Decision Trees (AQA A-Level Business): Revision Notes
Decision trees
What are decision trees?
A decision tree is a visual diagram that helps managers choose between different options when the outcomes are uncertain. It displays the various choices available, the likelihood of different results, and the potential financial returns of each option.
Decision trees are particularly useful when:
- A business faces several possible alternatives
- Each alternative has uncertain outcomes
- The decision involves financial costs and returns
- Managers need to compare options objectively
The tree structure shows risks and rewards clearly, making it easier to identify which choice offers the best potential value.
How to construct a decision tree
Starting the tree
Every decision tree begins with a square. This square represents the decision point – the choice that needs to be made.
Adding branches for options
From the initial square, at least two lines (branches) extend outward. Each line represents a different option the business could choose. There may also be a third line showing the "do-nothing" option, where the business takes no action.
Showing uncertain outcomes
Each option leads to a circle, which represents a chance node. This shows that the outcome is uncertain – it could result in success or failure.
From each circle, further branches extend to show the possible results. These final branches end with arrows indicating the outcome.
Decision tree symbols:
- Square = decision to be made
- Circle = uncertain outcome (chance)
- Line/branch = option or possible result
- Arrow = final outcome
Remember: "Square for choice, Circle for chance"
Labelling the decision tree
To properly evaluate a decision tree, every branch must be fully labelled with three key pieces of information:
- The cost of each option – how much the business needs to invest
- The potential outcomes – the financial returns (revenue or profit)
- The probabilities – the likelihood of each outcome occurring (expressed as a decimal, such as 0.7 for 70%)
Without complete labelling, it's impossible to calculate which option provides the best return. All three elements (Cost, Outcomes, Probabilities) must be present on every branch.
Worked example: XYZ plc
Worked Example: Choosing Between Relaunch and New Product
XYZ plc is considering whether to relaunch an existing product that has been underperforming or to develop and launch a completely new product. The company has gathered the following data:
| Relaunch existing product | New product | |
|---|---|---|
| Cost | $2.5m | $6m |
| Outcome: success | $8.5m | $12m |
| Outcome: failure | $0.5m | $2m |
| Probability: success | 0.7 | 0.6 |
| Probability: failure | 0.3 | 0.4 |
The decision tree shows:
- Initial decision point (square)
- Two main options: "Relaunch" (costing $2.5m) and "New product" (costing $6m)
- Each option leads to a chance node (circle)
- From each chance node, two possible outcomes branch off:
- Relaunch: Success (0.7 probability, $8.5m return) or Failure (0.3 probability, $0.5m return)
- New product: Success (0.6 probability, $12m return) or Failure (0.4 probability, $2m return)
- A third option showing "Do nothing" with $0 return
Calculating expected values
To determine which option offers the best return, managers calculate the expected value for each choice.
The calculation method
For each option:
- Multiply each outcome by its probability
- Add these figures together
- Subtract the initial cost
This gives the expected value – the average return the business can expect from that option.
Expected Value Formula:
XYZ plc calculations
Calculating Expected Values:
Relaunch option:
\text{Success outcome: } £8.5m \times 0.7 = £5.95m \\ \text{Failure outcome: } £0.5m \times 0.3 = £0.15m \\ \text{Total expected return: } £5.95m + £0.15m = £6.10m \\ \text{Subtract cost: } £6.10m - £2.5m = £3.6m \end{array}$$ **New product option:** $$\begin{array}{l} \text{Success outcome: } £12m \times 0.6 = £7.2m \\ \text{Failure outcome: } £2m \times 0.4 = £0.8m \\ \text{Total expected return: } £7.2m + £0.8m = £8.0m \\ \text{Subtract cost: } £8.0m - £6m = £2.0m \end{array}$$ **Conclusion:** Based on these calculations, the :success[relaunch option would provide the higher expected value (£3.6m compared to £2m)]. Therefore, relaunching the existing product appears to be the more financially attractive decision.Benefits of decision trees
Decision trees offer several advantages:
- They encourage analytical thinking – managers must quantify and evaluate decisions rather than relying purely on gut feeling
- They provide a clear visual comparison of different options
- They force managers to consider probabilities and risks systematically
- They make it easier to justify decisions to stakeholders using numerical evidence
Limitations of decision trees
While decision trees are useful analytical tools, they have important limitations:
Manager bias
Managers may be influenced by their personal preferences, making the estimated returns for their favoured option appear more attractive. This can lead to biased projections that justify a decision already made intuitively.
Probability estimates
The probabilities used in decision trees are often based on past experience or guesswork. Even with historical data, circumstances change, making these probabilities uncertain. In reality, they are often educated guesses rather than precise predictions.
Critical Limitation: Decision trees encourage quantitative analysis, but they shouldn't completely replace intuition and judgement. Business decisions involve many factors that can't easily be reduced to numbers. Experienced managers need to balance analytical findings with their understanding of the market, customers, and broader business context.
Other influences ignored
Decision trees focus primarily on financial outcomes. However, business decisions are also influenced by factors such as the company's mission and values, ethical considerations, and changes in the external environment (economic conditions, demographics, legal requirements). These factors may sometimes outweigh purely financial calculations.
Exam tips
Exam tip: Although the AQA specification doesn't require students to construct decision trees in exams, being able to do so will significantly help your understanding. Practice drawing decision trees and calculating expected values to build confidence in evaluating business decisions.
When answering questions about decision trees:
- Always show your working for calculations
- Remember to subtract costs from expected returns
- Consider both the numerical answer and the limitations
- Think about other factors beyond the financial calculations that might influence the final decision
Remember!
Key Points to Remember:
- Decision trees are visual tools that help businesses choose between options when outcomes are uncertain
- Squares represent decisions, circles represent chance (uncertain outcomes)
- Three things must be labelled: costs, outcomes, and probabilities
- Expected value formula:
- Limitations exist: probabilities are estimates, manager bias can affect results, and decision trees shouldn't replace all intuition and judgement