Risk Premiums?

Question

You have a $1,000,000 worth of equipment at this job site and wish to minimize your risk of direct property damage by taking out an insurance policy. The insurance company provides you with its statistical data as shown below:

Type of Damage / Probability% / Amt Of damage%

Total / 0.02 / 100

Medium / 0.08 / 40

Low / 0.10 / 20

No Damage / 99.8 / 0

If the insurance company uses expected value to calculate premiums, then how much would you expect the premium to be, assuming the insurance company adds on $300 for handing and profit?

Answer 1

This is a question out of a project management book (Kerzner's 9th edition, p. 768). It is not necessary to read too far into the question. The question relies more on mathematics ("expected value") to calculate the premium.

Expected value is the sum of all possible variables (referring, in this case, to types of damage), with each variable equal to a certain value multiplied by the probability of occurrence. We have all the necessary information (keep in mind we are determining the expected cost for the insurance company, not the expected gain for the insured):

E(All Damage Variables) = (Total) + (Medium) + (Low) + (None) = ($1 mil x 0.02) + ($400K x 0.08) + ($200K x 0.10) + ($0 x 99.8) = $72000

Don't forget to add the $300 for handling and profit (which I agree seems ludicrous for an insurance company to do), for a grand total of $72,300 (or $6025/month).