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 $610 million. The probability of loss is 1.35 percent in one year, and the relevant discount rate is 3.3 percent.

a. What is the actuarially fair insurance premium? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole dollar, e.g., 1,234,567.)

Insurance premium= __________

b. Suppose that you can make modifications to the building that will reduce the probability of a loss to .95 percent. How much would you be willing to pay for these modifications? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to the nearest whole dollar, e.g., 1,234,567.)

Maximum cost= __________

Answer #1

a). Expected Loss = (Probability of loss x Value of building) + [(1 - Probability of loss) x NPV for both]

= (0.0135 x $610M) + [(1 - 0.0135) x $0] = $8.235 million

PV of the expected loss = Expected loss / (1 +
K)^{t}

= $8.235M / 1.033 = $7,971,926.43, or $7,971,926

b). The most you would be willing to pay is the difference between the insurance premium before the modifications and the insurance premium after the modifications. The actuarially fair insurance premium after the modifications will be:

Insurance premium = (Asset value × Probability of loss) / (1 + R)

= ($610,000,000 × 0.0095) / (1 + 0.033) = $5,609,874.15, or $5,609,874

So, the most you would pay is:

Maximum payment for modifications = $7,971,926 - $5,609,874 = $2,362,052

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