FINA2342_A_2023_Review Questions 3_Solutions

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Nov 24, 2024

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1 of 3 THE UNIVERSITY OF HONG KONG HKU Business School 1 st Semester 2023-24 FINA2342_A_Insurance: Theory & Practice Tutorial Review Question #3 Textbook Questions ( Risk Management and Insurance, Harrington & Niehaus) Chapter 11 1 . Sommer Inc. is trying to determine how much to spend on safety equipment for its plant. The first column in the following table gives values for possible expenditures. The second column gives the expected number of worker injuries and the third column gives the expected severity per injury (cost to Sommer per injury) associated with each expenditure level. How much should Sommer spend on safety if it is trying to maximize firm value? Ignore the time value of money. Expenditure Expected Injuries Expected Severity per injury 0 10 $10,000 $15,000 7 8,000 30,000 5 7,000 45,000 4 5,000 60,000 3 5,000
2 of 3 3. Pottier Transportation is trying to decide whether to require its drivers to take a driver safety course. The firm has 100 drivers and the cost of the course per driver is $1,500, which includes the cost to the firm of people not working. If all 100 drivers take the course immediately, the insurance company will reduce the firm’s auto insurance premiums by $80,000 immediately, and by $45,000 in each of the next two years. In the managers’ view, the only benefit of the course is a reduction in insurance premiums. The firm’s chief financial officer says that the appropriate cost of capital is 7 percent. Should the firm require its drives to take the course?
3 of 3 Chapter 26 Q1 Use the following data to estimate the expected total losses for 2021 assuming that the probability distributions of frequency and severity have been and will continue to be stable. Year Frequency of Accidents Average Accident Severity Inflation Rate during Year 2014 33 $1,800 2.0% 2015 25 2,100 1.5 2016 35 3,000 2.5 2017 31 2,800 1.5 2018 29 3,100 2.0 2019 27 3,200 1.8 2020 34 3,500 1.5
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4 of 3 Chapter 20 Q6. Ambrose Motor Corp. has expected earnings before interest payments for the next year equal to $100 million if it does not lose a product liability lawsuit. Interest and principal payments on its debt equal $60 million, leaving $40 million for shareholders if it does not lose a product liability lawsuit. The probability of losing a product liability lawsuit is 2%, and the expected damage if a suit is lost equals $50 million. If the lawsuit is lost, the firm will be unable to make its promised payments to debtholders and it will have to renegotiate its debt payments. The legal and administrative costs of renegotiations equal $5 million. Should Ambrose Motor purchase a liability insurance policy with a $50 million limit for a premium of $1.2 million? Assuming the utility of the cash flow is In (CF). Case 1: If the company chooses not to purchase insurance, the (free) cash flow to the company will be: (in $million) E(U(CF)) = IN(45) x 2% + IN(100) x 98% = 4.5892 Case 2:If the company chooses to purchase insurance, then the (free) cash flow to the company will become: (in $million) U(CF) = IN(98.8) = 4.5931 Ambrose Motor should purchase a liability insurance.
5 of 3 Example from Lecture 3: Fire Insurance Suppose you own a luxury flat which is valued at $20 million. You figure that the chance of a fire is 0.1 and the damage in case of a fire would be $5 million. Assume the utility of overall wealth of homeowners is represented by ln(𝑊) . 1. What is your optimal amount of insurance you would buy? q* = L = $5M 2) What is the insurance premium per unit of protection to be charged by the insurance company if the insurance market is competitive? 𝝅 = p = 0.1 3) If the insurance market is not competitive, what would be the optimal demand for insurance? The optimal demand for insurance would depend on the unit premium charged by the insurer. The higher the premium charged by the insurer, the lower the demand for insurance.