More detailed investigation of probability distributions for each uncertainty showed that, in fact, there is a 50-50 chance of the market success being High or Low. There is a 10% chance that the actual Average Change in Price will be 8% per year, 40% chance that it will be 10% per year and 50% chance that the price change will be 14% per year. The decision diagram that we have built previously can be represented as a decision tree. Note that we are treating Change in Cost as known, thus it is not represented in the decision tree.
Every end point on the decision tree represents one of the possible outcomes, or prospects. For example, the very first end point represents a situation where the company had chosen Plan Alpha, then the Market Success turned out to be high and on average the market price was 8% per year. This scenario is expected to result in NPV of $94,108,906 over the next ten years. This dollar amount is then converted into the utility (u-value) using the utility function.
The numbers below each branch for uncertainties represents the probability of that outcome. For example, the probability of market Success being "High" is 50%. Note that this number is the same regardless of the plan chosen. This says that Market Success does not depend on the plan choice.
The expected utility of each alternative is calculated by multiplying the u-values of all prospects of the alternative by the corresponding probabilities and then summing them all up. The blue figure under each decision branch represents the u-value of each alternative. Using utilities instead of the values themselves allows to take into account the decision-maker's rick attitude.
Using the expected utility of each alternative the certain equivalent of that alternative can be calculated by using the inverse of the utility function.
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