Business Mathematics: Insurance - Property Insurance

To ensure that you have an appropriate amount of coverage for personal property, insurance policies include an indemnity clause which states that if you have a loss, the amount you will receive under the policy will not exceed the value of the property. Consequently, if you overinsure your property, you will be paying additional premiums, but will not be able to obtain excessive benefits.
 

Deductibles are used to eliminate trivial claims and also make the insured bear a part of the loss. The amount of the deductible is subtracted from the amount of loss before any benefit calculation is made.

Example
Mr. Jones has a $500 deductible on the theft portion of his homeowner’s insurance. If Mr. Jones has a robbery and suffers a $4,000 loss, he will receive $3,500 from his insurance company.
Most insurance claims are not total losses. If your property is worth, say, $100,000, experience shows that it is unlikely that you will have a full $100,000 loss. To deter property owners from underinsuring their properties, most policies contain a coinsurance clause.

Let us say your coinsurance rate is 80%, which is typical of many policies. If your insurance coverage is at least 80% of the replacement value of your property, the insurance company will pay to replace what was destroyed, up to the face value of your policy.

If you are insured for less than 80% of replacement value, however, and have a partial loss, your benefit will be proportional to the ratio of your policy limit to 80% of the replacement value of the property.

Example
Bob Allen’s TV repair shop is worth $50,000. However, it is underinsured for only $30,000, and his policy has an 80% coinsurance clause. One day a heavy rain causes a flood and does $4,000 worth of damage. Bob will receive only $3,000 from the insurance company.

If Bob had a policy whose face value was $40,000, he would have received the full $4,000.

Example
Suppose that Bob (see Example 5) has a $500 deductible in his policy. The deductible is always applied first so the insurance company will compute his settlement on the basis of $3,500.

Solved Problems:

10.6   Samuel has a property damage policy which has a deductible of $500. During a storm, a tree falls on his house and does $2,250 worth of damage. Assuming that he has sufficient coverage for his property, how much will he receive from the insurance company?
 

Solution
He will receive a benefit of $2,250–$500 = $1,750.

10.7   Bill Sawyer’s home has a replacement value of $350,000. When he purchased the home 5 years ago, he insured it for $200,000 and never updated his policy. His policy has an 80% coinsurance clause. One day, a pipe burst and caused $22,000 worth of water damage. How much will Bill collect on his policy?
 

Solution
Since his policy has a face value of less than 80% of his home’s replacement value, Bill cannot collect his full damages.


10.8   When a car drove through Jim and Emma Brown’s summer home, the cost of repairs was $14,200. The replacement value of the home is $140,000, and they carried an insurance policy of $120,000 with a $500 deductible and an 80% coinsurance clause. How much will the insurance company pay toward repairs?
 

Solution
Since their $120,000 policy was in excess of 80% of the $140,000 replacement cost of the home, the insurance company will pay for the repairs in full, less the deductible amount. Therefore the Browns will get a check for $14,200–$500 = $13,700.

10.9   Jacque owns a French restaurant whose value is $400,000. The restaurant has a fire which does $60,000 worth of damage. How much will Jacque receive if
(a)  He has insurance in the amount of $350,000 with a $2,000 deductible?
(b)  He has insurance in the amount of $300,000 with a $2,000 deductible?
 

Solution
(a)  Since the face value of the policy exceeds 80% of the value of his restaurant (80% of $400,000 = $320,000), Jacque will receive $60,000 less the $2,000 deductible from the insurance company. His total benefit will be $58,000.
(b)  Now Jacque is underinsured. The deductible is applied first so the insurance company will compute his benefit on the basis of a loss of $60,000–$2,000 = $58,000.