IB Business Management

1. Break-even: the arithmetic and the judgement

Learning goal: Calculate break-even output and decide what it means.

Break-even analysis finds the level of output at which total revenue equals total costs, so profit is zero. Fixed costs, such as rent, do not change with output in the short run. Variable costs, such as materials, rise with each unit made. Contribution per unit is the selling price minus the variable cost per unit. Break-even output equals fixed costs divided by contribution per unit.

Margin of safety is the gap between actual (or planned) output and break-even output. A large margin means sales can fall a long way before the firm makes a loss. A small margin means the firm is exposed to a fall in demand. To find profit at any output, multiply output by contribution per unit and subtract fixed costs. A change in price or variable cost changes contribution, so it moves the break-even point.

The method has limits that an evaluation should name. It assumes that all output is sold, that the price stays constant at every level of output, and that variable cost per unit is constant. In real firms, discounts for large orders, rising wages and wasted stock break these assumptions. Fixed costs are also fixed only within a range of output; a new factory raises them in steps. For a new product the forecast of sales is a guess, so the result is only as good as the forecast.

Use the result to support a decision, not to make it alone. If break-even output is 2 000 units and market research suggests that sales will be 1 500, the plan looks risky, and a manager may look at raising the price or cutting costs. If the firm is already above break-even, the question changes to how far it can lower the price to win customers. Always state the assumption, calculate, then judge. All figures in these exercises are invented teaching numbers.

Worked example

A firm has fixed costs of 12 000 dollars, a price of 20 dollars and variable cost of 8 dollars. Find break-even output.

1. Contribution = 20 - 8 = 12.
2. Break-even = 12 000 / 12.
3. = 1 000 units.
4. If sales are 1 400, margin of safety = 400 units.

Mental model: Break-even equals fixed costs divided by contribution.

Common trap: Dividing by price instead of contribution.

2. Profit margins: gross, net and what the gap tells you

Learning goal: Calculate margins and interpret differences.

Profit has several levels. Gross profit is revenue minus cost of sales, the direct cost of the goods sold. Operating profit is gross profit minus overheads such as rent, wages and marketing. Net profit is what is left after interest and tax. Each level answers a different question, so the margins at each level help to find where a business is strong or weak.

A margin is a profit divided by revenue and multiplied by 100. Gross profit margin = gross profit / revenue x 100. Net profit margin = net profit / revenue x 100. A gross margin of 40 percent means that 40 cents of each dollar of sales remain after paying for the goods. The gap between gross and net margin shows how much the overheads, interest and tax take.

Interpretation needs a comparison. A margin means little alone. Compare it with last year, with a competitor in the same industry, or with a target. A supermarket often has a low margin and high volume, while a luxury brand has a high margin and low volume, so a margin should not be compared across very different industries. If gross margin falls while net margin falls by the same amount, the cause is likely the cost of sales. If gross margin is steady but net margin falls, look at overheads.

Possible actions follow from the diagnosis. To raise gross margin, a firm can raise prices, find cheaper suppliers or change the product mix. To raise net margin, it can control overheads, refinance debt or improve efficiency. Each action has a risk: a higher price may lower sales, and a cheaper supplier may lower quality. Margins are also affected by accounting choices, so say what the data cannot show. All numbers here are invented.

Worked example

Revenue is 200 000, cost of sales 120 000 and net profit 30 000. Find gross and net margin.

1. Gross profit = 80 000.
2. Gross margin = 80 000 / 200 000 = 40 percent.
3. Net margin = 30 000 / 200 000 = 15 percent.

Mental model: Divide gross profit by revenue.

Common trap: Margin is profit divided by revenue.

3. Return on capital: efficiency, not just size

Learning goal: Calculate and interpret ROCE.

Return on capital employed (ROCE) measures how well a firm uses the money invested in it. ROCE = operating profit / capital employed x 100. Capital employed is equity plus non-current liabilities, which is the long-term funding of the business. A firm with a large profit may still be inefficient if it needed a very large investment to earn it.

Consider two firms. One earns 50 000 on 500 000 of capital, so ROCE is 10 percent. The other earns 30 000 on 200 000, so ROCE is 15 percent. The first firm has the larger profit, but the second uses capital more effectively. This is why profit alone is a poor measure of performance and ROCE is used for comparing firms or years.

To interpret ROCE, compare with the cost of borrowing and with alternatives. If a firm can borrow at 6 percent and earns 12 percent on the money, expansion looks sensible. If ROCE is below the interest rate, then growth funded by debt will reduce value. Compare also with competitors in the same industry and with the firm's own trend. A falling ROCE can result from lower profit or from a rising capital base without extra profit yet.

Ways to improve ROCE are to raise operating profit, for example by cutting costs or raising prices, or to reduce capital employed, for example by selling unused assets. Note the limits: ROCE uses accounting values that may be out of date, new investment may take time to pay back, and a short-term focus on ROCE may cut spending that builds future profit. All figures in the exercises are invented.

Worked example

Operating profit is 45 000. Capital employed is 300 000. Find ROCE.

1. ROCE = 45 000 / 300 000 x 100.
2. = 15 percent.

Mental model: Profit divided by capital employed.

Common trap: ROCE = operating profit / capital employed x 100.

4. Liquidity: can the business pay its bills?

Learning goal: Use current and acid-test ratios.

Liquidity is the ability of a firm to pay its short-term debts when they fall due. A profitable firm can still fail if it runs out of cash. The current ratio = current assets / current liabilities. Current assets include cash, receivables and inventory; current liabilities include payables and short-term loans. It is often written as a ratio such as 1.5 : 1.

The acid-test ratio removes inventory, because stock may be slow to sell. Acid-test ratio = (current assets - inventory) / current liabilities. It is a stricter test. A firm with a current ratio of 2 but an acid-test ratio of 0.6 holds most of its assets as stock, so it may struggle to pay bills quickly if the stock does not sell. A textbook guide is a current ratio of 1.5 to 2 and an acid-test ratio of at least 1, but the right level depends on the industry.

Industry matters. A supermarket gets cash daily and sells stock fast, so it can run with a low ratio. A shipbuilder has slow cash inflows and needs a higher one. Compare with the same firm over time and with competitors. A very high ratio is not always good, because it can mean cash and stock sit idle instead of being invested.

Ways to improve liquidity include collecting receivables faster, negotiating longer payment terms with suppliers, reducing stock, selling unused assets, or taking a long-term loan instead of a short-term one. Each has a cost: faster collection may upset customers, and a long-term loan adds interest. Ratios use the balance sheet date, so they are a snapshot and can be affected by seasonal trade. All figures here are invented.

Worked example

Current assets 90 000, inventory 40 000, current liabilities 50 000. Find both ratios.

1. Current = 90 000 / 50 000 = 1.8.
2. Acid test = 50 000 / 50 000 = 1.0.

Mental model: Remove inventory first.

Common trap: Acid test = (CA - inventory) / CL.

5. Investment appraisal: payback with partial years

Learning goal: Calculate payback period and judge the limits of the method.

Investment appraisal helps a firm decide whether a project is worth the money. The payback period is the time taken for the cash inflows to repay the initial cost. Add the yearly net cash flows until the total equals the investment. If the repayment happens part way through a year, work out the fraction: the remaining amount divided by that year's cash flow, multiplied by 12 for months.

Take an invented project: a machine costs 100 000 and returns 30 000, 40 000 and 50 000 in years 1, 2 and 3. After two years 70 000 is repaid. The remaining 30 000 is divided by year 3's 50 000, which gives 0.6 of a year. Payback is 2.6 years, or 2 years and about 7 months. Present months by multiplying the fraction by 12 and rounding.

Payback is popular because it is simple and favours quick returns, which suits a firm with cash problems or in a fast-changing market. Its limits matter. It ignores the cash flows after the payback date, so a project that earns heavily in later years may look worse than a quick but short-lived one. It also ignores the time value of money and the size of overall profit.

Use payback alongside other methods such as average rate of return and net present value in the syllabus. State what the firm wants: speed, profit, or low risk. Comparing two projects, the one with the shorter payback is not automatically better, because a longer project may have a much higher total return. All numbers are invented teaching values; the true cash flows are only forecasts and could be wrong.

Worked example

Cost 80 000. Cash flows are 20 000, 30 000, 40 000. Find the payback period.

1. After 2 years: 50 000 repaid.
2. Remaining 30 000 / 40 000 = 0.75.
3. Payback = 2.75 years.

Mental model: Add years until repaid.

Common trap: Use the remaining amount over the final year flow.

6. Decision trees: expected value and risk

Learning goal: Calculate expected value and weigh risk.

A decision tree maps a decision, the possible outcomes and their probabilities. Squares mark choices and circles mark chance events. Each outcome has a payoff, and each chance branch has a probability; the probabilities leaving one circle add up to 1. The expected value (EV) of a branch is the sum of each probability times its payoff.

To solve a tree, work from right to left. Calculate the EV at each chance node, then subtract the cost of the choice to get the net gain. Compare the net gains and choose the highest, unless risk changes the view. Take an invented example: launching a product costs 40 000, with a 0.6 chance of a 100 000 return and a 0.4 chance of a 20 000 return. EV = 0.6 x 100 000 + 0.4 x 20 000 = 68 000. Net gain = 68 000 - 40 000 = 28 000.

Expected value is an average over many repeats, not a promise for one decision. A choice with a high EV can have a chance of a large loss, which a small firm may not survive. Managers also weigh the best case and the worst case, and their attitude to risk. A risk-averse firm may choose a lower EV with a safer outcome.

Limits of the method: the probabilities are estimates, often from opinion or limited research, and a small change in them can change the answer. Payoffs may ignore non-financial factors such as reputation. The tree gives quantitative support for a decision but does not replace judgement. Test the result by asking how sensitive the choice is to the probabilities. All numbers are invented.

Worked example

Cost 10 000. Probability 0.5 of 30 000 and 0.5 of 6 000. Find net gain.

1. EV = 0.5 x 30 000 + 0.5 x 6 000 = 18 000.
2. Net gain = 18 000 - 10 000 = 8 000.

Mental model: Multiply each probability by payoff.

Common trap: EV = sum of p x payoff.

7. Price elasticity: sign, size and strategy

Learning goal: Calculate PED and use it to advise on price.

Price elasticity of demand (PED) measures how much the quantity demanded changes when price changes. PED = percentage change in quantity demanded / percentage change in price. Because price and demand normally move in opposite directions, PED is negative, though many courses quote the size only. State which you use.

If the size is greater than 1, demand is elastic: quantity changes by a larger percentage than price. If it is less than 1, demand is inelastic: quantity changes by a smaller percentage. A size of exactly 1 is unit elastic. Take an invented case: price rises 10 percent and quantity falls 25 percent. PED = -25 / 10 = -2.5, so demand is elastic.

The result guides pricing strategy. If demand is elastic, a price rise lowers revenue because the fall in quantity outweighs the higher price, and a price cut raises revenue. If demand is inelastic, a price rise increases revenue. Products with many substitutes, such as a branded snack, tend to be elastic; necessities with few substitutes, such as fuel for a commuter, tend to be inelastic, though the real value must be measured.

Limits of PED: it is estimated from past data, other factors such as income and competitors' prices change at the same time, and the value differs at different price levels and over time. Use it as one input. Advice should say what the figure implies for revenue, what could make it wrong, and what other marketing factors matter. All numbers are invented.

A final point is the time frame. Demand often responds slowly, so a price change may show only a small effect in the first weeks and a larger one months later. Advice should say over what period the PED was estimated.

Worked example

Price rises 5 percent. Quantity falls 15 percent. Find PED.

1. PED = -15 / 5 = -3.
2. Size 3 is greater than 1, so elastic.

Mental model: Divide the percentage changes.

Common trap: PED = %change quantity / %change price.

8. Labour turnover: measure, then diagnose

Learning goal: Calculate turnover and use it in a recommendation.

Labour turnover measures how many employees leave in a period. Labour turnover rate = number of employees who left during the year / average number of employees x 100. A firm with 12 leavers and an average of 80 staff has a rate of 15 percent. The measure is easy to calculate but says nothing about why people left.

High turnover has costs: recruitment and training, lost knowledge, lower morale and, in customer service, weaker customer experience. Some turnover is healthy because new staff bring fresh ideas and it helps firms to change. What counts as high depends on the industry; fast food has typically higher turnover than a law firm, so compare with the same sector and the firm's own trend.

To diagnose, look for evidence on causes. Exit interviews, staff surveys and pay comparisons help. Common causes are low pay, poor management, few promotion chances and dull work. Use the syllabus theories, such as Herzberg's hygiene and motivating factors, to link a cause to an action. If pay is a hygiene factor, a raise removes dissatisfaction but may not motivate; a role with more responsibility may motivate.

Recommend actions that fit the cause and cost, such as better induction, training, flexible hours or a pay review. Weigh the cost of the action against the cost of turnover, and say how you would check whether it worked, for example by measuring the rate again after a year. Be careful: turnover alone could be affected by the local job market. All numbers are invented.

Worked example

20 employees left. Average staff was 160. Find the rate.

1. 20 / 160 x 100 = 12.5 percent.

Mental model: Divide leavers by average staff.

Common trap: Rate = leavers / average staff x 100.

9. Capacity utilisation: efficiency and the cost of idle capacity

Learning goal: Calculate utilisation and recommend an operations response.

Capacity utilisation shows how much of a firm's maximum possible output is being used. Capacity utilisation = actual output / maximum capacity x 100. A factory that can make 10 000 units a month and makes 7 500 is working at 75 percent. The rest is idle capacity, which still carries fixed costs.

Because fixed costs are spread over the units made, a higher use of capacity lowers the fixed cost per unit. This is the link between utilisation and unit cost. With invented fixed costs of 60 000 a month, producing 6 000 units gives fixed cost of 10 per unit, and producing 10 000 units gives 6 per unit. Higher utilisation usually means lower average cost and a better chance of a profit.

But running near 100 percent is not always wise. There is little room for maintenance, a rush order or a breakdown, and staff can become tired, so quality may fall. Underuse has its own problems: idle capacity wastes money and may signal weak demand. A firm should compare its figure with a target, the industry and its trend.

Options when utilisation is low include finding new customers, cutting prices, subcontracting work for other firms, closing a plant or selling a machine. When utilisation is too high, the firm can add a shift, outsource, or invest in more capacity. Judge by cost, the time the effect takes, and whether demand is a lasting change or temporary. All numbers are invented.

Seasonal demand also matters. A firm that sells most of its output in four months of the year will show low utilisation for the rest, so an annual average can hide the problem. Look at monthly figures before choosing a response.

Worked example

Capacity 5 000 units, output 4 000 units. Find utilisation.

1. 4 000 / 5 000 x 100 = 80 percent.

Mental model: Divide fixed cost by output.

Common trap: Fixed cost per unit = fixed costs / output.

10. Cash-flow forecasts: timing is what sinks firms

Learning goal: Build and read a simple cash-flow forecast.

A cash-flow forecast predicts the cash coming in and going out month by month. Net cash flow = cash inflows - cash outflows. The opening balance of a month is the closing balance of the month before, and closing balance = opening balance + net cash flow. Profit and cash are different: a sale on credit is revenue now but cash later.

This is why profitable firms fail. A firm may sell 50 000 of goods in March but be paid in May, while wages, rent and suppliers must be paid in March. The forecast shows when a negative closing balance will occur, which gives time to arrange an overdraft, delay a payment or collect debts sooner. Take an invented case: opening balance 5 000, inflows 12 000, outflows 20 000. Net cash flow is -8 000 and closing balance is -3 000.

Read a forecast by looking for the first negative balance, the lowest point and the trend. Seasonal firms such as ice cream makers have big swings. Then match the remedy to the gap: a short gap suits an overdraft, a permanent gap needs a loan or a change in prices or costs. Always ask how reliable the inputs are, since forecasts for sales rely on estimates and can be wrong by a large amount.

Limits of forecasts: they depend on assumptions about sales, customer payment habits and costs, and unexpected events cause errors. A forecast should be updated often and compared with actual cash flow, which is called variance. Managers use the result to support decisions on credit terms, stock levels and borrowing. All figures here are invented teaching numbers.

Worked example

Opening 10 000, inflows 15 000, outflows 22 000. Find closing balance.

1. Net = 15 000 - 22 000 = -7 000.
2. Closing = 10 000 - 7 000 = 3 000.

Mental model: Add net cash flow to the opening balance.

Common trap: Closing = opening + inflows - outflows.

11. Stakeholders and ethics: who gains, who pays

Learning goal: Identify stakeholder interests and weigh an ethical decision.

Stakeholders are the people or groups affected by a business or with an interest in it. Internal stakeholders include owners, managers and employees. External ones include customers, suppliers, lenders, the government, local communities and pressure groups. Their interests differ: shareholders want profit, workers want pay and security, communities want low pollution.

Conflicts arise when a decision helps one group and harms another. Closing a factory may raise profit for owners but cost jobs and hurt the local community. A good analysis names the groups affected, says what each wants, and assesses their power and interest: powerful and interested groups, such as large customers or regulators, must be managed closely. A stakeholder map helps to organise this.

Ethics asks what is right, not only what is legal or profitable. A firm may use cheaper materials from a supplier with poor labour conditions. This lowers costs but damages reputation if discovered. Some firms adopt corporate social responsibility (CSR) to show care for society. CSR can cost money, but it may raise brand trust and help recruit staff, though the evidence for the size of the benefit varies.

When judging an ethical decision, give both sides with reasons, consider short and long run effects, and reach a conclusion. Avoid claims that cannot be checked. Use real information from the case study you are given. A balanced answer says which stakeholder is most affected, why, and what the firm could do to reduce harm, such as retraining staff or offering a phased closure. All example firms are hypothetical.

Worked example

A firm plans to move production abroad to cut costs. Name two stakeholders and their interests.

1. Owners want lower cost and higher profit.
2. Local employees want job security.
3. These interests conflict.

Mental model: Subtract internal from the total.

Common trap: Total minus internal.

12. Marketing mix and segmentation

Learning goal: Link the four Ps to a target segment.

Market segmentation divides customers into groups with shared needs, by age, income, location or lifestyle. A firm then targets a segment and builds a marketing mix to suit it. The classic mix has four Ps: product, price, place (distribution) and promotion. Extended versions add people, process and physical evidence for services.

The Ps must fit together. A premium watch uses a high price, selective shops and image-based advertising. A budget watch uses low price, supermarkets and price promotions. A mix with a high price and discount shops would confuse customers. When analysing a case, start with the target segment and test each P against it.

Market research supports the decision. Primary research, such as surveys, is collected by the firm; secondary research, such as published reports, already exists. Sampling choices affect reliability: a small or biased sample may mislead. Use research to estimate demand before launch. Be careful with claims about market size; use only the figures given in a case or from a named source.

Evaluate the mix by asking whether it meets the segment's needs, whether it is affordable and whether competitors can copy it. Changes over the product life cycle matter: a new product may need heavy promotion, while a mature one may need price cuts or new features. A strong answer links the choice to evidence and notes risks. All examples are hypothetical.

Remember the time value of the forecast. A cash-flow forecast for the next three months is usually more reliable than one for the next year, so managers revisit the early months often and treat later months as rough guides only.

Worked example

A firm targets students on a low budget. Suggest a price and a place choice.

1. Price: low or with student discounts.
2. Place: online and near campuses.
3. Both fit the segment's income and habits.

Mental model: Count the Ps.

Common trap: The classic mix has four.

13. Lean production and just-in-time

Learning goal: Explain lean methods, benefits and risks.

Lean production aims to cut waste while keeping quality. Waste includes overproduction, waiting, extra stock, unneeded movement and defects. Just-in-time (JIT) delivers materials only when they are needed, so the firm holds almost no stock. This reduces storage costs and frees cash, which links back to liquidity.

Other lean tools include kaizen, or continuous improvement, where workers suggest small changes, and cell production, where small teams make a complete product. These methods can raise quality and motivation, since staff have a say. They require training, a good relationship with suppliers and a workforce willing to change.

The risks are clear. With JIT, a late delivery stops the line, since there is no buffer stock. A strike at a supplier or a storm can halt production. Firms may then hold some safety stock, which is a trade-off between cost and security. JIT also suits steady demand better than uncertain demand.

To evaluate, compare the savings against the risks and the cost of change. Consider the industry: car makers use JIT widely, while a firm in a remote region with unreliable transport may not. Ask how the firm would measure success, such as stock held, defect rate and unit cost. All examples are hypothetical and no savings figures are claimed.

A short example shows the use. A firm sees that its closing balance goes negative in month four. It can ask customers to pay in 20 days, not 30, or ask suppliers for 45 days. Each choice affects relationships, so the manager must weigh them.

Worked example

A firm moves from 20 days of stock to 5. Explain one benefit and one risk.

1. Benefit: less storage cost and cash tied up.
2. Risk: a supplier delay halts production.

Mental model: Subtract.

Common trap: Difference in days.

14. Managing change: forces for and against

Learning goal: Use force field analysis to plan and judge a change.

Organisations change because of new technology, competition, laws or a new strategy. Change often meets resistance, because people fear loss of status, jobs or familiar routines. Lewin's force field analysis lists the driving forces that push for a change and the restraining forces that hold it back. Change happens when driving forces outweigh restraining ones.

To use the tool, list each force and give it a weight, for example from 1 to 5, using evidence from the case. The weights are judgements and not measurements. Then plan to strengthen the driving forces or, usually more effectively, to weaken the restraining ones. Removing a fear by giving training and clear information may do more than pushing harder.

Good change management involves communication, involving staff in the design, training and visible support from leaders. Kotter's steps or Lewin's unfreeze, change, refreeze model offer a structure. Unfreeze means preparing people by explaining why the change is needed. Change is the action, and refreeze means making it the new normal with rewards and updated procedures.

Evaluate by asking what is at stake, how much time there is, and how great the resistance is. A big change in a crisis may need a fast, top-down approach, while a gradual change allows participation but takes longer. Name the risks, such as lost morale or key staff leaving. All case examples here are hypothetical.

Another point is the product life cycle. Early on, a firm may use a high price and heavy promotion to reach early adopters. Later, when competitors enter, the firm may cut price or add features. The right mix changes over time with the stage.

Worked example

A firm adopts new software. Give one restraining force and one way to reduce it.

1. Restraining force: staff fear they cannot learn it.
2. Reduction: provide training before launch.

Mental model: Subtract.

Common trap: Net = driving - restraining.

15. Case-study technique: command terms and structure

Learning goal: Plan answers to command terms using case evidence.

Business Management papers use command terms such as define, outline, explain, analyse, discuss and evaluate. Each asks for a different depth. Define needs a short precise meaning. Explain needs a reason. Analyse needs the parts and how they connect. Discuss and evaluate need both sides and a justified conclusion. Match your depth to the command term and the marks.

Evidence is the key to higher marks. Use facts from the case, such as figures or stakeholder positions, and apply a tool. If the case gives costs, calculate the break-even; if it gives staff data, calculate the rate. Quote the numbers and units. A response that could be written about any firm cannot score well because it is not applied.

A good structure for longer answers is a point, evidence, explanation and link back to the question. For evaluation, finish with a conclusion that makes a choice and gives reasons. Examples of reasoning words are because, therefore, however and as a result. Plan in short notes first. Keep to the time the marks suggest: about one minute per mark is a common rule of thumb, which you should check against the real paper.

Check the current assessment details on the official page, since the paper structure and the pre-released case study rules may change. Practice with past papers and mark schemes provided by your school. The weightings and timings are not stated here because they were not extracted from a fetched official page. All examples in this course are hypothetical.

Quality is the other side of the argument. If JIT leads to rushed checks, defects may rise and cost more than the stock savings. Lean firms therefore build quality into each step, so that workers can stop the process when they see a fault.

Worked example

Planning to answer Evaluate whether a firm should cut price. List a plan.

1. Calculate PED from case data.
2. State effect on revenue.
3. Give a risk or limit.
4. Conclude with a choice.

Mental model: Multiply.

Common trap: Marks times minutes per mark.

16. Using the toolkit across change, ethics and sustainability

Learning goal: Apply concepts and tools to a contemporary decision.

Real decisions combine several tools. Suppose a firm considers a sustainable packaging line. A break-even calculation tests whether sales can cover the cost. Payback shows how fast the investment returns. Stakeholder analysis shows who gains and who loses. Each tool answers a different question, and none answers all of them.

Start with the facts of the case and the objective. Choose two or three tools that fit the question and avoid using every tool you know. Calculate carefully and state the units. Then interpret: what does each number mean for the firm, and how reliable is it? Numbers from a forecast should be treated with caution because they rely on assumptions.

Sustainability adds long-run and social effects. Costs such as energy use and waste can fall, but the starting investment is higher. Customers and regulators may reward the change; the size of the effect depends on the market and cannot be assumed. Ethical questions include fairness to workers and honest claims about environmental benefits.

Finish with a recommendation that names the choice, gives two or three reasons, and states a condition or risk that could change it. Offer a way to check the result, such as comparing actual sales with the forecast after a year. A balanced answer shows both the numerical evidence and the judgement. All figures in this course are invented teaching numbers.

Finally, practise with real command terms. Take a past question from your school, underline the command term, and write a one-line plan before writing. Then compare your answer with the mark scheme to see which kind of point earns the marks.

Worked example

A firm invests 50 000 and receives 20 000 a year. Find the payback.

1. 50 000 / 20 000 = 2.5 years.
2. Payback is 2.5 years.

Mental model: Divide cost by yearly return.

Common trap: Equal flows: cost / flow.