Decision Trees

Decision trees are a key quantitative tool in AQA A-Level Business for analysing and evaluating business decisions under conditions of uncertainty. They allow managers to map out different options, assign probabilities and financial values, and calculate the expected value of each course of action. This lesson covers how to construct, interpret, and evaluate decision trees.

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What Is a Decision Tree?

Key Definition: A decision tree is a diagrammatic representation of a business decision that shows the different options available, the possible outcomes of each option, the probabilities of those outcomes, and the expected financial returns.

Decision trees are a tool of scientific decision making — they impose structure and quantitative rigour on complex decisions.

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Key Components of a Decision Tree

Symbol	Meaning	Description
Square node (□)	Decision point	Represents a choice the manager must make
Circle node (○)	Chance node	Represents an uncertain outcome (with probabilities)
Branch (line)	Option or outcome	Connects nodes — labelled with the option, probability, and/or financial value

Structure

A typical decision tree reads from left to right:

1. Start with a decision node (square) — the initial choice
2. Each branch from the decision node represents an option (e.g., launch Product A or Product B)
3. Each option leads to a chance node (circle) — representing uncertainty
4. Branches from the chance node represent possible outcomes (e.g., high demand, low demand), each with a probability and a financial value

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Constructing a Decision Tree: Worked Example

Scenario

A company is deciding whether to launch a new product. The two options are:

• Option A: Launch nationally — Costs £500,000

  • 60% probability of high demand → Revenue of £1,200,000
  • 40% probability of low demand → Revenue of £300,000

• Option B: Launch regionally — Costs £200,000

  • 70% probability of high demand → Revenue of £600,000
  • 30% probability of low demand → Revenue of £150,000

Step 1: Draw the Tree

                        High demand (0.6) → £1,200,000
           Option A ──○
          (£500,000)    Low demand (0.4) → £300,000
□
          Option B ──○  High demand (0.7) → £600,000
          (£200,000)    Low demand (0.3) → £150,000

Step 2: Calculate Expected Values (EV)

Key Definition: The expected value (EV) of a decision is the weighted average of all possible outcomes, calculated by multiplying each outcome's financial value by its probability and summing the results.

Formula: EV = Σ (Probability × Financial Value)

Option A: EV = (0.6 × £1,200,000) + (0.4 × £300,000) EV = £720,000 + £120,000 = £840,000

Option B: EV = (0.7 × £600,000) + (0.3 × £150,000) EV = £420,000 + £45,000 = £465,000

Step 3: Calculate Net Gain

Key Definition: Net gain is the expected value minus the initial cost of the option. It represents the expected profit (or loss) from the decision.

Formula: Net Gain = Expected Value − Cost

Option A: Net Gain = £840,000 − £500,000 = £340,000

Option B: Net Gain = £465,000 − £200,000 = £265,000

Step 4: Make the Decision

Based on expected value, Option A (national launch) has the higher net gain (£340,000 vs £265,000) and should be chosen.

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Another Worked Example

Scenario

A restaurant owner is deciding whether to expand into a second location or refurbish the existing restaurant.

• Expand — Cost: £300,000

  • 50% chance of success → Revenue: £800,000
  • 50% chance of failure → Revenue: £100,000

• Refurbish — Cost: £100,000

  • 80% chance of success → Revenue: £350,000
  • 20% chance of failure → Revenue: £80,000