1. Whitley Transport Company is a regional trucking company headquartered in a southeastern city of the U. S. The company's risk manager is trying to decide whether to recommend to senior management that all of the company's drivers be required to take a driver safety course.
The firm has 500 drivers and the cost to take the course is $2,500. If all 500 drivers take the course immediately, the insurance company will reduce the firm's auto insurance premiums by $180,000 immediately and by $60,000 in each of the next 4 years. At this point, the management team has not be able to identify any other benefits for the course other than the reduction in insurance premiums The firm's Board has determined that the appropriate cost of capital for the company is 8%.
2. Southern manufacturing has substantial warehousing needs for raw materials. It currently faces the choice of building a single $18 million facility, or building three separate $6 million facilities. Each facility faces the following loss distribution. (The separate facilities are statistically independent.)
Probability
of Loss Percent of
Value Lost
.04 100
.03 50
.94 0
a) What is the expected loss for each warehousing choice?
b) What is the probability of an $18 million loss for each warehousing choice?
c) Assume that a direct loss of $18 million loss will cause the firm to have to pay extra expenses of $2million to stay in business. What will be the impact of Buckeye's warehousing choice on its expected indirect losses?
3. Draw a graph of an insurer's probability distribution for total claims assuming the insurer has expected claims cost of $1.0 billion.
a. On the graph, identify the probability of insolvency if the insurer has economic capital (surplus) of $1.5 billion.
b. Assume the insurer cedes a portion of its liabilities to a reinsurer under a treaty. Show on the graph how the reinsurance impacts the insurer's probability of insolvency.
4. Jones Petroleum Company 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 claim severity per injury associated with each expenditure level.
Loss Control
Expenditures Number of
Worker Injuries Injury
Severity
$0 10 $10,000
$15,000 7 8,000
$30,000 5 7,000
$45,000 4 5,000
$60,000 3 5,000
$75,000 2 5,000
How much should Jones Petroleum spend on safety equipment if its object is to maximize the firm's value?
5. XYL Insurance Corp. estimates that its assets, which are currently worth $1,000 million, will earn a return at the end of the year that is normally distributed with an expected value of 0.05 and a standard deviation of 0.06. It estimates that its liabilities from policies at the end of the year will be normally distributed with an expected value of $850 million and a standard deviation of $50 million. The correlation between asset returns and liabilities equals zero.
Is XYL's probability of insolvency greater than or less than 0.01? Please show your supporting calculations to show how you arrived at your conclusion.