
Formula to convert partiallyCOLA'd pension to equivalent COLA'd amount?
11182009, 11:18 PM

#1

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Formula to convert partiallyCOLA'd pension to equivalent COLA'd amount?
OK all you math gurus out there, I need your help. I am still trying to figure out my "Magic Number"—how much I need to have in my retirement account to leave my job with reasonable security. My pension has a quirk that makes it difficult for me to say how much of a shortfall my savings need to be able to make up. It's a defined benefit pension, with a fixed increase of 1.5% a year plus a guarantee that it will never go below 65% of the original purchasing power. Since inflation is almost always more than 1.5% a year, this isn't a fully COLA'd pension. If I live long enough (and I definitely intend to) it will almost certainly hit the 65% floor. OTOH, it isn't a fixed amount. Eventually the shrinkage of purchasing power will stop. By playing around with spreadsheets, I've found that, assuming constant 4% inflation, it takes about 23 years to hit the floor. I hope to retire before age 60 and am assuming I live to be 100, so 23 years is only about half of the time span the model needs to consider. This feature of the pension makes it tricky to figure out how much income my portfolio needs to produce. Even the financial planner I went to last year didn't have software that could model the pension accurately. The Monte Carlo simulations she did for me assumed the purchasing power of the pension would never stop shrinking, and IMO the "magic number" she calculated was grossly overestimated as a result.
It occurred to me a while ago that it might be possible to treat this pension in a way that made it equivalent to a fully COLA'd pension with a smaller benefit. Obviously, it could be considered a fully COLA'd pension for 65% of the starting benefit. But if I only spend 65% of the starting benefit, I could invest the remainder and at a SWR of say 3%*, generate a COLA'd stream of income from it also. The first year's income stream {1} would be 3% x 35%=1.225% of the original pension. If I did this for n years, until the pension had shrunk to 65% of its original buying power, I'd have what amounts to a COLA'd pension at 65% of the original benefit amount, plus a series of COLA'd income streams {1} through {n}. Put together, it would all add up to a fully COLA'd stream of income for (65+1.225+{2}+...+{n})% of the starting benefit amount. What I'd like to know is the formula, if there is one, to calculate what percentage of the original benefit all those income streams add up to. By playing with the spreadsheets some more, I found that with constant 4% inflation my partly COLA'd pension would be equivalent to a fully COLA'd pension up to age 100, for between 71 and 72 percent of the original amount. I haven't quite figured out how to make the spreadsheet tell me what happens when the inflation rate varies. I suspect that the equivalent amount will be strongly affected by the sequence of rates. My guess is that a few years of high inflation at the beginning of a scenario would have a drastic negative influence, just like a bear market during the first few years of withdrawals makes it more likely that the portfolio will be exhausted.
*I used a SWR of 3% rather than 4% because the amounts have to last longer than 30 years, and because it might not be possible to defer tax on all of the "remainders".




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11192009, 12:48 AM

#2

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Nice analysis, especially your observation that "the equivalent amount will be strongly affected by the sequence of rates." Yep..... you can't work with an "average" number such as 2.5%/yr since the sequence is important.
Unfortunately, since we don't know what inflation will be, determining what impact it will have on a notcola'd pension or a pension with a fixed annual adjustment such as yours is a guess at best. My DW has a similar situation to yours although, fortunately, the annual adjustment is higher. Unfortunately she doesn't have a "buying power floor." I SWAG hers into FireCalc by putting half of her pension amount as notcola'd and half as cola'd. I think you could do something similar but perhaps go 70/30 as your spreadsheet indicated.
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11192009, 07:56 AM

#3

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You could do your retirement income and expense computations without adjusting dollar values for inflation, so that dollars in 2040 would be worth a lot less than dollars today, due to inflation. I am not sure this is feasible in FIRECalc, but it would be something to try in any projections you might be doing yourself manually. You would have to make some assumptions about inflation, to adjust your expenses and other income streams.
Another (completely different and separate) approach would be to just assume that it is completely nonCOLA'd for purposes of your retirement computations, and just assume that the excess would be use for a little bit more "fun money". This is the approach that I would probably use.
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11192009, 08:43 AM

#4

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How much of your annual spend will come from this pension? If it is 100%, you are correct that the drift from real inflation could indeed be a big deal over 40 years. As it moves down towards 50% or less, a progressively smaller deal (but I still see why you want to try to model it).
Either way, I think youbet's suggestion is about as good as you can do. After that, there are probably bigger variables that we may not even know about.
Maybe you could enter some steps of increased spending at years 10, 15, 20 or so, to simulate the purchasing power degrading over time? Like youbet says, this won't really be modeled against historic inflation moves.
Or (similar to W2R's second suggestion), you could just start it out at 65% of its value, knowing that is conservative and accepting that a slightly lower success% isn't really that bad. Again, if the pension represents near 100% of your income stream, that probably isn't going to give you the lifestyle you want. DW will get a 3% each year semiCOLA, but it will be so small I have not even entered it. It is just a little more positive fudge factor for us.
ERD50



11192009, 08:48 AM

#5

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The Life of the Party
well I am only a sexmaster and not a math guru.
Since future inflation rates are unknown an exact answer is unknowable.
However I would use an approach like this...
Convert your payment stream back to a netpresentvalue lump sum. Then from that lump sum you can use the SWR rules to estimate an equivalent income stream.
To calculate the lump sum use a netpresentvalue calculator. Pick a discount rate that seems reasonable (or maybe your plan uses one already), subtract off the 1.5 percent increase from the discount rate to compute the lump sum equivalent.
For fun and also to entertain your friends at cocktail parties, you could vary the discount rate to come up with different answers.
Compare that result to the lump sum with a discount rate fully discounted by your estimate of inflation times the 65% floor.



11192009, 10:34 AM

#6

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Quote:
Originally Posted by W2R
You could do your retirement income and expense computations without adjusting dollar values for inflation, so that dollars in 2040 would be worth a lot less than dollars today, due to inflation. I am not sure this is feasible in FIRECalc, but it would be something to try in any projections you might be doing yourself manually. You would have to make some assumptions about inflation, to adjust your expenses and other income streams.

My brains get all tangled up when I try to work in constant dollars. For some reason it's easier for me to keep things straight in my mind if I think in terms of inflation doubling the cost of everything after a certain number of years, rather than inflation cutting my dollars in half over the same time span. It's the same thing really, but somehow I can't get a mental grip on it the second way.
Quote:
Another (completely different and separate) approach would be to just assume that it is completely nonCOLA'd for purposes of your retirement computations, and just assume that the excess would be use for a little bit more "fun money". This is the approach that I would probably use.

This is more or less what my FP did. It makes a huge difference in the outcome. The online Monte Carlo model I used can approximate this pension (I put it in as nonCOLA'd until it's down to the 65% value, and COLA'd at the lower benefit after that). It says, if I can retire if I keep doing what I'm doing for another 4 years (or even 3 if Mr Market is nice). The FP's models said, impossible (like my entire salary) savings levels for several years longer than that will not be sufficient. But the Monte Carlo simulator doesn't spit out a number so I can tell myself, "when your retirement account hits this number, you can pull the plug".



11192009, 10:49 AM

#7

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Quote:
Originally Posted by ERD50
How much of your annual spend will come from this pension? If it is 100%, you are correct that the drift from real inflation could indeed be a big deal over 40 years. As it moves down towards 50% or less, a progressively smaller deal (but I still see why you want to try to model it).
Either way, I think youbet's suggestion is about as good as you can do. After that, there are probably bigger variables that we may not even know about.
Maybe you could enter some steps of increased spending at years 10, 15, 20 or so, to simulate the purchasing power degrading over time? Like youbet says, this won't really be modeled against historic inflation moves.
Or (similar to W2R's second suggestion), you could just start it out at 65% of its value, knowing that is conservative and accepting that a slightly lower success% isn't really that bad. Again, if the pension represents near 100% of your income stream, that probably isn't going to give you the lifestyle you want. DW will get a 3% each year semiCOLA, but it will be so small I have not even entered it. It is just a little more positive fudge factor for us.
ERD50

I'm "test driving" the pension now, by basing my budget this year on how much spendable cash I'd have if I had retired in January (as it happens this is just about what's left after I max contributions and catchup to my taxdeferred account). I can squeak by, but it's uncomfortably tight at times. I think I would be able to live quite cozily on the benefit I'll be eligible for in 3 or 4 years, which is several hundred dollars a month more. So, at the beginning, the pension will be 100% of my income, especially since I will (hopefully) be under 591/2 and not able to take out of my retirement accounts yet. I do have fudge factors in my calculations, but this pension is such a big fraction of the whole I don't really feel I can treat the nonCOLA'd part of it as another one—35% of starting annual income is a pretty big fudge factor!



11192009, 10:56 AM

#8

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Quote:
Originally Posted by MasterBlaster
well I am only a sexmaster and not a math guru.
Since future inflation rates are unknown an exact answer is unknowable.
However I would use an approach like this...
Convert your payment stream back to a netpresentvalue lump sum. Then from that lump sum you can use the SWR rules to estimate an equivalent income stream.
To calculate the lump sum use a netpresentvalue calculator. Pick a discount rate that seems reasonable (or maybe your plan uses one already), subtract off the 1.5 percent increase from the discount rate to compute the lump sum equivalent.
For fun and also to entertain your friends at cocktail parties, you could vary the discount rate to come up with different answers.
Compare that result to the lump sum with a discount rate fully discounted by your estimate of inflation times the 65% floor.

Last night I thought of another method: get an annuity quote for my pension, then find out how big a COLA'd annuity I could buy for the same amount of money (but I don't know where I'd get that info either). Is that essentially the same thing you are describing above? Unfortunately, I don't know how to do that calculation either. Can you suggest a book or link that would guide me through it step by step?



11192009, 11:13 AM

#9

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here is one link to a pension lump sum calculator:
https://www.pensionbenefits.com/calc...em=lumpsum_cal
For a simpler calculation just find a calculator that computes net present value.
<from wikipedia>
Net present value ( NPV) or net present worth ( NPW) [1] is defined as the total present value (PV) of a time series of cash flows. It is a standard method for using the time value of money to appraise longterm projects. Used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met.
Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is the sum of all terms , where
t  the time of the cash flow i  the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.) Rt  the net cash flow (the amount of cash, inflow minus outflow) at time t (for educational purposes, R0 is commonly placed to the left of the sum to emphasize its role as (minus the) investment.
<more from wikipedia>
Net present value  Wikipedia, the free encyclopedia



11192009, 11:43 AM

#10

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Quote:
Originally Posted by kyounge1956
I'm "test driving" the pension now, by basing my budget this year on how much spendable cash I'd have if I had retired in January (as it happens this is just about what's left after I max contributions and catchup to my taxdeferred account). I can squeak by, but it's uncomfortably tight at times. I think I would be able to live quite cozily on the benefit I'll be eligible for in 3 or 4 years, which is several hundred dollars a month more. So, at the beginning, the pension will be 100% of my income, especially since I will (hopefully) be under 591/2 and not able to take out of my retirement accounts yet. I do have fudge factors in my calculations, but this pension is such a big fraction of the whole I don't really feel I can treat the nonCOLA'd part of it as another one—35% of starting annual income is a pretty big fudge factor!

how does 4% of your portfolio compare to 35% of your starting pension?



11202009, 02:13 AM

#11

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Quote:
Originally Posted by jdw_fire
how does 4% of your portfolio compare to 35% of your starting pension?

Right now? It's a little over 8x (starting monthly benefit three years hence x 12 x 0.35). Nowhere near big enough yet, I know.



11202009, 02:36 PM

#12

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Quote:
Originally Posted by kyounge1956
Right now? It's a little over 8x (starting monthly benefit three years hence x 12 x 0.35). Nowhere near big enough yet, I know.

hmmm not sure i understand your answer. are you saying
1) 4% * (your portfolio value) = 8 * (starting monthly benefit three years hence x 12 x 0.35)
or
2) (your portfolio value) = 8 * (starting monthly benefit three years hence x 12 x 0.35)
if 1) then you have no problem as you can more cover a 35% loss of pension purchasing power right now with WDs from your portfolio
if 2) then your current portfolio can cover 11.2 % of your starting pension value. and using your estimate of inflation (4%) the 2nd year of your retirement you would need a .8925% WD to cover the lost purchasing power. if you chose to use your portfolio to maintain your pension's purchasing power while maintaining a SWR or better for your portfolio you can get not quite 5 years (about 12.2% since what you dont use grows grows some) of pension purchasing power protection.



11202009, 03:28 PM

#13

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Quote:
Originally Posted by jdw_fire
hmmm not sure i understand your answer. are you saying
1) 4% * (your portfolio value) = 8 * (starting monthly benefit three years hence x 12 x 0.35)
or
2) (your portfolio value) = 8 * (starting monthly benefit three years hence x 12 x 0.35)
if 1) then you have no problem as you can more cover a 35% loss of pension purchasing power right now with WDs from your portfolio
if 2) then your current portfolio can cover 11.2 % of your starting pension value. and using your estimate of inflation (4%) the 2nd year of your retirement you would need a .8925% WD to cover the lost purchasing power. if you chose to use your portfolio to maintain your pension's purchasing power while maintaining a SWR or better for your portfolio you can get not quite 5 years (about 12.2% since what you dont use grows grows some) of pension purchasing power protection.

I meant 2. Obviously the portfolio is much too small to allow me to retire yet, even if I ignored the fact that the benefit I'd get if I retired now is significantly less than what it will be in 3 years.
Maybe I should just say: Magic Number=25 x [8 * (starting monthly benefit three years hence x 12 x 0.35)]. A 4% withdrawal rate would be cutting things a little close if the COLA'd part was the whole pension, but since it isn't the whole pension, my withdrawal rate won't reach a full 4% until long after I retire (23 years with constant 4% inflation). Using that, and given the current size of the portfolio, maximum contribution, estimated growth rate etc, the Magic Number is sounding more like four years hence than three. Maybe three and a half, because the benefit amount will go a little higher too. That will give housing prices some time to recover, because I am counting on my house to provide almost 30% of the Magic Number (i.e. the "sell it and buy one in a lessexpensive location" plan).



11202009, 05:35 PM

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It looks to me like you've done a lot of good work already. I think your approach of splitting it into a COLA'd pension of 65% of your initial benefit plus a side fund is the best route.
I'd simply assume that I can put the side fund into TIPS yielding inflation + 2.5%, then go ahead and run the spreadsheet the way I think you are already running it. Your results will still be impacted by inflation, but I'm guessing that you can run a number of inflation rates and convince yourself that the variation isn't too bad. It's certainly less than the variation you've got due to an unknown date of death.



11202009, 05:54 PM

#15

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Quote:
Originally Posted by Independent
It looks to me like you've done a lot of good work already. I think your approach of splitting it into a COLA'd pension of 65% of your initial benefit plus a side fund is the best route.
I'd simply assume that I can put the side fund into TIPS yielding inflation + 2.5%, then go ahead and run the spreadsheet the way I think you are already running it. Your results will still be impacted by inflation, but I'm guessing that you can run a number of inflation rates and convince yourself that the variation isn't too bad. It's certainly less than the variation you've got due to an unknown date of death.

I was planning to use I Bonds for the "remainders", because you don't have to pay the income tax until you cash them, but it's the same general idea. I will have to go look up the rates. I thought they were very low at the moment, but maybe I have confused the inflation adjustment and the interest rate. Anyway, they are guaranteed to keep up with CPI, and that's the important thing.



11232009, 04:29 AM

#16

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Quote:
Originally Posted by kyounge1956
Maybe I should just say: Magic Number=25 x [8 * (starting monthly benefit three years hence x 12 x 0.35)].

Magic Number=25 x [8 * (starting monthly benefit three years hence x 12 x 0.35)]
Magic Number= 25 * 8 * (starting monthly benefit three years hence x 12 x 0.35)
Magic Number= 200 * (starting monthly benefit three years hence x 12 x 0.35)
again i am not understanding. you said in 1 of your posts that you can live on 100% of your pension payment at the time you start your pension, so why do you need such a hi multiple (200 times) of the total possible loss of purchasing power of your pension as a portfolio "magic number"?



11232009, 05:06 AM

#17

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I would view it as a COLA'd pension of .65 the original amount, with some bonus money thrown in.
If inflation were to run at 6%, it would only take 10 years for your pension's purchasing power to erode to the point where the .65 limit kicks in. If inflation runs at 4.5%, it would only take 15 years. At 7.5%, it would take only 7 years.
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11232009, 10:32 AM

#18

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Quote:
Originally Posted by jdw_fire
Magic Number=25 x [8 * (starting monthly benefit three years hence x 12 x 0.35)]
Magic Number= 25 * 8 * (starting monthly benefit three years hence x 12 x 0.35)
Magic Number= 200 * (starting monthly benefit three years hence x 12 x 0.35)
again i am not understanding. you said in 1 of your posts that you can live on 100% of your pension payment at the time you start your pension, so why do you need such a hi multiple (200 times) of the total possible loss of purchasing power of your pension as a portfolio "magic number"?

It's a booboo—8 is on the same key as *, maybe I somehow hit them both. Either that or when I copied & pasted from my earlier post I mistakenly added 25 in front instead of changing the 8 to 25. It should just be 25X the amount in brackets, not 200x.




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