$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. What considerations may change your decision?

The cost of the emergency generator is $80,000, and if it is installed (I), no losses from this type of incident will be incurred.
If the generator is not installed (I'), there is a 12% chance that a power outage (P) will occur during a year.
If there is a power outage, there is a 0.07 probability that the resulting losses will be very large (HL), or approximately $7 million in net aggregated loss.
Alternatively, it is estimated that there is a 0.93 probability of only slight losses (SL) of around $1 million.

Consider the decision tree attached below.

The loss that will be incurred after the generator is installed is, $80,000.

Compute the loss that will be incurred if the generator is not installed as follows:

[tex]E(\text{Loss})=P(HL|P)P(P)\times \$7000000+P(SL|P)P(P)\times \$1000000[/tex]

[tex]=(0.07\times 0.12\times \$7000000)+(0.93\times 0.12\times \$1000000)\\=58800+111600\\=170400[/tex]

The loss that will be incurred if the generator is not installed is $170,400.

The loss from not installing the generator is more than from installing it.

Thus, SPEA should have install the new power generator.