Business have to make decisions all the time. Frequently there is no formal process to help the decision making process. The use of a decision tree can assist with this process says John Davison.

Decision trees

A decision tree will examine the various alternatives and determine the best options according to the choices available and the chances of events happening. It has two elements, costs and consequences. Whist some elements are objective (such as the expected cost) some are subjective, such as the chance of an event occurring. Thus, there is always an element of judgement when using a decision tree.

There are four elements when constructing a decision tree:

  • Identify the choices to be made, this leads to the different outcomes of these choices, these are the branches of the tree;

  • What are the costs or benefits of these choices;

  • What are the chances, probabilities, of these outcomes; and

  • What are the consequences of these decisions, the payoff for each decision

The decision tree will be used to calculate the Expected Monetary Value (EMV) of decisions; this is the consequence of the decision. The EMV is the probability multiplied by the impact of the decision. It should be noted that there are other possible outcomes other than financial such as reputational risk, and these elements also need to be noted in the decision tree. This newsletter will only consider the financial outcomes.

A decision tree is built using branches that represent the possible paths leading from the present to the future. This contains:

  • Decision nodes (green squares) represent the decision gates with all available options;

  • Chance nodes (red circles) represent uncertain future events with impacts and probabilities; and

  • End nodes (blue triangles) represent the final outcome given the decisions made and uncertainty revealed along the way.

Example

As an example, consider that you are a business that is using a poor computer system that needs updating. It is estimated that the cost of the current system is about £10,000 a day due to its inefficiencies. There are two contractors that can provide a solution. The costs have been estimated as follows:

Supplier 1

Supplier 2

Cost

$1 million

$1.3 million

Time to install

30 days

20 days

Possibility of delay

30%

10%

Potential delay

10 days

10 days

This is obviously a very simple example and will only result in a couple of branches of a decision tree. Decision trees are effective where there are multiple branches to help calculate the EMV of multiple decisions.

Prepare the decision tree

The first step is to prepare the decision tree for the various decisions or outcomes that can arise.

Assign Monetary Values

It is then necessary to assign monetary values to the decisions.

Once the various values of the decisions have been calculated and the risks of the outcomes calculated, the EMV can be calculated.

Calculate the Economic Monetary Value

For Supplier One the EMV is the initial cost ($1 million), plus the likelihood of the outcomes. In this case there is a 70% chance of the process taking 30 days at £10,000 a day, and a 30% chance of the process taking 40 days at £10,000 a day. That is:

£1m + (30 X £10,000 X 70%) + (40 X £10,000 X 30%) = £1,330,000.

For Supplier Two the EMV is the initial cost ($1.3 million), plus the likelihood of the outcomes. In this case there is a 90% chance of the process taking 20 days at £10,000 a day, and a 10% chance of the process taking 30 days at £10,000 a day. That is:

£1.3m + (20 X £10,000 X 90%) + (30 X £10,000 X 10%) = £1,510,000.

Decision

If cost alone was the main criteria the choice would be supplier 1. There may, however, be other factors that need to be considered, such as the impact on other areas of the business of the poor computer system. Obviously, for most decisions there will more complex issues which will lead to more branches and a more complex EMV calculation.

Decision trees are useful tools in helping making decisions. But, as with all tools, they only provide assistance and should not be taken at face value or a guarantee of the correct decision. Your own business judgements is also required.

Last reviewed 10 February 2020