Question

The SPEA’s administration was concerned about the potential loss that might occur in the event of a power failure. The school estimated that the loss from one of these incidents could be as much as $10 million, including losses due to interrupted student service and potential loss of data collected for years in NSF and DoD sponsored projects. One alternative the school is considering is the installation of an emergency power generator. The cost of the emergency generator is $80,000, and if it is installed, no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 12% chance that a power outage will occur during a year. If there is an outage, there is a .07 probability that the resulting losses will be very large, or approximately $7 million in net aggregated loss. Alternatively, it is estimated that there is a .93 probability of only slight losses of around $1 million. Using decision tree analysis, determine whether the SPEA should have install the new power generator.

Answer 1

Solution:

Decision tree enclosed.

Computation of probabilities:

At a cost of $8 Million:

Construction; Loss probability = 0.5 * 0 = 0

No Construction; No loss probability = 0.5 * 0 = 0.5

At a cost of $7 Million:

No Construction; Loss probability = 0.5 * 0.12 * 0.07 = 0.0042

At a cost of $1 Million:

No Construction; No loss probability =0.5 * 0.12 * 0.93 = 0.0558

Thus best choice will be not to construct.