Life, Health and Disability Insurance

1
Life, Health and Disability Insurance

• Personal Financial Planning
• Business 4099

2
Key Issues

• mortality tables form the basis for pricing life
  insurance
• the Income Approach and the Expense Approach are
  the two alternative ways to calculate the amount
  of life insurance required.
• it is important that you learn the meaning of the
  terms and the types of insurance.

3
Key Issues

• In addition, you must complete the assigned
  problems in the Chapterthese will give you
  insight and experience in the use of mortality
  tables, as well as in the pricing of life
  insurance products.
• You can expect to be tested on these concepts in
  the final exam.

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Problem 9 - 1

• a. At age 50 there are 93,325 males surviving out
  of the original 100,000. At age 56 there are
  90,072. The probability of survival, given that
  the man has already reached 50, is
• 90,072 / 93,325 96.5
• b. At age 30, there are 98,608 females surviving
  out of the original 100,000. At age 34 there are
  98,405. The probability of survival, given that
  the woman has already reached 30, is
• 98,402 / 98,608 99.8

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Problem 9 - 2

• Assume a 500,000 term insurance. Using
  Appendix B
• The mortality rate of 48-year-old males is
  .0037.
• Therefore, the pure premium is
• 500,000 (.0037/1.08) 1,712.95

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Problem 9 - 3

• The solution to this problem can be modeled after
  example 9.4 (p. 171) of the text.
• Net Single Premium NSP amount of insurance
  coverage sought times the sum of the present
  values of the condition probability of death of
  the individual for each year given that they
  survived to that year
• The easiest way to do this is on a spreadsheet

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Problem 9 - 3

• See handout spreadsheet
• NSP 11,688.14
• NAP 1,040.15
• You first need to input the statistical data from
  the mortality table
• Calculate the individual probabilities for each
  year
• Calculate the joint probabilities for each year
• Discount the joint probabilities for each year
  then sum
• Multiply the sum of the PV of joint probabilities
  against the size of the insurance policy to get
  NSP
• Sum the PV of individual probabilities and divide
  that into the NSP to get NAP

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Problem 9 - 4

• See handout spreadsheet
• You need to reconstruct Table 9.5 on page 180 of
  the text.
• You are basically asked to redo Example 9.5 of
  the text assuming different after-tax rates of
  return that might be realized on the savings if
  you choose the term insurance route.
• Balance in at an after-tax rate of
• 3 13,292
• 6 18,591
• 10 29,290

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Problem 9 - 5

• In the event of Getta Lifes insolvency, Mr.
  Greens life is covered up to a maximum of
  200,000
• The life time pay out limit of his health and
  dental plan is 60,000 per member of his family.
• His RRSP account at the other company is only
  secured up to 60,000 of the total current amount
  of 70,000.
• His mothers, wifes, and childrens life
  insurance policies are well secured, since their
  individual coverage is well below the CompCorps
  limits of compensation.
• His disability is only covered for the first
  24,000 p.a. or 2,000 per month.

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Problem 9 - 6

• Assuming Laura is a non-smoker and using age 35
  data (Table 9.2 page 174)
• She is currently paying an annual premium for her
  whole life policy of 340 200,000/1.70
• 20 year term 340 250,000/267.50 317,757
• 10 year term 340250,000/197.50 430,380
• She should consider if she needs life insurance
  beyond the 10 year or 20 year term. The premium
  on term life beyond the fixed term of a policy
  will rise with age, while it is constant with a
  whole-life policy.

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Problem 9 - 7

• Assumptions
• real rate of return is 3 p.a.
• rule of thumb tax adjustment is 75
• work to age 65
• both are non-smokers
• they will purchase a 20 year term life.
• Insurance on Mary Qi
• further assume
• overall family expenses decrease by 20,000 p.a.
• Tony will have a marginal tax rate of 20

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Problem 9 - 7 ...

• Insurance Required on Marys Life
• Income shortfall 70,000 - (20,000 15,000)
  35,000
• Before-tax income required 43,750
  (35,000/.8)
• PV required (PVIFAn36,k 3) 43,750
  955,161
• Tax-adjusted .75 (955,161) 716,370
• Premium 262.50(716,370/250,000) 752.20 p.a.

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Problem 9 - 7 ...

• Insurance on Tony
• Further assume
• net effect of lost income, reduced living
  expenses and lost services is 12,000
• Mary will have a marginal tax rate of 45
• Income shortfall 12,000
• Before-tax income required 21,818
  12,000/.55
• PV required (PVIFAn34,k 3) 21,818
  461,054
• Tax-adjusted .75 (461,054) 345,791
• Premium 267.50(345,791/250,000) 370.00 p.a.

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Problem 9 - 8

• Life Insurance
• Using the Income Approach
• (Assume)
• Real rate of return is 3
• Rule of thumb tax adjustment is 75
• Added child care expenses equal to reduction in
  living expenses plus CPP payable to Maria and
  children on death of Walter.
• All the values are in real dollars
• Work to age 65.

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Problem 9 - 8 ...

• Insurance on Walter
• PV of added stuff at death
• lump sum CPP 3,000
• Life insurance 62,000
• 65,000
• (This is the income replacement approach. The
  other assets of the family are accumulated from
  past income.
• PV required (PVIFAn35,k3)31,000 - 65,000
  666,160 - 65,000
• 601,104
• Tax-adjusted .75 (601,104) 450,828

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Problem 9 - 8 ...

• Insurance on Maria
• Assume
• - that child care expenses increase by 3,000 on
  her death
• - Walter will have a marginal tax rate of 30
• Income shortfall 4,000 3,000 7,000
• Before-tax income required 7,000/(1 - .3)
  10,000
• PV required 10,000(PVIFAn36, k3) 218,323
• Tax-adjusted .25 (218,323) 163,742

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Problem 9 - 8

• Using the Expense Approach
• in either death, the mortgage is paid off with
  some of the insurance proceeds. This is
  tax-efficient, since mortgage interest is not
  tax-deductible, but interest on the insurance
  proceeds is taxable. In addition, it allows us
  to simplify the calculation of amount G in Table
  9.1 that follows to an annuity. The mortgage
  would be paid off sometime during the dependency
  period, reducing expenses very significantly.
• Estimate the amount of the mortgage payments
  roughly, as follows. Assume an 8 nominal rate,
  annual payments, 25 years to maturity. Annual
  payment 5,152.23. Round it to 5,000.

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Problem 9 - 8

• Using the Expense Approach
• the familys expenditures will remain at 29,000
  p.a. (their current expenses now Walters
  after-tax income of 25,000 plus Marias income
  of 4,000) minus the mortgage payment of 5,000
  24,000. The savings on the death of Walter are
  offset by increases in child care expenses.
  Marias death leads to an net increase in
  expenses of 3,000 due to increased child care
  and housekeeping costs. The familys total
  expenditures are thus 29,000 3,000 -
  5,000(mortgage) 27,000 Walter loses
  Maria as a tax credit for life. He can claim one
  child as equivalent-to-married, losing only the
  child tax credit, and can also claim part of the
  child care costs. The net tax effect is small
  and we ignore it in the analysis.

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Problem 9 - 8

• Using the Expense Approach
• the real rate of interest is 3
• Assume a 20 adjustment on the amount G in Table
  9.1 for Walter and 15 for Maria (since more of
  her money will come from the tax-paid insurance
  principal, her average tax rate will be lower).
  Her tax on the income other than the insurance is
  assumed to be zero, since she can claim one of
  the children as equivalent-to-married.
• Funeral expenses 15,000
• they wish to provide to age 85 for her, and to
  age 80 for him (approximately the mean life
  expectancy)
• the detailed calculations are found in the
  attached tables.

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Problem 9 - 8

• Using the Expense Approach
• Calculate the cost of insurance
• Assume both are non-smokers.
• For Walter 267.50 (403,702/250,00) 432 p.a.
• For Maria 262.50(144,551/250,000) 152 p.a.
• In reality it might be a bit lower for Walter and
  higher for Maria, since the fixed costs of the
  policy are spread over a different base from the
  250,000 quoted.

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Table 9.1Calculation of the Amount of Insurance
Needed
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Table 9.1continued after Walters death
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Table 9.1Calculation of the Amount of Insurance
Needed
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Table 9.1continued after Marias death