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 $600 million. The probability of loss is 1.31 percent in one year, and the relevant discount rate is 4.2 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 .80 percent. How much would you be willing to pay for these modifications?

Answer 1

1.

Expected Loss =(Probability of loss x Value of building) + (1 - Probability of loss) x NPV for both=0.0131*600+(1-0.0131)*0= 7.86 million

PV of the expected loss =Expected loss / (1 + K)^t= 7.86/1.042= $ 7,543,186.18

Fair premium (which is usually paid in advance) is $ 7,543,186.18

2.

Expected Loss =(Probability of loss x Value of building) + (1 - Probability of loss) x NPV for both=0.0080*600+(1-0.0080)*0= 4.80 million

PV of the expected loss =Expected loss / (1 + K)^t= 4.80/1.042= $4,606,525.912

Maximum amount to pay for the modifications =PV of the original premium - PV of the new premium=7543186.18-4606525.912=2,936,660.268