Decision Trees (9BS0 3.3.3)
Decision trees map choices, chance outcomes and payoffs, letting managers compare options using expected values. Edexcel regularly sets calculation questions on them, so you must be able to compute expected value and net gain accurately and then criticise the technique.
How decision trees work
A decision tree is drawn left to right. Decision nodes (squares) show points where managers choose; chance nodes (circles) show uncertain outcomes with estimated probabilities that must sum to 1 at each node. Each branch ends in a payoff — the estimated financial result.
To evaluate an option, calculate its expected value (EV): multiply each payoff by its probability and add the results. Then subtract the option's initial cost to find the net gain. Comparing net gains across options identifies the best choice on purely financial grounds.
- EV = sum of (probability x payoff)
- Net gain = EV minus cost of the option
- Always work right to left when trees have multiple stages
Rejected branches are struck through with double lines in a full diagram.
Worked calculation
A snack manufacturer is deciding whether to launch a new protein bar. Launching costs £800,000. Market research suggests a 0.6 probability of success, giving a payoff of £2,400,000, and a 0.4 probability of failure, giving a loss of £500,000. Not launching has zero cost and zero payoff.
| Step | Calculation | Result |
|---|---|---|
| Success branch | 0.6 x £2,400,000 | £1,440,000 |
| Failure branch | 0.4 x (−£500,000) | −£200,000 |
| Expected value | £1,440,000 − £200,000 | £1,240,000 |
| Net gain | £1,240,000 − £800,000 | £440,000 |
Since £440,000 is greater than the £0 of not launching, the tree recommends launching. Show every stage in the exam — method marks are available even if arithmetic slips. A sensible final check: the expected value must lie between the worst and best payoffs, so if it falls outside that range a multiplication or sign error has crept in somewhere.
Strengths and limitations
Strengths: decision trees force managers to set out options explicitly, attach numbers to uncertainty and compare alternatives on a consistent basis. They make risk visible — the £500,000 downside above is in plain sight — and support discussion between departments before money is committed.
Limitations are just as examinable. Probabilities are usually estimates, often little better than guesses, and small changes can reverse the recommendation; a success probability of 0.4 instead of 0.6 would make the launch unattractive. Payoffs are forecasts subject to the same bias. The technique ignores qualitative factors — brand fit, staff morale, competitor reaction — and reflects the attitude to risk of whoever built it: a positive net gain may still be rejected by a risk-averse board facing a possible £500,000 loss. Trees also date quickly in dynamic markets. Use them as one input, tested with sensitivity analysis, rather than a verdict.
Key terms
Practice questions
Explain one advantage to a business of using decision trees when making an investment choice. [4 marks]
Model answer guidance: Decision trees make managers quantify uncertainty by attaching probabilities and payoffs to each option. This turns vague hunches into comparable numbers, so options can be ranked on expected financial return. For example, a firm can see that a launch with a net gain of £440,000 beats doing nothing. The discipline of building the tree also exposes assumptions that can then be challenged before money is spent.
Using the data in the extract, calculate the net gain of launching the product. You are advised to show your working. (Launch cost £800,000; 0.6 probability of £2,400,000; 0.4 probability of −£500,000.) [4 marks]
Model answer guidance: Expected value = (0.6 x £2,400,000) + (0.4 x −£500,000) = £1,440,000 − £200,000 = £1,240,000. Net gain = £1,240,000 − £800,000 = £440,000. Since the net gain is positive and exceeds the alternative of not launching, the decision tree supports the launch. Full working shown at each stage secures method marks.
Discuss the limitations of decision trees as a decision-making technique. [8 marks]
Model answer guidance: The probabilities in a tree are estimates, often based on limited research, and the recommendation can flip if they are slightly wrong — reducing success probability from 0.6 to 0.4 in a typical launch decision can turn a positive net gain negative. Payoffs are equally uncertain forecasts. Trees also exclude qualitative factors such as brand fit, employee impact and competitor response, and they can be manipulated by managers who want a project approved. They remain useful for structuring choices, but only when tested with sensitivity analysis and combined with judgement.
Assess the value of decision trees to a business operating in a fast-changing market. [10 marks]
Model answer guidance: In fast-changing markets, decision trees still add value by forcing explicit thinking about outcomes and by making downside risks visible before commitment, which supports faster, structured board decisions. However, their inputs decay quickly: probabilities estimated this quarter may be obsolete next quarter, and rivals' moves can change payoffs entirely. Static trees can therefore give a false sense of scientific rigour. Their value depends on how they are used — as regularly updated, sensitivity-tested models they help; as one-off justifications they mislead. In volatile markets, speed of revision matters more than the initial calculation.
Evaluate whether quantitative techniques such as decision trees should determine major strategic decisions. (20) [20 marks]
Model answer guidance: Quantitative techniques bring discipline: decision trees rank options by expected value, expose assumptions and reduce the influence of office politics, which is valuable when hundreds of thousands of pounds are at stake. A calculated net gain of £440,000 versus zero is a clear starting point. However, major strategic decisions involve factors numbers cannot capture — culture, brand, stakeholder reaction, competitor retaliation — and the inputs are subjective estimates dressed as facts. Overreliance can produce confident errors, especially where managers game probabilities to favour pet projects. The better position is that quantitative tools should inform, not determine: they frame the financial case, while judgement weighs strategic fit and risk appetite. The final decision should depend on how reliable the data is — the more novel the situation, the less weight the numbers deserve.
Examiner tips
- Show probability x payoff for every branch separately before summing — method marks survive arithmetic errors.
- Check probabilities at each chance node sum to 1 before calculating; examiners sometimes include distractor data.
- In evaluation, question where the probabilities came from — market research quality is the weak point of every tree.
In The Business School simulation your students make these exact decisions in a live market against rival firms — every choice mapped to the specification. Free teacher demo, no installs, students join with a PIN.