3.3 Costs and break-even analysis
- Syllabus
- 2026
- Topic
- 3.3
- Level
- —
Learning objectives
3.3.1Revenue, costs, profit and lossUnderstand and calculate revenue, fixed costs, variable costs, total costs, profit and loss. Use revenue = selling price × quantity sold, total costs = fixed costs + variable costs, and profit = revenue − total costs in business contexts.3.3.2Break-even analysisThe concept of break-even and calculation of break-even (from formula or diagram):• break-even level of output.3.3.3Interpretation of break-even chartsInterpretation of break-even charts:• the impact of changes in revenue and costs• limitations of break-even charts.
Build revenue, cost and profit from units
Revenue is sales income; costs are resources used to operate/produce; profit or loss is the difference between total revenue and total costs for the same period and output.
| Quantity | Meaning | Behaviour as output changes |
|---|---|---|
| fixed cost | cost that does not change with output within the relevant period/range, such as premises rent | total fixed cost remains constant even at zero output |
| variable cost | cost that changes with output, such as direct materials | total variable cost rises as more units are made/sold; variable cost per unit may be given |
| total cost | fixed cost plus all variable cost | starts at fixed cost and rises with output |
revenue=sellingpriceperunit×quantitysold;totalvariablecost=variablecostperunit×quantity;totalcost=fixedcost+totalvariablecost;profit=revenue−totalcost
| 200 bowls per day | Calculation | Result (£) |
|---|---|---|
| revenue at £12 each | 12 × 200 | 2,400 |
| variable cost at £3 each | 3 × 200 | 600 |
| total cost with £600 fixed cost | 600 + 600 | 1,200 |
| profit | 2,400 - 1,200 | 1,200 |
If total cost exceeds revenue, the result is a loss: loss = total cost - revenue. Profit can rise if revenue increases by more than any added cost or costs fall without causing a larger fall in revenue.
Classify cost behaviour for the stated period and output range. A salary may be fixed when paid regardless of units, while piece-rate labour is variable; ‘fixed’ does not mean the amount can never change in the future.
Calculate the output where revenue equals cost
Break-even is the output at which total revenue equals total cost, so profit is zero. Each unit's contribution first covers fixed cost; after fixed cost is covered, further contribution becomes profit.
contributionperunit=sellingpriceperunit−variablecostperunit;break−evenoutput=fixedcosts/contributionperunit
| Ice-cream case | Calculation |
|---|---|
| selling price per tub | £2.50 |
| variable cost per tub | £1.10 |
| contribution per tub | £2.50 - £1.10 = £1.40 |
| fixed costs per day | £77 |
| break-even output | £77 / £1.40 = 55 tubs |
Below 55 tubs, total contribution has not covered fixed costs and the business makes a loss. At 55 it breaks even. Above 55, each additional tub contributes £1.40 toward profit, assuming price and unit variable cost stay unchanged.
Compare the calculated output with realistic demand and capacity. Managers can test how price, unit variable cost or fixed cost changes affect the target before deciding whether a product or expansion is viable.
If contribution per unit is zero or negative, selling more units cannot cover fixed costs under the formula. Break-even output is a number of units; break-even revenue is that output multiplied by selling price and is a different answer.
Read shifts and assumptions on a break-even chart
On a break-even chart, output is on the horizontal axis and money is on the vertical axis. The total-revenue line starts at zero; fixed cost is horizontal; total cost starts at fixed cost and rises with variable cost. Revenue and total cost intersect at break-even.
| Change, all else equal | Line effect | Break-even effect |
|---|---|---|
| selling price rises | revenue line becomes steeper | break-even output falls |
| selling price falls | revenue line becomes flatter | break-even output rises |
| variable cost per unit rises | total-cost line becomes steeper | break-even output rises |
| variable cost per unit falls | total-cost line becomes flatter | break-even output falls |
| fixed cost rises | fixed-cost and total-cost intercept shift upward | break-even output rises |
| fixed cost falls | fixed-cost and total-cost intercept shift downward | break-even output falls |
To the left of the intersection, total cost exceeds revenue: loss. To the right, revenue exceeds total cost: profit. The vertical gap between revenue and total cost at a chosen output shows the profit or loss amount on the chart's money scale.
A simple chart assumes constant selling price and unit variable cost, fixed costs unchanged over the range, straight-line relationships, all output sold and reliable demand/cost estimates. Discounts, capacity steps, waste, unsold inventory, competitors and uncertainty can make actual results differ.
Use break-even as one planning input: test alternative assumptions and combine it with demand, capacity, cash flow, quality and strategic evidence. A low break-even target is helpful only if the assumptions and expected sales are credible.
Break-even does not forecast demand or guarantee profit. Moving one line can have consequences elsewhere—for example, a higher price steepens revenue only if customers still buy the assumed output.