Title: LIFE INSURANCE III: MEASURING THE COST OF INSURANCE
1LIFE INSURANCE IIIMEASURING THE COST OF
INSURANCE
2LIFE INSURANCE PRICING
- Mortality table
- Age cohort
- radix, lx, dx
- Net premium
- Gross premium
3LIFE INSURANCE COST COMPARISON METHODS
- Traditional/Projected net cost method
- Interest-adjusted cost methods
- Surrender cost index
- Net payment cost index
- Belths Formula
4TRADITIONAL 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)
5TRADITIONAL 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
-
6TRADITIONAL 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
7TRADITIONAL 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)
8INTEREST-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)
9INTEREST-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
10INTEREST-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)
11INTEREST-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
12BELTHS 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
13BELTHS 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