Question 1: Suppose that a liability insurance policy with a coverage limit of $100,000 (i.e., the insurer will pay liability claims up to $100,000) has a premium of $600. For each of the following people, what is the premium per dollar of personal wealth protected if the policy were purchased?
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Person
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Person's Wealth
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Mary
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$ 5,000
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Curly
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$ 50,000
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Moe
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$100,000
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Alice
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$150,000
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Nancy
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$200,000
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Question 2. Suppose that Skipper's insurer views him as having the following distribution for the present value of losses:
Loss = $20,000 with probability 0.02
Loss = $5,000 with probability 0.04
Loss = $1,000 with probability 0.10
Loss = 0 with probability 0.84
A) What is the fair premium for full coverage if the competitive loading (administrative costs and capital costs) equals 15 percent of expected claim costs?
B) Suppose that Skipper believes his probabilities of losses are one-half of what the insurer believes. What is the loading on the policy from Skipper's perspective?
Question 3. Suppose that a business expects to have profits of $100,000 if it is not sued over the coming year. The probability of a suit is 0.04 and the loss if a suit occurs is $250,000. The firm's tax rate if it earns positive profits is 30 percent. If it makes negative profits, it pays a 0 percent rate.
A) What is the firm's before-tax expected profit without insurance? What is its after-tax expected profit without insurance?
B) Suppose the firm can purchase a liability insurance policy with full coverage for a premium of $11,000. From the insurer's point of view, does this policy have a positive loading?
C) What is the firm's expected before and after-tax profit if it purchases the insurance policy (assume that the premium is a tax-deductible expense)?
D) Compare the expected after-tax profits with and without insurance. Explain.