diagram.
☐ Read break-even, profit and loss from a diagram.
☐ Explain the effect of a price change.
☐ Explain the effect of a change in costs.
☐ Explain the limitations of break-even.
Summary
✓ 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) Always subtract the variable cost from the price before dividing. Your answer is in units, not pounds. |
Exam Practice: Break-Even Analysis
Answer all questions. Show your working in calculations. · 25 minutes
▸ Question 1 · 1 mark · Define. Define the term 'margin of safety'.
▸ Question 2 · 2 marks · Calculate. A business has fixed costs of £12,000. It sells its product for £20 and the variable cost is £8 per unit. Calculate the break-even level of…
▸ Question 3 · 2 marks · Calculate. The same business sells 1,300 units. Using your answer above, calculate its margin of safety. You are advised to show your working.
▸ Question 4 · 2 marks · Outline. Outline one benefit to a new business of calculating its break-even output.
▸ Question 5 · 3 marks · Explain. Explain one impact on a business's break-even output of an increase in the variable cost per unit.
Question 1 · 1 mark · Define
|
“Define the term 'margin of safety'.” |
HOW TO ANSWER IT Command word: Define. Worth 1 mark, so plan before writing.
Question 1 · mark scheme
1 mark available. Award a mark for each point made.
▸ Actual / budgeted sales minus break-even output. 1 mark
▸ Model answer. The difference between a business's actual sales and its break-even level of output.
Question 2 · 2 marks · Calculate
|
“A business has fixed costs of £12,000. It sells its product for £20 and the variable cost is £8 per unit. Calculate the break-even level of output. You are advised to show your working.” |
HOW TO ANSWER IT Command word: Calculate. Worth 2 marks, so plan before writing.
Question 2 · mark scheme
2 marks available. Award a mark for each point made.
▸ Correct method: fixed costs ÷ (price - variable cost per unit). 1 mark
▸ Correct answer: 1,000 units. 1 mark (award 2 marks for the correct answer with no working)
▸ Model answer. £12,000 ÷ (£20 - £8) = £12,000 ÷ £12 = 1,000 units
Question 3 · 2 marks · Calculate
|
“The same business sells 1,300 units. Using your answer above, calculate its margin of safety. You are advised to show your working.” |
HOW TO ANSWER IT Command word: Calculate. Worth 2 marks, so plan before writing.
Question 3 · mark scheme
2 marks available. Award a mark for each point made.
▸ Correct method: actual sales - break-even output. 1 mark
▸ Correct answer: 300 units. 1 mark (own figure rule applies)
▸ Model answer. 1,300 - 1,000 = 300 units
Question 4 · 2 marks · Outline
|
“Outline one benefit to a new business of calculating its break-even output.” |
HOW TO ANSWER IT Command word: Outline. Worth 2 marks, so plan before writing.
Question 4 · mark scheme
2 marks available. Award a mark for each point made.
▸ A benefit identified, e.g. sets a sales target / shows if the idea is viable / helps get a loan. 1 mark
▸ Developed: why this helps the business. 1 mark
▸ Model answer. It shows the owner how many units they must sell to avoid a loss (1), so they can judge whether their sales target is realistic before spending money on the business (1).
Question 5 · 3 marks · Explain
|
“Explain one impact on a business's break-even output of an increase in the variable cost per unit.” |
HOW TO ANSWER IT Command word: Explain. Worth 3 marks, so plan before writing.
Question 5 · mark scheme
3 marks available. Award a mark for each point made.
▸ An impact identified: break-even output rises. 1 mark
▸ First linked point of explanation. 1 mark
▸ Second linked point of explanation. 1 mark
▸ Model answer. The break-even output will rise (1). Each unit sold now contributes less towards paying the fixed costs, because the gap between price and variable cost is smaller (1). This means the business must sell more units before it covers its costs, and its margin of safety falls (1).