Contribution, break-even point, charts, margin of safety
📈 Quantitative topic⏱ 18 min📝 3 practice questions
Learning Objectives
By the end of this lesson you will be able to…
Distinguish between fixed and variable costs with examples
Calculate contribution per unit and total contribution
Calculate the break-even point using the formula
Interpret a break-even chart and identify key features
Calculate and explain the margin of safety
Cost Types
Fixed Costs vs Variable Costs
Fixed Costs
Costs that do not change with the level of output. Paid regardless of how much is produced.
•Rent / mortgage on premises
•Salaries of permanent staff
•Insurance premiums
•Loan repayments
Variable Costs
Costs that change directly with output. Zero if nothing is produced.
•Raw materials / ingredients
•Packaging
•Direct labour (paid per unit)
•Delivery costs per order
Total Costs = Fixed Costs + (Variable Cost per unit × Quantity produced)
Key Concept
Contribution Per Unit
Definition
Contribution is the amount each unit sold contributes towards covering fixed costs — and eventually towards profit.
Formula
Contribution per unit = Selling Price − Variable Cost per unit
Worked Example
Selling price per unit£20
Variable cost per unit£8
Contribution per unit£12
Each unit sold contributes £12 towards fixed costs and profit
The Key Formula
Break-Even Point
Definition
The break-even point is the level of output at which total revenue equals total costs — the business makes neither profit nor loss.
Break-Even Formula
BEP = Fixed Costs ÷ Contribution per unit
Worked Example
Fixed costs£36,000
Selling price per unit£15
Variable cost per unit£9
Contribution per unit£6
Break-even point£36,000 ÷ £6 = 6,000 units
Break-Even Chart
Reading a Break-Even Chart
X-axis: Output (units produced/sold)
Y-axis: Revenue and costs (£)
Fixed cost line: Horizontal — constant regardless of output
BEP: Where the Revenue and Total Cost lines cross — neither profit nor loss
Key Concept
Margin of Safety
Definition
The margin of safety is the difference between actual output and the break-even output. It shows how much output can fall before the business makes a loss.
Formula
Margin of Safety = Actual Output − Break-Even Output
Worked Example
Break-even point6,000 units
Actual output8,500 units
Margin of safety8,500 − 6,000 = 2,500 units
Interpretation: Output can fall by up to 2,500 units before the business starts making a loss. A larger margin of safety = lower risk.
Evaluation
Uses and Limitations of Break-Even
Uses
Helps set a minimum sales target
Supports pricing decisions — what price ensures viability?
Helps secure a bank loan (shows awareness)
Evaluates impact of cost changes
Compares scenarios (e.g. different prices)
Limitations
Assumes all output is sold — unrealistic
Assumes variable costs are constant — may not be (bulk discounts)
Static model — doesn't account for market changes
Ignores quality or strategic factors
Only as good as the estimates used in the inputs
Practice Question 1 of 3
A business sells candles for £12 each. The variable cost per candle is £4. What is the contribution per unit?
A£4
B£12
C£8
D£16
Correct: C — £8. Contribution per unit = Selling Price − Variable Cost = £12 − £4 = £8. This means each candle sold contributes £8 towards covering fixed costs (and then profit once fixed costs are covered).
Practice Question 2 of 3
A business has fixed costs of £20,000, a selling price of £10 per unit and a variable cost of £6 per unit. What is the break-even output?
A2,000 units
B3,333 units
C5,000 units
D20,000 units
Correct: C — 5,000 units. Contribution per unit = £10 − £6 = £4. Break-even = Fixed Costs ÷ Contribution = £20,000 ÷ £4 = 5,000 units. At this level, total revenue (£50,000) exactly equals total costs (£20,000 fixed + £30,000 variable).
Practice Question 3 of 3
A business has a break-even point of 4,000 units and is currently producing 5,500 units. What is the margin of safety?
A1,500 units
B4,000 units
C9,500 units
D5,500 units
Correct: A — 1,500 units. Margin of Safety = Actual Output − Break-Even Output = 5,500 − 4,000 = 1,500 units. This means production can drop by up to 1,500 units before the business starts making a loss. It's a measure of how much buffer the business has.
Quick Reference
Formula Summary
Contribution per unit
SP − VC per unit
Break-Even Point
FC ÷ Contribution per unit
Margin of Safety
Actual − Break-Even output
Exam approach: Always show your working. Write out each formula, substitute values, then state your answer with units. Even if the final answer is wrong, you can earn method marks.