Revenue and Costs
Sales Volume and Sales Revenue
Sales volume: the number of units a business sells in a period, such as a week, a month or a year.
Sales revenue: the money a business receives from selling its output, before any costs are taken off. It is also called total revenue or turnover.
Sales revenue is the selling price multiplied by the number of units sold: \[ \text{Sales revenue} = \text{Price} \times \text{Sales volume} \] A barber who charges £18 a haircut and does 120 haircuts in a week has sales revenue of 120 × £18 = £2,160 for the week.
The same formula rearranges to find sales volume: \[ \text{Sales volume} = \frac{\text{Sales revenue}}{\text{Price}} \] If revenue next week is £2,520, the barber must have done 2,520 ÷ 18 = 140 haircuts. Questions often give you two of the three figures and ask for the third.
Two things to keep in mind. Revenue is not profit: costs still have to be paid (see unit 1.6.3). And raising the price does not always raise revenue, because sales volume usually falls, by how much depending on price elasticity of demand (Theme 2).
Fixed and Variable Costs
Fixed costs: costs that do not change when output changes, at least in the short run. Rent, business rates, insurance and the salaries of permanent staff are all fixed costs. They have to be paid even in a month when the business makes nothing.
Variable costs: costs that rise and fall with output. Raw materials, packaging, the energy used by machines and delivery charges are variable costs. Make nothing and they fall to zero.
Total variable costs are the variable cost of one unit multiplied by output. A firm that spends £2.50 on materials for each unit and makes 1,000 units has total variable costs of 1,000 × £2.50 = £2,500.
Fixed costs are only fixed up to a point. A business that grows may need bigger premises or more salaried staff, so its fixed costs jump to a new level. In the long run, every cost can change.
Total and Average Costs
Total costs: the whole cost of producing a given level of output, found by adding fixed and variable costs: \[ \text{Total costs} = \text{Fixed costs} + \text{Variable costs} \]
Average cost: the cost of producing one unit, found by dividing total costs by output: \[ \text{Average cost} = \frac{\text{Total costs}}{\text{Output}} \] It is also called unit cost.
Average cost usually falls as output rises, because the same fixed costs are shared across more units.
Worked Example: A Candle Maker's Costs
Rosa makes scented candles in a rented workshop. Her fixed costs are £2,000 a month for rent, insurance and her website. Each candle uses £4 of wax, jars, wicks and packaging.
| Candles a month | Fixed costs | Variable costs | Total costs | Average cost |
|---|---|---|---|---|
| 200 | £2,000 | £800 | £2,800 | £14.00 |
| 500 | £2,000 | £2,000 | £4,000 | £8.00 |
| 1,000 | £2,000 | £4,000 | £6,000 | £6.00 |
Variable costs are £4 times output, and average cost is total costs divided by output. Fixed costs stay at £2,000, so the fixed cost carried by each candle drops from £10 at 200 candles to £2 at 1,000. That is why average cost falls from £14 to £6. If Rosa sells her candles at £12, making only 200 a month means each one costs more to make than she charges for it. At 500 a month she is £4 a candle ahead.
Percentage Change
Data questions often ask how much a figure has changed, as a percentage. Take the change, divide it by the original value and multiply by 100:
\[ \text{Percentage change} = \frac{\text{New value} - \text{Original value}}{\text{Original value}} \times 100 \]
Suppose Rosa's monthly sales revenue rises from £6,000 to £7,500. The change is £1,500, so the percentage change is 1,500 ÷ 6,000 × 100 = 25%.
A negative answer means a fall. When Rosa's output goes from 200 to 500 candles, her average cost goes from £14 to £8. That is (8 − 14) ÷ 14 × 100 = −42.9%, a fall of 42.9% to one decimal place. Write out the formula and each step, so the examiner can follow your method.
Always divide by the original value. A rise from £6,000 to £7,500 is 25%, but a fall from £7,500 back to £6,000 is only 20%, because the starting figure is bigger. Take care when the figures are already percentages, too: an interest rate going from 4% to 5% has risen by one percentage point, which is a 25% increase.
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