Quantitative skills contributing to the 10% minimum
- Syllabus
- 2017
- Topic
- —
- Level
- A2
Learning objectives
—QS1—Ratios, averages and fractionsCalculate, use and understand ratios, averages and fractions.—QS2—Percentages and percentage changesCalculate, use and understand percentages and percentage changes.—QS3—Standard graphical formsConstruct and interpret a range of standard graphical forms.—QS4—Index numbersInterpret index numbers.—QS5—Cost, revenue, profit and break-evenCalculate cost, revenue, profit and break-even.—QS6—Investment appraisalCalculate investment-appraisal outcomes and interpret the results.—QS7—Price and income elasticity of demandInterpret values of price elasticity and income elasticity of demand.—QS8—Quantitative and non-quantitative decisionsUse and interpret quantitative and non-quantitative information to make decisions.—QS9—Analysing business informationInterpret, apply and analyse information in written, graphical and numerical forms.
Ratios, fractions and averages keep the reference quantity visible
A ratio compares quantities measured on a compatible basis; a fraction expresses a part relative to a whole; an average summarises a set of observations. Before calculating, label the quantities and convert them to compatible units so that the result has a clear business meaning.
| Skill | Method | Interpretation check |
|---|---|---|
| ratio | write comparable quantities as a:b and simplify both by the same factor | state what each side represents |
| fraction | part ÷ whole | confirm the numerator belongs inside the denominator |
| arithmetic mean | sum of observations ÷ number of observations | retain the unit and check for unusual values |
| weighted average | sum of value × weight ÷ sum of weights | use when observations contribute unequally |
If three branches earn £120k, £150k and £180k, mean revenue is £450k ÷ 3 = £150k. If 30 of 120 workers are part-time, the fraction is 30/120 = 1/4 and the full-time:part-time ratio is 90:30 = 3:1.
Do not average percentages that describe unequal-sized groups unless the task permits it: use a weighted average. A ratio of 3:1 is not a fraction of 3/1; it means four equal parts in total, so the first quantity is 3/4 of the combined amount.
A percentage needs a base; percentage change needs the original base
A percentage is meaningful only when its base is identified. To find a percentage of an amount, multiply the total by percentage ÷ 100. To express a part as a percentage, calculate part ÷ whole × 100.
| Question | Calculation | Business meaning |
|---|---|---|
| amount from a percentage | percentage/100 × total | the monetary or physical part |
| percentage of a total | part/whole × 100 | the part's share of the chosen whole |
| percentage change | (new − original)/original × 100 | growth if positive; decline if negative |
Sales rise from £240,000 to £276,000. The change is £36,000, so percentage change = 36,000 ÷ 240,000 × 100 = 15%. If labour cost is 30% of the new sales total, labour cost = 0.30 × £276,000 = £82,800.
The original value is the denominator for percentage change, not the new value. Keep percentage points separate: a margin rising from 20% to 25% rises by 5 percentage points but by 25% relative to its original level. Always name the base before interpreting the answer.
A graph is valid only when its structure and change are explicit
Construct a graph so another reader can recover what was measured: give it a relevant title, label both axes with variables and units, choose an even scale, plot accurately and include a key when more than one series appears.
| Reading move | Question to answer |
|---|---|
| level | what value does the point, bar or curve show? |
| change | what is the absolute or percentage difference between two points? |
| pattern | is there growth, decline, fluctuation, correlation or a turning point? |
| comparison | which series is higher, faster-growing or more volatile on the same basis? |
| exception | is an anomaly changing the overall conclusion? |
In a supply-and-demand diagram, a subsidy that lowers producers' costs shifts supply to the right, other things equal. The new intersection normally has a lower equilibrium price and higher equilibrium quantity. State the shifted curve and direction before interpreting the new equilibrium.
A visual pattern is not automatically a causal relationship. Check the scale, time period, units, omitted observations and whether two series are genuinely comparable. A truncated vertical axis can exaggerate a small movement; a well-labelled graph should still be interpreted in its business context.
An index shows relative movement from a base of 100
An index number converts a series to a common base, usually 100, so relative movement is easy to compare. Index = current value ÷ base value × 100. The index has no physical unit because it expresses a relationship to the base.
| Index | Correct interpretation |
|---|---|
| 100 | equal to the base-period level |
| 125 | 25% above the base-period level |
| 80 | 20% below the base-period level |
| 150 then 165 | a 10% rise between these observations: 15/150 × 100 |
If a firm's base-year advertising spend is £40,000 and current spend is £46,000, the index is 46,000 ÷ 40,000 × 100 = 115. Current spending is therefore 15% above the base-year amount.
A 15-point rise in an index is not always a 15% rise: calculate the movement relative to the starting index. An index alone does not reveal the original cash amount, and two indexed series can be compared for relative change without showing which has the larger absolute value.
Cost, revenue, profit and break-even form one linked calculation
Keep output quantity consistent across the calculation. Total revenue = selling price × quantity. Total variable cost = variable cost per unit × quantity. Total cost = fixed cost + total variable cost, and profit = total revenue − total cost.
| Measure | Calculation | Use |
|---|---|---|
| contribution per unit | price − variable cost per unit | amount each unit contributes to fixed cost and profit |
| total contribution | contribution per unit × quantity | fixed-cost coverage at the chosen output |
| break-even output | fixed cost ÷ contribution per unit | output at which total revenue equals total cost |
| margin of safety | actual or forecast output − break-even output | output that can be lost before a loss begins |
At a price of £30, variable cost of £18 and fixed cost of £24,000, contribution is £12 per unit and break-even output is 24,000 ÷ 12 = 2,000 units. At 2,500 units, profit is total contribution £30,000 minus fixed cost £24,000 = £6,000.
Do not divide fixed cost by selling price: break-even depends on contribution. The model assumes the relevant selling price, unit variable cost and fixed cost remain valid over the output range; capacity limits, stepped costs or changing demand can weaken the forecast.
Payback, ARR and NPV answer different investment questions
Investment appraisal compares a project's initial outlay with its expected cash flows or profit. Use the method requested, show the time basis and then interpret the result rather than treating one calculation as a complete decision.
| Method | Procedure | Interpretation |
|---|---|---|
| payback | accumulate net cash inflows until the outlay is recovered; use the fraction of the next period if needed | shorter payback improves liquidity and reduces exposure |
| ARR | average annual profit ÷ initial investment × 100 | compare the forecast accounting return with a target |
| NPV | sum each cash flow × its discount factor, including the negative initial outlay | positive NPV means discounted inflows exceed the outlay |
Payback emphasises timing but ignores cash flows after recovery. ARR includes profits across the project but ignores their timing. NPV recognises the time value of money, yet depends on forecast cash flows and the chosen discount rate.
Do not mix profit with cash flow or compare projects with inconsistent time periods. A positive NPV, high ARR or short payback supports a project only under the assumptions used; strategic fit, risk, capacity, employees and environmental consequences can alter the final judgment.
PED uses magnitude; YED uses sign and magnitude
Price elasticity of demand (PED) estimates responsiveness of quantity demanded to a price change: percentage change in quantity demanded ÷ percentage change in price. Its value is normally negative, so classification usually uses the absolute magnitude. Income elasticity of demand (YED) = percentage change in demand ÷ percentage change in income; its sign is essential.
| Measure | Value | Interpretation |
|---|---|---|
| PED | < 1 | |
| PED | > 1 | |
| YED > 0 | normal good; above 1 indicates income-elastic demand | |
| YED < 0 | inferior good; demand moves opposite to income |
If PED = −1.5 and price rises by 4%, estimated quantity demanded falls by about 6%, other things equal. If YED = 0.6 and income rises by 5%, demand is estimated to rise by about 3%. State the direction, size and business implication.
Do not discard the sign of YED, and do not call PED of −0.4 elastic because it is negative. Elasticity estimates depend on the observed range, time period and other conditions; they support pricing and forecasting but do not guarantee an exact outcome.
A decision needs numbers, conditions and non-quantitative consequences
Quantitative information expresses measurable scale, cost, return or risk. Non-quantitative information captures factors that may resist reliable measurement, such as employee capability, customer trust, strategic fit or environmental impact. Sound decisions use both forms in the same context.
| Evidence type | Examples | Required check |
|---|---|---|
| quantitative | sales, cost, cash flow, market share, elasticity, NPV | source, units, time period, comparability and forecast assumptions |
| non-quantitative | quality, culture, ethics, reputation, stakeholder response | relevance, credibility, affected groups and possible bias |
| decision condition | objective, finance, time horizon, risk tolerance | whether evidence addresses the actual constraint |
Define the decision and success criterion; compare the relevant numerical outcomes; expose the assumptions and uncertainty; add non-quantitative effects on stakeholders and implementation; then make a conditional recommendation. Explain what new evidence could change it.
Numbers are not automatically objective: forecasts can embed selective assumptions, while non-quantitative evidence can still be systematic and important. Do not list pros and cons without weighting them. A higher calculated return may be rejected when finance, risk, ethics or implementation makes it unsuitable.
Analyse business information by building one evidenced causal claim
Business information may be written, graphical or numerical, but analysis uses the same discipline: identify the issue, extract relevant evidence, apply it to the named business and explain a causal chain from the evidence to an outcome.
| Step | Action |
|---|---|
| orient | identify the business, decision, period and units |
| extract | select a relevant statement, plotted value, pattern or number |
| process | calculate a comparable figure where useful and show the method |
| apply | connect the evidence to the firm's objective, constraint or stakeholder |
| analyse | explain cause → immediate effect → business consequence |
| qualify | test an assumption, limitation, alternative factor or time horizon |
If a graph shows unit sales rising 8% while a written source reports a 12% price cut, do not merely repeat both figures. Explain how the lower price may have increased demand, then test whether the sales response is large enough to support revenue and whether competitor action or capacity changes the outcome.
Description reports what the source shows; analysis explains why it matters. Do not force every number into the answer, infer causation from correlation or compare mismatched bases. A justified conclusion should follow the evidence and remain conditional where information is incomplete.