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)

Answer 1

1.
Expected Loss =(Probability of loss x Value of building) + (1 - Probability of loss) x NPV for both
=0.0125*245 million+(1-0.0125)*0= $3.0625 million

PV of the expected loss =Expected loss / (1 + K)^t=3.0625*10^6/1.04= 2944711.5385

A fair premium (which is usually paid in advance) is $2,944,711.5385)

2.
Expected Loss =0.009*245 million+(1-0.009)*0=2.2050 million

PV of the expected loss =Expected loss / (1 + K)^t=2.2050*10^6/1.04= $2,120,192.3077

Maximum amount to pay for the modifications =PV of the original premium - PV of the new premium=2944711.5385-2120192.3077=824,519.2308