Problem: Your firm faces a 9% chance of a potential loss of $10 million next year. If your firm implements new policies, it can reduce the chance of this loss to 4%, but these new policies have an upfront cost of $100,000. Suppose the beta of the loss is 0, and the risk-free interest is 5%.
a. If the firm is uninsured, what is the NPV of implementing the new policies?
b. If the firm is fully insured, what is the NPV of implementing the new policies?
c. Given your answer to part (b), what is the actuarially fair cost of full insurance?
d. What is the minimum-size deductible that would leave your firm with an incentive to implement the new policies?
e. What is the actuarially fair price of an insurance policy with the deductible in part (d)?