Key Answer Department of Policy Analysis and Management PAM 423: Risk Management and Policy Problem Set 3 Spring 2008
1. A product manufactured by Harrington, Inc. in 2000 injures Greg Niehaus in 2005. Harrington purchased annual liability insurance coverage for all years 2000-2008, with coverage renewing each year on January 1. Niehaus sues Harrington for damages in 2007. A. If Harrington's insurance is occurrence-based coverage, which year's policy provides coverage for the lawsuit? The 2005 policy. B. If Harrington's insurance is claims-made coverage with the retroactive date for each policy set to 2000, which year's policy provides coverage for the lawsuit? The 2007 policy. C. Assume that Harrington's insurance coverage has a self insured retention (SIR) of $100,000 and a primary per occurrence limit of $400,000. Harrington also has a first excess layer with $2 million per occurrence limit in excess of $500,000, and a second excess layer with $5 million per occurrence limit in excess of $2,500,000. Illustrate Harrington's insurance program with a coverage chart.
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Either of the following coverage charts is correct:
$7,500,000
Excess 2 Excess 2 $2,500,000 to $7,500,000 Excess 1 $500,000 to $2,500,000 Primary $100,000 to $500,000 SIR $0 to $100,000 $2,500,000 Excess 1
$500,000 Primary 2
$100,000 SIR D. Harrington's insurance companies settle the lawsuit with Niehaus for $3 million. $0 How much, if anything, will each insurer (primary, first excess, second excess) have to pay? How much, if anything, will Harrington have to pay? Harrington will pay $100,000. Primary insurer will pay $400,000. First excess insurer will pay $2,000,000. Second excess insurer will pay $500,000. 2. Consider the following three year finite risk contract: (1) the insured firm pays $2 million premiums per year; (2) the insurer deducts a fee equal to 10 percent of each year's premium; (3) the insurer credits interest at 5 percent per year on the year's beginning balance less its fee; (4) the insurer pays a maximum of $9 million in losses over the three year contract period. Assume that premiums and fees are paid at the beginning of each year and losses are paid at the end of each year. Ignore discounting. A. Show the annual cash flows under the contract if losses equal $2 million in year 1, $4 million in year 2 and $1 million in year 3.
Year 1 Initial Balance Premium Fee Beginning Balance Loss Interest Ending Balance Year 2 Year 3 $0 -$110,000 -$2,225,500 $2,000,000 $2,000,000 $2,000,000 -$200,000 -$200,000 -$200,000 $1,690,000 -$4,000,000 $84,500 -$2,225,500 -$425,500 -$1,000,000 -$21,275 -$1,446,775
$1,800,000 -$2,000,000 $90,000 -$110,000
B. Briefly explain the benefits to the policyholder from purchasing this finite risk contract. The insured transfers the loss-timing risk to the insurer (smoothes losses over time), and receives a more certain tax deduction by paying premiums to the insurer (rather than just being able to deduct losses at the time they are paid out); the fact that the insured pays only some portion of any ending deficit to the insurer also means that the contract provides some (small) amount of risk transfer to the insurer.
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3. Consider the following retrospectively rated policy: insurance the premium equals 75 percent of the loss amount experienced, except that it is subject to a minimum premium of $50,000 and a maximum premium of $200,000. A. Illustrate on a carefully labeled graph the premium charged to the insured firm as a function of the losses it experiences. Slope=.75 200,000 50,000 66,667 266,667 Loss
B. What will the premium charge be if the firm's losses are $80,000 during the year? Premium= .75(80,000)= 60,000 C. What will the premium charge be if the firm's losses are $350,000 during the year? Premium= .75(350,000)= 262,500. Since this is greater than 200,000, the maximum, they will only have to pay 200,000. 4. Griffin Go-Carts currently purchases liability insurance of $150 million in excess of a $5 million self insured retention (SIR). The premium for this insurance coverage is $50,000. With the $5 million SIR, Griffin expects to pay retained losses for accidents during the year equal to $1 million. Griffin expects that of the retained losses will be paid at the end of the current and the other will be paid at the end of the next year. Griffin is considering changing its SIR to $2 million. With this SIR its liability insurance premium will be $170,000 and its expected value of retained losses for accidents that occur during the year will be $900,000. Griffin expects that of the retained losses will be paid at the end of the current and the other will be paid at the end of the next year. Griffin's discount rate is 10 percent per year and its income tax rate is 34 percent. Griffin's decision horizon is 1 year because it can change its SIR again next year (note, however, that cash flows for retained losses extend over 2 years). A. Calculate the discounted present value of expected after-tax costs of each insurance program. Based on this comparison, which SIR should Griffin choose? Current insurance program: $50,000 .34($50,000)/1.10 + $500,000(1-.34)/1.10 + $500,000(1-.34)/1.102 =$607,272.72
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New insurance program: $170,000 = .34($170,000)/1.10 + $450,000(1-.34)/1.10 + $450,000(1-.34)/1.102 =$632,909.10 The firm should choose the current program based on this comparison. B. Calculate the discounted present value of expected after-tax costs of each insurance program assuming that retained losses equal the retention limits (of $5 million and $2 million, respectively) rather than the expected values. Based on this comparison, which SIR should the company choose? Current insurance program: $50,000 - .34($50,000)/1.10 + $2,500,000(1-.34)/1.10 + $2,500,000(1-.34)/1.102 =$2,898,181.81 New insurance program: $170,000 - .34($170,000)/1.10 + $1,000,000(1-.34)/1.10 + $1,000,000(1-.34)/1.102 =$1,262,909.10 The firm should choose the new program based on this comparison. C. How (if at all) should Griffin use the calculations in part B in its risk management decision making? Part B is a sensitivity analysis (the "worst case scenario") that Griffin should use to help it determine the cost of uncertainty associated with each plan. By looking at the highest possible cost and considering what the consequences for the company would be under that scenario, Griffin can determine whether it has the capability to bear that risk.
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