Business calculations: profit margins and ARR
Gross profit and gross profit margin (recap and extension)
Gross profit = Revenue − Cost of goods sold (COGS)
Gross profit margin (GPM) % = (Gross profit ÷ Revenue) × 100
The GPM tells you the percentage of each pound of revenue remaining after paying for the direct costs of the goods/services sold (raw materials, manufacturing labour, direct distribution costs).
Example: A clothing retailer has revenue of £180,000 and COGS of £108,000. Gross profit = £180,000 − £108,000 = £72,000. GPM = (72,000 ÷ 180,000) × 100 = 40%.
Interpretation: 40p of every £1 of revenue remains after paying for the clothes themselves. This 40p must then cover rent, staff wages, marketing, and all other overheads.
Net profit and net profit margin
Net profit = Gross profit − Other operating expenses (overheads: rent, salaries, utilities, marketing, depreciation)
Net profit margin (NPM) % = (Net profit ÷ Revenue) × 100
Continuing the example: Operating expenses = £48,000. Net profit = £72,000 − £48,000 = £24,000. NPM = (24,000 ÷ 180,000) × 100 = 13.3%.
Interpretation: after ALL costs, the retailer keeps 13.3p per £1 of revenue as profit.
GPM vs NPM: if GPM stays stable but NPM falls, the problem is rising overheads (not COGS). If GPM falls, the business is paying more for its inputs relative to its selling price.
Average Rate of Return (ARR)
ARR is an investment appraisal method that calculates the average annual profit generated by an investment as a percentage of the initial investment.
ARR (%) = (Average annual profit ÷ Initial investment) × 100
Where:
Average annual profit = Total profit over lifetime ÷ Number of years
And:
Total profit = Total revenue from investment − Initial investment cost
Worked example: FreshJuice Ltd invests £50,000 in a new juice-pressing machine. Over 5 years, the machine generates total revenue of £95,000 (before costs). The cost of goods processed in that time (materials, power, maintenance) is £20,000. So:
Net inflows over 5 years = £95,000 − £20,000 = £75,000. Total profit = £75,000 − £50,000 = £25,000. Average annual profit = £25,000 ÷ 5 = £5,000. ARR = (5,000 ÷ 50,000) × 100 = 10%.
Interpretation: the machine returns 10% per year on the initial investment. Compare this to the interest rate on borrowing (if the machine was financed by a loan at 6%, ARR of 10% suggests the investment is worthwhile).
Using ARR to compare investments
A business can compare multiple investment options:
- Investment A: ARR = 12% — better annual return.
- Investment B: ARR = 8%.
If choosing on ARR alone, choose A. However, ARR ignores the timing of cash flows (£5,000 received in year 1 is worth more than £5,000 in year 5 due to the time value of money). This is a key limitation of ARR.
Limitations of ARR
- Ignores timing of cash flows: treats all years as equal; does not account for the time value of money.
- Uses profit, not cash flow: profit and cash flow differ (depreciation, payment timing).
- Does not account for risk: a 10% ARR on a high-risk project is not directly comparable to a 9% ARR on a safe one.
- Assumption of stable returns: in reality, annual returns fluctuate.
Common calculation mistakes
- Forgetting to deduct the initial investment when calculating total profit: don't divide total inflows by years — first subtract the initial investment to find total profit.
- Using total profit (not average annual profit) in the ARR formula: the formula requires annual average.
- Dividing GPM by costs instead of revenue: always divide by revenue.
AI-generated · claude-opus-4-7 · v3-edexcel-business