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 $620 million. The probability of loss is 1.39 percent in one year, and the relevant discount rate is 2.4 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.)
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? (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.)

Answer 1

a. The actuarially fair insurance premium is computed as shown below:

= (Insurance value x Probability of loss) / (1 + discount rate)

= ($ 620,000,000 x 0.0139) / (1 + 0.024)

= $ 8,416,015.625 or $ 8,416,016 Approximately

b. The amount is computed as shown below:

= $ 8,416,015.625 - (Insurance value x Probability of loss) / (1 + discount rate)

= $ 8,416,015.625 - ($ 620,000,000 x 0.0085) / (1 + 0.024)

= $ 8,416,015.625 - $ 5,146,484.375

= $ 3,269,531 Approximately

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