SEPP calculation - Fixed annuitization Method - annuity factor ?

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indexlover
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Joined: Mon May 11, 2015 10:39 am

SEPP calculation - Fixed annuitization Method - annuity factor ?

Post by indexlover » Mon May 25, 2020 9:04 am

Does anyone know how the Fixed Annuitization Method annuity factor is calculated? I am looking for a formula that references the Appendix B Mortality table ? I am not good with math , please explain like i am 6 year old or something. :-) Thank you

In this example below , for a 50 year , i see Qx = 0.002409 and Ix = 966677 ( i guess Qx is the probability that a person exact age x will die within one year. and Ix is the number of persons surviving to exact age x. and the interest rate is 2.98%. How does it compute to the annuity factor 21.345. Thanks

Reference: https://www.irs.gov/retirement-plans/re ... c-payments
https://www.irs.gov/pub/irs-drop/rr-11-10.pdf

Fixed annuitization method

The fixed annuitization method consists of an account balance, an annuity factor and an annual payment. The annuity factor is calculated based on the mortality table in Appendix B of Rev. Rul. 2002-62 and an interest rate of not more than 120% of the federal mid-term rate. Once an annual distribution amount is calculated under this method, the same dollar amount must be distributed in subsequent years.

Under this method the annual distribution amount is equal to the account balance ($400,000) divided by an annuity factor that would provide one dollar per year over Bob’s life, beginning at age 50. The age 50 annuity factor (21.345) is calculated based on the Rev. Rul. 2002-62 Appendix B mortality table and an interest rate of 2.98%. The annual distribution amount is calculated as $400,000/21.345 = $18,740.



Appendix B mortality table:
https://www.irs.gov/pub/irs-irbs/irb02-42.pdf

Definitions:
https://www.ssa.gov/OACT/HistEst/PerLif ... itions.pdf
Last edited by indexlover on Mon May 25, 2020 10:18 am, edited 1 time in total.
“If a statue is ever erected to honor the person who has done the most for American investors, the hands-down choice should be Jack Bogle.” - Mr. Buffett - Berkshire Hathaway ’s 2016 annual report.

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JoMoney
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Re: SEPP calculation - Fixed annuitization Method - annuity factor ?

Post by JoMoney » Mon May 25, 2020 9:17 am

For what it's worth, I've always just ignored the 'fixed annuitization method'.
When I've used SEPP 72t calculators like https://www.dinkytown.net/java/72t-calculator.html
The 'annuitization menthod' tends to be close to, but slightly lower than, the 'fixed amortization method'.
I have a formula for amortization, and the RMD method is pretty easy... so I just ignore the 'annuitization method' when playing with calculations. I don't know why it would be useful, since it seems more complex, results in a lower amount, and if I desired a lower amount I can create that by just using the amortization method and lowering the interest rate.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

rkhusky
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Re: SEPP calculation - Fixed annuitization Method - annuity factor ?

Post by rkhusky » Mon May 25, 2020 10:13 am

JoMoney wrote:
Mon May 25, 2020 9:17 am
... if I desired a lower amount I can create that by just using the amortization method and lowering the interest rate.
Or putting less in the SEPP.

Topic Author
indexlover
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Re: SEPP calculation - Fixed annuitization Method - annuity factor ?

Post by indexlover » Mon May 25, 2020 10:37 am

As an academic exercise, I tried to do the same calculations in the current rate environment and this what i got for the same situation:
(I wish i knew how the annuity factor is calculated which was my question in OP)

120% of the applicable federal mid-term rate for June 2020: 0.22%
https://www.irs.gov/pub/irs-drop/rr-20-12.pdf

Required minimum distribution method:
The annual distribution amount is : 400,000/34.2 = $11,695

Fixed amortization method :
https://www.calculator.net/amortization ... x=113&y=30
The annual distribution amount is 12,142.44

Fixed annuitization method :
https://afc.soa.org/#Calculator
Annuity factor: 34.423 ( based on valuation yeat 2011 , mid-term rate is 0.22% and age 50)
The annual distribution amount is : 400000/34.423 = 11620.14

@JoMoney
Fixed amortization still seems to be the choice
“If a statue is ever erected to honor the person who has done the most for American investors, the hands-down choice should be Jack Bogle.” - Mr. Buffett - Berkshire Hathaway ’s 2016 annual report.

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JoMoney
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Re: SEPP calculation - Fixed annuitization Method - annuity factor ?

Post by JoMoney » Mon May 25, 2020 11:02 am

OP,
I know it doesn't help with the specific math/formula question for 'annuitization method', maybe one of the math wizards will chime in on that, but like I said, I just ignore that method for not being useful for any purpose to me.

But if you're considering early retirement withdrawals, I would also draw your attention to "Roth IRA Conversion Ladder" method. If I decide to retire early, it will likely be what I do, since it allows for more flexibility in the amounts, or even stopping withdrawals altogether should I decide to get a side job and earn other income.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

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Horton
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Re: SEPP calculation - Fixed annuitization Method - annuity factor ?

Post by Horton » Mon May 25, 2020 11:22 am

Bankrate has a calculator:

https://www.bankrate.com/retirement/cal ... alculator/

Here's how you can match their calculation:

1) Copy / paste the mortality table referenced above into Excel; specifically, the age, qx, and lx data.

2) Get the age, qx, and lx data into three columns (A:C). When you copy / paste it will be in six. qx is the probability of death at the specific age. lx is the number of people remaining alive at a given age based upon a starting population of 1,000,000 at age 0.

3) In column D, calculate px (the probability of survival to a specified age) as the lx of the current age divided by the lx of the starting age. So, if starting at age 50, then p_50 = l_50 / l_50 = 1, p_51 = l_51 / l_50 = .997591, etc.

4) In column E, add the interest rate. I'm using 2.36% because that what they are using at bankrate.

5) In column F, show a payment of 1

6) In column G, add time (x) starting at 0.

7) In column H, calculate the present value at age x = (F * D) / (1 + E) ^ (G)

8) Sum up the values in column H. 23.364062, if starting at age 50.

9) Take account balance divided by the sum. $100,000 / 23.364062 = $4,280.

Here is the data in csv format:

Code: Select all

age,qx,lx,px,ix,payment_x,x,pv_x,,
50,0.002409,966677,1.000000,2.36%,1,0,1.000000,,
51,0.002646,964348,0.997591,2.36%,1,1,0.974590,,
52,0.002896,961796,0.994951,2.36%,1,2,0.949601,,
53,0.003167,959011,0.992070,2.36%,1,3,0.925021,,
54,0.003453,955974,0.988928,2.36%,1,4,0.900832,,
55,0.003754,952673,0.985513,2.36%,1,5,0.877023,,
56,0.004069,949097,0.981814,2.36%,1,6,0.853587,,
57,0.004398,945235,0.977819,2.36%,1,7,0.830513,,
58,0.004736,941078,0.973519,2.36%,1,8,0.807797,,
59,0.005101,936621,0.968908,2.36%,1,9,0.785435,,
60,0.005509,931843,0.963965,2.36%,1,10,0.763411,,
61,0.005975,926709,0.958654,2.36%,1,11,0.741701,,
62,0.006512,921172,0.952926,2.36%,1,12,0.720271,,
63,0.007137,915173,0.946721,2.36%,1,13,0.699082,,
64,0.007854,908641,0.939963,2.36%,1,14,0.678090,,
65,0.008670,901505,0.932581,2.36%,1,15,0.657253,,
66,0.009591,893689,0.924496,2.36%,1,16,0.636533,,
67,0.010620,885118,0.915630,2.36%,1,17,0.615893,,
68,0.011778,875718,0.905905,2.36%,1,18,0.595303,,
69,0.013072,865404,0.895236,2.36%,1,19,0.574728,,
70,0.014519,854091,0.883533,2.36%,1,20,0.554137,,
71,0.016139,841690,0.870704,2.36%,1,21,0.533501,,
72,0.017950,828106,0.856652,2.36%,1,22,0.512789,,
73,0.019958,813241,0.841275,2.36%,1,23,0.491973,,
74,0.022198,797010,0.824484,2.36%,1,24,0.471038,,
75,0.024699,779318,0.806182,2.36%,1,25,0.449963,,
76,0.027484,760070,0.786271,2.36%,1,26,0.428731,,
77,0.030582,739180,0.764661,2.36%,1,27,0.407335,,
78,0.034010,716574,0.741276,2.36%,1,28,0.385773,,
79,0.037807,692203,0.716064,2.36%,1,29,0.364061,,
80,0.042010,666033,0.688992,2.36%,1,30,0.342221,,
81,0.046652,638053,0.660048,2.36%,1,31,0.320285,,
82,0.051766,608287,0.629256,2.36%,1,32,0.298303,,
83,0.057392,576798,0.596681,2.36%,1,33,0.276340,,
84,0.063583,543694,0.562436,2.36%,1,34,0.254474,,
85,0.070397,509124,0.526674,2.36%,1,35,0.232800,,
86,0.077892,473283,0.489598,2.36%,1,36,0.211422,,
87,0.086124,436418,0.451462,2.36%,1,37,0.190459,,
88,0.095238,398832,0.412580,2.36%,1,38,0.170043,,
89,0.105068,360848,0.373287,2.36%,1,39,0.150301,,
90,0.115518,322934,0.334066,2.36%,1,40,0.131408,,
91,0.126487,285629,0.295475,2.36%,1,41,0.113548,,
92,0.137876,249501,0.258102,2.36%,1,42,0.096899,,
93,0.149419,215101,0.222516,2.36%,1,43,0.081613,,
94,0.161176,182961,0.189268,2.36%,1,44,0.067818,,
95,0.173067,153472,0.158762,2.36%,1,45,0.055576,,
96,0.185008,126911,0.131286,2.36%,1,46,0.044898,,
97,0.196920,103431,0.106996,2.36%,1,47,0.035748,,
98,0.210337,83063.4,0.085927,2.36%,1,48,0.028046,,
99,0.224861,65592.1,0.067853,2.36%,1,49,0.021636,,
100,0.241017,50843,0.052596,2.36%,1,50,0.016385,,
101,0.259334,38589,0.039919,2.36%,1,51,0.012149,,
102,0.280356,28581.6,0.029567,2.36%,1,52,0.008791,,
103,0.303142,20568.6,0.021278,2.36%,1,53,0.006180,,
104,0.329482,14333.4,0.014827,2.36%,1,54,0.004208,,
105,0.359886,9610.8,0.009942,2.36%,1,55,0.002756,,
106,0.394865,6152.01,0.006364,2.36%,1,56,0.001724,,
107,0.434933,3722.8,0.003851,2.36%,1,57,0.001019,,
108,0.480599,2103.63,0.002176,2.36%,1,58,0.000563,,
109,0.532376,1092.63,0.001130,2.36%,1,59,0.000285,,
110,0.590774,510.94,0.000529,2.36%,1,60,0.000130,,
111,0.656307,209.09,0.000216,2.36%,1,61,0.000052,,
112,0.729484,71.8628,0.000074,2.36%,1,62,0.000018,,
113,0.810817,19.44,0.000020,2.36%,1,63,0.000005,,
114,0.900819,3.67772,0.000004,2.36%,1,64,0.000001,,
115,1.000000,0.36476,0.000000,2.36%,1,65,0.000000,,

Alan S.
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Re: SEPP calculation - Fixed annuitization Method - annuity factor ?

Post by Alan S. » Mon May 25, 2020 5:44 pm

It's noteworthy that the sudden and dramatic reduction of the AFR to historical lows has reduced the SEPP payout using the usual amortization method to just 3% of the account balance. Earlier this year, the payment would have been in the 4.5% range depending on age at plan inception. This means that your account balance now needs to be nearly 50% higher to generate the same payout it would have just a few months ago.

It also means that the amortization payout has now dipped to only slightly more than the RMD method generates. The RMD method should not have been used before except by those making the permitted one time switch to RMD to reduce the distribution amount if you no longer needed the original distribution amount and wanted to preserve your IRA balance for later. Again, there are some variances based on inception age, and in these examples age 50 was selected.

In these examples the RMD calculation was only 3.7% lower than the amortization method.
However, if the proposed RMD table revisions are adopted by the IRS beginning in 2021 as expected, the new RMD calculation would then be 8.8% less than amortization.

For many people suddenly out of work due to Covid, the prime problem is having an IRA balance large enough to generate the SEPP payout needed. But those that qualify for a CRD (100k max) and for who 33k a year will suffice, they are set for 3 years since there will be no penalty on the CRD and taxable income of 1/3 the distribution can be reported for each of those 3 years. If the SEPP can be avoided for 3 years, perhaps it will not be needed at all.

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Re: SEPP calculation - Fixed annuitization Method - annuity factor ?

Post by #Cruncher » Tue May 26, 2020 8:25 am

Horton wrote:
Mon May 25, 2020 11:22 am
Bankrate has a calculator:
https://www.bankrate.com/retirement/cal ... alculator/
Choose "uniform life table" in the drop-down for life expectancy table.
Horton, continuing in same post, wrote:Here's how you can match their calculation:
Here is Horton's calculation in more compact form where the discount rate, 2.98%, is stored in cell B1.
21.365 = SUM(D55:D120)

Code: Select all

Row  Col A    Col B     Col C     Col D
  1   Rate    2.98%
             Number  Fraction Discounted
      Age     Alive     Alive   Fraction

Code: Select all

 55    50   966,677   1.00000    1.00000
 56    51   964,348   0.99759    0.96872
 57    52   961,796   0.99495    0.93820
 58    53   959,011   0.99207    0.90841
 59    54   955,974   0.98893    0.87933
 60    55   952,673   0.98551    0.85094
 61    56   949,097   0.98181    0.82321
 62    57   945,235   0.97782    0.79614
 63    58   941,078   0.97352    0.76970
 64    59   936,621   0.96891    0.74389
 65    60   931,843   0.96397    0.71867
 66    61   926,709   0.95865    0.69403
 67    62   921,172   0.95293    0.66992
 68    63   915,173   0.94672    0.64630
 69    64   908,641   0.93996    0.62312
 70    65   901,505   0.93258    0.60033
 71    66   893,689   0.92450    0.57791
 72    67   885,118   0.91563    0.55580
 73    68   875,718   0.90591    0.53399
 74    69   865,404   0.89524    0.51243
 75    70   854,091   0.88353    0.49109
 76    71   841,690   0.87070    0.46996
 77    72   828,106   0.85665    0.44899
 78    73   813,241   0.84127    0.42818
 79    74   797,010   0.82448    0.40749
 80    75   779,318   0.80618    0.38691
 81    76   760,070   0.78627    0.36644
 82    77   739,180   0.76466    0.34605
 83    78   716,574   0.74128    0.32576
 84    79   692,203   0.71606    0.30558
 85    80   666,033   0.68899    0.28551
 86    81   638,053   0.66005    0.26560
 87    82   608,287   0.62926    0.24589
 88    83   576,798   0.59668    0.22641
 89    84   543,694   0.56244    0.20724
 90    85   509,124   0.52667    0.18845
 91    86   473,283   0.48960    0.17011
 92    87   436,418   0.45146    0.15232
 93    88   398,832   0.41258    0.13518
 94    89   360,848   0.37329    0.11876
 95    90   322,934   0.33407    0.10321
 96    91   285,629   0.29548    0.08864
 97    92   249,501   0.25810    0.07519
 98    93   215,101   0.22252    0.06295
 99    94   182,961   0.18927    0.05199
100    95   153,472   0.15876    0.04235
101    96   126,911   0.13129    0.03401
102    97   103,431   0.10700    0.02691
103    98    83,063   0.08593    0.02099
104    99    65,592   0.06785    0.01609
105   100    50,843   0.05260    0.01211
106   101    38,589   0.03992    0.00893
107   102    28,582   0.02957    0.00642
108   103    20,569   0.02128    0.00449
109   104    14,333   0.01483    0.00304
110   105     9,611   0.00994    0.00198
111   106     6,152   0.00636    0.00123
112   107     3,723   0.00385    0.00072
113   108     2,104   0.00218    0.00040
114   109     1,093   0.00113    0.00020
115   110       511   0.00053    0.00009
116   111       209   0.00022    0.00004
117   112        72   0.00007    0.00001
118   113        19   0.00002    0.00000
119   114         4   0.00000    0.00000
120   115         0   0.00000    0.00000
Here are the formulas in cells C55 and D55 that are copied down to row 120:
C55: 1.00000 = B55 / B$55
D55: 1.00000 = C55 / (1 + B$1) ^ (A55 - A$55)


You can omit column D and just use the Excel NPV function on column C.
21.365 = NPV(B1, C55:C120) * (1 + B1)

(The " * (1 + B1)" is needed because the NPV function assumes payments are at the end of each period, while the procedure here assumes they occur at the beginning.)

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