Revenue, costs and profit
Three calculations underpin everything else in this sub-topic, and they must be recalled:
revenue = price × quantity sold total costs = fixed costs + variable costs profit = revenue − total costs
Revenue is the money coming in from sales. It is not profit, and it is not what the business keeps — that confusion costs marks more often than any other in this topic.
Profit and loss. If revenue is greater than total costs the business makes a profit; if total costs are greater the business makes a loss. A loss is written as a negative figure.
Interest is the cost of borrowing money, or the reward for saving it. When a business takes out a loan it repays the amount borrowed plus interest, so borrowing raises total costs. Interest is normally expressed as a percentage per year.
interest = amount borrowed × interest rate × number of years
total repayment = amount borrowed + interest
Worked example
A business sells 900 units at £14 each. Fixed costs are £4200 and variable costs are £6 per unit. Calculate revenue, total costs and profit.
- Revenue = price × quantity = 14 × 900 = £12 600.
- Total variable costs = variable cost per unit × quantity = 6 × 900 = £5400.
- Total costs = fixed + variable = 4200 + 5400 = £9600.
- Profit = revenue − total costs = 12 600 − 9600.
- State the unit — these answers are money, so they need a £ sign.
Answer: Revenue £12 600, total costs £9600, profit £3000.
Common mistake
Variable cost per unit is not the same as total variable costs. Multiply it by the number of units before adding it to fixed costs — forgetting to is the single most common error in these calculations.
- Revenue
- the money coming in from sales, calculated as price × quantity sold
- Fixed costs
- costs that do not change with the level of output, such as rent
- Variable costs
- costs that change with the level of output, such as materials
- Profit
- revenue minus total costs
Break-even and margin of safety
The break-even level of output is the number of units a business must sell so that revenue exactly equals total costs — the point at which it makes neither a profit nor a loss.
break-even output = fixed costs ÷ (selling price per unit − variable cost per unit)
The bracket at the bottom is called the contribution per unit: what each sale contributes towards covering the fixed costs, once the variable cost of making that unit has been paid.
The margin of safety is how far above break-even the business is currently selling — in other words, how much sales could fall before it starts making a loss.
margin of safety = actual output − break-even output
Worked example
Fixed costs are £4200, the selling price is £14 and the variable cost is £6 per unit. Calculate the break-even output, and the margin of safety if the business sells 900 units.
- Find the contribution per unit first: 14 − 6 = £8.
- Break-even output = fixed costs ÷ contribution = 4200 ÷ 8.
- = 525 units.
- Margin of safety = actual output − break-even output = 900 − 525.
- Check it makes sense against the earlier profit figure: 375 units × £8 contribution = £3000, which matches the profit calculated above.
Answer: Break-even output is 525 units, and the margin of safety is 375 units. Sales could fall by 375 units before the business made a loss.
Common mistake
Break-even output is measured in units, not pounds. And divide by the contribution per unit — price minus variable cost — not by the price alone.
- Break-even level of output
- the number of units a business must sell so that revenue exactly equals total costs, making neither a profit nor a loss
- Margin of safety
- the amount by which current output exceeds the break-even level of output
- Contribution
- selling price per unit minus variable cost per unit
Interpreting break-even diagrams
The specification asks for four things to be read off a break-even diagram, and the chart above labels all four: the break-even level of output, the margin of safety, profit and loss, and the impact of changes in revenue and costs.
Reading the lines:
• Fixed costs are horizontal, because they do not change with output. • Total costs start at the fixed cost level, not at the origin — a business with no output still pays rent. • Revenue starts at the origin, because selling nothing earns nothing. • Where revenue crosses total costs is break-even. Left of it the business makes a loss; right of it, a profit. • The vertical gap between the revenue line and the total cost line at any output is the profit or loss at that level.
Worked example
Using the figures above, the landlord raises rent so fixed costs become £5400. Calculate the new break-even output and comment on the margin of safety.
- The contribution per unit is unchanged, because neither price nor variable cost has changed: still £8.
- New break-even output = 5400 ÷ 8.
- = 675 units.
- New margin of safety = 900 − 675 = 225 units.
- Compare with before and say what it means for risk.
Answer: Break-even output rises from 525 to 675 units, and the margin of safety falls from 375 to 225 units. The business is now closer to making a loss, so a fall in sales would be more dangerous than before.
The limitations of break-even analysis are worth knowing for evaluation questions. It assumes everything produced is sold, that the selling price stays the same however many units are sold, and that costs rise in a straight line — none of which is reliably true. It is also only as good as the forecast figures it is built from.
Before you practise
- revenue = price × quantity; total costs = fixed + variable; profit = revenue − total costs.
- Fixed costs do not change with output; variable costs do. Multiply variable cost per unit by quantity first.
- Interest is the cost of borrowing, and it raises total costs.
- contribution per unit = selling price − variable cost per unit.
- break-even output = fixed costs ÷ contribution per unit, measured in units.
- margin of safety = actual output − break-even output.
- On the diagram: fixed costs horizontal, total costs starting at the fixed cost level, revenue from the origin.
- Higher fixed or variable costs, or a lower price, all raise break-even output and shrink the margin of safety.
- Break-even analysis assumes all output is sold at a constant price with costs rising in a straight line.