Question

You own a house worth $800,000 that is located on a river bank. If the river floods moderately, the house will be completely destroyed. This happens about once every 50 years. If you build a seawall, the river would have to flood heavily to destroy your house, which only happens about once every 200 years. What would be the annual premium for a flood insurance policy that offers full insurance? For a policy that pays only 70% of the home value, what are your expected costs with and without a seawall? Do the different policies provide an incentive to be safer (i.e., to build the seawall) ?

Short answer

If the yearly expense of the structure and keeping a seawall is under $\$11,200$each year, we can say that neither the insurance policy will be better or worse.

Step-by-step solution

Content Introduction

The annual project cost is the projection sum that might be brought about in finishing a predetermined task. It is a piece of capital planning used to decide real fixed-cost agreements with different parties.

Content Explanation

With full insurance the expected loss is $800,000\times 0.02=16,000$

With a seawall, the expected loss is localid="1649654243299" $800,000\times 0.005=4000$

The estimated loss will be charged as a premium by the insurance company. The premium is the annual expense you can expect in either circumstance.

With partial insurance,

Without a seawall, the expected loss is $0.7\times 80,000\times 0.02=11,200$

With a seawall, the expected loss is $0.7\times 800,000\times 0.005=2,800$

The estimated loss will be charged as a premium by the insurance company. The premium is the annual expense you can expect in either circumstance.

Without the seawall, $[0.02\times (5,60,000-800,000)+0.98(0\left)\right]-11.200=-16,000$

With a seawall, $[0.005\times (5,60,000-800,000)+0.98]-2,800=-4000$

Tragically, neither the insurance contract is better nor it is regrettable. Although the expenses under the fractional are lower, the normal expense every year is equivalent to full protection.

Regardless you will build the seawall if the annual cost of building and maintaining a seawall is under $11,200 each year.