Introduction to Decision Trees

We use Decision Trees to clarify the expected value of capital investment opportunities. Decision Trees can also be helpful in business operations, where companies continuously struggle with big decisions on product development, operations management, human resources, and others. With Decision Tree analysis, we can better evaluate the alternative options. However, we should not use the technique for every minor decision the business faces. Decision Trees only give a general framework to determine solutions and manage them.

This analysis method lets us explore the ranging elements influencing a decision. Trying to determine all the critical variables leads us to create very complex decision trees. However, this technique is still an essential tool in the decision-making process and investment analysis.

We can also present Decision Trees as pay-off tables, showing all the events and choices we can take.

Decision Tree Analysis

Decision Trees are made up of two elements: nodes and branches.

Each branch represents an alternative course of action or a decision. At the end of each branch, there’s a node representing a chance event – whether or not some event will occur. Branches to the right of nodes are the alternative outcomes of a chance event. For each complete course of action through the decision tree, there is a pay-off, shown right of the last branch. It is a common practice to mark decision forks with squares and chance forks with circles when illustrating a Decision Tree.

We base the outcomes for different sequences of decisions and events on the current information available to us. We don’t try to identify all decisions and events when building a Decision Tree. Instead, we focus only on those that are relevant and important to our analysis and the outcomes we want to compare.

Usually, only the first decision point has to be made right away, as the following decision points (if any) are further in time. Executives take into account the costs for each option and the probabilities for the possible outcomes when they evaluate potential actions to take.

Stakeholders and Risk

The expected gains must be looked at together with the inherent risks for each course of action. Different stakeholders in a decision usually look at it from different perspectives. Therefore, we must consider all views when performing our Decision Tree analysis. Let’s look at the example of an investment opportunity to build a new factory, that our business has. The parent company investing the funds expects some investments across their portfolio of subsidiaries to fail and have hedged against that by diversifying their risk exposures. The sales manager of the company has a lot to gain in regards to increased product quality to offer to potential clients, and nothing to lose if the project is not successful. However, for the plant manager that will be in charge of building the new modernized factory, failure may mean losing his job.

Such a situation where we have a significant number of different stakeholder points of view introduces an undesirable element of politics in the decision-making process. To mitigate the risk of such politics leading to wrong decisions, we need to ask who bears the risk and what is the risk and look at each decision from the perspective of each stakeholder, when performing our analysis.

Uncertainty of Alternatives

To account for the uncertainty of options at each decision point, we seek to present it discretely. If we expect a variable to fall within a range (e.g., net cash flows from financing activities is forecasted to be between EUR 50 thousand and EUR 480 thousand), we can break it down into smaller ranges and treat those as discrete options.

Evaluate Investment Opportunities With Decision Trees

Keep in mind that Decision Trees don’t show information that was not already known by the management. Decision Trees have great value in laying out what management knows in a way that enables systematic analysis and leads to a more robust and rigorous decision-making process. The technique is excellent for illustrating the structure of investment decisions, and it can be crucial in the evaluation of investment opportunities.

Decision Trees in financial analysis are a Net Present Value (NPV) calculation that incorporates different future scenarios based on how likely they are to occur. The cash flows for a given decision are the sum of cash flows for all alternative options, weighted based on their assigned probability

To prepare a Decision Tree analysis, we take the following approach:

1. Identify the points of decision and the alternative options available at each of them;
2. Identify aspects of uncertainty and type or range of alternative outcomes;
3. Estimate the values for the analysis:
   • Probabilities of events and results from actions;
   • Costs of and possible gains from various events and activities;
4. Analyze alternative amounts and choose a course (calculate the present value for each state).

Decision Trees don’t provide a ready answer. They instead help management determine which alternative at a particular choice point will give the maximum return, based on the available information.

Rollback

The concept of rolling back is applied when evaluating a Decision Tree. We value each branch and then discount it back to the first decision point. Then we can compare options.

It is important to note that Decision Tree analysis does not provide an answer to which discount rate to use. We usually discount the branches using the Weighted Average Cost of Capital (WACC) of the company, as it shows the blended cost of capital across all sources, both equity and debt. We can also use the expected return on investment calculated via the Capital Asset Pricing Model (CAPM).

Perform Decision Tree Analysis in Excel

Let us perform a Decision Tree analysis to evaluate a potential investment in a new modernized factory for alloy frames, to replace our current steel frames factory. The project will cost EUR 250 thousand. Based on the development of the market, we expect to achieve cost savings of either EUR 135 thousand per year for five years in favorable market conditions, or EUR 100 thousand per year for three years in unfavorable conditions. Our market research shows that there’s an 85% chance of favorable conditions and 15% chance of unfavorable ones.

There’s also a 2% chance the government may introduce anti-dumping legislation on alloy frames, which will turn our project into a failure, as we will not be able to produce alloy frames if such legislation is accepted.

If we decide not to invest in a new factory for alloy frames, we face a 35% chance that we will need to perform significant repairs on our existing production machinery, which will cost us EUR 80 thousand spread equally over two years.

Building our Decision Tree for the option to invest in a new factory, we have the following branches with two chance nodes – one for the anti-dumping legislation and one for the market development.

The next thing we do is evaluate the two possibilities for market development. For the market growth case, we have a five-year cost savings period of EUR 135 thousand per year. We calculate the present value of future cash flows using the company’s WACC of 10%.

Subtracting the initial investment amount, we get the NPV of this state.

We do the same for the possibility where the market shrinks.

For the alternative option to not invest in a new factory, we have the following branches and one chance node, representing the possibility of a break down in production machinery.

We approach the cash outflows for repairs in a similar way to arrive at the following present value of future cash flows.

Now that we have the discounted cash flows for each node of our decision tree, we have a much better visual representation of the possible results of different courses of action.

We then calculate the net present values at each chance point by weighing the possibilities with the probabilities assigned to them.

The table summarizes our calculations. We see that investing in a new factory will have a positive effect on our cash flows, even when taking into account the risks this action faces. Basing our strategy only on the decision tree analysis will mean we select the option to invest, as it appears to be a more economically sound decision.

Conclusion

The unique benefit of Decision Trees analysis is that it combines analytical approaches like Discounted Cash Flows (DCF) and NPV with a clear image of decision points and events. The technique clarifies the connection between current and future decisions and uncertain circumstances. Having such information enables management to consider the available courses of action with more ease and clarity.

Although Decision Tree Analysis is challenging to apply when multiple sources of uncertainty are present, it remains a widely used technique to determine the value of investment opportunities.

Don’t forget to download the Excel file with the example below: