LIFE INSURANCE III: MEASURING THE COST OF INSURANCE

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LIFE INSURANCE IIIMEASURING THE COST OF
INSURANCE
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LIFE INSURANCE PRICING

• Mortality table
• Age cohort
• radix, lx, dx
• Net premium
• Gross premium

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LIFE INSURANCE COST COMPARISON METHODS

• Traditional/Projected net cost method
• Interest-adjusted cost methods
• Surrender cost index
• Net payment cost index
• Belths Formula

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TRADITIONAL NET COST METHOD

• Total premiums paid over t years
• ? Dividends received over t years
• Net premiums paid over t years
• ? Policy cash value at end of t years
• Net insurance cost
• Net cost per year Net insurance cost/t years
• Net cost per 1000 Net cost per year/face
  (000s)

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TRADITIONAL NET COST EXAMPLE

• Assume
• - 25-year old male
• - 25,000 death benefit
• - two cash value policies
• nonparticipating policy
• annual premium 250.75
• participating
• annual premium 341.50

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TRADITIONAL NET COST-contd

• Nonpar Policy-10 years
• Premiums 2507.50
• Dividends ? 0
• Terminal Div. ? 0
• Cash Value ?1750.00
• Net Cost 757.50
• Net cost per year
• 757.50/10 75.75
• Net cost per 1000
• 75.75/25 3.03

Participating Policy-10 Years Premiums
3415.00 Dividends ????? 854.00 Terminal Div. ?
250.00 Cash Value ? 2000.00 Net Cost
311.00 Net cost per year 311.00/10
31.10 Net cost per 1000 31.10/25 1.24
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TRADITIONAL NET COST-contd
Nonpar Policy-20 Years Premiums
5015.00 Dividends 0 Terminal
div. ?? 0 Cash value ?
5100.00 Net cost (85) Net cost per
year (85)/20 (4.25) Net cost per 1000
(4.25)/25 (.17)
Participating Policy-20 Years Premiums
6830.00 Dividends ? 2625.75 Terminal
div. ???? 450.00 Cash value ?
5475.00 Net cost (1720.75) Net cost per
year (1720.75)/20 (86.04) Net cost per
1000 (86.04)/25 (3.44)
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INTEREST-ADJUSTED COST METHODSURRENDER COST
INDEX

• Rationale Assume the insured survives t years,
  then surrenders the policy for its cash value.
  IASC is equivalent annual cost per 1000 of
  coverage, given opportunity rate.
• t years premiums compounded at opportunity rate
• ? t years dividends compounded at opportunity
  rate
• Net interest-adjusted premiums paid over t years
• ? Cash surrender value at end of t years
• Interested-adjusted insurance cost (IAIC) at
  year t
• Interested-adjusted surrender cost (IASC)
  IAIC/FVIFA i,t ? (1 i)
• Surrender cost index IASC/face (000s)

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INTEREST-ADJUSTED SURRENDER COST INDEX

• Nonpar Policy-10 years
• FV Prem. _at_ 5 3311.60
• FV Div. _at_ 5 ???????????????0
• Terminal Div.-yr 10 ? ????????0
• Cash Value-yr 10 ???1750.00
• Interest-adjusted
• insurance cost (IAIC) 1561.60
• Interest-adjusted surrender cost (IASC) per year
• 1561.60/13.2068 118.24
• IASC per 1000 at end of yr 10
• 118.24/25 4.73
• Future value annuity due

Participating Policy-10 Years FV Prem. _at_ 5
4510.12 FV Div. _at_ 5
??1018.76 Terminal Div.-yr 10 ?
250.00 Cash Value-yr 10 ?
2000.00 Interest-adjusted insurance cost (IAIC)
1241.36 Interest-adjusted surrender cost
(IASC) per year 1241.36/13.2068
93.99 IASC per 1000 at end of yr 10
93.99/25 3.76 Future value annuity due
Future value ordinary annuity
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INTEREST-ADJUSTED COST METHODNET PAYMENT COST
INDEX

• Rationale Assume insured dies at end of
  comparison period --therefore, ignore the
  terminal dividend and the end-of-period cash
  values in computing the net payment cost values.
• t years premiums compounded at opportunity rate
• ? t years dividends compounded at opportunity
  rate
• Net interest-adjusted premiums paid over t years
• Net payment cost (NPC) at year t
• Net interest-adjusted premiums/FVIFA i,t
  ??(1i)
• NPC index NPC/face (000s)

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INTEREST-ADJUSTED SURRENDER COST INDEX

• Nonpar Policy-10 years
• FV Prem. _at_ 5 3311.60
• FV Div. _at_ 5 ???????????????0
• Interest-adjusted
• payment cost (IAPC) 3311.60
• Interest-adjusted payment cost (IAPC) per year
• 3311.60/13.2068 250.75
• IAPC per 1000 at end of yr 10
• 250.75/25 10.03
• Future value annuity due

Participating Policy-10 Years FV Prem. _at_ 5
4510.12 FV Div. _at_ 5
??1018.76 Interest-adjusted payment cost (IAPC)
3491.36 Interest-adjusted surrender cost
(IAPC) per year 3491.36/13.2068
264.36 IAPC per 1000 at end of yr 10
264.36/25 10.57 Future value annuity due
Future value ordinary annuity
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BELTHS FORMULA

• (P CVP)(1 i) - (CV D)
• BF
  (DB - CV)(0.001)
• where BF yearly price per 1000 of
  protection
• P annual premium
• CVP cash value at end of preceding year
• i insureds opportunity rate
• CV cash value at end of current year
• D dividend in current year
• DB death benefit at end of year
• Compare BF to age-adjusted benchmark values

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BELTHS FORMULAAGE-ADJUSTED BENCHMARKS

• Age Benchmark Price
• Under 30 1.50
• 30-34 2.00
• 35-39 3.00
• 40-44 4.00
• 45-49 6.50
• 50-54 10.00
• 55-59 15.00
• 60-64 25.00
• 65-69 35.00
• 70-74 50.00