Alex Daisy Posted December 29, 2007 Posted December 29, 2007 Can someone tell me how the Annual Percentage Rate (APR) is determined for cross testing? I see a lot of liturature with the following: The participant is age 55, the interest rate is 8.5%, and the UP-1984 Mortality Table is used. In most examples I see, the ARP is 95.38 or the Actuarial Factor is .035155. Can someone explain to me how these numbers are arrived at? I assume they come from a table. Is this true? Thank you in advance.
John Feldt ERPA CPC QPA Posted December 29, 2007 Posted December 29, 2007 I get a factor of 95.38 for a testing age of 65, not for age 55. This number comes from an actuarial mortality table. To explain in laymen's terms as much as I can, it sort of goes like this (warning: I am not an actuary): If you want to pay someone $1 per month for the rest of their life, starting at age 65, and they are currently age 65 now, then: the question is: how much cash should you have on hand right now if you could invest that cash at 8.50% (and assume that person is just one of many people in a large group whose deaths would each occur statisically equal to the probabilities of death as shown in the UP84 mortality table). The answer is $95.38 (thus, the 95.38 factor). The $95.38 cash on hand now (at age 65) would give you approximately the amount needed to pay them up until their life expectancy date. Again, I've only stated this just to help you with understanding the issue in general - the life expectancy age is not really the exact answer, but hopefully it helps you to understand it better. The UP84 table shows the probabilty of death each year, then at age 110 is shows 100% probability. So, to get that age 65 factor (it's an age 65 present value factor) you adjust the $12 per year benefit to account for the monthly timing of these payments, and then discount that to today's date by 8.5% for each year as well as discounting it by the probbaility of death in each year. Thus, the annual payment at age 66 is adjusted and discounted by 8.5% to the current year (age 65) and that amount is also adjusted by the probability that the participant may not live until age 66. Similarly, the annual payment at age 67 is adjusted and discounted for 2 years by 8.5% to the current year (age 65) and that amount is also adjusted by the probability that the participant may not live until age 67. This continues for each age, until age 110, where thereafter those payments have no present value because the table assumes a zero percent chance of survival past 110. Here are some of the "probabilities" of death (qx's) for the UP84 table: Age qx 50 0.005616 51 0.006196 52 0.006853 53 0.007543 54 0.008278 55 0.009033 56 0.009875 57 0.010814 58 0.011863 59 0.012952 60 0.014162 61 0.015509 62 0.017010 63 0.018685 64 0.020517 65 0.022562 66 0.024847 67 0.027232 68 0.029634 69 0.032073 70 0.034743 71 0.037667 72 0.040871 73 0.044504 74 0.048504 75 0.052913 76 0.057775 77 0.063142 78 0.068628 79 0.074648 80 0.081256 81 0.088518 82 0.096218 83 0.104310 84 0.112816 85 0.122079 86 0.132174 87 0.143179 88 0.155147 89 0.168208 90 0.182461 91 0.198030 92 0.215035 93 0.232983 94 0.252545 95 0.273878 96 0.297152 97 0.322553 98 0.349505 99 0.378865 100 0.410875 101 0.445768 102 0.483830 103 0.524301 104 0.568365 105 0.616382 106 0.668696 107 0.725745 108 0.786495 109 0.852659 110 0.924666 111 1.000000
Alex Daisy Posted December 30, 2007 Author Posted December 30, 2007 Thanks for this detailed explanation. So, if I understand you correctly, if the normal retirement age is 65, I can use the Annual Percentage Rate (APR) of 95.43 for every participant, regardless of their age? What about the Actuarial Factor is .035155. Would you know how this is calculated? I get a factor of 95.38 for a testing age of 65, not for age 55.This number comes from an actuarial mortality table. To explain in laymen's terms as much as I can, it sort of goes like this (warning: I am not an actuary): If you want to pay someone $1 per month for the rest of their life, starting at age 65, and they are currently age 65 now, then: the question is: how much cash should you have on hand right now if you could invest that cash at 8.50% (and assume that person is just one of many people in a large group whose deaths would each occur statisically equal to the probabilities of death as shown in the UP84 mortality table). The answer is $95.38 (thus, the 95.38 factor). The $95.38 cash on hand now (at age 65) would give you approximately the amount needed to pay them up until their life expectancy date. Again, I've only stated this just to help you with understanding the issue in general - the life expectancy age is not really the exact answer, but hopefully it helps you to understand it better. The UP84 table shows the probabilty of death each year, then at age 110 is shows 100% probability. So, to get that age 65 factor (it's an age 65 present value factor) you adjust the $12 per year benefit to account for the monthly timing of these payments, and then discount that to today's date by 8.5% for each year as well as discounting it by the probbaility of death in each year. Thus, the annual payment at age 66 is adjusted and discounted by 8.5% to the current year (age 65) and that amount is also adjusted by the probability that the participant may not live until age 66. Similarly, the annual payment at age 67 is adjusted and discounted for 2 years by 8.5% to the current year (age 65) and that amount is also adjusted by the probability that the participant may not live until age 67. This continues for each age, until age 110, where thereafter those payments have no present value because the table assumes a zero percent chance of survival past 110. Here are some of the "probabilities" of death (qx's) for the UP84 table: Age qx 50 0.005616 51 0.006196 52 0.006853 53 0.007543 54 0.008278 55 0.009033 56 0.009875 57 0.010814 58 0.011863 59 0.012952 60 0.014162 61 0.015509 62 0.017010 63 0.018685 64 0.020517 65 0.022562 66 0.024847 67 0.027232 68 0.029634 69 0.032073 70 0.034743 71 0.037667 72 0.040871 73 0.044504 74 0.048504 75 0.052913 76 0.057775 77 0.063142 78 0.068628 79 0.074648 80 0.081256 81 0.088518 82 0.096218 83 0.104310 84 0.112816 85 0.122079 86 0.132174 87 0.143179 88 0.155147 89 0.168208 90 0.182461 91 0.198030 92 0.215035 93 0.232983 94 0.252545 95 0.273878 96 0.297152 97 0.322553 98 0.349505 99 0.378865 100 0.410875 101 0.445768 102 0.483830 103 0.524301 104 0.568365 105 0.616382 106 0.668696 107 0.725745 108 0.786495 109 0.852659 110 0.924666 111 1.000000
John Feldt ERPA CPC QPA Posted December 30, 2007 Posted December 30, 2007 "if the normal retirement age is 65, I can use the Annual Percentage Rate (APR) of 95.43 for every participant, regardless of their age?" No, the factor is 95.38. You use that for participants whose testing age is 65, but anyone who is older you need to use another factor, for example, if their retirement age is 72, then I would use a factor of 79.23 (UP84 8.5%) "What about the Actuarial Factor is .035155. Would you know how this is calculated?" Can you give us an example of how that factor is being used with your data, what it is used to derive?
Tom Poje Posted December 31, 2007 Posted December 31, 2007 a correction on the term being used APR stands for Annuity Purchase Rate. you have determined someones 'lump sum' at a testing age. now you 'purchase an annuity' to provide a monthly benefit. ........... now, the govt gives you a slection of tables that are permissible to be used. I believe UP 84 has the lowest APR 95.38 and 1983 IAF has the largest APR 115.39 (at testing age 65). if all (and I stress all) people have the same testing age, then it doesn't matter what APR you use because the APR will be a constant. (If you do NOT IMPUTE DISPARITY) if you impute disparity then generally you would want to use a larger APR. you can not simply say "I can use 95.43 for all participants". it has to be possible that such an APR factor would exist. now, since the range for a testing age 65 falls between 95.38 and 115.39, then it should be possible by using an interest rate other than 8.5 (you get to choose between 7.5 and 8.5) and a different mortality table to generate such a factor.
Alex Daisy Posted December 31, 2007 Author Posted December 31, 2007 I meant to say the factor was 95.38, not 95.43. My apologies. Below is an example of where the Actuarial Factor is being used. How is this number arrived at: Employee Compensation Allocation Actuarial Factor PV Factor EBAR Ann - 55 $170,000 $17,000 .035155 5,976.35 2.84% Bob - 45 $100,000 $10,000 .015549 1,554.90 6.43% Cathy - 25 $20,000 $2,000 .003042 60.84 32.87% "if the normal retirement age is 65, I can use the Annual Percentage Rate (APR) of 95.43 for every participant, regardless of their age?"No, the factor is 95.38. You use that for participants whose testing age is 65, but anyone who is older you need to use another factor, for example, if their retirement age is 72, then I would use a factor of 79.23 (UP84 8.5%) "What about the Actuarial Factor is .035155. Would you know how this is calculated?" Can you give us an example of how that factor is being used with your data, what it is used to derive?
Tom Poje Posted December 31, 2007 Posted December 31, 2007 well, I have no clue what the actuarial factors or pv factors are, though I can get the same results by the following: Ann has 10 years to retirement, 170,000 comp and 17,000 contribution. in 10 years what will 17,000 grow to? 17,000 * 1.085^10 (assuming 8.5% interest rate) = 38,436.72 now, instead of taking this in one lump sum, an annuity is purchased. (hence APR or Annuity Purchase Rate) 38,436.72 / 95.38 = 402.985 monthly benefit 402.985 * 12 = 4835.82 annual benefit benefit / comp = e bar 4835.82 / 170,000 = 2.84% EBar which equals what you indicated. this should work for the other people as well.
Alex Daisy Posted January 5, 2008 Author Posted January 5, 2008 Mike: The actuarial facor and PV factors are referenced on page 11-8 (example 11-1), question Q 11:12 of the Coverage and Nondiscrimination Answer Book (3rd Edition). My question is where do these numbers come from. Thanks in advance. well, I have no clue what the actuarial factors or pv factors are, though I can get the same results by the following:Ann has 10 years to retirement, 170,000 comp and 17,000 contribution. in 10 years what will 17,000 grow to? 17,000 * 1.085^10 (assuming 8.5% interest rate) = 38,436.72 now, instead of taking this in one lump sum, an annuity is purchased. (hence APR or Annuity Purchase Rate) 38,436.72 / 95.38 = 402.985 monthly benefit 402.985 * 12 = 4835.82 annual benefit benefit / comp = e bar 4835.82 / 170,000 = 2.84% EBar which equals what you indicated. this should work for the other people as well.
Tom Poje Posted January 7, 2008 Posted January 7, 2008 Mike: when people refer to me as an actuary, I am terribly insulted. I still have some personality and a sense of humor. it may be off the wall, but at least I still have one. Alex: as for the actuarial factor above, it can be calculated as follows. (but before doing so a bit of explanation. In the example referred to above from the Coverage and Nondiscrimination Answer Book, there is an example and the book provides two different ways of arriving at the same answer. I provided the second method, the previous author provided the first, which uses the term 'actuarial factor' and pulls a 'magical' number from some table hidden in the deep caverns of wherever.) ok, all kidding aside at 8.5% interest and 10 years to retirement you have 1.085 ^ 10 = 2.260983 annualized would be 2.260983 * 12 = 27.1318 the APR was 95.38 so 95.38 / 27.1318 = 3.515 which is the actuarial factor (well ok, if you divide by 100 it is the same value)
ak2ary Posted January 8, 2008 Posted January 8, 2008 Tom- This is the second or third time I have seen someone ask essentially the same question...can you teach me the basics of compound interest and show me how to calculate EBARS. The last time, someone was questioning the EBARs on a practicioners report, so the practicioner thought he should come on to benefitslink and see how those darned things are calculated so he could tell the auditor. Now I appreciate people wanting to learn more and I have spent alot of my time teaching, but it really concerns that people are asking these questions on benefitslink and that forever they will use the answer that you provide as the basis for all their work without understanding why they get the number but simply having rote directions on how to get the number. When I first entered the business I was shown how to calculate the ILP Normal Cost for a benefit by hand... in theory, so I could check the computer output. I was taught that you take the current yeaar's benefit and subtract the prior years benefit. This gives you the benefit for the normal cost. You multiply that benefit by the age 65 number in column 7 from this chart and divide that by the current age number in column 4 of the chart. This gives you the change in normal cost that you add to last years Problem was that if you gave them a chart with columns in different order, nobody could do nothin' It scares me that there are people out there that do cross testing and consult to clients that can't calculate EBARs and don't know what these magic numbers represent. Maybe thats why you changed your name to Mike..so when they screw up they cant say..it was that Mike Poje This may not be fair to Alex, it sounds as if he/she is just starting to leaarn about this area and if so, I praise his/her motivation to try and find answers...I really do It just reminded me so much of the last post where everyone tried to teach EBARs http://benefitslink.com/boards/index.php?showtopic=37078
ak2ary Posted January 8, 2008 Posted January 8, 2008 Picked a bad year to switch to Sanka..or something like that
Mike Preston Posted January 8, 2008 Posted January 8, 2008 Ouch. I am now officially "in need" of caffeine because of my thirst for tea. You DO NOT want to be around me if I've gone 24 hours without my Brisk ... or something like that.
austin3515 Posted January 8, 2008 Posted January 8, 2008 Does anyone know where I can find the APR rates for all of the different mortality tables? I am trying to expand my cross-testing spreadsheet by allowing the user to specify what mortality table to use, to see which produces the best results. Austin Powers, CPA, QPA, ERPA
John Feldt ERPA CPC QPA Posted January 8, 2008 Posted January 8, 2008 I'd think there may be an actuary who could lend you a spreadsheet, maybe even allowing you to vary the interest rates and the retirement ages. I'd attach mine if I could figure out how to attach it in here, but I'm not sure you'd want that since I am not an actuary. Really, I hoped my comments had scared away anyone from actually trying to calculate the APRs ...
Tom Poje Posted January 8, 2008 Posted January 8, 2008 Austin and others: as I have indicated before, the basic formula for the e-bar is the follwoing you stick a CONTRIBUTION in the bank for a number of years. the number of years is how many you have to retirement. the interest at this wonderful bank is between 7.5% and 8.5%, because the govt says that is what they have to pay. so at retirement I will have this much $$ (or in the case of Mr Preston $$$$$$$$$$) Contribution * 1.085 ^ yrs to age 65 (assuming an 8.5% interest rate and retirement age 65) you divide this by the APR, which gives you a monthly benefit, multiply by 12 to annualize it and then divide by comp to give you an E-Bar again, if everyone has the same retirement age, then the APR is a constant, and really has no effect on anything, so it doesn't matter what mortality table you use. (If you impute disparity it will make a bit of a difference) thus, what becomes important is the range - which table produces the largest APR and which table produces the smallest APR. All other tables would fall imbetween these 2 values, and thus wouldn't make much of a difference in testing, or put another way, at least in my humble opinion, you don't really need to know all the tables. at 8.5% 1983 iaf apr = 115.39 up 84 = 95.38 so really those should be the only tables used (unless the govt 'blesses' a new GAR table (or whatever they call it) that would fall outside those boundaries)
austin3515 Posted January 8, 2008 Posted January 8, 2008 Sounds good! Does anyonme have the APR table for the 83 table? I want to be able to accomodate any testing age. Austin Powers, CPA, QPA, ERPA
austin3515 Posted January 9, 2008 Posted January 9, 2008 J4KBC, just give me what you got! When you add a reply, right after the main text box is a tool that lets you upload files. Whatever anyone gives me, actuary or not, will be proved against Relius, so not to worry about accuracy. I'm betting its perfectly fine. Austin Powers, CPA, QPA, ERPA
John Feldt ERPA CPC QPA Posted January 11, 2008 Posted January 11, 2008 Well, FWIW. I'll see if it actually attaches... ... ... ... ... ... ... ... ... ... ... ... ... ... ... Hmmm..... .... ... .... ... ... ... ... Yeah. I'm not sure it will ever complete the upload. I'll try to send it to you directly. PensionMonster 1
John Feldt ERPA CPC QPA Posted January 14, 2008 Posted January 14, 2008 One more try... Hey - I think it worked! You can load in your own table in there too if you want, I left one blank.
austin3515 Posted January 14, 2008 Posted January 14, 2008 I know, I know, beggers can't be choosers, but your table doesn't include the Immediate Annuity Factor one, which Tom inidcated is the outside range table!!! Anyone?? Austin Powers, CPA, QPA, ERPA
Tom Poje Posted January 14, 2008 Posted January 14, 2008 actually the immediate annuity factor falls imbetween (at least at 8.5% interest) if I said otherwise, I apologize. the tables at either end were UP84 and 1983IAF. by the way, the regs list which tables are allowed to be used 1.401(a)(4)-12 definitions: standard mortality table so you cant use just any table. the last sentance says: the applicable mortality table under section 417(e)(3)(A)(ii)(I) is also a standard table. otherwise you couldn't use the new table that gets released every few years for those DB folks to pay lump sums.
Mike Preston Posted January 15, 2008 Posted January 15, 2008 Starting in 2008, we are going to be getting annual updates to that table.
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