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life insurance iii: measuring the cost of insurance

LIFE INSURANCE PRICING. Mortality tableAge cohortradix, lx, dxNet premiumGross premium. LIFE INSURANCE COST COMPARISON METHODS. Traditional/Projected net cost methodInterest-adjusted cost methodsSurrender cost indexNet payment cost indexBelth's Formula. TRADITIONAL NET COST METHOD. Total premiums paid over t years ? Dividends received over t yearsNet premiums paid over t years ? Policy cash value at end of t years

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life insurance iii: measuring the cost of insurance

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    1. LIFE INSURANCE III:MEASURING THE COST OF INSURANCE

    3. LIFE INSURANCE COST COMPARISON METHODS Traditional/Projected net cost method Interest-adjusted cost methods Surrender cost index Net payment cost index Belth’s Formula

    4. 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)

    5. 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

    6. TRADITIONAL NET COST-cont’d 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

    7. TRADITIONAL NET COST-cont’d

    8. INTEREST-ADJUSTED COST METHOD:SURRENDER 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)

    9. INTEREST-ADJUSTED SURRENDER COST INDEX Nonpar Policy-10 years FV Prem. @ 5%* $ 3311.60 FV Div. @ 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

    10. INTEREST-ADJUSTED COST METHOD:NET 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 ??(1+i)] NPC index = NPC/face (000s)

    11. INTEREST-ADJUSTED SURRENDER COST INDEX Nonpar Policy-10 years FV Prem. @ 5%* $ 3311.60 FV Div. @ 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

    12. BELTH’S 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 = insured’s 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

    13. BELTH’S 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

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