The purpose and key components of decision trees

Decision trees are tools that enable businesses to evaluate various options by factoring in the likelihood of different results and their potential financial returns. They assist in making informed choices by combining estimates of probability with expected financial outcomes.

Key concepts in decision trees

• Probability - This measures the chance of a particular event occurring. Managers typically estimate probabilities based on past experiences or available data, expressing them as decimals (e.g., 0.7 for a 70% chance). The probabilities for an event occurring and not occurring always sum to 1, representing certainty.
• Expected monetary value (EMV) - This calculates the anticipated financial outcome by multiplying the probability of each result by its pay-off and summing these values for a given option.
• Net gain - This determines the overall financial benefit of an option after deducting the initial costs from the EMV.

Formula for expected monetary value

$\text{EMV}=\sum (\text{probability of outcome}\times \text{pay-off of outcome})$

Where:

• Probability of outcome = Likelihood of that result (as a decimal)
• Pay-off of outcome = Financial return if that outcome occurs (£)

Formula for net gain

$\text{Net gain}=\text{EMV}-\text{initial costs}$

Where:

• EMV = Expected monetary value (£)
• Initial costs = Upfront expenses for the option (£)

Features of decision trees

Decision trees use a diagram to represent choices and their potential consequences visually. They include specific symbols and elements to show decisions, uncertainties, and outcomes.

Symbols and elements in decision trees

• Decision node - Shown as a square, this indicates a point where the business must choose between different options.
• Courses of action - Lines extending from the square represent possible choices, with associated costs noted alongside.
• Chance node - Depicted as a circle, this shows points of uncertainty where different outcomes could occur.
• Alternative outcomes - Lines branching from the circle illustrate possible results, each labelled with a probability (as a decimal) and a pay-off value (in monetary terms, such as £).

How to create and use decision trees

Creating a decision tree involves mapping out options systematically and calculating their potential value. Businesses use this process to select the most promising path based on quantitative analysis.

Steps to create a decision tree

1. Identify the main decision and possible courses of action.
2. For each action, outline potential outcomes and assign probabilities to them.
3. Estimate the financial pay-off for each outcome.
4. Calculate the EMV for each course of action by multiplying probabilities by pay-offs and summing the results.
5. Subtract initial costs to find the net gain for each option.
6. Compare net gains and typically select the option with the highest value.

Worked example - Calculating EMV and net gain

A business is deciding whether to launch a new product. The initial cost is £12,000. There are two possible outcomes: success with a probability of 0.7 and a pay-off of £35,000, or failure with a probability of 0.3 and a pay-off of -£4,000 (a loss). Calculate the EMV and net gain for this option.

Step 1: Identify the values

• Initial cost = £12,000
• Success: Probability = 0.7, Pay-off = £35,000
• Failure: Probability = 0.3, Pay-off = -£4,000

Step 2: Calculate EMV

$\text{EMV}=(0.7\times \pounds \mathrm{35,000})+(0.3\times -\pounds \mathrm{4,000})$ $\text{EMV}=\pounds \mathrm{24,500}-\pounds \mathrm{1,200}=\pounds \mathrm{23,300}$

Step 3: Calculate net gain

$\text{Net gain}=\pounds \mathrm{23,300}-\pounds \mathrm{12,000}=\pounds \mathrm{11,300}$

Advantages of decision trees

• Encourage detailed analysis - They force managers to assess probabilities and potential financial returns systematically.
• Require specific data - They demand numerical estimates, avoiding vague claims like "sales will improve."
• Provide visual clarity - The diagram format makes it easier to understand and compare options at a glance.
• Enable objective comparison - Options can be evaluated quantitatively, reducing reliance on intuition.
• Effective in known scenarios - They work well when the business has sufficient experience to make reliable estimates.

Disadvantages of decision trees

• Focus on numbers only - They emphasise quantitative data and overlook qualitative factors, such as staff views on decisions.
• Unreliable estimates - Probabilities and pay-offs are often subjective and may not reflect actual events accurately.
• Potential for bias - The values depend on the creator's perspective, which could skew results towards preferred outcomes.
• Incomplete outcomes - They may not capture all possible scenarios, such as partial successes or varying durations of results (e.g., short-term gains versus long-term failures).
• Dependence on quality of data - If based on inaccurate information, the entire analysis can lead to poor decisions.