Decision Trees

In a capital budgeting exercise, the decision-maker has to identify and evaluate the various alternative courses of action leading to the investment decision. A decision tree captures these alternatives in form of a diagram and is useful for clarifying the range of alternative course of action, assessing possible outcomes.

In a statistical sense, when a sequential series of conditional decisions are required to be taken under conditions of uncertainty, decision tree model comes in handy to visualize and evaluate all possible options for action.

Consider this example. The purchase of an asset could lead to an increase in sales. This increase can either be low, medium or high with probabilities of 0.5, 0.3 and 0.2 respectively. Each of these could be referred to as a branch and may yield differing contributions and fixed costs, and in turn to differing profit levels giving rise to various outcomes. Such possibilities are captured in decision tree.

There are two stages in preparing decision tree. The first step is drawing the decision tree itself, in a manner that reflects all outcomes and choices. The second step is to incorporate probabilities, relevant values and derive expected monetary values.

Rules for drawing a decision tree diagram

Some basic rules in drawing the decision tree are:

Rule 1 : A decision tree begins with a decision point. A decision point ( also known as node) is represented by a rectangle. An outcome point (also known as chance node) is denoted in circle.

Rule 2 : Decision alternatives (e.g. sales volume in the preceding example) are shown by a straight line originating from decision node.

Rule 3 : A decision tree diagram is drawn from left to right. The rectangles and circles are sequentially numbered.

Rule 4 : Values and probabilities for each branch are then incorporated.

Evaluation and decision rules

A decision tree is analyzed and evaluated using toll-back method. That is the value of each circle and each square is computed by evaluating from right to left. This technique proceeds from last decision in the sequence, wand works back to the first, for each of the possible decisions. There are two rules in this evaluation.

Rule 1 : The expected monetary value at a chance node (branches emanating from a circle) is aggregate of the expected values of the various branches and emanate from the chance node.

Rule 2 : The expected value at a decision node (branches emanating from a square) is the highest amongst the expected values of the various branches that emanate from the decision node.

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