Basic Calculations of Single Premium and Regular Premium Investment-linked Policies and their Death Benefits 整付保費和定期繳費的投資相連保單及其死亡保險金的基本計算

Basic Calculations of Single Premium Policies 整付保費保單的基本計算

A single premium policy starts with one premium paid to an authorised insurer. Charges may be collected when the premium is received or at monthly, annual or other specified intervals during the policy. Their timing affects the amount available for investment.

Premium Application Method One converts the whole premium into units and then cancels enough units to pay charges. Method Two deducts charges first and purchases units with the balance. Identical cash charges can therefore leave different numbers of units.

Read prices from the insurer's perspective: the policyholder purchases units at the insurer's offer price and realises them at its bid price. The following calculations assume life cover only, no riders and one investment fund. Displayed prices and unit numbers use two decimal places, and later calculations carry forward those displayed figures.

Premium Application Method One 保費應用方法一

Assume a single premium of HK$50,000, a unit NAV which is also the bid price of HK$12, and a spread calculated as 5% of the bid price. The offer price is 12 × 1.05 = HK$12.60. The whole premium initially purchases 50,000 ÷ 12.60 = 3,968.25 units.

The policy fee is HK$1,000. Administrative and mortality charges for the whole policy duration are assumed to be 2.5% of the premium, or HK$1,250. Assuming all these charges are collected at inception, the total is HK$2,250.

Units are cancelled at the bid price to pay charges: 2,250 ÷ 12 = 187.50 units. The balance is 3,968.25 − 187.50 = 3,780.75 units. Using the offer price for cancellation would be wrong; the different purchase and cancellation prices explain the effect of the spread.

Top-up Application 額外投資保費

Assume the policyholder pays a HK$20,000 top-up two years after inception. If unit prices grow steadily at 8% a year from their initial levels, the bid price after two years is HK$14.00 and the offer price is HK$14.70. This is a calculation assumption, not a guaranteed return.

Under Method One, the whole top-up first purchases 20,000 ÷ 14.70 = 1,360.54 units. The top-up fee is HK$200 and the administrative charge is 1.5% of the top-up, or HK$300, making total charges of HK$500.

Paying charges requires cancellation of 500 ÷ 14.00 = 35.71 units at the bid price. The net addition is 1,360.54 − 35.71 = 1,324.83 units. Added to the existing 3,780.75 units, the total holding becomes 5,105.58 units.

Partial Withdrawal (Partial Surrender) Benefit 局部提取利益（局部退保）

A partial withdrawal realises some units at the bid price while leaving the rest in the policy. Withdrawal or surrender charges may apply, and some policies specify minimum withdrawal or surrender amounts. Do not assume that any amount can be withdrawn free of charge.

Assume a holding of 5,105.58 units, a bid price of HK$18 and a HK$9,000 withdrawal with no withdrawal charge. Cancel 9,000 ÷ 18 = 500 units, leaving 5,105.58 − 500 = 4,605.58 units. The 500 units are those cancelled, not those remaining.

Surrender Value 退保現金價值

Full surrender realises all units at the bid price and ends the policy and its cover. Surrender value equals units held × applicable bid price, less any surrender charge. A policy value before surrender charges may therefore differ from the cash actually payable.

If all 5,105.58 units are surrendered directly at a bid price of HK$18, without first withdrawing HK$9,000, the value is 5,105.58 × 18 = HK$91,900.44, less any surrender charge. If a partial withdrawal has already occurred, use the remaining unit balance instead.

Death Benefit 死亡保險金

For Increasing Death Benefit (IDB), add the chosen death cover to the unit value at death. With 4,605.58 units and a bid price of HK$20, the unit value is HK$92,111.60. In this example, chosen death cover remains 150% of the original HK$50,000 single premium, or HK$75,000, giving an IDB of HK$167,111.60.

Level Death Benefit (LDB) takes the higher of the unit value at death and the chosen death cover, rather than adding them. Comparing HK$92,111.60 with HK$75,000 therefore gives a death benefit of HK$92,111.60.

A 105 Plan pays 105% of the policy account value at death: 92,111.60 × 1.05 = HK$96,717.18. The percentage applies to account value, not premiums paid or chosen death cover. This type of plan generally has a smaller insurance protection element.

For ease of comparison, these figures assume the same unit value for all three options. Actual mortality charges depend on the option: other things being equal, IDB costs more than LDB, while most 105 Plans have minimal insurance charges. Higher charges reduce unit accumulation, so actual holdings need not be identical.

Return on Gross Premium 毛保費回報

Return on gross premium starts with the premium actually paid before deductions. Assume only the original HK$50,000 premium, leaving 3,780.75 units after charges, with no top-ups or withdrawals. At 8% annual growth, the bid price rises from HK$12 to HK$25.91 after 10 years, giving 3,780.75 × 25.91 = HK$97,959.23.

Let r be the compound annual return. Then 50,000 × (1 + r)^10 = 97,959.23. Therefore, r = (97,959.23 ÷ 50,000)^(1 ÷ 10) − 1, approximately 6.96%. Dividing the total percentage gain by 10 does not produce the compound annual rate.

An 8% annual increase in unit price does not mean an 8% annual return on gross premium: the spread and charges reduced the initial unit holding. These figures exclude the HK$20,000 top-up and HK$9,000 withdrawal and do not represent a guaranteed return.

Premium Application Method Two 保費應用方法二

Method Two deducts charges before purchasing units. From the HK$50,000 single premium, deduct the HK$1,000 policy fee and administrative and mortality charges of 50,000 × 2.5% = HK$1,250. The net premium for investment is HK$47,750.

Purchasing at the HK$12.60 offer price gives 47,750 ÷ 12.60 = 3,789.68 units, slightly more than Method One's 3,780.75 units. The HK$2,250 used for charges never passes through a unit purchase and cancellation, so that portion avoids the bid-offer spread.

A single premium policy can also collect policy fees, administrative charges and mortality charges periodically, such as monthly throughout its life. A single premium does not necessarily mean all charges are collected at inception. Top-ups, withdrawals, surrender and death benefits still use their relevant prices and formulae.

Basic Calculations of Regular Premium Policies 定期繳費保單的基本計算

Regular premium policies receive premiums in instalments but use similar unit purchase and charging principles to single premium policies. Subject to the terms, policyholders can vary regular premiums, make top-ups or skip payments for a period. These facilities do not automatically stop charges.

Initial distribution and policy issuance costs can absorb a substantial part of early premiums. Units may first be allocated and then cancelled to meet initial charges, potentially leaving no investment units after the first year's payments.

One illustrative investment allocation scale is 0% in year 1, 50% in year 2 and 100% from year 3 onwards. Years 1 and 2 involve initial charges and monthly administrative and mortality charges. Monthly administrative and mortality charges continue from year 3, so 100% allocation does not mean no charges. This scale is an example, not a uniform arrangement.

Spreading initial charges over a longer period can leave some units in the account during year 1. However, an insurer may impose surrender charges to recover initial costs still outstanding when a policy ends early. Having units in the first year does not make early surrender cost-free.

Monthly Application of Regular Premium 每月繳交保費

Authorised insurers in Hong Kong normally apply monthly premiums using Method One: purchase units with the whole premium, then cancel units for monthly charges. Mortality charges are calculated monthly and deducted from the investment account. A later request to increase life cover requires evidence of insurability.

Assume an annual life cover rate of HK$6 per HK$1,000, chosen death cover of HK$500,000, 400 opening units, a HK$12 bid price, a HK$12.60 offer price, a HK$500 monthly premium and a HK$30 monthly policy fee. Opening account value is HK$4,800, and the premium purchases 500 ÷ 12.60 = 39.68 units.

For IDB, the amount at risk is the HK$500,000 chosen cover. Monthly mortality charges are (6 ÷ 1,000) × (1 ÷ 12) × 500,000 = HK$250. Including the policy fee, HK$280 requires cancellation of 280 ÷ 12 = 23.33 units, leaving 400 + 39.68 − 23.33 = 416.35 units. Using opening account value, the death benefit is HK$504,800.

For LDB, the amount at risk using opening account value is 500,000 − 4,800 = HK$495,200. Monthly mortality charges are HK$247.60. Including the policy fee, HK$277.60 cancels 23.13 units, leaving 416.55 units; the death benefit using opening account value is HK$500,000. LDB covers only the excess of chosen cover over account value, producing lower charges in this example.