Calculation
- Syllabus
- 2026
- Topic
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- Level
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Learning objectives
—Percentages and percentage changesCalculate and use percentages and percentage changes in business contexts.—AveragesCalculate and use averages in business contexts.—Revenue, costs and profitCalculate revenue, costs and profit in business contexts.—Gross and net profit marginsCalculate gross profit margin and net profit margin ratios in business contexts.—Average rate of returnCalculate average rate of return in a business context.—Cash-flow forecast calculationsCalculate total costs, total revenue and net cash flow within cash-flow forecasts.
Calculate a percentage and the direction of change
A percentage expresses a part relative to a whole. Percentage change compares the change with the original value, so the original—not the new value—is the denominator.
percentage=part/whole×100;percentagechange=(newvalue−originalvalue)/originalvalue×100
| Task | Direct route | Worked result |
|---|---|---|
| find 70% of 43,000 employees | 43,000 × 0.70 | 30,100 employees |
| add 3% to £23,546 | £23,546 × 1.03 | £24,252.38 |
| reduce 285 by 12% | 285 × 0.88 | 250.80 |
| change from 4.7m to 4.9m | (4.9 − 4.7) ÷ 4.7 × 100 | about 4.26% increase |
State whether the result is a percentage amount, a new total or a percentage change. Keep currency/people/volume units, show substitution and round only at the end to the requested precision.
A 15% discount means pay 85% of the original price. Percentage-point change differs from percentage change: a rate moving from 20% to 25% rises by 5 percentage points but by 25% relative to 20%.
Choose an average that answers the business question
An average summarises several observations as one representative value. In most calculation questions, the arithmetic mean is total of the values divided by the number of values; identify what is being averaged and keep its unit.
mean=sumofallvalues/numberofvalues
If 9,000 vehicles are sold across 6 showrooms, average sales = 9,000 ÷ 6 = 1,500 vehicles per showroom. The denominator is showrooms, not vehicles or years.
| Measure | Useful when | Limitation |
|---|---|---|
| mean | every value should contribute to a total-per-item result | extreme values can pull it away from a typical case |
| median | the middle value is needed and extremes are misleading | ignores the size of values away from the middle |
| mode | the most frequent category/value matters, such as popular size | may be absent or more than one mode |
Use the average with spread, time period and sample context. Two shops can have the same mean sales but very different consistency, so an average alone may hide operational risk.
Do not average percentages or ratios blindly when their group sizes differ; combine the underlying totals or use an appropriate weighted mean. Always name the denominator and unit.
Build revenue, cost and profit from the same activity
Revenue is income from sales; costs are resources used; profit or loss compares both for the same period and activity. Keep fixed and variable costs separate before forming total cost.
revenue=sellingpriceperunit×quantitysold;totalvariablecost=variablecostperunit×quantity;totalcost=fixedcost+totalvariablecost;profit=revenue−totalcost
| Given | Calculation | Result |
|---|---|---|
| fixed costs £1,150,000 | — | £1,150,000 |
| variable costs £4,250,000 | — | £4,250,000 |
| total cost | 1,150,000 + 4,250,000 | £5,400,000 |
| revenue | — | £4,850,000 |
| result | 4,850,000 − 5,400,000 | −£550,000: loss £550,000 |
A profit can rise because price or quantity raises revenue by more than added cost, or because cost falls without a larger revenue loss. Separate the arithmetic from the business explanation.
Cash inflow is not automatically revenue, and cash outflow is not automatically cost for the same period. Profit is an accounting result; it is not the closing cash balance.
Convert profit into a comparable margin
A profit margin shows profit earned from each 100 of revenue, allowing businesses or periods of different size to be compared. Use the profit line named in the question and revenue from the same period.
grossprofit=revenue−costofsales;grossprofitmargin=grossprofit/revenue×100;netprofitmargin=netprofit/revenue×100
| Statement data | Calculation | Result |
|---|---|---|
| revenue £200,000; cost of sales £120,000 | gross profit = 200,000 − 120,000 | £80,000 |
| gross margin | 80,000 ÷ 200,000 × 100 | 40% |
| net profit £30,000 | 30,000 ÷ 200,000 × 100 | 15% |
The gross margin reflects pricing and direct/cost-of-sales control; the net margin also reflects further expenses included before net profit. Compare like definitions, periods and business models, then inspect the underlying figures before explaining a change.
Do not divide profit by cost: that produces a markup/return measure, not a profit margin. The specification's formula appendix labels operating profit margin separately; when a question asks net profit margin, use the exact net-profit line and formula supplied for that task.
Calculate the annual return on an investment
Average rate of return (ARR) expresses average annual profit as a percentage of the initial investment. First calculate profit over the whole project, then convert it to an annual average.
totalprofit=totalreturns−initialinvestment;averageannualprofit=totalprofit/projectyears;ARR=averageannualprofit/initialinvestment×100
| Five-year project | Calculation | Result |
|---|---|---|
| initial investment | — | £100,000 |
| total returns | — | £150,000 |
| total profit | 150,000 − 100,000 | £50,000 |
| average annual profit | 50,000 ÷ 5 | £10,000 |
| ARR | 10,000 ÷ 100,000 × 100 | 10% |
A higher ARR may indicate a stronger accounting return, but compare projects using consistent assumptions and consider risk, cash timing, finance, strategic fit and the required return.
ARR uses average annual profit, not total return, total profit or one year's cash inflow. It does not show when cash arrives or discount future money, so it cannot decide an investment alone.
Complete each cash-flow forecast period in order
A cash-flow forecast tracks expected cash moving into and out of a business by period. Add every row once, preserve the sign and carry each closing balance forward as the next period's opening balance.
totalcashinflow=sumofinflows;totalcashoutflow=sumofoutflows;netcashflow=totalinflow−totaloutflow;closingbalance=openingbalance+netcashflow
| One month | Amount (£) |
|---|---|
| opening balance | 20,000 |
| total cash inflow | 28,000 |
| total cash outflow | 56,000 |
| net cash flow | 28,000 − 56,000 = −28,000 |
| closing balance | 20,000 + (−28,000) = −8,000 |
Within the forecast, total revenue/cash sales and total costs are calculated by summing the relevant forecast rows or by the unit relationships provided. Classify each figure before adding it; do not count a subtotal again.
A negative net cash flow means outflows exceed inflows in that period; a negative closing balance means the accumulated cash position is below zero. Use forecast patterns to plan timing, finance or payments, while testing assumptions against actual results.
Net cash flow is not profit, and a negative monthly net flow does not automatically mean the closing balance is negative if the opening balance is large enough. Forecasts are estimates whose timing and values can differ from reality.