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# Decision Tree Risk Analysis

## Decision tree analysis – and Expected Monetary Value

These are one of the techniques used when carrying out the process ‘perform quantitative risk analysis’, and is used as the first step in determining the uncertainties within the project in all of to get better information upon which to make a judgment.

This technique will normally occur by using subject matter experts all people with experience with this type of project.  The focus here will be on the determining those risks that may impact upon schedule or cost of the project.

The Decision Tree analysis will enable you to make better decisions, and to determine the most appropriate actions  for both risk threats and opportunities – and hence assist in the Plan Risk Responses process.

### Expected monetary value (EMV) within the decision tree

The decision tree technique is there to establish a costs order point that based on various risk scenarios, so the decision tree needs to be drawn up correctly and logically.

The best way to do this is to arrange a meeting or workshop so that the various risk scenarios can be brainstormed and probability of the scenario estimated.  From the list, the monetary value must be determined that is associated with each outcome by multiplying the risk probability times the monetary value of each outcome.

The monetary value of the Decision Tree risk outcomes can now be added to get the expected monetary value of the risk of decision.

This is best understood by using a simple example:

Dave owns a condo in the Far East and is considering buying a new apartment in Italy, but his wife would rather spend the money on modernizing their current condo.

Dave had previously considered modernizing your condo, but purchasing or importing modern furniture in your city has been a problem in the Far East.

Remodelling costs of the condo if new furniture and fittings are available will cost \$ 45,000, but there is a 50/50 chance that the furniture is not available locally and will need to be imported which will then cost \$65,000.

Dave has found an old townhouse in Naples but it will need a lot of work to make it habitable. The price is \$ 105,000. He has found a local builder and he has given you a best case cost of \$55,000 and a worst case cost of \$75,000.  The builder advises that the best case is 60% likely.

Dave expects to get \$160,000 for the sale of his condo, and now needs to discuss the possible outcomes with his wife. Draw a decision tree and calculate the Net Path Value (Expected Monetary Value).

Laying out this scenario as a Decision Tree with the various outcomes might look like the left-hand side diagram below:

So once you have the Decision Tree drawn, it is fairly straightforward to calculate the numbers.

Take the assumption of the furniture being available for purchase, this is 50% likely to happen and if it did it would cost \$45,000. So the math is just 0.5 times \$45,000 = \$22,500.

Summing the EMV for the refurbish condo option gives \$57,000, and similarly for the move to Italy, gives \$63,000.

Doing this for each of the outcomes will give you the right-hand side diagram above:

So this suggests a lower risk cost for refurbishing.

Notice that the selling and buying of the properties have not been factored in here for simplicity.

In the real world, this would need to have other factors added, such as the cost of selling and  buying, the likely market situation to do that, the  time frames involved and so on. However, this example is typical of a PMP exam question.