Decision tree is the main component of finance, philosophy and decision analysis in university courses. However, many students and graduates fail to understand their purpose, even though these statistics indicate that they play an indispensable role in the company’s financial and economic forecasts.

## Decision Tree Basics

The decision tree is organized as follows: Individuals make major decisions, such as conducting capital projects or choosing between two competing companies. These decisions, which are usually described by decision nodes, are based on the expected results of a specific course of action. An example of such a result is “the estimated increase in revenue by $5 million.” However, since the event indicated by the end node is speculative in nature, the chance node also specifies the probability of achieving a specific prediction.

Since the list of potential outcomes that depends on previous events becomes more dynamic with complex decisions, Bayesian probability models must be implemented to determine the prior probabilities.

Use decision trees in finance

## Binomial Option Pricing in Decision Tree Analysis

Decision tree analysis is usually applied to option pricing. For example, the binomial option pricing model uses discrete probabilities to determine the value of options at expiration. The most basic binomial model assumes that the value of the underlying asset will rise or fall according to the calculated probability of the expiry date of the European option.

However, the situation for American options has become more complicated, where options can be exercised at any time before expiration. The binary tree will consider multiple paths that the underlying asset price may take over time. As the number of nodes in the binomial decision tree increases, the model eventually converges to the Black-Scholes formula.

Although the Black-Scholes formula provides a simpler alternative to option pricing on a decision tree, computer software can create a binomial option pricing model with “unlimited” nodes. This type of calculation usually provides more accurate pricing information, especially for Bermuda options and dividend-paying stocks.

## Use decision trees for real options analysis

The evaluation of real options, such as expansion options and abandon options, must be done using decision trees, because their value cannot be determined by the Black-Scholes formula. Real options represent actual decisions that the company may make, such as whether to expand or contract operations. For example, an oil and gas company can buy a piece of land today, and if the drilling operation is successful, it can buy additional land cheaply. If the drilling is unsuccessful, the company will not exercise the option and it will be worthless when it expires. Because real options provide important value for corporate projects, they are an integral part of capital budgeting decisions.

Individuals must decide whether to purchase options before the project starts. Fortunately, once the probabilities of success and failure are determined, decision trees help clarify the expected value of potential capital budgeting decisions. Companies usually accept items that initially appear to be negative net present value (NPV), but once the real option value is considered, the NPV actually becomes positive.

## Decision tree application for competing projects

Similarly, decision trees apply to business operations. The company constantly makes decisions on issues such as product development, staffing, operations, and mergers and acquisitions. Using a decision tree to organize all considered alternatives, these ideas can be systematically evaluated at the same time.

This is not to say that decision trees should be used to consider every micro decision. But decision trees do provide a general framework for determining solutions to problems and managing the realized consequences of major decisions. For example, decision trees can help managers determine the expected financial impact of hiring employees who fail to meet expectations and must be fired.

## Pricing of Binomial Tree Interest Rate Tool

Although not strictly a decision tree, a binomial tree is constructed in a similar way for the similar purpose of determining the impact of volatility/uncertain variables. Fluctuations in interest rates have a significant impact on the prices of fixed income securities and interest rate derivatives. Binary trees allow investors to accurately evaluate bonds with embedded call options and use the uncertainty of future interest rates to set reserves.

Since the Black-Scholes model is not suitable for the valuation of bonds and interest rate-based options, the binomial model is an ideal alternative. The valuation of enterprise projects usually uses decision trees, which take into account the various possible alternative states of the economy. Similarly, the value of bonds, interest rate lower and upper limits, interest rate swaps, and other types of investment instruments can be determined by analyzing the impact of different interest rate environments.

## Decision tree and business analysis

Decision trees allow individuals to explore ranging elements that may have a significant impact on their decisions. Before playing a multi-million dollar Super Bowl ad, a company’s goal was to determine the different possible outcomes of its marketing campaign. Various issues can affect the ultimate success or failure of expenditures, such as business attractiveness, economic prospects, product quality, and competitors’ advertisements. Once the impact of these variables is determined and the corresponding probabilities are assigned, the company can formally decide whether to advertise.

## Bottom line

These examples provide an overview of typical assessments, which can benefit from using decision trees. Once all the important variables are determined, these decision trees can become very complex. However, these tools are usually essential tools in the investment analysis or management decision-making process.

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