The value of an exhausting annuity can be calculated by breaking it down into two separate parts. The first part is the portion of the annuity that does not exhaust. The second part is the final payment made in the period that the annuity exhausts.
§25.7520-3(b)(2)(v), example 5 describes a case where a donor, age 60, sets up a $1,000,000 trust to pay a 10% annuity for the life of the donor. The §7520 rate used is 6.8%. This annuity is calculated to exhaust in 18 years, with a final payment in year 18 equal to $32,712. To value this annuity, break it down into two separate parts: $100,000 lasting for 17 years; and a single payment of $32,712 in the 18th year. Once the pieces are known, value each one individually and then add them together. The annuity factor for an annuity lasting for the shorter of 17 years or until the prior death of a person age 60 is 8.6121. The annuity factor for the shorter of 18 years or until the prior death of a person age 60 is 8.7957. Given these factors (which can be obtained from example 11 in IRS Pub. 1457), the valuation of the annuity is:
Value = [$100,000 * 8.6121] + [$32,712 * (8.7957 - 8.6121)]
= $861,210 + $6006
Of course, these numbers get more complicated when the annuity is payable more frequently than annually, but the basic methodology is still the same. For example, take the above case, but make it payable quarterly instead of annually. Now the $100,000 payments only last 16½ years. The final payment, made in the 3rd quarter of the 16th year, is $5,414.41. Transforming this single payment into an annual amount by multiplying it by the number of payments per year (in this case 4), yields an annuity of $21,657.64 lasting 16¾ years. Valuing partial-year annuities requires interpolation. An annuity lasting 16½ years is valued by taking ½ the value of the same annuity lasting for 16 years plus ½ the value of it lasting for 17 years. An annuity lasting for 16¾ years is valued by adding taking ¼ the value of the same annuity lasting for 16 years plus ¾ the value of it lasting for 17 years. Getting back to the example:
Annuity Factor for 16½ years = (½ x 8.4055) + (½ x 8.6121) = 8.5088
Annuity Factor for 16¾ years = (¼ x 8.4055) + (¾ x 8.6121) = 8.56045
Of course, the frequency of payments still has to be taken into account. The payout frequency factor from Table K (IRS Pub. 1457) is 1.0252. Therefore, the annuity is valued:
Value = 1.0252 x [$100,000 * 8.5088] + [ $21,657.64 x (8.56045 - 8.5088) ]
= 1.0252 x ($850,880 + $1,118.62)
The above examples ignore the calculation of both when the annuity exhausts, and the amount of the final payment. These two numbers, however, are critical to calculating a proper annuity valuation. The program provides two different methods for calculating these numbers: the Illustrated Method and the IRS Annuity Factor Method.
Annuities paid at the beginning of the period are treated in the same manner as annuities paid at the end of each period. First, the trust is reduced by the value of the first payment. The above analysis is then performed for the annuity, assuming payments occur at the end of each period. Finally, the first payment is added to the annuity value.