Making Financial Decisions
Business calculations
Contents
Gross profit is the profit a business makes from its core trading activity. It is found by subtracting cost of sales from sales revenue. Cost of sales are the direct costs of the goods sold, such as materials or stock.
Gross profit = sales revenue − cost of sales. You need to memorise this formula because it is not given in the exam. Gross profit is a money amount, such as £19,000, not a percentage. It shows the core profitability of the trading activity before other operating expenses, such as rent and wages, and interest are paid.
Worked example: Harbour Cycle Repairs has sales revenue of £48,000 and cost of sales of £29,000. Gross profit = £48,000 − £29,000 = £19,000. The business kept £19,000 from its core trading after paying for the parts and stock it sold, before other operating expenses and interest.
You can rearrange the formula to find cost of sales: Cost of sales = sales revenue − gross profit. If Harbour Cycle Repairs has sales revenue of £48,000 and gross profit of £19,000, cost of sales = £48,000 − £19,000 = £29,000. This is useful when you know sales revenue and gross profit but need to work out cost of sales.
Net profit is the money a business keeps once other operating expenses and interest have been taken off its trading profit. It is what is left from gross profit after you subtract those costs.
Other operating expenses are the running costs that are not part of cost of sales, such as rent, wages, marketing and administration. Interest is the cost of borrowing money.
The formula
Net profit = gross profit − other operating expenses and interest
Learn this by heart. It is not given in the exam, so you need to recall it and use it accurately. Work through it in two steps: pick out the gross profit, then add together every operating expense and interest charge before you subtract.
Worked example
A garden centre has gross profit of £72,000. Its rent, wages, marketing and administration come to £44,000, and interest on a loan is £5,500, so its other operating expenses and interest total £49,500.
Net profit = £72,000 − £49,500 = £22,500
The garden centre has turned £72,000 of trading profit into £22,500 of overall profit, because £49,500 was used up by running the business and paying for borrowed money.
What a net loss means
If other operating expenses and interest are greater than gross profit, net profit is negative. The business has made a net loss. Suppose the same garden centre had expenses and interest of £80,000. Then £72,000 − £80,000 gives a net loss of £8,000. Trading made money, but not enough to cover everything else. You would write this as −£8,000 or as a net loss of £8,000.
Net profit shows the overall profit after other operating expenses and interest have been paid, so it shows how well a business controls those costs. It is a money amount, always written with the currency unit used in the question, never as a percentage. A percentage version is covered by net profit margin.
The gross profit margin measures a business's gross profit as a percentage of sales revenue. It tells you what share of every pound taken from sales the business keeps as gross profit, before other operating expenses and interest are paid.
The formula must be memorised:
Gross profit margin (%) = (gross profit ÷ sales revenue) × 100
The figure on top is gross profit, never net profit, and the figure underneath is always sales revenue. You may be given cost of sales rather than gross profit: work out gross profit first by subtracting cost of sales from sales revenue, then use it in the margin formula.
What a higher margin tells you
A higher gross profit margin means a larger proportion of sales revenue is kept as gross profit at that stage. That usually points to tighter control of direct costs such as materials and stock, or to a higher selling price relative to those costs.
A business with £150,000 of sales revenue and £60,000 of cost of sales makes £90,000 gross profit. Its margin is (£90,000 ÷ £150,000) × 100 = 60%. The business keeps 60p of every £1 of sales as gross profit.
Why percentages help comparisons
Money figures alone can mislead you, because a bigger business will usually show bigger profits simply because it sells more. Percentages put businesses of different sizes on a level footing.
| Business | Sales revenue | Gross profit | Gross profit margin |
|---|---|---|---|
| Birchwood Bakery | £250,000 | £75,000 | 30% |
| Hollin Farm Shop | £40,000 | £15,600 | 39% |
Birchwood Bakery has the larger gross profit in money terms, but Hollin Farm Shop keeps a bigger share of its sales. The percentages make that difference clear, so gross profit margin is useful for comparing product lines within one business or for comparing rival firms in the same industry, where cost structures are similar.
Writing your answer
A gross profit margin is always an answer in percentage form, so multiply by 100 rather than leaving the decimal. If a question asks for a set number of decimal places, give exactly that many, rounding correctly.
Net profit margin expresses net profit as a percentage of sales revenue. It shows how much of each pound of sales revenue is converted into net profit after other operating expenses and interest have been deducted.
Net profit margin (%) = (net profit ÷ sales revenue) × 100. You must memorise this formula. A higher margin suggests the business converts sales into net profit more efficiently and controls its costs more tightly.
Worked example
Riverside Cycles has sales revenue of £250,000 and net profit of £18,000. Net profit margin = (£18,000 ÷ £250,000) × 100 = 7.2%. This means 7.2p of every £1 of sales becomes net profit.
Gross and net margins
A high gross profit margin does not guarantee a high net profit margin, because other operating expenses and interest may still be high. For example, a business with sales revenue of £600,000 and gross profit of £240,000 has a gross profit margin of 40%. If other operating expenses and interest total £180,000, net profit is £60,000, so the net profit margin is only 10%. Most of the gross profit has been used up by other operating expenses and interest.
Give a net profit margin as a percentage. If a question asks for a certain number of decimal places, round to exactly that many.
The average rate of return (ARR) measures how profitable an investment or capital project is expected to be. It shows the average annual profit as a percentage of the money spent to set the project up, so you can judge whether a project is worth the money it costs.
The formula
ARR (%) = (average annual profit ÷ cost of investment) × 100
The cost of investment is the initial amount the project costs to start, such as the price of a new refrigerated van. Average annual profit is the total profit the project is expected to make over its whole life, shared out evenly across the years:
Average annual profit = total profit ÷ number of years
- Find the total profit over the project's life.
- Divide it by the number of years to get the average annual profit.
- Divide that by the cost of investment.
- Multiply by 100 to turn it into a percentage.
Worked example
A farm shop spends £80,000 on a new cold storage room. It expects the room to make £128,000 of profit in total over 8 years.
- Average annual profit = £128,000 ÷ 8 = £16,000
- ARR = (£16,000 ÷ £80,000) × 100 = 20%
Write the final answer as a percentage, such as 20%, not as a money amount. If a question asks for a set number of decimal places, round to exactly that many: 27.55% to one decimal place is 27.6%.
Using ARR to make decisions
The higher the ARR, the more profitable the investment is expected to be for each pound spent. A business can compare the figure with a target return it has set, or with the ARR of rival projects, and pick the one offering the best return.
ARR is only an estimate because it uses forecast profits. The real return may differ, and a business may still choose a project with a lower ARR if it brings other benefits, such as faster production or a stronger reputation.
Looking at profit as a money amount can mislead you when businesses are different sizes. A £22,500 profit sounds stronger than a £14,400 profit, but it depends on the sales revenue needed to earn it. A percentage such as a profit margin shows profit relative to sales revenue, so it allows a fairer comparison.
| Business | Net profit | Sales revenue | Net profit margin |
|---|---|---|---|
| Harbour Sports | £22,500 | £180,000 | 12.5% |
| Willow Crafts | £14,400 | £57,600 | 25% |
Willow Crafts earns less profit in money terms, but it keeps 25p of net profit from every £1 of sales, compared with 12.5p for Harbour Sports. Relative to its sales, Willow Crafts is more profitable.
Money amounts and percentages
Gross profit and net profit are money amounts. Gross profit margin, net profit margin and average rate of return are percentages. A money figure tells you size; a percentage tells you the rate or proportion. You need both to judge performance fairly. Average rate of return does the same job for investments: it expresses the average annual profit as a percentage of the cost of the investment, so projects of different sizes can be compared.
Finding profit from a margin
If you know sales revenue and a margin, rearrange the margin formula: Profit = (margin ÷ 100) × sales revenue. For example, a stationery shop has sales revenue of £48,000 and a net profit margin of 15%. Net profit = 0.15 × £48,000 = £7,200.
Being able to switch between money and percentage forms helps you interpret financial data and answer questions that ask you to compare performance.
Every business calculation sits inside a scenario — a garden centre, a phone repair shop or a small bakery — so read the question twice and pick out only the figures you need, along with their labels. Financial data often arrives in a table or a short extract: sales revenue, cost of sales, other operating expenses and interest, total profit, the number of years the project lasts and the cost of investment. In an investment question the lifespan and cost may be buried in the sentences rather than the table, so note them down with their labels before you choose a formula.
Show your workings
A calculator is allowed, but write the formula and the figures you put into it. Correct workings can still earn credit when the final number goes wrong — a two-mark calculation usually gives one mark for the right formula or correctly substituted figures and one mark for the right answer. For example, writing (42,000 ÷ 140,000) × 100 shows an examiner exactly what you did, and they can follow it even if you press a key wrongly.
Units and rounding
Match the unit used in the question. A profit or revenue answer, or the cost of an investment, is money, written in the same currency unit as the data. A margin or average rate of return answer is a percentage, so remember to multiply by 100 before writing it — 0.3 is not the same answer as 30%. If the question asks for a set number of decimal places, give exactly that many digits after the point and round the last digit correctly.
Finish with one clear final answer, in its unit, in the answer space: show your workings, then write something like “Gross profit margin = 30%” underneath, rather than leaving several scattered half-finished sums.