A Level Business · Topic guide

Decision Trees and Quantitative Decision-Making

A decision tree is a quantitative, diagrammatic technique used to evaluate two or more strategic options by calculating and comparing their expected values (EV). Each decision (a choice the business controls) is shown as a square node, and each chance event (an outcome outside the business's control, such as high or low demand) is shown as a circle node, with a probability attached to each branch leading from it; the probabilities on branches from the same chance node must sum to 1. The expected value of an outcome is calculated by multiplying its financial result by its probability, and the expected values of all branches from a chance node are summed and then reduced by the cost of that option to give the net gain, which is what the business compares between options. Decision trees force managers to quantify uncertainty, but the probabilities are usually estimates rather than certainties, so the technique should support, not replace, managerial judgement.

Year 12-13 (A Level)Decision making to improve performanceAQAWJECEduqas

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Corporate Objectives, Mission and Ansoff's Matrix

Method

Identify the decision nodes (squares, options the business is choosing between) and the chance nodes (circles, uncertain outcomes such as high or low demand) on the diagram.
Check that the probabilities on the branches from each chance node sum to 1; if a question gives only one probability for a two-outcome event, find the other by subtracting from 1.
Calculate the expected value of each chance node: multiply each outcome's financial value by its probability, then add the results together.
Subtract the cost of that option (the initial outlay) from its expected value to find the net gain for each option.
Compare the net gains and recommend the option with the higher net gain as the quantitative answer.
For an evaluate question, go beyond the numbers: probabilities are estimates and may be wrong, the technique ignores qualitative factors (staff morale, brand fit, competitor reaction), and a smaller net gain may still be preferable if it carries much lower risk, so a supported judgement is needed, not just the biggest number.

Worked example

A business is choosing between launching Product A, which costs 100,000 pounds, with a 0.6 probability of high sales generating revenue of 400,000 pounds and a 0.4 probability of low sales generating revenue of 150,000 pounds, or launching Product B, which costs 60,000 pounds, with a 0.7 probability of high sales generating revenue of 250,000 pounds and a 0.3 probability of low sales generating revenue of 90,000 pounds. Use decision tree analysis to recommend which product to launch.

Check probabilities: Product A, 0.6 + 0.4 = 1. Product B, 0.7 + 0.3 = 1. Both valid.
Expected value of Product A's outcomes: (0.6 x 400,000) + (0.4 x 150,000) = 240,000 + 60,000 = 300,000 pounds.
Net gain of Product A: 300,000 - 100,000 (the launch cost) = 200,000 pounds.
Expected value of Product B's outcomes: (0.7 x 250,000) + (0.3 x 90,000) = 175,000 + 27,000 = 202,000 pounds.
Net gain of Product B: 202,000 - 60,000 (the launch cost) = 142,000 pounds.
Compare: 200,000 pounds is greater than 142,000 pounds, so the quantitative recommendation is to launch Product A, though a full answer should also weigh how reliable the 0.6/0.4 probability estimates are.

Practice questions

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Q1What shape represents a decision node on a decision tree?Show answer

Answer: A square.

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Q2What shape represents a chance (outcome) node on a decision tree?Show answer

Answer: A circle.

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Q3A chance node has two branches. One has a probability of 0.35. What is the probability of the other branch?Show answer

Answer: 0.65, because the probabilities on branches from the same chance node must sum to 1 (1 - 0.35 = 0.65).

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Q4An option has outcomes of 500,000 pounds (probability 0.3) and 200,000 pounds (probability 0.7). Calculate its expected value.Show answer

Answer: (0.3 x 500,000) + (0.7 x 200,000) = 150,000 + 140,000 = 290,000 pounds.

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Q5State one weakness of using decision trees to make business decisions.Show answer

Answer: The probabilities used are usually estimates or forecasts rather than certain figures, so the calculated expected value can be inaccurate if the real-world probability turns out to be different.

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Q6Why must the net gain, not just the expected value, be compared between two options with different costs?Show answer

Answer: Because the expected value alone ignores how much each option costs to set up; subtracting the cost gives the net financial benefit, which is the fair basis for comparing options of different sizes.

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Exam-style questions

Written in the style of a A Level Business exam paper, with a full mark scheme.

Q1[9 marks]

Analyse the benefits to a business of using decision trees when choosing between two investment options.

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Tick each line you got. Your score builds from the marks on the scheme.

basic, undeveloped identification of a benefit, e.g. states decision trees allow comparison of options, with little or no application.3 marks
one benefit is explained with a chain of reasoning, e.g. decision trees quantify uncertain outcomes into a single expected value, which lets managers compare options on a common numerical basis rather than relying on instinct.2 marks
two or more benefits analysed in depth with clear application to a business context, e.g. quantifying risk supports a case for finance to lenders or shareholders, and the visual layout helps communicate complex reasoning to stakeholders who were not part of the original discussion.2 marks
Credit content on: reducing bias/gut-feel decisions, forcing explicit probability estimates, showing the effect of costs on net gain, and aiding communication/justification of the chosen option.2 marks

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Q2[25 marks]

Hartfield Engineering is deciding between two ways to expand capacity. Option 1 is to build a new factory, costing 500,000 pounds, with a 0.55 probability of strong demand generating revenue of 1,200,000 pounds and a 0.45 probability of weak demand generating revenue of 400,000 pounds. Option 2 is to upgrade its existing site, costing 200,000 pounds, with a 0.65 probability of strong demand generating revenue of 650,000 pounds and a 0.35 probability of weak demand generating revenue of 250,000 pounds. Using the data and decision tree analysis, evaluate whether Hartfield Engineering should choose Option 1 or Option 2.

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Tick each line you got. Your score builds from the marks on the scheme.

limited or no calculation, unsupported assertion of which option to choose.7 marks
partial or minor-error calculation of expected value/net gain for one option, one-sided discussion.6 marks
correct calculations for both options (Option 1: EV = (0.55 x 1,200,000) + (0.45 x 400,000) = 660,000 + 180,000 = 840,000; net gain = 840,000 - 500,000 = 340,000 pounds. Option 2: EV = (0.65 x 650,000) + (0.35 x 250,000) = 422,500 + 87,500 = 510,000; net gain = 510,000 - 200,000 = 310,000 pounds), with analysis that Option 1's higher net gain (340,000 vs 310,000 pounds) is the quantitative case for it.6 marks
balanced evaluation going beyond the numbers, e.g. Option 1's weak-demand outcome (400,000 pounds revenue against a 500,000 pound cost) risks an outright loss, while Option 2's weak-demand outcome (250,000 pounds revenue against a 200,000 pound cost) stays in profit even if demand disappoints, so Option 2 is the lower-risk choice; a justified conclusion considers Hartfield's ability to raise 500,000 pounds, its attitude to risk, and how reliable the given probabilities are before recommending an option.6 marks

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Next topics

Critical Path Analysis: Network Diagrams and the Critical Path SWOT Analysis and Choosing a Strategic Option Corporate Objectives, Mission and Ansoff's Matrix

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