I've been having some fun with the mathematical side of ERE, which led me to write a post on my blog which you can find here.
Feel free to look around and if you have any questions or comments, just let me know. It's only part I, another post will follow later.
Playing with numbers
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Robert Muir
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I didn't have time to look into your formula deeply, but shouldn't you be subtracting your monthly savings from your monthly income at the beginning of the formula? Assuming that your net income after subtracting savings would be your monthly expenses.
What you want is:
(swr*nestegg)/12 = income - saved.
years = ((((income-saved/swr)12)-nestegg)/saved)/12
So in your initial calculation, you would only need 30 years vs 55 years and 19 years vs 44 in the second.
What you want is:
(swr*nestegg)/12 = income - saved.
years = ((((income-saved/swr)12)-nestegg)/saved)/12
So in your initial calculation, you would only need 30 years vs 55 years and 19 years vs 44 in the second.
Thought I would share the equation I use in excel:
=NPER(rr,-sr,-pp,(1.0-sr)/swr)
rr= inflation adjusted annual rate of return
sr = savings rate (I use as percent of net income)
pp = principal (initial savings) as percent of net income (principle/net income)
swr = annual safe withdrawal rate. I use 3%
Two things not accounted for:
1. This does not account for salary growth (this formula assumes salary grows with inflation). Accounting for salary growth makes the calculation extremely complicated.
2. Taxes are not perfectly accounted for (SWR changes based on taxes and therefore income in retirement). Using net income controls for taxes while earning.
So for a 4% inflation adjusted return, 80 percent savings rate, 0 principal, 3% swr and 0 inflation adjusted salary growth:
n = 7.33 years
You can use data tables in excel to see this while letting the variables change. For example, tweaking only the savings rate, we have:
sr---- n
0.60- 16.21563
0.62- 15.22918
0.64- 14.26837
0.66- 13.33158
0.68- 12.41729
0.70- 11.52414
0.72- 10.65088
0.74- 9.796354
0.76- 8.959498
0.78- 8.139333
0.80- 7.334953
0.82- 6.545517
0.84- 5.770245
0.86- 5.00841
0.88- 4.259333
=NPER(rr,-sr,-pp,(1.0-sr)/swr)
rr= inflation adjusted annual rate of return
sr = savings rate (I use as percent of net income)
pp = principal (initial savings) as percent of net income (principle/net income)
swr = annual safe withdrawal rate. I use 3%
Two things not accounted for:
1. This does not account for salary growth (this formula assumes salary grows with inflation). Accounting for salary growth makes the calculation extremely complicated.
2. Taxes are not perfectly accounted for (SWR changes based on taxes and therefore income in retirement). Using net income controls for taxes while earning.
So for a 4% inflation adjusted return, 80 percent savings rate, 0 principal, 3% swr and 0 inflation adjusted salary growth:
n = 7.33 years
You can use data tables in excel to see this while letting the variables change. For example, tweaking only the savings rate, we have:
sr---- n
0.60- 16.21563
0.62- 15.22918
0.64- 14.26837
0.66- 13.33158
0.68- 12.41729
0.70- 11.52414
0.72- 10.65088
0.74- 9.796354
0.76- 8.959498
0.78- 8.139333
0.80- 7.334953
0.82- 6.545517
0.84- 5.770245
0.86- 5.00841
0.88- 4.259333
By, the way, to show how much you have to save yearly, you should use the annuity formula with a target savings (FV) of expenses/swr. This site goes through the math and rearranges to solve for n (the number of years it will take to reach your goal)
http://www.frickcpa.com/tvom/TVOM_FV_Annuity.asp
n=LN(iFV/PMT+1)/(LN(1+i))
This is the equivalent to =nper(i,-PMT,0,FV) in Excel and is the formula needed for no principal
If you wanted to get the equation for nper with principal,you would have to solve for n in this formula:
FV=PMT(((1+i)^n-1)/i)+[P(1+i))^n] (where P is principal)
The bracketed part is what the principle grows to in the future and is a modification of the annuity formula from the link above.
Solving for n gets
n=ln((iFV+P)/(iPV+P))/ln(1+i)
which matches
=nper(i,-PMT,-P,FV)
Using your 55 year example in excel
= nper(.05,-600*12,-25000,800*12/.03)
we get 20.7 years of saving required.
http://www.frickcpa.com/tvom/TVOM_FV_Annuity.asp
n=LN(iFV/PMT+1)/(LN(1+i))
This is the equivalent to =nper(i,-PMT,0,FV) in Excel and is the formula needed for no principal
If you wanted to get the equation for nper with principal,you would have to solve for n in this formula:
FV=PMT(((1+i)^n-1)/i)+[P(1+i))^n] (where P is principal)
The bracketed part is what the principle grows to in the future and is a modification of the annuity formula from the link above.
Solving for n gets
n=ln((iFV+P)/(iPV+P))/ln(1+i)
which matches
=nper(i,-PMT,-P,FV)
Using your 55 year example in excel
= nper(.05,-600*12,-25000,800*12/.03)
we get 20.7 years of saving required.
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George the original one
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@Nagerusu - don't get hung up on the exact numbers because investment returns are exceedingly variable.
For example: Jacob exceeded his $6k/yr expenses well before reaching $100k and I've had a similar experience. 2 or 3 good years like that and you'll be well ahead of the carefully plotted curve.
On the other hand, substantially negative returns in, say, the third or fourth year of saving, have a very profound ability to lengthen the years you need for reaching your goal.
And, on the third hand, one's fixed expenses can unexpectedly take a turn for the worse. It is rare for expenses to take a turn for the better!
For example: Jacob exceeded his $6k/yr expenses well before reaching $100k and I've had a similar experience. 2 or 3 good years like that and you'll be well ahead of the carefully plotted curve.
On the other hand, substantially negative returns in, say, the third or fourth year of saving, have a very profound ability to lengthen the years you need for reaching your goal.
And, on the third hand, one's fixed expenses can unexpectedly take a turn for the worse. It is rare for expenses to take a turn for the better!
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George the original one
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- Joined: Wed Jul 28, 2010 3:28 am
- Location: Wettest corner of Orygun
Using Dan's formula and starting with zero principal, 80% savings rate, and going for a 4% SWR, getting to ERE in 5 years requires 11.3% inflation adjusted return.
That's in the realm of possible, but certainly requires some unusually positive investment returns... as I recall, MikeBOS's rental income is in that ballpark.
It's easier if you already have saved, say, 20% of their annual net income (not an uncommon scenario for someone just discovering ERE). Then inflation adjusted return only needs to be 8.4%, which is not too far above a realistic number for sn investor who is slightly above average.
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Applying all this to my own situation, counting only the taxable accounts: n=14 years with the 8.4% inflation adjusted return and n=12 years with the 11.3% return.
Counting all accounts, it looks much better. n=9.7 and n=8.1, respectively. Technically, it's much better than that since one of the retirement accounts is a pension that provides an income well above it's 4% SWR.
That's in the realm of possible, but certainly requires some unusually positive investment returns... as I recall, MikeBOS's rental income is in that ballpark.
It's easier if you already have saved, say, 20% of their annual net income (not an uncommon scenario for someone just discovering ERE). Then inflation adjusted return only needs to be 8.4%, which is not too far above a realistic number for sn investor who is slightly above average.
***
Applying all this to my own situation, counting only the taxable accounts: n=14 years with the 8.4% inflation adjusted return and n=12 years with the 11.3% return.
Counting all accounts, it looks much better. n=9.7 and n=8.1, respectively. Technically, it's much better than that since one of the retirement accounts is a pension that provides an income well above it's 4% SWR.
@George: I actually have a graph the displays expenses vs. passive income. When they cross, I can live of the investments. It does not take into account the income I get from actively buying and selling stocks, so that would even give me a buffer.
Thouhg that graph is more trustworthy, there are a couple of things to note:
1. Passive income can fluctuate too
2. It shows me what happens right now, not when it's probably going to happen
3. You can never be certain about anything
That being said, I do those calculations to give me more confidence about reaching my goals and also to give me an indication when it will happen. If some changes happen along the way, I can recalculate everything, adjust my plan accordingly and have an idea of the impact of those changes on the duration of the journey.
We can not fixate on the numbers,
but how else could we know when the time is right to step into ERE?
Thouhg that graph is more trustworthy, there are a couple of things to note:
1. Passive income can fluctuate too
2. It shows me what happens right now, not when it's probably going to happen
3. You can never be certain about anything
That being said, I do those calculations to give me more confidence about reaching my goals and also to give me an indication when it will happen. If some changes happen along the way, I can recalculate everything, adjust my plan accordingly and have an idea of the impact of those changes on the duration of the journey.
We can not fixate on the numbers,
but how else could we know when the time is right to step into ERE?
"We can not fixate on the numbers, but how else could we know when the time is right to step into ERE?"
The answer as I see it, is funnily enough, fixating on the numbers ( the numbers that you have control over only)and erring on the side of caution.
like say, when you reach the point where the returns on your somewhat low risk and somewhat inflation proof (ranging from rentals to dividend stocks) investments cover say, 1.5 times your current (EREish) expenses(how else would you know your average expenses over a long period precisely but by fixating on those numbers?)
----fixate by all means..but on the right numbers..which is expenses, outflow etc- something TOTALLY in your control..unlike the returns on investments----
Now also assume your diligent tracking of your expenses shows that you could further reduce it by another 25% or so IF NEED BE ( by taking on some inconveniences which you surely would rather live without, but could live with too, without being much affected by..if need be only)
So there's 2 buffers right there: your needs are being met with 2/3rds of your passive income, and there is also the possibility of reducing your needs by another 25%.
At this stage you can be pretty sure you could now practice your martial arts out in the open rather than in front of the computer
The answer as I see it, is funnily enough, fixating on the numbers ( the numbers that you have control over only)and erring on the side of caution.
like say, when you reach the point where the returns on your somewhat low risk and somewhat inflation proof (ranging from rentals to dividend stocks) investments cover say, 1.5 times your current (EREish) expenses(how else would you know your average expenses over a long period precisely but by fixating on those numbers?)
----fixate by all means..but on the right numbers..which is expenses, outflow etc- something TOTALLY in your control..unlike the returns on investments----
Now also assume your diligent tracking of your expenses shows that you could further reduce it by another 25% or so IF NEED BE ( by taking on some inconveniences which you surely would rather live without, but could live with too, without being much affected by..if need be only)
So there's 2 buffers right there: your needs are being met with 2/3rds of your passive income, and there is also the possibility of reducing your needs by another 25%.
At this stage you can be pretty sure you could now practice your martial arts out in the open rather than in front of the computer
in the post above, I'd suggested not fixating with the returns-numbers, but doing so with the expenses-number.
if anyone's wondering whether i think 1.5's not a number ( i'd said.."your somewhat low risk and somewhat inflation proof investments cover say, 1.5 times your current expenses"..well I sure think that's a number all right
to not fixate only means not going..'OMG..my returns this month from equities is 1/3rd the historical number for this month'...or 'OMG...my portfolio has depreciated 3% this week compared to the last week'. that's fixation..which is very counter-productive wrt returns-numbers. whereas..calculating that you have managed an average of 15% returns from equities over 5 years is not. (notwhthstanding the fact that the data of last 5 years may not be one bit representative of the returns you may see in the next 5..but that's the best we can do)
ironically, fixating on the expenses-numbers is very productive..like going 'OMG..i've spent 100 dollars this month on something whereas it looks like I'd spent only about 30 dollars every other month in this year on that something..i wonder what makes this month different..was it worth it etc'. Doing this over a long period of time with everything results in a highly value-for-money and finely tweaked expenses-tracking-mechanism which can drastically reduce the outflow..and it becomes second nature after a while ( i'm not saying all this from experience...i don't put my expenses on paper..mostly as all my expenses are of a repetitive nature and I can track them easily..but it couldn't hurt to write them down. Note to self: to track expenses more thoroughly on paper.
if anyone's wondering whether i think 1.5's not a number ( i'd said.."your somewhat low risk and somewhat inflation proof investments cover say, 1.5 times your current expenses"..well I sure think that's a number all right
to not fixate only means not going..'OMG..my returns this month from equities is 1/3rd the historical number for this month'...or 'OMG...my portfolio has depreciated 3% this week compared to the last week'. that's fixation..which is very counter-productive wrt returns-numbers. whereas..calculating that you have managed an average of 15% returns from equities over 5 years is not. (notwhthstanding the fact that the data of last 5 years may not be one bit representative of the returns you may see in the next 5..but that's the best we can do)
ironically, fixating on the expenses-numbers is very productive..like going 'OMG..i've spent 100 dollars this month on something whereas it looks like I'd spent only about 30 dollars every other month in this year on that something..i wonder what makes this month different..was it worth it etc'. Doing this over a long period of time with everything results in a highly value-for-money and finely tweaked expenses-tracking-mechanism which can drastically reduce the outflow..and it becomes second nature after a while ( i'm not saying all this from experience...i don't put my expenses on paper..mostly as all my expenses are of a repetitive nature and I can track them easily..but it couldn't hurt to write them down. Note to self: to track expenses more thoroughly on paper.
@slacker: I understand that and that's also what I do. I was just trying out formula's to give me an estimate on how long it's going to take me. That's very difficult to predict (actually, there's no way of knowing for sure).
But still, having an estimate that you can follow by entering data in a formula is a good way to stay inspired and keep the motivational juices flowing.
And the only way to do that, is by starting from a mathematical formula, that needs to be fed some numbers. That's close to fixating, but I see no other way of estimating how long it should take...
But still, having an estimate that you can follow by entering data in a formula is a good way to stay inspired and keep the motivational juices flowing.
And the only way to do that, is by starting from a mathematical formula, that needs to be fed some numbers. That's close to fixating, but I see no other way of estimating how long it should take...
@nagerusu: yeah, it sure helps with motivation but like you've said so yourself, it's next to impossible to predict (my biggest dilemma wrt ERE)..and I've always believed no map's better than a wrong one..so I just do the best I can wrt saving in the hope that when the time's right I'll somehow know ( how naive is that?)...or I'll be forced into ERE via retrenchment etc (but what if that never happens anytime?)
actually i never gave much thought to it....always saying to myself something like: when the stress gets too much (it already is too much but i'm not FI yet) I'll put ERE into action (not the saving part..but the deciding to live off of your savings part)
@jacob ( and anyone else here who's ERE already): how did you decide what was the right time? when your savings crossed a threshold or the bullshit at work crossed a threshold? but if i remember correctly, you worked for 2-3 years after you were FI, right? (not the latex gig..but the physics career). So what was the motivation to stop adding more buffer to the savings and go ERE finally?
actually i never gave much thought to it....always saying to myself something like: when the stress gets too much (it already is too much but i'm not FI yet) I'll put ERE into action (not the saving part..but the deciding to live off of your savings part)
@jacob ( and anyone else here who's ERE already): how did you decide what was the right time? when your savings crossed a threshold or the bullshit at work crossed a threshold? but if i remember correctly, you worked for 2-3 years after you were FI, right? (not the latex gig..but the physics career). So what was the motivation to stop adding more buffer to the savings and go ERE finally?
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jacob
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@slacker - It was a combination of 1) Not wanting to continue in the same career (nice cozy government job managing a scientific database and writing white papers for the next 25 years); 2) Not being able to switch track within "the company" (wrong citizenship); and 3) Having the opportunity to do something else (nonprofit startup).
I have never had a specific financial target number/date(*) with which I meant to retire once I hit it. It was more of a fallback in case work no longer interested me. In terms of work I'm mainly interested in "building cathedrals". I don't really care for things I can't put my stamp on so to speak.
(*) However, I did know the number and the date years in advance and my predictions turned out to be quite accurate (within a couple of months).
I have never had a specific financial target number/date(*) with which I meant to retire once I hit it. It was more of a fallback in case work no longer interested me. In terms of work I'm mainly interested in "building cathedrals". I don't really care for things I can't put my stamp on so to speak.
(*) However, I did know the number and the date years in advance and my predictions turned out to be quite accurate (within a couple of months).
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George the original one
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Zounds! I've been looking into what my pension's value actually is... yes, there's a lump sum option, but it is a fraction of the value of the payments.
Plugging that number into the equation with a 6% adjusted inflation return moves n down to 5.25 years. Which is the same ballpark as my other estimates for "bridging the gap" until the pension kicks in at age 58.
Plugging that number into the equation with a 6% adjusted inflation return moves n down to 5.25 years. Which is the same ballpark as my other estimates for "bridging the gap" until the pension kicks in at age 58.
George, are your pension payments inflation adjusted? One of my parents is retiring soon and I keep warning about the inflation risk (with high inflation you'll wish you took the lump sum). Parent is dead set on low inflation or deflation. I find this very hard to believe given current and foreseeable monetary leadership.
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George the original one
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- Joined: Wed Jul 28, 2010 3:28 am
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The pension payments would be partially inflation adjusted, which is why the cash value is tough to calculate. Unless the laws are changed again (and they very well could be, a lot can happen in the decade before I can claim them), the payments get an annual COLA, but the COLA caps at 2%.
The payments would be 28% of the cash value that is reported to me annually. When I claim retirement (but not before), the cash value is matched, so the "full formula" payments work out to 14% of cash value.
The payments would be 28% of the cash value that is reported to me annually. When I claim retirement (but not before), the cash value is matched, so the "full formula" payments work out to 14% of cash value.