FIN 322
Insurance and Risk Management
Prof. Thistle
Spring 2011
EXAM 2
Multiple Choice
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. B A A B B B B C A A C A B C A D C C C B C C B C c Part B. Essay (10 pts each) WRITE ALL ANSWERS IN THE EXAM BOOK Please write legibly (If I can’t read it, it’s wrong). 31. The three approaches to calculating the amount of life insurance to purchase are the human life value approach, the needs approach and the capital requirements approach. For the human life value approach: (a) Describe the basic steps in the calculation. (b) Explain the weaknesses of that approach. Human Life Value Approach: (A) (1) Estimate the individual's average annual earnings over his or her productive lifetime, (2) Deduct taxes, insurance premiums, and the costs of self‐maintenance, (3) Determine the number of years to the contemplated age of retirement, (4) Using a reasonable discount rate, determine the present value of the family's share of earnings for the period determined in step c. (B) Weaknesses: (1) Ignores other sources of income, (2) Simple forms assume constant earnings and expenses, (3) Income allocated to family can change, (4) Choice of discount rate critical. 32. Sonja purchased a $100,000 ordinary life insurance policy on her life. The waiver‐of‐premium and guaranteed purchase options are attached to the policy. In each of the following situations, indicate the extent of the insurer’s obligation, if any, to Sonja or to Sonja’s beneficiary. Identify the appropriate policy provision or rider that applies in each case. Treat each situation separately. (a) Sonja fails to pay the second premium due on January 1. She dies on January 15. (b) Sonja commits suicide three years after the policy was purchased. (c) At Sonja’s death at age 43, the insurer discovers that Sonja deliberately lied about her age. She indicated her age was 25 when she was in fact 26 at the time the policy was purchased.. (d) Sonja is seriously injured in an automobile accident. After six months, she is still unable to return to work, has no income and cannot afford to continue paying the life insurance premiums. a. The death claim must be paid since the insured died during the grace period when the policy was still in force. b. The death claim is paid since the two‐year suicide period has expired. c. The policy proceeds will be reduced. Under the misstatement‐of‐age clause, the amount payable is the amount that the premium would have purchased at the correct age. d. Under the waiver‐of‐premium provision, all premiums would be waived after a six‐month waiting period if she is totally disabled. A retroactive refund of the premiums paid during the first six months would be paid. 33. A participating ordinary life insurance policy in the amount of $100,000 is issued to an individual aged thirty‐five. The following cost data are given. Assume a 5 % discount rate and a 20 year time horizon. Annual Premium $445 Annual Dividend $0 annually, years1‐5 $50 annually, years 6‐20 Cash value at 20 years $5709 (a) Compute the cost of the policy using the surrender cost index. (b) Compute the cost of the policy using the net payment cost index. (a) Surrender Cost Index Future Value of Premiums $15,450.07 Less Future Value of Dividends ‐1,078.93 Less Cash Value ‐5,709.00 Net Future Value $8,662.14 FVAD interest factor 35.7193 Annual Cost $249.49 (C) Net Payment Cost Index Future Value of Premiums $15,450.07 Less Future Value of Dividends ‐1,078.93 Net Future Value $14,371.14 FVAD interest factor 35.7193 Annual Cost $402.34 34. Both fixed and variable annuities can provide lifetime income to annuitants, but they differ in important ways. Compare and contract fixed and variable annuities with respect to:. (a) Determining how premiums are invested (b) Stability of income payments after retirements (c) Death benefits is the annuitant dies before retirement. (a) The insurer determines how the premiums are invested in a fixed annuity. As such, the investment risk falls on the insurer. The annuity owner determines how the premiums are invested in a variable annuity. The annuity owner has a choice of investment portfolios in which the premiums are invested, such as a growth stock fund, bond fund, or international fund. The investment risk falls on the annuity owner. (b) The income payments in a fixed annuity are guaranteed and fixed and generally do not change. The income payments in a variable annuity change periodically depending on the value of the annuity units. (c) In a fixed annuity, the death benefit prior to retirement is usually the gross premiums paid without interest, or the cash value of the contract if larger. In a variable annuity, the death benefit is the amount invested in the contract, or the value of the account at the time of death, whichever is larger. Some variable annuities pay enhanced death benefits, such as periodically adjusting the value of the account to lock in investment gains. 35. Brittany, age 28, purchased a individual major medical insurance policy with a lifetime limit of $1 million, a calendar year deductible of $1000, an 80‐20 coinsurance provision. Brittany had emergency surgery for an inflamed appendix. Covered medical expenses are $31,000. Brittany also lost $1000 in wages because she could not work for one week. (a) What is the amount paid by insurer? (b) What is the amount paid by the Brittany? (c) What is the amount paid by the insurer if the policy has an annual stop‐loss limit of $3,000? (a)Covered medical expenses are $31,000. Brittany must meet a $1000 deductible. In the absence of a stop‐loss provision, the insurer would pay 80 percent of $30,000, or $24,000. A major medical policy does not cover the loss of wages. (b)Brittany must meet a $1000 deductible. In the absence of a stop‐loss provision, Brittany would pay 20 percent of $30,000, or $6000. (c) With a stop‐limit, Brittany would pay only $3000 plus the deductible of $1000, so the insurer would pay$27,000. FORMULAS PV = FV
1
(1 + r )
T
FV = PV (1 + r ) T
1⎡
1 ⎤
PVA = C × ⎢1 −
⎥
r ⎣⎢ (1 + r ) T ⎥⎦
FVA = C ×
[
]
1
(1 + r ) T − 1
r
PVAD = (1 + r ) PVA
FVAD = (1 + r ) × FVA