# How Do Decision Trees Work

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## Introduction

A decision tree is a managerial tool that helps corporate managers quantify the potential outcomes of management decisions. A decision tree is a type of graphical model that incorporates the odds of various outcomes occurring as well as the potential payoffs for each of those outcomes. Decision trees create an easily understood structure for evaluating complex decisions and are particularly useful in helping managers decide between various strategies, projects or investment alternatives. Decision trees are widely used in situations in which resources are limited and the prioritization of opportunities is critical.

## Outline of a Decision Tree

A decision tree starts with the central decision that a manager must make. Draw a small square on the left side of the page to represent the central decision, and draw lines out from the square to represent each possible solution. Write a small description of each solution (i.e. "introduce new product", "redevelop existing product", etc.) along each line. At the end of each line, write the possible outcomes for each solution. If the outcome is uncertain, draw a circle; if the outcome leads to another decision that you will need to make, draw a square. Then, starting from the new decision squares, draw additional lines that represent possible decisions that you could make. From the circles, draw lines representing possible outcomes. Write small descriptions of the decisions and possible outcomes along each line to keep things organized. Continue this process until you have mapped out all of the possible decisions and outcomes that might come from the central decision.

## Assign Probabilities and Values

The next step is to assign monetary values to each potential outcome from the decision tree. Record the potential value for each outcome on the far right side of the page, next to the corresponding outcome line. Once monetary values are assigned, you must assign probabilities to each potential outcome. Start at each circle (decision point) on the tree, and assign probabilities to each potential outcome from that decision point. Keep in mind that all probabilities must add up to 100 percent.

## Calculate Expected Values

The final step is to calculate the expected value of each outcome. First, record the cost associated with each decision below the line describing that decision. Next, calculate the expected value for each decision by multiplying the probabilities of the associated possible outcomes by the values of those outcomes and adding the numbers together. That calculation will give you the expected gross proceeds from the decision, and you must subtract the costs of the decision to calculate expected profits. Suppose a particular decision has a cost of \$40,000 and three possible outcomes: good (40 percent probability with a \$100,000 payoff); moderate (40 percent probability with a \$50,000 payoff); and poor (20 percent probability with a \$2,000 payoff). The expected profit associated with this decision is: [(40% x \$100,000) + (40% x \$50,000) + (20% x \$2,000)] - \$40,000 = \$20,400. Continue this process until you have calculated an expected value for each decision path. Choose the decision path that has the highest expected profits based on your calculations.

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