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Decision Trees
A clear guide to decision trees, expected value, net gain and how businesses use quantitative decision-making under uncertainty.
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Created by an experienced Head of Business and examiner
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KEY POINTS
Decision trees help managers compare different options when outcomes are uncertain.
A square shows a decision point, while a circle shows chance outcomes that depend on probability.
Expected value is calculated by multiplying each outcome by its probability and adding the results.
Net gain is calculated by subtracting the cost of the option from its expected value.
Decision trees support scientific decision-making, but managers must still consider qualitative factors, data reliability and risk.
KEY DEFINITION
Decision tree
A decision tree is a quantitative decision-making model that maps out choices, possible outcomes, probabilities and expected financial values to help managers compare options under uncertainty.
Main Explanation
Decision trees are a quantitative decision-making technique used to help managers compare options where future outcomes are uncertain. They are especially useful when a business faces a choice that could lead to several possible results, such as launching a product, entering a new market, opening a new site or investing in new equipment.
A decision tree starts with a decision point. This is usually shown as a square and represents the choice the business has to make. From this point, branches show the possible options. For example, a business might choose to launch a new product, modify an existing product or do nothing.
Some branches then lead to chance points. These are usually shown as circles and represent uncertain outcomes. Each outcome is given a probability. Probabilities show the estimated likelihood of each outcome happening, and the probabilities from a chance point should add up to 1. For example, a new product may have a 0.6 probability of high demand and a 0.4 probability of low demand.
The expected value of an option is calculated by multiplying each possible outcome by its probability and then adding the results together. This gives a probability-weighted financial value. It does not predict exactly what will happen, but it gives managers a way to compare the average financial outcome of different options.
Net gain is calculated by subtracting the initial cost of the option from its expected value. This is important because one option may have a high expected value but also a high cost. In many exam questions, the option with the highest net gain appears to be the best financial choice.
However, students should not assume that the highest net gain automatically means the best decision. Decision trees are based on estimates, so the outcome values and probabilities may be inaccurate. If the market is changing quickly or the business has poor data, the calculations may give a false sense of accuracy.
Decision trees also focus mainly on financial outcomes. They may ignore important qualitative factors such as brand reputation, customer reaction, employee morale, ethics, environmental impact and competitor response. A decision with a lower expected financial return may still be better if it protects the business from serious risk or supports long-term objectives.
Managers may also have different attitudes to risk. A business with strong cash flow may be willing to accept a risky option with a high possible return. A smaller business with limited finance may prefer a safer option, even if the expected value is lower. This means decision trees should support judgement rather than replace it.
Overall, decision trees are useful because they force managers to think logically about options, outcomes, probabilities, costs and risk. The strongest exam answers use the numbers carefully, but then evaluate whether the data is reliable and whether other non-financial factors should affect the final decision.
✎ EXAMINER TIP
Do not just pick the option with the highest net gain. Explain how reliable the figures are and whether qualitative factors could change the final decision.
KEY FORMULAS(s)
Profit and Profitability Formulas
These key formulas help you calculate different profit measures and profitability ratios used in business.
Gross Profit
Gross profit = Revenue − Cost of sales
The profit made after deducting direct costs.
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Remember: profit shows how much money has been made, while profitability shows how efficiently revenue is being turned into profit.
DATA TABLE
Income Statement for North Coast Coffee Ltd
This statement shows how revenue is converted into gross profit, operating profit and net profit.
Revenue
£250,000
Output
Fixed Costs
Variable Costs
Total Costs
Revenue
Profit / Loss
0 candles £1,200 £0 £1,200 £0 -£1,200
Net profit is the final profit remaining after all costs and expenses have been deducted from revenue.
WORKED EXAMPLE
Worked Example: North Coast Coffee
How many coffees must be sold to break even?
Fixed Costs
£1,800
equity + long-term debt
Break-even output = Fixed costs ÷ Contribution per unit
Contribution per unit = Selling price − Variable cost
£3.50 − £1.10 = £2.40
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Step 1: Calculate contribution
£3.50 − £1.10 = £2.40
Contribution per unit is the amount each coffee contributes towards fixed costs.
BREAK-EVEN OUTPUT:
750 coffees per month
EXAM TIP
Always explain what the number means for the business. Do not just calculate the break-even point.
Decision Trees: Choices, Chances and Expected Value
So in this diagram, the decision to launch generates a much higher return than the 'Do Not Launch' option.
APPLICATION
Ryanair
Ryanair is a useful real business context for decision trees because airlines regularly face uncertain decisions about routes, capacity and costs. A low-cost airline may need to decide whether to launch a new route from a regional airport, increase flights on an existing route or keep aircraft capacity elsewhere.
A decision tree could help Ryanair compare the possible financial outcomes of launching a new route. For example, the route may have a high-demand outcome if ticket sales are strong and aircraft load factors are high, but a low-demand outcome if passengers do not book enough seats. Each outcome could be given a probability based on market research, booking data, airport catchment area, tourism demand and competitor activity.
The expected value calculation would help managers estimate the weighted financial return of the route. If the expected value of launching the route is higher than the expected value of using the aircraft elsewhere, this may suggest that the new route is worth considering. The business would then subtract the initial costs, such as marketing, airport fees, crew scheduling and operational set-up, to calculate the net gain.
However, the decision tree would only be as reliable as the estimates used. Demand for flights can be affected by fuel prices, airport charges, exchange rates, consumer confidence, weather disruption, air traffic control issues and competitor actions. If the probability estimates are weak, the decision tree may produce a misleading result.
Ryanair would also need to consider qualitative factors. A route with a lower expected net gain may still be strategically useful if it strengthens the airline’s network, improves aircraft utilisation or helps build a presence at an important airport. Alternatively, a route with a high expected return may be rejected if airport fees are rising or if it creates operational complexity.
This example shows that decision trees can support scientific decision-making by making risk and financial outcomes clearer. However, managers should combine the calculations with judgement, market knowledge and strategic analysis before making the final decision.
This independent educational case study is not affiliated with, endorsed by or sponsored by Greggs plc. Any financial figures used alongside this example should be treated as simplified or hypothetical estimates created for teaching purposes.
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ANALYSIS
EXAM FOCUS
Analysis questions require you to examine a business concept or issue in detail, breaking it down into its component parts. You should explain how and why something happens and consider its impact on the business.
How to Approach Analysis Questions
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Identify the key issue or concept
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Break it down
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Explain how and why
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Reach a reasoned conclusion
Read the question carefully and highlight the focus of the analysis.
Consider the different factors, causes or impacts related to the issue.
Provide clear explanations using business terms and links points to context.
Evaluate the overall implications for the business.
Example Analysis Question
North Coast Coffee is considering using break-even analysis before opening a second café.
Advantages
• Sales forecasts may be inaccurate.
• Assumes costs and revenue remain constant.
• External factors may reduce reliability.
• Ignores qualitative business factors.
Disadvantages
• Sales forecasts may be inaccurate.
• Assumes costs and revenue remain constant.
• External factors may reduce reliability.
• Ignores qualitative business factors.
Key Exam Tip
If you find it difficult to expand your answer and show the type of depth that an examiner is looking for in a top response, consider using the 'so what' approach.
Tesco carry out market research - so what? - this allows them to better understand customer needs - so what? as a result Tesco can provide goods more likely to sell - so what? - this will increase Tesco profit and ensure higher levels of customer satisfaction - so what? this means that customers are likely to become more loyal to Tesco.
Avoid These Exam Traps
Students often lose marks on calculation and analysis questions by making these mistakes. Watch out for them in your exam!
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Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
Tip:
Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
2
Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
Tip:
Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
3
Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
Tip:
Helvetica Light is an easy-to-read font, with tall and narrow letters, that works well on almost every site.
Be precise. Read the question carefully. Show your working.
Small mistakes can cost big marks.
EXAM PRACTICE
Practice Question
Apply your knowledge of profit and profitability to answer this exam-style question.
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MINI CASE STUDY
North Coast Coffee Ltd is a premium coffee business which sells freshly roasted coffee beans through its online store and a small chain of independent cafés. The business has experienced strong sales growth due to increasing demand for high-quality speciality coffee products.
The business generates annual revenue of £250,000. Its cost of sales, including coffee beans, packaging and direct production costs, totals £100,000. North Coast Coffee Ltd also faces operating expenses of £80,000, including marketing, employee wages, rent and administration costs. In addition, the business pays £20,000 in interest and taxation each year.
The owner, Mia Thompson, is reviewing the company’s profitability because rising wage costs and increased competition in the premium coffee market have started to place pressure on operating profit margins. She is considering increasing prices slightly in order to protect profitability while still maintaining customer demand.
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EXAM QUESTION
Analyse the possible reasons for BrightBite’s falling profit margins and evaluate strategies it could use to improve profitability.
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HOW TO ANSWER
P
Point
E
Explain
A
Apply
C
Consequence
H
However...
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MODEL ANSWER
P
Point
Increasing prices could improve the profitability of North Coast Coffee Ltd because each sale would generate a larger amount of revenue and potentially increase profit margins.
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EXAMINER TIP
For full marks, make sure you analyse causes rather than just listing them, and evaluate realistic strategies with clear judgement. THINK: Which strategy would have the biggest impact and why?
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