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 $245 million. The probability of loss is 1.25 percent in one year, and the relevant discount rate is 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 2 decimal places, e.g., 1,234,567.89). b. Suppose that you can make modifications to the building that will reduce the probability of a loss to .90 percent. How much would you be willing to pay for these modifications? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16). a. Insurance premium b. Maximum cost

Answer 1

1a). Actuarially fair insurance premium = expected loss/(1+ discount rate)

= 1.25%*245,000,000/(1+4%) = 2,944,711.54

1b). If probability of loss is 0.9% then expected loss = 0.9%*245,000,000 = 2,205,000

Actuarially fair insurance premium would be 2,205,000/(1+4%) = 2,120,192.31

Maximum cost which should be paid for the modifications are = 2,944,711.54 - 2,120,192.31 = 824,519.23

2). Loss = (closing price for March futures - price at expiration)*10

= (1,974 - 1,965)*10 = 90.00