Appendix 3: Quantitative skills — Edexcel A-Level Business

Almost every judgement in this subject is a comparison, and this is how business makes comparisons fair. The change is the new value minus the original value, divided by the original value, then multiplied by one hundred, and the original value on the bottom is the part students lose marks on. The same arithmetic runs the margins, where gross profit divided by revenue and operating profit divided by revenue each give a percentage; it runs market growth and market share; and it runs both elasticities, since price elasticity of demand is the change in quantity demanded divided by the change in price, both expressed in percentage terms. A large rise on a tiny starting figure looks dramatic and means very little, which is exactly where the evaluation marks are earned.

Charts in this subject are evidence rather than decoration, and the credit is for what the picture tells the business. Bar charts compare categories such as sales by region, line graphs show a trend over time, pie charts show composition, scatter graphs suggest a relationship between two variables, and a break even chart puts total revenue and total costs on the same axes so the crossing point and the margin of safety can be read straight off. Interpretation means naming the trend, quoting an actual value from the axis and then saying what it implies for a decision. Watch the scale, because an axis that starts above zero exaggerates a small movement, and a correlation on a scatter graph is never proof that one variable caused the other.

An index rewrites a series as a comparison with a chosen starting point, which is set at one hundred, so movement can be read at a glance without wrestling with the underlying units. Each value is that period's figure divided by the base period figure and multiplied by one hundred, so a reading of one hundred and eighteen means eighteen per cent above base. Business uses indices for consumer prices, commodity and freight costs, share prices and export volumes, and the practical job is usually deflating: money sales growing faster than the price index have grown in real terms, and sales growing more slowly have shrunk. The trap is that a movement between two readings is measured against the earlier reading, not against the base.

These are the four figures a business is actually run on, and the whole set falls out of a handful of relationships. Total revenue is selling price multiplied by quantity sold, total cost is fixed cost plus variable cost per unit multiplied by output, and profit is the difference between the two. Contribution per unit is selling price minus variable cost per unit, and the output at which the firm covers everything is fixed costs divided by contribution per unit, an answer in units rather than in pounds. Fixed costs of sixty thousand pounds with a contribution of four pounds a unit give an answer of fifteen thousand units, and anything planned above that is the margin of safety. The model assumes all output is sold, costs behave in straight lines and price never moves, which is where evaluation starts.

Pearson wants three techniques and, far more heavily, the ability to say what each number tells a named firm. Payback counts the time until cumulative net cash inflow covers the initial outlay, the part year found by dividing the sum still outstanding by that year inflow and multiplying by twelve, and it answers a liquidity question rather than a profit one. Average rate of return takes average annual profit as a percentage of the outlay, so it can be set against the interest a bank pays or a target return in the extract. Net present value discounts each year inflow back to today money and takes the outlay off, giving a figure in pounds that supports investing when it is positive. All three rest on forecast cash flows, so the interpretation marks come from questioning the forecast rather than from the arithmetic.

Elasticity is examined as a reading rather than as a definition. Price elasticity of demand is the percentage change in quantity demanded over the percentage change in price, so it is normally negative and it is the size of the figure, sign ignored, that drives the decision: bigger than one means demand is responsive and a price rise cuts total revenue, smaller than one means demand is unresponsive and a price rise lifts it. Income elasticity of demand puts the percentage change in quantity demanded over the percentage change in real income; a positive figure marks a normal good, a negative one an inferior good, and a figure above one a luxury whose sales swing hard through a recession. Both guide pricing, promotion and the spread of the product range, and both assume every other influence holds still.

No decision in this qualification is settled by the table alone. The numerical side is the extract figures, ratios, forecasts, survey results and appraisal outcomes; the other side is everything numbers cannot carry, such as brand reputation, staff morale, supplier relationships, ethics, the objectives of the founder and the likely reaction of pressure groups. A strong answer weighs the two and then says which carries more weight here and why, using reliability as the lever: how old the data is, how big the sample was, who paid for it, and whether the forecast quietly assumes the market stands still. A decision tree shows the pattern neatly, because an expected value in pounds is only as sound as the probabilities somebody estimated, and the lower valued branch may still be chosen to protect a reputation.

The paper hands over evidence in three shapes and expects the same business judgement from each. A chart needs its axes read first: the units, whether the scale starts at zero, and whether the line plots sales or the rate of growth of sales, because a falling growth rate still means sales are rising. An index number needs its base year found before any comparison, since a reading of 112 says twelve per cent above the base and nothing else. A break even chart is read where total revenue crosses total cost, with the margin of safety measured as current output less break even output. Written extracts supply the context that decides which figure matters. Application marks come from putting the figure and the business into one sentence, not from describing the picture.