Costs, Revenue, Profit & Break-Even

Why costs, revenue and profit matter

Every business needs to know whether it is making money. To work this out, owners track how much they spend (costs), how much they earn (revenue) and the difference between the two (profit). This chapter pulls these ideas together and uses them to answer one of the most important questions in business: how much do we need to sell just to cover our costs? That is the job of break-even analysis.

Key terms Costs – the payments a business makes to produce its goods or services.

Revenue – the income a business receives from selling its products (also called sales or turnover).

Profit – the surplus left when total costs are taken away from revenue.

Fixed, variable and total costs

Costs are split into two types depending on whether they change with output.

Fixed costs do not change with the level of output. The business pays them whether it makes 0 units or 10,000 units. Examples include rent, salaries, insurance and loan repayments.

Variable costs do change directly with output. The more you produce, the higher they are. Examples include raw materials, packaging and the wages of workers paid per unit. Variable cost per unit is usually constant; total variable cost rises as output rises.

Total costs (TC) are simply the two added together at a given level of output:

$$\text{Total costs} = \text{Total fixed costs} + \text{Total variable costs}$$

$$\text{Total variable costs} = \text{variable cost per unit} \times \text{quantity}$$

Worked example A bakery has fixed costs of £2,000 per month. Each loaf costs £0.50 in ingredients and packaging (the variable cost per unit). It bakes 3,000 loaves.

Total variable cost $= £0.50 \times 3{,}000 = £1{,}500$.

Total cost $= £2{,}000 + £1{,}500 = £3{,}500$.

Watch out Don't confuse variable cost per unit (stays the same, e.g. £0.50 each) with total variable cost (rises with output). Read the question carefully to see which one is given.

Revenue

Revenue is the money coming in from sales. It is found by multiplying the selling price by the number of units sold:

$$\text{Revenue} = \text{price} \times \text{quantity}$$

Worked example The bakery sells its 3,000 loaves at £1.50 each.

Revenue $= £1.50 \times 3{,}000 = £4{,}500$.

Revenue is not the same as profit. A business with huge revenue can still make a loss if its costs are higher.

Profit

Profit is the reward for taking risk and the sign that a business is succeeding:

$$\text{Profit} = \text{total revenue} - \text{total costs}$$

If the answer is negative the business has made a loss.

Worked example Bring the bakery figures together:

Revenue $= £4{,}500$, Total costs $= £3{,}500$.

Profit $= £4{,}500 - £3{,}500 = £1{,}000$ per month.

Exam tip Show every line of your working. If your final number is wrong but your method is right, you can still pick up most of the marks. Always add the unit (£) and the time period (per month, per year) to your answer.

Contribution per unit

Before we reach break-even we need one more idea: contribution. Each unit sold contributes towards paying off the fixed costs. Once the fixed costs are fully covered, every further unit's contribution becomes profit.

$$\text{Contribution per unit} = \text{selling price} - \text{variable cost per unit}$$

Worked example The bakery's loaf sells for £1.50 and costs £0.50 to make.

Contribution per unit $= £1.50 - £0.50 = £1.00$.

Each loaf sold puts £1 towards covering the £2,000 of fixed costs.

Break-even

The break-even point is the level of output at which total revenue exactly equals total costs. At this point the business makes neither a profit nor a loss. Selling above it makes a profit; selling below it makes a loss.

The formula uses contribution:

$$\text{Break-even output} = \frac{\text{fixed costs}}{\text{contribution per unit}}$$

Worked example The bakery has fixed costs of £2,000 and a contribution of £1 per loaf.

Break-even $= \dfrac{2{,}000}{1} = 2{,}000$ loaves per month.

The bakery must sell 2,000 loaves just to cover its costs. Its 3,000 loaves are comfortably above this, which is why it makes a profit.

Key terms Break-even point – the output where total revenue equals total costs (zero profit, zero loss).

Contribution – selling price minus variable cost per unit; the amount each sale contributes towards fixed costs and then profit.

The break-even chart

A break-even chart shows costs and revenue on the same graph so you can see the break-even point. Output is on the horizontal axis and money (£) on the vertical axis. Three lines are drawn:

Fixed cost line – horizontal, because fixed costs stay the same at every level of output.
Total cost line – starts at the fixed cost level (output of 0) and slopes upward as variable costs are added.
Revenue line – starts at the origin (0 sales = £0) and slopes upward more steeply.

Where the revenue line crosses the total cost line is the break-even point. Drop a line down to the output axis to read off the break-even quantity.

The margin of safety

The margin of safety shows how far current sales are above the break-even point. It is the cushion a business has before it starts making a loss.

$$\text{Margin of safety} = \text{actual sales} - \text{break-even output}$$

Worked example The bakery sells 3,000 loaves and breaks even at 2,000 loaves.

Margin of safety $= 3{,}000 - 2{,}000 = 1{,}000$ loaves.

Sales could fall by 1,000 loaves before the bakery makes a loss. A large margin of safety means lower risk.

Using break-even to make decisions

Break-even analysis can answer useful "what if?" questions.

Worked example The bakery wants to know the effect of a price rise to £2.00 (variable cost stays £0.50).

New contribution $= £2.00 - £0.50 = £1.50$.

New break-even $= \dfrac{2{,}000}{1.50} = 1{,}334$ loaves (rounded up).

A higher price lowers the break-even output, because each loaf now contributes more towards fixed costs.

Break-even can also work out the output needed to hit a profit target:

$$\text{Output for target profit} = \frac{\text{fixed costs} + \text{target profit}}{\text{contribution per unit}}$$

Worked example The bakery wants £1,000 profit. Contribution is £1 per loaf.

Output $= \dfrac{2{,}000 + 1{,}000}{1} = 3{,}000$ loaves. This matches its actual sales, confirming the earlier £1,000 profit.

Uses and limitations of break-even analysis

Uses (advantages):

Shows how many units must be sold to avoid a loss, which helps with setting sales targets.
Helps when applying for a loan, as banks like to see the figures.
Lets managers test "what if?" scenarios (changing price, costs or output) quickly.
Shows the margin of safety, giving a clear measure of risk.

Limitations (disadvantages):

It assumes everything produced is sold – in reality there may be unsold stock.
It assumes selling price and variable cost per unit stay constant, but discounts and bulk-buying change them.
The chart shows lines as straight, when in real life costs and revenue may not be perfectly linear.
It is only as accurate as the data put in; estimates can be wrong.
It is a snapshot and the market can change quickly.

Real world A new café will often draw a break-even chart in its business plan before it opens. It helps the owners judge whether the number of customers needed each day is realistic for their location, and shows the bank that they understand their numbers.

Exam tip "Evaluate" or "discuss" questions on break-even want both sides. State the uses, then the limitations, and finish with a justified judgement, such as: "Break-even is a useful planning tool but its assumption that all output is sold means the results should be treated with caution."