Decision trees

• A decision tree is a quantitative and methodical organizational planning tool based on the mathematical concept of probability trees. As a visual tool, it allows managers to see possible options and the probable outcomes, thereby helping them to make more informed decisions.

Conventions in drawing a decision tree are outlined below:

• A square represents a decision node, i.e., a decision that needs to be made

• A circle represents a chance node (or probability node), i.e., the probable outcomes of different decisions

• Probabilities of the different outcomes are shown as decimal numbers, e.g., 0.65 means a 65% chance of the outcome occurring.

• Cross out lines (or strike out lines) indicate the options that are rejected based on quantitative reasoning and logic.

The diagram below shows a decision of a firm to invest in either Project Widmore (which costs $13.5m) or Project Redlands (which costs $10m).

Consider the following scenario for the two projects, and then take a look at the decision tree diagram below that corresponds with these figures:

• Project Widmore has a 65% chance of success, which would generate $20 million in sales revenue. Thus, the likely outcome is $20m × 0.65 = $13m.

• Project Widmore has a 35% chance of failing, which would generate only $11.5m in sales revenue. Hence, the likely outcome is $11.5m × 0.35 = $4.025m.

• Hence, the combined probable outcome for Project Widmore is $13m + $4.025m = $17.025m. After deducting the cost of the project, the probable return on investment is $17.025m – $13.5m = $3.525m.

• For Project Redlands, there is a 75% chance of success in earning $16m. This is a higher probability than success for Project Widmore, even though the return is less ($20m compared with $16m). The probable outcome of success for Project Redlands is $16m × 0.75 = $12m.

• There is a 25% expectation that Project Redlands will fail, in which case the forecast earnings is $11m in sales revenue. Hence, the probable outcome is $11m × 0.25 = $2.75m.

• Hence, the combined probable outcome for Project Redlands is $12m + $2.75m = $14.75m. As the project costs $10m, the probable profit from Project Redlands is therefore $14.75m – $10m = $4.75m.

• The probable profit from Project Redlands at$4.75m is higher than that for Project Widmore at $3.525m.

• Two parallel lines are used in the decision tree diagram to cut through a “branch” which shows the option that is rejected. In this case, as Project Redlands has a higher expected return on investment, Project Widmore is not chosen.

 Top tip!

Remember that examiners will expect a key (legend) to a decision tree diagram. Make sure squares (decision nodes), circles (chance nodes) and crossed out lines (rejected options) are all correctly labelled.

 Top tip!

Check that your probabilities for each chance node in a decision tree diagram adds up to 1.0, i.e. 100%.

The advantages of using decision trees as a decision-making tool include:

• As a planning tool, decision trees offer managers a visual representation of different decisions and choices, with probable and quantifiable outcomes. This makes decision making more informed, objective, and logical.

• It helps managers to consider the various financial risks involved with different choices options, not just the potential financial rewards.

• The results are easy to understand, with tangible quantitative results to support decision making.

• It is a flexible organizational planning tool that can be applied to many different situations and decisions.

The limitations of using decision trees as a decision-making tool include:

• As a purely quantitative planning tool, decision trees ignore qualitative factors (non-financial information) that often affect decision making. For example, there is no consideration of the role of intuitive, emotion or ethical issues in the decision-making process.

• The probabilities are, at best, only forecasts even if based on market research data. This means the predicted outcomes are still unknown. Changes in the external business environment can easily change the probably outcomes, i.e. the data used to construct a decision tree can become out of date by the time managers follow through with their decision.

• As a quantitative decision-making technique, the use of decision trees does not necessarily reduce the amount of risks, whatever the predicted net outcome figures might reveal.

• For very complex decisions with numerous and interconnected options, it can be difficult to construct a decision tree diagram that is concise and succinct.