Question

In calculating insurance premiums, the actuarially fair insurance premium is the premium that results in a zero NPV for both the insured and the insurer. As such, the present value of the expected loss is the actuarially fair insurance premium. Suppose your company wants to insure a building worth $280 million. The probability of loss is 1.44 percent in one year, and the relevant discount rate is 3.6 percent.

  

a.	What is the actuarially fair insurance premium? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Round your answer to the nearest whole dollar amount, e.g., 32.)

Insurance premium

$

b.

Suppose that you can make modifications to the building that will reduce the probability of a loss to .85 percent. How much would you be willing to pay for these modifications? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to the nearest whole dollar amount, e.g., 32.)

  

Maximum payment

$

Answer 1

ANSWER

a) Calculate the actuarially fair Insurance Premium as follows

Insurance Premium=Value of asset* Probability of loss/(1+Discount rate)

                                                =$280,000,000*1.44% / (1+0.036)

                                                =4,032,000/1.036

                                                =$3,891,891

So

The Actuarially fair Insurance Premium is =$3,891,891

b)

The maximum amount that the company would be willing to pay for the modification is the difference between the previous expected loss and the current expected loss

Compute the revised insurance premium as follows

Insurance Premium=Value of asset* Probability of loss/(1+Discount rate)

                                =280,000,000*0.85/(1+.036)

=$2,380,000/1.036

                                =$2,297,297

Thus, The revised insurance premium is =$2,297,297

Maximum Amount to pay for the Modifications=PV of the original Premium- PV of the new premium

                                                                         =$3,891,891-$2,297,297

                                                                         =$1,594,594

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