Break-Even Analysis

Break-even output is the level of production at which a business makes neither a profit nor a loss — total revenue exactly equals total costs.

To find the break-even point, first calculate contribution per unit.

Contribution per unit = Selling Price − Variable Cost per Unit

Contribution is the amount each unit sold contributes toward paying the fixed costs. Once fixed costs are fully covered, any additional contribution becomes profit.

Break-even output = Fixed Costs ÷ Contribution per Unit

Worked example:

A phone case business has:

• Fixed costs: £5,000/month
• Selling price: £20 per case
• Variable cost per case: £12

Step 1 — contribution per unit:

$\text{Contribution}=\pounds 20-\pounds 12=\pounds 8$

Step 2 — break-even output:

$\text{Break-even}=\frac{\pounds 5,000}{\pounds 8}=625\text{ units}$

Verification: At 625 units:

• Revenue = 625 × £20 = £12,500
• Variable costs = 625 × £12 = £7,500
• Total costs = £7,500 + £5,000 = £12,500
• Profit = £12,500 − £12,500 = £0 ✓

The business must sell at least 625 phone cases per month to cover all its costs.

The margin of safety measures how far actual output is above the break-even point. It shows how much output could fall before the business starts making a loss.

Margin of Safety = Actual Output − Break-Even Output

Worked example — continuing from above:

If the business currently produces and sells 800 cases per month:

$\text{Margin of safety}=800-625=175\text{ units}$

This means output could fall by up to 175 units before the business reaches break-even and begins making a loss.

Profit at 800 units:

$\text{Revenue}=800\times \pounds 20=\pounds 16,000$

$\text{Variable costs}=800\times \pounds 12=\pounds 9,600$

$\text{Total costs}=\pounds 9,600+\pounds 5,000=\pounds 14,600$

$\text{Profit}=\pounds 16,000-\pounds 14,600=\pounds 1,400$

Alternatively, profit can be calculated as:

$\text{Profit}=\text{Margin of safety}\times \text{Contribution per unit}=175\times \pounds 8=\pounds 1,400✓$

Exam tip: A larger margin of safety means the business is further from making a loss — it is less financially vulnerable to a drop in sales.

A break-even diagram plots revenue and costs against output on a graph. Examiners may ask you to sketch, interpret, or annotate one.

The diagram below plots the phone case business (fixed costs £5,000, selling price £20, variable cost £12 per unit). The revenue and total cost lines cross at 625 units — the break-even point.

Key features of the diagram:

Feature	Description
Fixed cost line	Horizontal — same value at every output level
Total cost line	Starts at the fixed cost on the y-axis; slopes upward (adds variable costs)
Revenue line	Starts at the origin (0 units = £0 revenue); slopes upward
Break-even point	Where the revenue line and total cost line cross
Loss zone	To the left of break-even — total costs exceed revenue
Profit zone	To the right of break-even — revenue exceeds total costs
Margin of safety	Horizontal distance between current output and break-even output

The steeper the revenue line compared to the total cost line, the fewer units are needed to break even.

Break-even analysis is most useful when a business considers changing its prices or costs. Each change shifts one of the lines.

If fixed costs rise (e.g., rent increases):

• The fixed cost line moves up
• The total cost line also shifts up (it starts higher)
• The revenue line is unchanged
• The break-even point moves to the right — more units must be sold to break even
• The margin of safety decreases

If variable costs rise (e.g., raw material price increase):

• The total cost line becomes steeper
• The fixed cost line is unchanged
• The revenue line is unchanged
• Break-even point moves to the right

If the selling price rises:

• The revenue line becomes steeper (more revenue per unit)
• Cost lines are unchanged
• The two lines cross sooner — break-even point moves to the left
• The margin of safety increases

If the selling price falls:

• The revenue line becomes less steep
• Break-even point moves to the right
• The margin of safety decreases

Worked example — impact of a cost rise:

Using the phone case business (FC = £5,000, SP = £20, VC = £12, current break-even = 625 units):

Fixed costs rise to £6,000:

$\text{New break-even}=\frac{\pounds 6,000}{\pounds 8}=750\text{ units}$

If actual output is still 800 units:

$\text{New margin of safety}=800-750=50\text{ units}$

The margin of safety has shrunk from 175 to 50 units — the business is now much closer to making a loss.

Break-even analysis helps business owners and managers make decisions about pricing, costs and output targets.

Strengths of break-even analysis:

• Quick and simple to calculate
• Gives a clear output target for the business to aim for
• Helps assess the financial risk of a new product or venture
• Supports negotiations with banks when seeking finance (shows when loans can be repaid)

Limitations of break-even analysis:

• Assumes all output is sold — in reality, businesses may have unsold stock
• Assumes selling price is constant — businesses often offer discounts
• Assumes variable cost per unit is constant — bulk buying may reduce unit costs
• Does not account for changes in the external environment (competition, recession)
• More useful as a planning tool than as a predictor of actual results

Exam tip: In a "Do you think break-even analysis is useful for this business?" question, present at least one strength and one limitation, then give a justified conclusion based on the business context described.

1. Calculate contribution before break-even

The break-even formula requires contribution per unit. Students who try to go straight to break-even often confuse the fixed cost with something else. Always: Contribution = SP − VC, then Break-even = FC ÷ Contribution.

2. Verify your break-even with a profit check

Multiply your break-even output by the selling price. That should equal Total Costs at the same output. If it doesn't, recheck your working.

3. Margin of safety is about output, not money

Margin of safety = units of output (or sometimes % of current output). Don't give a £ figure unless the question specifically asks for it in value terms.

4. Drawing the diagram — label everything

Examiners award marks for: both axes labelled, fixed cost line in the right place, total cost line starting at FC (not at origin), revenue line starting at origin, break-even point clearly marked.

5. Interpreting changes — state the direction

Don't just say "break-even changes" — say whether it moves left (fewer units needed) or right (more units needed), and what that means for risk.

Scenario	Effect on Break-Even Output
Fixed costs increase	Increases (moves right)
Fixed costs decrease	Decreases (moves left)
Variable cost per unit increases	Increases (revenue and TC cross later)
Selling price increases	Decreases (revenue line steeper)
Selling price decreases	Increases (revenue line less steep)