Your firm faces? a(n) 9% chance of a potential loss of $10 million next year. If

Question

Your firm faces? a(n) 9% chance of a potential loss of $10 million next year. If your firm implements new? policies, it can reduce the chance of the 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 rate is 5%.

a. If the firm is? uninsured, what is the NPV of implementing the new? policies? (round to the nearest dollar) ________________________

b. If the firm is fully? insured, what is the NPV of implementing the new? policies? (round to the nearest dollar) __________________________

c. Given your answer to ?(b?), what is the actuarially fair cost of full? insurance? (round to the nearest dollar) _________________________

d. What is the? minimum-size deductible that would leave your firm with an incentive to implement the new? policies? (round to three decimal places) ______________

e. What is the actuarially fair price of an insurance policy with the deductible in part ?(d?)? ? (Round to the nearest? dollar.)__________________________________

Explanation / Answer

As per rules I am answering the first 4 sub parts of this question

a. Reduction in loss = 9% – 4% = 5%,

Savings = 5% × $10 million = $500,000.

NPV = – 100,000 + 500,000/1.05 = $376,190.

b. If the firm is fully insured, then the loss will be covered by insurance.

So there will be no gain to the firm from the new policies.

NPV in this case = –100,000.

c. If the firm is fully insured it will not be useful to implement the new policies.

Loss expected will be 9%.

Actuarially fair premium = 9% × $10 million/1.05 = $857,143.

d. Let D be the amount of the deductible.

NPV of the new policies = –100,000 + 5%(D)/1.05.

0 = -100000+ 5%D/1.05

D = $2.1 million.

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