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Old 03-04-2011, 03:50 PM   #21
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i didn't read all of your post.

But, Lets beat this thing to death...

Why the 16X model doesn't work so well. It doesn't account for different collection spans. Therefore some sort of correction need be added to compare

lets suppose the 62 year old lives to 82. That's 20 years of pension he gets. We estimated the presnt value of his pension at 62 to be around $156k. And we discounted it back to 55 estimeted at $111k.

The 55 year old also lives to 82 which is 27 years of pension. Here the 16X model underestimates relative to the 62 year old (16X model) by 7 years. The $29k extra was an attempt to correct the model.

This is a correction above and beyond, the 16X discounted cash flow.
maybe you should have read all my post. let me now show you why you dont have to discount twice (of course you will need to read this post). first, you are correct about the need to correct for time but all i am saying is you dont need to correct twice (in fact doing so makes the comparison incorrect). i will show you with both of the ways i said you could account for the difference in when the payments start. it is conceptually easier to explain by comparing the value of the 2 pensions at the age of 62. to get the value of all the payments going forward for each pension at the age of 65 we use the same formula (i.e. 16x). thats fair, right? those values, as pointed out by you, are
Quote:
The present value of your ($346/mo) pension using the 16x formula is

12X346X16 = 66432

.... the $813 pension is

12X 813X16 = 156096.
value of pension A = $66,432
value of pension B = $156,096

any problem so far? remember we are determining the value of these pensions at age 65. but what about all those payments already made? well seems like they need to be added to the above values. i will again use your numbers.
Quote:
The 55 year old gets 7 more years of income than the 62 year old. The 55 year old gets an extra 7 years X 12 months/year X 346 ==> $29064 extra.
so making that addition we get
value of pension A = $66,432 + $29,064 = $95,496
value of pension B = $156,096 + 0 = $156,096
(which i said in my 1st post and showed in my 3rd post, the 1 you didnt read.) remember these are the values of both pensions at age 62

now if you want the values of both pensions at age 55 you need to discount the values of both pensions soo using your work in that area too
Quote:
But that value needs to be discounted at (lets say for example) 5% per year. IE. How much money do I need now that compounds at 5%/yr will give me 156096.

using a 5% discount rate for 5 years I get that the present value of the income stream at 62 is ~$111k
we see that discounting a cash flow value from the value it has age 62 to its value at age 55 (7 years) using your assumed discount rate of 5% we can multiply its value at age 62 by ~0.711 ($156,096*0.711=~$111,000). there is the value of 1 pension but the value of the other 1 at age 62 also needs to be discounted (we need to be consistant) so it becomes $95,496*0.711=~$67,898. now this last paragraph is a convoluted way of arriving at the value of pension A at the age of 55 but i did this to be consistant. it does show that the 16x formula isnt consistant with a 5% discounting but that isnt really the point.

the point i am trying to make is when you discounted pension B using 5% you got the value of pension B at age 55 (and that is all you needed to do because you already had the value of pension A at age 55) but when you added all the payments made from pension A to the 16x formula for that pension you had the value of pension A at age 62 (not age 55). in essence you double discounted and as such you were comparing apples to oranges. you need to pick 1 date to which you calculate the value of both pensions, not compare values at different dates.

and oh btw, instead of beating this to death how bout you read my posts before commenting on them?
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Old 03-04-2011, 04:07 PM   #22
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I believe that you are still mistaken.

The value of the 55 year old pension at age 55 was $66k. If I was given that cash and invested it at 5% for seven years until 62 it would be worth around $92k.

Previously we estimated that at 65 the higher pension was worth $156k.

But there was a problem in that our 16X present value model didn't take into account that the 55 year old would collect for maybe 27 years and the 62 year old would collect for 20 years. Therefore direct present value comparisons corrected to either a 55 year old or a 62 year old aren't valid.

I estimated the correction for the extra payments to the 55year old at $29k when he was 55. But that money invested at 5% for 7 years until he is 62 would be worth ~$40k.

Therefore the present value of the lower pension at 62 years old is (($66k)/.71) + ($29k/.71) = $133k

The higher pension at 62 had a (at 62) present value of $156k and wins the little ballpark analysis. Still they are close enough and my analysis has been simple.

Therefore I suspected that per the rules, discount rates, and mortality models of the OPs pension plan they were probably actuarily equivalent.
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Old 03-04-2011, 04:47 PM   #23
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I believe that you are still mistaken. no, it is you who is mistaken, you are correcting the value of pension A to its value at 62 but you also are also correcting the value of pension B to its value at age 55. apples and oranges

The value of the 55 year old pension at age 55 was $66k. If I was given that cash and invested it at 5% for seven years until 62 it would be worth around $92k.

Previously we estimated that at 65 the higher pension was worth $156k.

But there was a problem in that our 16X present value model didn't take into account that the 55 year old would collect for maybe 27 years and the 62 year old would collect for 20 years. Therefore direct present value comparisons corrected to either a 55 year old or a 62 year old aren't valid.

I estimated the correction for the extra payments to the 55year old at $29k when he was 55. But that money invested at 5% for 7 years until he is 62 would be worth ~$40k. so now to try and make your point you are changing the numbers? i used your numbers to show you that your method was wrong, why muddy the waters by changing the numbers?

Therefore the present value of the lower pension at 62 years old is (($66k)/.71) <-this is totally inappropriate, it should not be divided by anything + ($29k/.71) <-and this is where you are mudding the waters = $133k <-this is now very incorrect

The higher pension at 62 had a (at 62) present value of $156k and wins the little ballpark analysis. Still they are close enough and my analysis has been simple.

Therefore I suspected that per the rules, discount rates, and mortality models of the OPs pension plan they were probably actuarily equivalent. nope
how bout instead of making your wild claims and changing the parameters, you go through my explanation and show me where there is an error in my method (you wont be able to, if the numbers are wrong remember i used your numbers). try doing that to my explaination of the value of both pensions at age 62.
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Old 03-04-2011, 04:57 PM   #24
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lets keep this Civil !

I haven't changed the numbers. Go read my first ballpark post.

I believe what has confused you is that the error correction for the longer payment regarding the 16X model is almost identical to the delta increase from the $66k present value at 55 to the present value at 62. Both are worth about $29k but refer to two separate and very different things.
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Old 03-04-2011, 05:36 PM   #25
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Here is another way of evaluating, it assumes the money is saved and earns 4% per year. Not inflation indexed so the comparison is valid. Assumes zero inflation.

Looks like the breakeven point is age 68. Do note that at age 83, you will have collected about 50% more money = $100k +
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Old 03-04-2011, 06:25 PM   #26
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why wont you go through my explanation and show me the error in my method? and why wont you read my posts?


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Originally Posted by MasterBlaster View Post
lets keep this Civil !

I haven't changed the numbers. Go read my first ballpark post. i did read your post, i used your numbers. but now you are inflating both the original value of pension A but also you are inflating the value of the payments made between 55 and 62.

I believe what has confused you is that the error correction for the longer payment regarding the 16X model is almost identical to the delta increase from the $66k present value at 55 to the present value at 62. Both are worth about $29k but refer to two separate and very different things.
i am not confused but i think you are. we are using the 16x method of determining the PV of a nonCOLAed lifetime income stream at some date once the stream has started. therefore whenever you value a pension from some date forward that value will always be 16x. since you put a value of 16x on pension B's future starting at age 62 then it makes sense to value the future payments of pension A starting at age 62 the exact same way. in fact it doesnt make sense to not value them the same way, especially since it is the same persons pension.

think of getting the PV of pension A at age 62 as the sum of 2 values 1) the value of the payments that at that time will already have been paid and 2) the PV of the future (beyond age 62) payments. in your 1st post you gave 1) to be $29,064, so i used your number. since we are using the 16x method of getting the PV of a future income stream starting now, 2) is 12X346X16 = 66432 (per you too) there fore the value of pension A at age 62 is $29,064+$66,432=$95,496, which i said in my post that you admittedly didnt read.

now, again per you and the 16x method, the value of pension B at age 62 is 12X 813X16 = 156096

so AT AGE 62 the total value of pension A is $95,496 (this includes all the payments already made by that age) and the value of pension B is $156,096. you do not discount pension B because we are using age 62 as the date of valuation.
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Old 03-04-2011, 10:19 PM   #27
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Yet again, I commend the moderators for their patience!
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Old 03-04-2011, 11:15 PM   #28
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SKIRacer:

This isn't a trivial exercise. You need to assume a discounted rate of return and a mortality model. You can go here and play around with their calculator: https://www.pensionbenefits.com/calc...item=cash_flow(snip).
I tried to use the calculator, but ran into a snag. I don't know what "determination date" means, and it isn't defined in the "click here for help" pop-up either.

Please explain.
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Old 03-05-2011, 10:26 AM   #29
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why wont you go through my explanation and show me the error in my method? and why wont you read my posts?
.
JDF_Fire;

I thought some more about this issue and realize now that there is an error in my approach.

Please forgive me.
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Old 03-05-2011, 10:27 AM   #30
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I tried to use the calculator, but ran into a snag. I don't know what "determination date" means, and it isn't defined in the "click here for help" pop-up either.

Please explain.
I would suppose that "determination date" is the date at which interest rates, and mortality rates are chosen and frozen. Some plans only change interest rates once a year even though they fluctuate all year long. The determination date may be very different than the retirement date.
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Old 03-05-2011, 10:51 AM   #31
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Good grief! This has been way more complicated a discussion than I expected. Flaming arrows and all.

My first reply to the OP somewhat simplified the analysis that I had done on my own pensions. I have several very small pensions. Two are discounted at 3% per year and two at 6% against the "normal" retirement age of 65.

Everything, of course, depends on the discount rate used in calculating the NPV of the various income streams. What I decided using an ultra safe discount rate is that the 3% discounts provide little value in delaying taking the money as soon as it is available. The 6% discount is worth delaying as long as intermediate US bonds are yielding below 5 or 6%.

This also assumes that one's health is good and no reason exists to assume you won't exit this world one the early side of your mortality table.

Effectively, you are choosing to "buy" an annuity by delaying. You could also go through the drill of saying "how much would it cost in year X to buy an annuity to make up for the lost annual payment by taking my pension early?"
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Old 03-05-2011, 01:45 PM   #32
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Lordy, one could acquire a headache reading all these convoluted theories. To the OP: my observation is that most pensions that give you the choice of age to begin receiving payments *generally* have a (simplistic) breakeven age in the mid-70's, give or take a year this way or that. There are many ways to add mathematical layers to that breakeven guesstimate to try to divine the *best* choice. But....often there is no loud and clear answer. The preponderance of votes are going to be for delaying, but I caution you to look at the impact it will have on the taxability of your SSI. If you delay, you push more of your pension dollars into your SSI years, and could subject your SSI dollars to income taxes. This impact may be enough to argue taking your pension at 55. Figuring that one out is a spreadsheet exercise, no doubt...depends on so many moving parts!!

Good luck!
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Old 03-05-2011, 07:32 PM   #33
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JDF_Fire;

I thought some more about this issue and realize now that there is an error in my approach.

Please forgive me.
thank you. done.
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Old 03-06-2011, 06:07 AM   #34
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Good grief! This has been way more complicated a discussion than I expected. ...

Because it is complicated and there are a number of assumptions that need to be made and varied using well defined models (note the plural models) to understand the possible dynamics of the future (how it might turn out). As is the case with most complex problems that incorporate risk (finance, engineering, actuarial sciences, etc).... one needs to be fairly well acquainted with the general aspects of topic and the math, modeling, etc.

Take care and do a lot of checking and cross-checking... it is easy to introduce a mistake (even if your model is appropriate for what you are attempting to analyze).


I was going to describe my approach... but it would take too much effort to describe it. I built several models in spreadsheets where I could adjust the key (important) variables to see how it moved (sensitivity analysis) under different assumptions. The insight yielded from my effort caused me to adjust my decision (as opposed to what I had assumed for many years). I probably put in about 40 hours work (building the models and analysis). That 40 hours of work had a big payback. If I had made my decision based on my early assumptions.... it would have cost me a lot of money and I would have taken on more risk.

Some of my analysis was not in a spreadsheet.... it had to do with the my personal situation (health, wealth, longevity, cashflow needs, etc) and the health of the pension fund, my exposure to a variety of other risks, etc.

IMO - That is just a warm up exercise... (or possibly a cross-check determine if the other analysis from one's own models is on the right track). If I were beginning this type of analysis... One simple exercise I would perform (which does rely on some assumptions that may not turn out to be exactly accurate) is to use an annuity as an approximation for the purchase of the pension. I would get annuity quotes for the payout at each age. This gives an indication of the value of each stream at each age... what does it look like? Which is more valuable? Take the Premium cost for the 55 payout stream and determine the compounded rate of return I would need to achieve (using the invested 55 premium amount, invested for 7 years) with the goal of buying the larger payout stream at 62 (remember the quotes have the insurance company's full model built in... actuarial assumptions). I would use the immediate annuity web site for convenience. For me to accomplish a similar outcome using the OP's payout amounts as an example (using a single life annuity).... I would need to make a 10.6% compounded return (net of any taxes) to buy the larger payout at 62. One basic question I would ask myself: can I double my money in 7 years (using investments with an equivalent risk profile... very high grade bonds, with very high yield that mature in a short time frame) so I am very confident (relatively low risk of not achieving the goal) that I will have the premium needed to buy the larger payout annuity at 62?


BTW - I edited that last part several times to try to communicate the idea accurately... Sorry if there are any stray words left in that confuse the idea... as stated by 2B... it is a complicated topic... because there a several non-determinant factors to consider.
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Old 03-06-2011, 03:30 PM   #35
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...

IMO - That is just a warm up exercise... (or possibly a cross-check determine if the other analysis from one's own models is on the right track). If I were beginning this type of analysis... One simple exercise I would perform (which does rely on some assumptions that may not turn out to be exactly accurate) is to use an annuity as an approximation for the purchase of the pension. I would get annuity quotes for the payout at each age. This gives an indication of the value of each stream at each age... what does it look like? Which is more valuable? Take the Premium cost for the 55 payout stream and determine the compounded rate of return I would need to achieve (using the invested 55 premium amount, invested for 7 years) with the goal of buying the larger payout stream at 62 (remember the quotes have the insurance company's full model built in... actuarial assumptions). I would use the immediate annuity web site for convenience. For me to accomplish a similar outcome using the OP's payout amounts as an example (using a single life annuity).... I would need to make a 10.6% compounded return (net of any taxes) to buy the larger payout at 62. One basic question I would ask myself: can I double my money in 7 years (using investments with an equivalent risk profile... very high grade bonds, with very high yield that mature in a short time frame) so I am very confident (relatively low risk of not achieving the goal) that I will have the premium needed to buy the larger payout annuity at 62?

...
the op's choices are $346/mo for life starting at age 55 or $813/mo for life starting at age 62. so the question is if the op starts at 55 and saves (invests) all the money he gets till age 62, what interest rate would he need to be able to buy a SPIA paying $813 - $346 = $467/mo when he reaches age 62? well todays cost of a SPIA paying $467/mo for a 62 y.o. male is $78,876 (per Immediate Annuities - Instant Annuity Quote Calculator.). so for $346/mo to grow to $78,876 in 7 years you need an after tax return of ~25% per year, compounded monthly (per my HP 12c). looks like waiting till 62 is the way to go.
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