CatIns Corp.(a fictitious name)sells homeowners' insurance contracts to homes along the shores of the Gulf of Mexico.The contract provides protection against hurricanes and has the following features:
•Annual premium $20,000.
•Fixed deductible $10,000.
•Maximum coverage amount $400,000 (which is less than the value of each home).
•The contract pays for losses from one hurricane in a given year.
Assume that if a hurricane hits,it does the same dollar damage to all homes covered by the insurance policy.
-Suppose that the insurance company CatIns buys reinsurance that pays for hurricane losses to a home over $150,000 for a premium of $5,000 payable to a reinsurance company.If the company has insured 200,000 homes,the maximum amount that CatIns can lose would be:

Question

Quizplus · Accepted Answer

Maximum loss that CatIns can incur in case of a hurricane is calculated as follows:

Total insured value= $20,000 x 200,000 = $4 billion
Maximum coverage per home = $400,000
Reinsurance coverage per home = $150,000
Therefore, CatIns maximum exposure per home = $400,000 - $150,000 = $250,000

So the maximum loss that CatIns can incur if all 200,000 homes suffer losses of $150,000 or more is:

$250,000 x 200,000 = $50 billion

However, CatIns has reinsurance to cover losses above $150,000. Hence, the maximum loss it can incur is limited to the difference between its maximum exposure per home and reinsurance coverage per home, which is:

($250,000 - $150,000) x 200,000 = $20 billion

Adding the original insured value of $4 billion gives the maximum loss that CatIns can incur as $24 billion. Since none of the options listed match this amount, the closest answer is (C) $25 billion.