University of Illinois at Urbana-Champaign s5

UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN College of Business D E P A R T M E N T O F F I N A N C E

Finance 230 Assignment 9 Fall, 2007 Due: November 2, 2007

For the first five questions, refer to the following whole life policy for a 30 year old male (at the time he purchased the policy):

Face Amount $500,000 Annual Premium 8,900 Dividends in year 20 7,000 first 20 years in total 38,000 Cash Values end of 19th year 189,600 end of 20th year 200,000 Accumulated Value of Dividends at the end of 20 years at 4.5% 57,300

1. What is the 20-year traditional net cost index per $1000 of coverage?

A. -7.93 B. -6.00 C. -3.66 D. 3.80 E. None of the above

Lecture 18 lists the formulas that you need for these first several cost-comparison problems.

Premiums Paid = 8,900/year x 20 years 178,000 -Dividends Received - 38,000 -Cash value at end of period -200,000 = Net cost -60,000 ÷ (Number of years x Policy Face per $1,000) = (20 x 500) ÷10,000 = Traditional Net Cost Index -6.00

2. What is the 20 year interest adjusted surrender cost index per $1000 of coverage based on a 4.5% interest rate?

A. -3.66 B. 2.10 C. 3.28 D. 3.45 E. None of the above

For the next several questions, you will need the annuity due factor.

Annuity due factor = (1+i)(n+1) - (1+i) = (1.045)(21) - (1.045) = 32.783 i 0.045

Accumulated value of premiums at interest = 8,900 x 32.783 291,769 -Accumulated value of dividends at interest -57,300 -Cash value at end of period -200,000 = Total interest adjusted cost =34,469 ÷ (Annuity due factor x $1,000 policy face) = (32.783 x 500) ÷16,391 = Interest adjusted surrender cost index 2.10 3. What is the 20 year interest adjusted net payment cost index per $1000 of coverage based on a 4.5% interest rate?

A. -3.66 B. 3.28 C. 14.30 D. 23.45 E. None of the above

The interest adjusted net payment index is similar to the interest adjusted surrender cost index but does not include the cash value at the end of the period.

Accumulated value of premiums at interest = 8,900 x 32.783 291,769 -Accumulated value of dividends at interest -57,300 = Total interest adjusted net payments =234,469 ÷ (Annuity due factor x $1,000 policy face) = (32.783 x 500) ÷16,391 = Net payments cost index 14.30

4. What is the equivalent level annual dividend per $1000 of coverage based on a 4.5% interest rate?

A. 2.32 B. 3.66 C. 5.73 D. 5.81 E. None of the above (3.50)

-Accumulated value of dividends at interest 57,300 ÷ (Annuity due factor x $1,000 policy face) = (32.783 x 500) ÷16,391 = Equivalent level annual dividend 3.50

5. What is the yearly rate of return for the 20th policy year if the foregone interest rate is 4.5% and the annual renewable term rate for this individual is $2.65 per $1000?

A. -0.53% B. 3.66% C. 4.68% D. 4.95% E. None of the above

The yearly rate of return method follows a complicated formula so you need to be careful and use the right numbers in the right places. Follow the subscripts carefully – they pertain to what year you should be looking at. Also, don’t forget to subtract 1 at the end

Yearly Rate of Return for Policy Year t = CVt + Dt + (YPt)(Ft - CVt)(.001) - 1 Pt + CVt-1 CV = cash value D = dividends YP = yearly price per $1000 of renewal term F = death benefit P = premium paid at beginning of year

Yearly Rate of Return for Policy Year 20 = 200,000 + 7,000 + (2.65)(500,000 – 200,000)(.001) - 1 8,900 + 189,600 6. Which of the following items in a bodily injury claim would represent punitive damages?

A. Hedonic losses B. Pain and suffering C. Hospital bills D. Loss of wages E. None of the above

Hospital bills and loss of wages would both be special damages since you have a specific economic loss associated with them. Hedonic losses (ie. Loss of pleasure from losing one of your senses) and pain and suffering do not have clear economic losses. They are both general damages. Punitive damages are damages intended solely to punish the wrongdoer with the intent of dissuading him or her from acting in such manner again. None of the choices above fits that description.

7. While you are walking to class, you are having an emotional conversation on your cell phone. You are not paying attention to where you are walking and you step into the street right in front of a car. A professor, who is driving under the speed limit, hits you with her brand new Mercedes. Although the professor could have swerved to avoid hitting you, she didn’t want to ruin the alignment on her tires. The professor sues you for denting her car. Which of the following is your best defense?

A. Assumption of risk B. Contributory negligence C. Comparative negligence D. Last clear chance E. None of the above

The Professor in this case had the last clear chance to avoid the accident but chose not to do so. Even though you were negligent because you were not paying attention, you may be able to successfully argue that the Professor should have avoided the accident altogether. You probably could not argue contributory negligence or comparative negligence since the Professor was driving carefully under the speed limit and therefore not negligently.

8. Your house is located on a lake next to a factory. Because the factory has been polluting the lake for 35 years, you figure it would be okay for you to dump your used motor oil into the lake after changing the oil on your car. Ten years later, the Environmental Protection Agency sues both you and the factory for pollution to the lake. An independent expert during the trial determines that the factory is 99.9% liable and you are 0.1% liable and establishes the total cleanup costs to be $100 million. The court awards the EPA $100 million in this case. By the time the verdict is delivered, the factory has burned down, the business is closed and the owners cannot be located. Under joint and several liability, how much are you personally liable for?

A. 0 B. $100,000 C. $1,000,000 D. $100,000,000 E. None of the above

Under joint and several liability, the plaintiff (the EPA in this case) can recover the losses in any proportion from any of the defendants, regardless of their share of liability. The plaintiff may not, however, recover more than the maximum amount of the losses. In other words, the EPA could collect $100,000,000 from either the factory or from you but it could not collect $100,000,000 from both.

9. You have obtained the following 20 year cost comparisons for a $1,000,000 whole life policy from insurers that all have similar very strong financial ratings using the same interest rate (5%). You are concerned that the participating policies will not pay the illustrated dividends, so you want to base your decision on the lowest Interest Adjusted Surrender Cost assuming no dividends are paid. Based on that criterion, which insurer is providing the best value?

Type of Interest Adjusted Equivalent Level Company Policy Surrender Cost Annual Dividend

A Participating 5.78 4.25 B Participating 3.45 3.59 C Participating 3.87 2.45 D Non-participating 6.50 0 E Non-participating 7.20 0

If you are worried about receiving dividends, you can add the equivalent level annual dividend to each company to figure out what the interest adjusted surrender cost would be if the company did not pay dividends. Note that both Company D and Company E are non-participating policies (ie. They do not pay dividends) so you don’t need to add an equivalent level annual dividend.

A = 5.78 + 4.25 = 10.03 B = 3.45 + 3.59 = 7.04 C = 3.87 + 2.45 = 6.32 D 6.50 E 7.20

After adjusting for the equivalent level annual dividend, company C has the lowest interst adjusted surrender cost index so you can say that they provide the best value.

10. Keith Green, the guest speaker on October 19, presented a slide that showed that the market-to- book value for insurance companies is highly correlated with the spread. How did he calculate the spread for this slide?

A. ROE – Equity Cost of Capital B. ROE – (Beta x Equity Cost of Capital) C. ROA x Financial Leverage D. ROE x ROA – Equity Cost of Capital E. None of the above