Endowment Reserve Certification Under a Valuation-Basis Change
A life insurer sold a 20-year endowment policy to a male aged exactly 40. The sum assured is IRR 1,000,000,000, payable at the end of the year of death or on survival to age 60. Annual premiums are payable in advance for 20 years. The net premium reserve is calculated on a 6% valuation interest rate and a standard mortality table. At issue, the actuarial factors are ä40:20 = 12.00 and A40:20 = 0.320. Immediately after the 10th premium is paid, the remaining-term factors are ä50:10 = 7.80 and A50:10 = 0.550. The insurer has just earned 8% on assets backing the policy, and the CEO wants to release IRR 100 million from the reserve as surplus. The regulator is consulting on moving the valuation rate to 4%. The actuary must certify the year-end reserve and advise on the dividend.
1. Calculate the net annual premium and the net premium reserve immediately after the 10th premium is paid. Show the prospective reserve formula.
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Net annual premium:
P = SA × A40:20 / ä40:20 = 1,000 × 0.320 / 12.00 = IRR 26.667 million.
Prospective net premium reserve after the 10th premium:
V_10 = SA × A50:10 − P × ä50:10 = 1,000 × 0.550 − 26.667 × 7.80 = 550 − 208.0 = IRR 342.0 million.
The reserve is a liability for future benefits, not accumulated past premiums. It equals the present value of remaining benefits less the present value of remaining net premiums, using the valuation assumptions.
2. The CEO says the 8% earned rate creates a 2% margin over the 6% valuation rate, so at least IRR 100 million of the reserve is excess and can be paid as a dividend. Evaluate this claim.
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The 8% earned rate is an experience result, not an automatic release. The 6% valuation rate is a conservative discount for guarantees; if assets actually earn 8%, the insurer may recognise an experience profit over time, but the reserve still supports future guaranteed benefits. Paying 100m immediately would reduce the reserve below the prospective best estimate and would require either (a) a demonstrated release of a valuation margin with regulatory approval, or (b) distributable surplus after all liabilities, expenses, and capital requirements are met. The actuary should not treat the 2% interest margin as free surplus. A dividend should be based on the insurer's audited surplus, solvency capital, and policyholder reasonable expectations. If the CEO wants a distribution, the actuary should show the reserve before and after the proposed release and the resulting coverage of the statutory reserve; if the release breaches the reserve, the actuary must refuse to certify.
3. If the valuation rate is reduced to 4%, will the reserve increase or decrease? Explain qualitatively and state one practical consequence for the CEO's dividend plan.
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A lower valuation rate increases the present value of future benefits and the annuity factor. At 4%, both A50:10 and ä50:10 would be higher than at 6%; the net premium reserve would generally increase, especially for an endowment with a large survival benefit. The exact increase depends on the mortality table and cash-flow timing. Practical consequence: the 4% basis would widen, not close, the solvency gap, so the CEO's 100m dividend plan becomes less feasible; the insurer may need to hold more capital, reduce dividends, or seek a phase-in. The actuary should quantify the reserve under both bases and disclose the sensitivity to the regulator and board.