A percentage is a share of a whole, scaled to 100. To find one, divide the part by the whole and multiply by 100. In FY2025/26 Kettle & Crumb's cafés took £1,528,800 of its £1,800,000 revenue: 1,528,800 ÷ 1,800,000 × 100 = 84.9%. The whole you divide by is the base, and most percentage mistakes are really base mistakes. Before you trust any percentage, ask: a percentage of what?

Percentage change compares a new figure with an old one, and the base is always the old figure: (new − old) ÷ old × 100. Kettle & Crumb's revenue went from £1,620,000 in FY2024/25 to £1,800,000, so the change is (1,800,000 − 1,620,000) ÷ 1,620,000 × 100 = 11.1%. Because the base moves, rises and falls do not cancel out. A price that rises 10% from £5.00 to £5.50 and then falls 10% ends at £4.95, not £5.00, because the fall is 10% of the larger figure.

Percentage points are for comparing two percentages. Suppose a campaign's sign-up rate rises from 20% to 25%. That is a rise of 5 percentage points, and also a 25% increase (5 ÷ 20 × 100). Both are true, but they answer different questions, and writers tend to pick whichever sounds bigger. A careful reader checks which one is meant; a careful writer always says.

Growth compounds: each year's percentage applies to the previous year's larger figure. £100,000 growing 10% a year becomes £110,000 after one year, £121,000 after two and £133,100 after three. "10% a year for three years" is a 33.1% rise, not 30%.

Three more traps catch people often. First, averaging percentages: a small shop growing from £10,000 to £15,000 (50%) and a large one staying at £90,000 (0%) have not grown by 25% between them; together they went from £100,000 to £105,000, which is 5%. Second, a percentage with no base: "sales are up 30%" means little until you know from what, since when and whose sales, as the Peak Pantry buyer's email showed. Third, big percentages of small numbers: doubling from two customers to four is a 100% rise, and still only four customers.

A correctly worded statement says what changed, from what, to what, over what period and in which unit: "Kettle & Crumb's revenue rose by 11.1%, from £1,620,000 in FY2024/25 to £1,800,000 in FY2025/26." Nobody can misread that.

Costs behave in two ways. Variable costs rise and fall with each sale: ingredients, packaging, delivery fuel. Fixed costs stay much the same in a period however much is sold: rent, salaried staff, insurance, a van lease. Real costs are not always so tidy (a busy week may need extra shifts), but the split is close enough for most marketing decisions.

Contribution is the selling price minus the variable costs of that sale. It is what each sale contributes, first towards the fixed costs and then, once they are covered, towards profit. For a £5.00 Kettle & Crumb café sale with £1.60 of ingredients and packaging, contribution is £5.00 − £1.60 = £3.40. The contribution ratio is contribution as a share of the price: £3.40 ÷ £5.00 = 68%. Here it matches the 68% gross margin you met in the profit and loss account in Module 1, because ingredients and packaging are the only variable costs of a café sale. When other costs also vary with sales, such as delivery fuel, the two figures part company.

Margin and markup use the same profit but divide it by different bases. Margin divides by the selling price: £3.40 ÷ £5.00 = 68%. Markup divides by the cost: £3.40 ÷ £1.60 = 212.5%. Mixing them up is expensive. A manager who wants a 50% margin but adds a 50% markup to a £2.00 cost charges £3.00, and earns a margin of only £1.00 ÷ £3.00 = 33.3%. Whenever someone quotes "our margin", ask whether they divided by price or by cost.

Why should marketers think in contribution rather than revenue? Because marketing decisions change how much is sold, and every extra sale adds its contribution, not its price, to profit. Discounts show this most sharply. A 50p discount on a £5.00 sale takes 10% off the price but the whole 50p off contribution, cutting it from £3.40 to £2.90: a loss of 0.50 ÷ 3.40 = 14.7% of what each sale contributed. To earn the same total contribution, sales must rise by 3.40 ÷ 2.90 = 1.172, so about 17.2% more transactions just to stand still. And some of the discounted sales would have happened at full price anyway. The lower a product's contribution ratio, the more volume a discount needs to pay for itself.

Every option has fixed costs that must be paid whatever happens, and every sale chips in its contribution towards them. Break-even is the point where total contribution exactly covers the fixed costs, so profit is zero. Below it the option loses money; above it every sale adds its contribution to profit.

Break-even volume = fixed costs ÷ contribution per unit. A fourth café in Hillsborough (Option A) would cost £221,000 a year to run in rent, staff and other fixed costs. Each £5.00 transaction contributes £3.40, so the café breaks even at 221,000 ÷ 3.40 = 65,000 transactions a year, or 65,000 ÷ 52 = 1,250 a week.

When you know revenue but not units, as with a wholesale contract, use the contribution ratio instead. Break-even revenue = fixed costs ÷ contribution ratio. If extra fixed costs are £38,000 and 40p of every pound of sales is contribution, break-even is 38,000 ÷ 0.40 = £95,000 of sales a year.

Break-even says nothing about whether an option will get there, so compare it with the forecast. Annual profit = expected contribution − fixed costs. The margin of safety shows how far sales could fall short before the profit disappears: (expected sales − break-even sales) ÷ expected sales. Dan forecasts 1,500 transactions a week for Option A, so its margin of safety is (1,500 − 1,250) ÷ 1,500 = 16.7%. Sales could fall about a sixth short of his forecast before the café loses money. A small margin of safety means an ordinary forecasting error could wipe out the profit.

Simple payback = set-up investment ÷ annual profit. It tells you roughly how long the money spent up front is at risk. A £180,000 fit-out repaid from £44,200 a year takes 180,000 ÷ 44,200 = 4.07 years, about 4.1.

These are deliberately simple models, so say what they leave out. They assume the forecast is reached from the first week, when a new outlet may take months to build trade. They ignore the timing of cash: the fit-out is paid before the first coffee is sold. They treat every cost as neatly fixed or variable. And payback ignores risk and the time value of money, the idea that a pound in four years' time is worth less than a pound today; methods such as net present value, taught in finance courses, deal with that. None of this makes the simple numbers useless. It makes them a first, honest test: an option that fails here rarely improves under more careful methods.

Many of the numbers marketers are judged on are about customers rather than products. Customer acquisition cost (CAC) is the marketing and sales spend needed to win one new customer: spend ÷ new customers won in the same period. Take a hypothetical gym, invented for this lesson, that spends £3,000 on a campaign and wins 60 new members: its CAC is 3,000 ÷ 60 = £50. Count only customers who are genuinely new, and only the spend that went on winning them.

Winning a customer is only the start. Retention is the share of customers at the start of a period who are still customers at the end; churn is the share who leave. They drive how long a customer stays. As a rough rule, if a steady 25% of members leave each year, the average member stays about 1 ÷ 0.25 = 4 years.

Customer lifetime value (CLV) puts these together: the profit a business expects from a customer over the whole relationship. A simple estimate is average spend × purchases a year × margin × years as a customer. For a Kettle & Crumb loyalty-app member, Dan assumes 1.2 visits a week at £5.00 and a three-year average membership. That gives £5.00 × 1.2 × 52 = £312 of spending a year; × 0.68 gross margin = £212.16 of gross profit a year; × 3 years = £636.48, or about £636.

Notice what kind of estimate that is. It uses gross margin, so it is profit before staff, premises and other overheads. It uses revenue × margin, not revenue alone: the same member's spending over three years is £936, which would flatter the figure. And it has no discounting: a pound earned in year three is counted the same as a pound today. Fuller CLV models discount future profit and vary retention year by year; this simple version is honest as long as you say it is simple and list its assumptions.

The point of CLV is comparison. Set it against CAC and you know roughly how much you can afford to spend to win a customer: if a typical member is worth about £636 of gross profit over three years, spending £50 to win one may be worthwhile, while spending £700 would not. The catch is that new customers may not behave like your most loyal ones, so check whose behaviour the assumptions describe.

CAC, retention and CLV make good KPIs of the kind you set in Module 2. Retention is a leading indicator: it moves before lifetime value does, so a fall in retention warns you early.

Numbers persuade, so they must be presented in a way that cannot mislead, even by accident.

Start with averages. The mean adds everything up and divides by the count; the median is the middle value when everything is put in order. One extreme value, an outlier, can drag the mean a long way. Five orders of £3, £4, £4, £5 and £34 have a mean of £10 but a median of £4, and £4 describes the typical order far better. When a few large values are possible, give the median, or give both and say why they differ.

Choose the chart for the question. Bars compare separate things, such as two options side by side. Lines show change over time, such as revenue by month. A table is better than any chart when the reader needs exact figures. Keep pie charts for a few parts of one whole, if you use them at all.

Watch the axis. A bar chart whose value axis starts at £1,500,000 rather than zero makes revenue of £1,620,000 and £1,800,000 look as if revenue grew two and a half times, when the real rise is 11.1%: the visible parts of the bars are £120,000 and £300,000 tall. Tufte (1983) called the ratio between the size of an effect shown in a graphic and its size in the data the "lie factor"; an honest chart keeps it close to 1. Bars should start at zero. Line charts may zoom in, but label the axis clearly.

Round consistently, and only as precisely as the inputs deserve. CLV of £636.48 suggests a precision that a three-year assumption cannot support; £636, or "about £640", is honest. Keep full figures in your working, show percentages to one decimal place throughout, and check that rounded shares still add up to 100%.

Then state your assumptions, each with its source: "1,500 transactions a week (Dan's assumption, about 77% of the existing café average)". Finally, run a sensitivity test: change one key assumption at a time and see what happens to the answer. If Option A sells 20% fewer transactions than forecast, 1,200 a week, its contribution is 1,200 × 52 × £3.40 = £212,160, less £221,000 of fixed costs: a loss of £8,840. If Option B earns 20% less revenue, £120,000, its contribution is £48,000, less £38,000: still a profit of £10,000. The margins of safety predicted this, since 20% is more than Option A's 16.7% and less than Option B's 36.7%. A decision-maker can see that risk in one line.