Insurance on Property - 2.2

State the amount the insured will be entitle to recover in each of the following cases. Give reasons for each answer and show your calculations.

In all cases, the full value of the property insured is $500,000. The fire policy is subject to an 80% coinsurance clause and a 2% waiver of coinsurance clause.

Amount of Insurance Amount of Loss
A. $300,000 $2,000
B. $450,000 $100,000
C. $350,000 $ 80,000
D. $300,000 $20,000

Answer:

The recovery for any loss under a policy with coinsurance before considering the waiver is calculated by this formula,

Amount of Recovery = Amount of Loss * Amount Carried / Amount Required

where the Amount Carried is the specified amount of insurance and Amount Required is the coinsurance of the total value of the property insured. In this case, the Amount Required is $400,000, which is the 80%, the coinsurance, of $500,000, the full value of the property.

The waiver of the coinsurance clause in the policy is 2%, which nullifies the coinsurance clause for losses less than 2% of the amount of insurance. Only when the loss exceeds 2%, the coinsurance clause will apply.

A. The waiver is 2%*$300,000 and results $6,000. The amount of loss is $2,000 and it doesn't exceed the waiver. Thus the coinsurance clause will not apply and the amount of recovery will be the full amount of loss, which is $2,000.

B. The waiver is 2%*$450,000 and results $9,000. The amount of loss is $100,000 and it exceed the waiver. The coinsurance clause will click. However, since the amount of insurance also exceeds the $400,000 minimum required by the coinsurance clause, the amount of recovery will the full amount of loss, $100,000.

C. The waiver is 2%*$350,000 and gets $7,000. The amount of loss is $80,000 and exceeds the waiver. The coinsurance clause will work. At the same time, the amount of insurance is less than $400,000 which is minimum required. We use the formula

$350,000/$400,000 * $80,000 = $70,000

Therefore, the amount of recovery is $70,000.

D. The waiver is 2%*$300,000, $6,000. The amount of loss $20,000 is greater than the waiver. The coinsurance clause will apply. The amount of insurance is less than the minimum required. We use the formula

$300,000/$400,000 * $20,000 = $12,000

The $12,000 is the amount of recovery which the insured entitles.