kyounge1956
Thinks s/he gets paid by the post
- Joined
- Sep 11, 2008
- Messages
- 2,171
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".
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".
