IB Business Management SL

BMT 6 – Decision Trees | Business Management Toolkit | IB Business Management SL

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Unit 6: Business Management Toolkit

BMT 6 - Decision Trees

Quantitative Decision-Making Tool Using Expected Values and Probabilities

1. What is a Decision Tree?

A decision tree is a visual, quantitative decision-making tool that maps out different decision options and their possible outcomes, incorporating probabilities and financial values to calculate expected values for each option.

Purpose:

  • Help businesses make complex decisions involving uncertainty
  • Compare different strategic options objectively
  • Calculate expected monetary value (EMV) of each decision
  • Visualize decision paths and potential outcomes
  • Support rational, data-driven decision-making

When to Use Decision Trees

Decision trees are particularly useful for:

  • Investment decisions: Choosing between different investment projects
  • Product launches: Deciding whether to launch a new product
  • Market expansion: Evaluating entry into new markets
  • Capacity decisions: Expanding production facilities or not
  • Research and development: Whether to invest in new technology
  • Marketing campaigns: Choosing between different promotional strategies

2. Components of a Decision Tree

Key Elements

1. Decision Nodes (Squares □):

  • Represent points where a decision must be made
  • Shown as squares or rectangles
  • Under management control
  • Example: "Launch Product A or Product B?"

2. Chance Nodes (Circles ○):

  • Represent uncertain outcomes or events
  • Shown as circles
  • Outside management control (depend on probability)
  • Example: "High demand or low demand?"

3. Branches (Lines):

  • Connect nodes and show decision paths
  • From decision nodes: different options available
  • From chance nodes: different possible outcomes

4. Probabilities:

  • Likelihood of each outcome occurring (0 to 1, or 0% to 100%)
  • Written on branches from chance nodes
  • Must sum to 1.0 (or 100%) for all outcomes from a chance node
  • Example: 0.6 probability of success, 0.4 probability of failure

5. Payoffs (Outcomes):

  • Financial results at the end of each branch
  • Can be profit, revenue, cost savings, or net present value
  • Written at the end of the tree (rightmost side)
  • Example: $500,000 profit or -$100,000 loss

6. Expected Values (EV):

  • Calculated average outcome considering probabilities
  • Written at chance nodes (after calculating)
  • Help determine best decision

Visual Representation of Components

Decision Node Option A Option B Chance Node P = 0.7 P = 0.3 Success: $500,000 Failure: -$100,000 P = 0.5 P = 0.5 Success: $400,000 Failure: -$50,000 Decision Node Chance Node Branch/Path P = 0.X Probability $XXX Payoff/Outcome

3. Expected Value (EV) Calculations

Expected Value (EV) is the weighted average of all possible outcomes, where each outcome is multiplied by its probability of occurring.

Formula:

\[ \text{Expected Value (EV)} = \sum (\text{Probability} \times \text{Payoff}) \]

Or written out:

\[ \text{EV} = (P_1 \times \text{Outcome}_1) + (P_2 \times \text{Outcome}_2) + ... + (P_n \times \text{Outcome}_n) \]

Where:

  • \( P_1, P_2, ..., P_n \) = Probabilities of each outcome
  • \( \text{Outcome}_1, \text{Outcome}_2, ..., \text{Outcome}_n \) = Financial payoffs
  • Sum of all probabilities must equal 1.0 (or 100%)

Simple Expected Value Example

Scenario: A business is considering launching a new product. There are two possible outcomes:

  • • Success (probability 0.6): Profit of $300,000
  • • Failure (probability 0.4): Loss of $50,000

Calculate Expected Value:

\[ \text{EV} = (0.6 \times \$300,000) + (0.4 \times -\$50,000) \] \[ \text{EV} = \$180,000 + (-\$20,000) \] \[ \text{EV} = \$160,000 \]

Interpretation: On average, considering the probabilities, this decision would result in an expected value of $160,000.

4. How to Construct a Decision Tree

Step-by-Step Process

  1. Draw from left to right: Start with the initial decision on the left, outcomes on the right
  2. Place decision node: Draw a square at the starting point
  3. Draw decision branches: One line for each option available
  4. Label each option: Write the name of each decision choice on its branch
  5. Add chance nodes: If outcomes are uncertain, add circles at end of decision branches
  6. Draw outcome branches: From each chance node, draw lines for each possible outcome
  7. Add probabilities: Write probability on each branch from chance nodes
  8. Add payoffs: Write financial outcome at the end of each final branch
  9. Calculate expected values: Work backwards from right to left
  10. Make decision: Choose option with highest expected value

Calculating Expected Values (Working Backwards)

Process of "rolling back" the tree:

  1. Start at the right: Identify all final payoffs
  2. Calculate EV at chance nodes: Multiply each outcome by its probability and sum
  3. Write EV at chance node: This becomes the "value" of that decision option
  4. Compare EVs at decision node: Look at all calculated EVs
  5. Choose highest EV: This is the recommended decision
  6. Cross out rejected options: Draw lines through branches not chosen

5. Comprehensive Decision Tree Example

Example: Product Launch Decision

Scenario:

A company must decide whether to launch a new product or not. If they launch, demand could be high or low. The decision also involves an initial investment.

Given Data:

  • Decision Options:
  • • Option 1: Launch the product (requires $100,000 investment)
  • • Option 2: Do not launch (no investment, no profit/loss)
  • If Launch - Possible Outcomes:
  • • High demand (probability 0.7): Revenue = $500,000
  • • Low demand (probability 0.3): Revenue = $150,000
  • • Initial investment for launch = $100,000
  • If Do Not Launch:
  • • No revenue, no investment = $0

Step 1: Calculate Net Payoffs

For "Launch" option (subtract initial investment from revenue):

  • • High demand net payoff: $500,000 - $100,000 = $400,000
  • • Low demand net payoff: $150,000 - $100,000 = $50,000

For "Do Not Launch" option:

  • • Net payoff: $0

Step 2: Calculate Expected Value for "Launch" Option

\[ \text{EV(Launch)} = (P_{\text{high}} \times \text{Payoff}_{\text{high}}) + (P_{\text{low}} \times \text{Payoff}_{\text{low}}) \] \[ \text{EV(Launch)} = (0.7 \times \$400,000) + (0.3 \times \$50,000) \] \[ \text{EV(Launch)} = \$280,000 + \$15,000 \] \[ \text{EV(Launch)} = \$295,000 \]

Step 3: Compare Expected Values

  • • EV(Launch) = $295,000
  • • EV(Do Not Launch) = $0

Decision: Launch the product because EV($295,000) > EV($0)

Interpretation: Based on expected value analysis, launching the product is the better decision. On average, considering the probabilities, the company can expect to gain $295,000.

Visual Decision Tree for This Example

Product Launch Decision Tree Launch Product Do Not Launch EV = $295,000 P = 0.7 High Demand P = 0.3 Low Demand $400,000 profit $50,000 profit $0 EV Calculation: (0.7 × $400k) + (0.3 × $50k) = $295k CHOOSE

6. Complex Decision Tree Example

Example: Market Expansion with Research Option

Scenario:

A company is considering expanding into a new market. They can either:

  • Option 1: Expand immediately without research ($50,000 investment)
  • Option 2: Conduct market research first ($20,000), then decide whether to expand ($50,000 if they proceed)
  • Option 3: Do not expand at all

If Expand Without Research:

  • • Success (P = 0.5): Revenue $300,000
  • • Failure (P = 0.5): Revenue $50,000

If Conduct Research First:

  • • Positive results (P = 0.6): Then expand
  •   - Success (P = 0.8): Revenue $300,000
  •   - Failure (P = 0.2): Revenue $50,000
  • • Negative results (P = 0.4): Do not expand

Calculations for Complex Tree

Option 1: Expand Without Research

Net payoffs (Revenue - Investment):

  • • Success: $300,000 - $50,000 = $250,000
  • • Failure: $50,000 - $50,000 = $0
\[ \text{EV(Expand Immediately)} = (0.5 \times \$250,000) + (0.5 \times \$0) = \$125,000 \]

Option 2: Research Then Decide

If research positive (decide to expand):

Net payoffs (Revenue - Research - Investment):

  • • Success: $300,000 - $20,000 - $50,000 = $230,000
  • • Failure: $50,000 - $20,000 - $50,000 = -$20,000
\[ \text{EV(Positive Research)} = (0.8 \times \$230,000) + (0.2 \times -\$20,000) \] \[ = \$184,000 - \$4,000 = \$180,000 \]

If research negative (do not expand):

  • • Only lose research cost: -$20,000

Overall EV for Research Option:

\[ \text{EV(Research)} = (0.6 \times \$180,000) + (0.4 \times -\$20,000) \] \[ = \$108,000 - \$8,000 = \$100,000 \]

Option 3: Do Not Expand

\[ \text{EV(Do Not Expand)} = \$0 \]

Decision:

  • • EV(Expand Immediately) = $125,000 ← HIGHEST
  • • EV(Research First) = $100,000
  • • EV(Do Not Expand) = $0

Recommendation: Expand immediately without research, as it has the highest expected value of $125,000.

7. Interpreting Decision Tree Results

What Expected Value Tells You

  • Average outcome: EV represents the average result if the decision were repeated many times
  • Not a guaranteed result: Actual outcome will be one of the specific payoffs, not the EV
  • Risk consideration: Higher EV doesn't always mean less risk
  • Comparative tool: Used to compare different options objectively

Limitations to Consider

  • EV ignores risk preference: Two options with same EV may have very different risk profiles
  • Example:
    • Option A: 100% chance of $100,000 (EV = $100,000)
    • Option B: 50% chance of $200,000, 50% chance of $0 (EV = $100,000)
    • Same EV, but Option A is risk-free while Option B is risky
  • Risk-averse businesses: May prefer lower EV with more certainty
  • Risk-seeking businesses: May accept lower EV for chance of very high payoff

Sensitivity Analysis

Sensitivity analysis tests how changes in probabilities or payoffs affect the decision.

Questions to ask:

  • How much would probability need to change to alter the decision?
  • What if the payoffs are 10% higher or lower?
  • Which factors have the most impact on the decision?

Purpose: Understand how robust the decision is to changes in assumptions

8. Advantages of Decision Trees

  • Visual and clear: Easy to understand diagram shows decision paths
  • Quantitative: Provides numerical basis for decisions (not just intuition)
  • Incorporates probability: Accounts for uncertainty in outcomes
  • Compares multiple options: Evaluates all alternatives side-by-side
  • Identifies best option: Objectively shows which choice has highest expected value
  • Shows sequential decisions: Can map out multi-stage decision processes
  • Communication tool: Helps explain decisions to stakeholders
  • Reduces bias: Structured approach minimizes emotional decision-making
  • Forces explicit thinking: Requires identifying all options, outcomes, and probabilities
  • Can be simple or complex: Scales from basic to sophisticated analyses

9. Disadvantages of Decision Trees

  • Probabilities are estimates: Difficult to accurately predict likelihoods of outcomes
  • Payoffs are estimates: Future financial outcomes uncertain
  • Garbage in, garbage out: Poor estimates lead to poor decisions
  • Ignores qualitative factors: Focuses only on financial outcomes
  • Risk attitude ignored: EV doesn't consider if business is risk-averse or risk-seeking
  • Can be oversimplified: May not capture full complexity of decision
  • Time-consuming: Gathering data and constructing tree takes effort
  • Becomes complex quickly: Many branches make tree difficult to analyze
  • Static analysis: Doesn't show how decision evolves over time
  • Ignores non-monetary factors: Employee morale, brand reputation, ethics not quantified
  • May give false precision: Exact numbers suggest more certainty than actually exists

10. IB Business Management Exam Tips

Key Formulas to Know

  • Expected Value: \( \text{EV} = \sum (\text{Probability} \times \text{Payoff}) \)
  • Two outcomes: \( \text{EV} = (P_1 \times \text{Outcome}_1) + (P_2 \times \text{Outcome}_2) \)
  • Net Payoff: \( \text{Revenue} - \text{Costs/Investment} \)

Common Exam Questions

  • "Calculate the expected value for Option A" (2-4 marks)
  • "Using decision tree analysis, recommend which option the business should choose" (6 marks)
  • "Construct a decision tree for the given scenario" (6 marks)
  • "Explain two limitations of using decision trees" (6 marks)
  • "Evaluate the usefulness of decision tree analysis for this business decision" (10 marks)

Drawing Decision Trees in Exams

Essential elements to include:

  • Decision nodes: Draw clear squares
  • Chance nodes: Draw clear circles
  • Label all branches: Write what each branch represents
  • Include probabilities: Write on branches from chance nodes
  • Include payoffs: Write at end of each branch
  • Calculate EVs: Show calculations and write EV at chance nodes
  • Indicate decision: Mark or note which option is chosen
  • Use ruler: Draw neat, straight lines

Calculation Tips

  • Show all working: Write out calculations step by step
  • Check probabilities sum to 1.0: From any chance node, probabilities must add to 100%
  • Be careful with signs: Costs and losses are negative
  • Calculate net payoffs first: Revenue minus costs/investment
  • Work right to left: Start with payoffs, calculate EV at chance nodes, compare at decision node
  • Label answers clearly: "EV(Option A) = $X"
  • Round appropriately: Usually to nearest dollar or whole number

Evaluation Questions

When asked to "evaluate usefulness of decision trees" consider:

Arguments FOR (advantages):

  • Provides quantitative basis for decision
  • Visual and easy to understand
  • Accounts for uncertainty through probabilities
  • Compares multiple options objectively

Arguments AGAINST (limitations):

  • Probabilities are estimates and may be inaccurate
  • Ignores qualitative factors (e.g., employee morale, brand reputation)
  • Doesn't consider risk attitudes
  • Can be oversimplified

Context considerations:

  • Type of business and industry
  • Size and resources of company
  • Availability of reliable data
  • Importance of non-financial factors

Conclusion: Make balanced judgment about usefulness in specific context

Common Mistakes to Avoid

  • Forgetting to subtract costs: Must calculate NET payoffs (revenue - costs)
  • Probabilities don't sum to 1.0: Check that P1 + P2 + ... = 1.0 from each chance node
  • Mixing up nodes: Squares for decisions, circles for chance events
  • Not showing calculations: Must show working for calculation marks
  • Wrong direction: Tree should flow left (decision) to right (outcomes)
  • Forgetting negative signs: Costs and losses should be negative
  • Not comparing all options: Must calculate EV for all choices
  • Ignoring the question: If asked for evaluation, must discuss advantages AND limitations

11. Practice Exercise

Try This: Restaurant Expansion Decision

A restaurant owner must decide whether to expand into a second location.

Options:

  • Option 1: Expand (Investment: $150,000)
  • Option 2: Do not expand

If Expand - Possible Outcomes:

  • • High success (P = 0.4): Annual profit $200,000
  • • Moderate success (P = 0.4): Annual profit $100,000
  • • Failure (P = 0.2): Annual profit $20,000

Tasks:

  1. Calculate the net payoffs for each outcome
  2. Calculate the expected value of expanding
  3. Recommend whether to expand or not
  4. Identify one limitation of this analysis

Solution:

1. Net Payoffs (Profit - Investment):

  • • High success: $200,000 - $150,000 = $50,000
  • • Moderate success: $100,000 - $150,000 = -$50,000
  • • Failure: $20,000 - $150,000 = -$130,000

2. Expected Value:

\[ \text{EV(Expand)} = (0.4 \times \$50,000) + (0.4 \times -\$50,000) + (0.2 \times -\$130,000) \] \[ = \$20,000 - \$20,000 - \$26,000 \] \[ = -\$26,000 \]

3. Recommendation:

DO NOT EXPAND. The expected value is negative (-$26,000), meaning on average the expansion would result in a loss.

4. Limitation:

The probabilities are estimates and may not be accurate. If the actual probability of high success is higher than estimated, the decision might change.

✓ Unit 6 - BMT 6 Summary: Decision Trees

You should now understand that decision trees are quantitative decision-making tools that visually map out different options and their possible outcomes using probabilities and financial values to calculate expected values. Decision trees consist of decision nodes (squares representing choices under management control), chance nodes (circles representing uncertain outcomes with probabilities), branches connecting nodes, probabilities (likelihood of outcomes summing to 1.0), payoffs (financial outcomes at branch ends), and expected values (weighted averages calculated by multiplying each outcome by its probability and summing). The Expected Value formula is EV = Σ(Probability × Payoff). Construction involves drawing left to right, starting with decision nodes, adding branches for options, placing chance nodes for uncertain outcomes, labeling probabilities and payoffs, then working backwards from right to left to calculate EVs at chance nodes and choosing the option with highest EV at decision nodes. Advantages include visual clarity, quantitative objectivity, probability incorporation, multiple option comparison, and structured analysis. Disadvantages include reliance on probability estimates, ignoring qualitative factors, not considering risk attitudes, potential oversimplification, and static nature. In IB exams, must show all calculations, draw clear diagrams with proper symbols, calculate net payoffs (revenue minus costs), verify probabilities sum to 1.0, compare all options, and for evaluation questions discuss both strengths and limitations in business context.

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