# Securing Longevity Insurance Through Income Annuities

I have published a few pieces in the past couple weeks on how income annuities are priced and used. Understanding how to use annuities can be a great benefit when planning for retirement. Let’s consider another possibility.

Another option is to consider treating the income annuity as longevity insurance. This involves paying for a deferred income annuity at age 65 and not receiving payments until a much higher age, such as 80 or 85. With a life-only version, this leverages the power of mortality credits, as the more costly nearer-term annuity payments have been removed from the calculus.

In Table 1, the income provided between ages 65 and 84 is \$0, so we only need to consider the income provided for ages 85 and beyond. The long period for annuitized assets to grow and earn interest combined with the lower probabilities for surviving to these advanced ages results in the annuity’s cost being dramatically lowered. Table 1 shows a cost of \$15,351. Compared to the immediate life-only income annuity, the cost for guaranteed income has fallen almost 90%. The payout rate from this annuity is the income divided by the cost, which has grown to 65.1%.

Longevity insurance is a unique tool for retirement income considering the relatively small amount of assets required for such long-term spending needs. This allows retirees to plan for a fixed horizon until income from the deferred annuity begins.

Table 1: Calculating the Cost of a \$10,000 Deferred Income Stream for a 65-Year Old Male (Longevity Insurance, Life Only)

 Discount Rate: 2.50% Age Income Discount Factor Discounted Value of Income Survival Probabilities* Survival-Weighted Discounted Value 65 \$0 100.0% \$0 100.0% \$0 66 \$0 97.6% \$0 98.9% \$0 67 \$0 95.2% \$0 97.7% \$0 … … … … … … 83 \$0 64.1% \$0 55.2% \$0 84 \$0 62.6% \$0 50.5% \$0 85 \$10,000 61.0% \$6,103 45.7% \$2,789 86 \$10,000 59.5% \$5,954 40.9% \$2,435 87 \$10,000 58.1% \$5,809 36.0% \$2,092 88 \$10,000 56.7% \$5,667 31.2% \$1,766 89 \$10,000 55.3% \$5,529 26.5% \$1,466 90 \$10,000 53.9% \$5,394 22.1% \$1,190 91 \$10,000 52.6% \$5,262 18.0% \$949 92 \$10,000 51.3% \$5,134 14.4% \$738 93 \$10,000 50.1% \$5,009 11.2% \$562 94 \$10,000 48.9% \$4,887 8.6% \$420 95 \$10,000 47.7% \$4,767 6.4% \$305 96 \$10,000 46.5% \$4,651 4.7% \$217 97 \$10,000 45.4% \$4,538 3.3% \$151 98 \$10,000 44.3% \$4,427 2.3% \$102 99 \$10,000 43.2% \$4,319 1.6% \$67 100 \$10,000 42.1% \$4,214 1.0% \$43 101 \$10,000 41.1% \$4,111 0.7% \$27 102 \$10,000 40.1% \$4,011 0.4% \$17 103 \$10,000 39.1% \$3,913 0.3% \$10 104 \$10,000 38.2% \$3,817 0.2% \$6 Present Value of the Annuity = Sum of Survival-Weighted Discounted Values: \$15,351 Annuity Payout Rate: 65.1% *Survival Probabilities are calculated from the IRS Mortality Tables for pension plan valuations.

In practice, deferred income annuities are used to prepay for retirement income, not as longevity insurance. For instance, a 55-year old might purchase a deferred income annuity which will begin income at 65. We have already determined that the cost of a life-only income annuity at 65 is \$148,492. If a 55-year male wanted to provide lifetime income starting at 65, we could further discount the price in two ways – by the ability to earn interest for 10 years before income starts, and by the probability that the 55-year old will live to 65.

The discount factor for 10 years of investment growth at 2.5% is 78.1%. The same mortality data also reveals a 94.7% chance that the 55-year old lives to 65. Multiplying these two factors by \$148,492 gives us a premium of \$109,246 for a deferred income annuity purchased at 55. This represents a 9.15% payout rate.

Pricing for an 85-Year Old Male

We looked at longevity insurance as it applies to a 65-year old male purchasing a deferred income annuity with income starting at 85. We may also consider the alternative of just waiting until age 85 and then buying an immediate annuity. During those 20 years, interest rates and mortality tables can change in unexpected ways, which impacts pricing calculations.

Table 2 shows the calculated cost for this income annuity if we assume that interest rates and mortality data remain the same. An 85-year old will experience higher mortality rates and a shorter time horizon, reducing the cost of an income annuity at this age. In this case, the premium is \$55,043, which raises the payout rate to 18.17%.

This payout rate is noticeably higher than that available at age 65, but it is lower than that available with the longevity insurance contract. Longevity insurance carries two key differences here: 20 years of asset growth within the contract, and the discount a 65-year-old receives thanks to his less than stellar chances of living to 85 (less than a 50% chance).

Waiting until 85 to make the purchase means sharing fewer mortality credits with the pool. As with our earlier calculation, if we discount this \$55,043 premium by the 45.7% survival probability from age 65 and by 20 years of investment growth at 2.5%, we arrive at the \$15,351 premium for the longevity insurance contract.

Table 2: Calculating the Cost of a \$10,000 Income Stream for an 85-Year Old Male (Life Only)

 Discount Rate: 2.50% Age Income Discount Factor Discounted Value of Income Survival Probabilities* Survival-Weighted Discounted Value 85 \$10,000 1.000 \$10,000 100.00% \$10,000 86 \$10,000 0.976 \$9,756 89.48% \$8,730 87 \$10,000 0.952 \$9,518 78.82% \$7,502 88 \$10,000 0.929 \$9,286 68.19% \$6,332 89 \$10,000 0.906 \$9,060 58.02% \$5,257 90 \$10,000 0.884 \$8,839 48.28% \$4,267 91 \$10,000 0.862 \$8,623 39.45% \$3,402 92 \$10,000 0.841 \$8,413 31.45% \$2,646 93 \$10,000 0.821 \$8,207 24.57% \$2,017 94 \$10,000 0.801 \$8,007 18.81% \$1,506 95 \$10,000 0.781 \$7,812 13.99% \$1,093 96 \$10,000 0.762 \$7,621 10.19% \$777 97 \$10,000 0.744 \$7,436 7.27% \$540 98 \$10,000 0.725 \$7,254 5.03% \$365 99 \$10,000 0.708 \$7,077 3.40% \$241 100 \$10,000 0.690 \$6,905 2.26% \$156 101 \$10,000 0.674 \$6,736 1.45% \$97 102 \$10,000 0.657 \$6,572 0.91% \$60 103 \$10,000 0.641 \$6,412 0.56% \$36 104 \$10,000 0.626 \$6,255 0.34% \$21 Present Value of the Annuity = Sum of Survival-Weighted Discounted Values: \$55,043 Annuity Payout Rate: 18.17% *Survival Probabilities are calculated from the IRS Mortality Tables for pension plan valuations.

Next, read 12 Principles of Intelligent Investors.

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