# The Money Mustache Community

## Learning, Sharing, and Teaching => Ask a Mustachian => Topic started by: gecko10x on December 16, 2014, 11:50:07 AM

Title: Simplify the Shockingly Simple Math?
Post by: gecko10x on December 16, 2014, 11:50:07 AM

However, it still isn't all that simple on the calculation side, and people still get hung up on it when thinking about pre-tax, post-tax, employer added income, etc.

But couldn't you re-formulate the table as a percentage of expenses? It seems that would be way easier to calculate. Like:
95% savings rate = 19x expenses -> <2yrs
50% savings rate = 1x expenses -> 17yrs
35% savings rate = 0.54x expenses -> 25yrs
25% savings rate = 0.33x expenses -> 32yrs
10% savings rate = 0.11x expenses -> 51yrs

Then, the calculation is really easy: I spent \$55k and saved \$32k (as in, this amount somehow made it into my various retirement accounts). So, 32/55 = 0.58, which is about 25yrs.

Does anyone have the spreadsheet for the math to verify if you can reformulate it this way? Did I miss something? (Probably! Or someone else would have already done it this way!)
Title: Re: Simplify the Shockingly Simple Math?
Post by: shuffler on December 16, 2014, 12:37:55 PM
But couldn't you re-formulate the table as a percentage of expenses? It seems that would be way easier to calculate.
Sure, you could.  Why do you think it's easier this way?  Why is "savings / spending" easier than "savings / net"?
Title: Re: Simplify the Shockingly Simple Math?
Post by: nereo on December 16, 2014, 12:54:38 PM
Quote
However, it still isn't all that simple on the calculation side, and people still get hung up on it when thinking about pre-tax, post-tax, employer added income, etc.
I think people get hung up and led astray with the "shockingly simple math".  Ultimately it's about what you save and what you'll need in ER.  If you have a current expense that you won't have in ER (e.g. paying college tuition, caring for a seriously-sick parent or paying rent for a larger & more expensive home you won't have when kids move out) your estimates will be completely off, often comically so.  You can also 'fudge' your savings rate depending on (as you said) whether you use pre/post tax, bonuses, job perks etc.

Whatever makes it easiest for you.  Personally, I find it most helpful to know my FI number (often 25x future expenses) and then that's what I need to 'win the game'.  Any number of online calculators can adjust for different savings rates and market returns to estimate how long it will take for me to get there.
YMMV
Title: Re: Simplify the Shockingly Simple Math?
Post by: gecko10x on December 16, 2014, 01:02:06 PM
But couldn't you re-formulate the table as a percentage of expenses? It seems that would be way easier to calculate.
Sure, you could.  Why do you think it's easier this way?  Why is "savings / spending" easier than "savings / net"?

It seems like a lot of people have trouble coming up with an accurate "net". I just thought the spending number might be a bit more concrete.

Plus I think it makes more sense because income has no bearing on the retirement numbers, but expenses do.
Title: Re: Simplify the Shockingly Simple Math?
Post by: Thegoblinchief on December 16, 2014, 01:17:38 PM
The shockingly simple math post is pretty flawed. Like nereo pointed out, one's budget in ER can vary drastically from during the accumulation phase. Ours will slightly. Users like arebelspy have noted they plan to spend more than 2x, I think mainly on travel.

So it's much more about using the right data and assumptions to come up with an accurate FIRE number and making progress towards that as fast (or as slow) as you desire.
Title: Re: Simplify the Shockingly Simple Math?
Post by: nereo on December 16, 2014, 01:20:51 PM
Plus I think it makes more sense because income has no bearing on the retirement numbers, but expenses do.
Yup, plus it's hard to integrate years when the earnings/savings ratio change.  What happens when your savings rate changes frequently because of differences in earning and/or large changes in spending.  "well, in '09 I had a SR of 35% on \$86k, in '10 it was 22% on \$58k and in '11 it was 40% on 91k...."

Like I said, whatever works for you.  Savings + future spending.
Title: Re: Simplify the Shockingly Simple Math?
Post by: No Name Guy on December 16, 2014, 01:51:55 PM
Uhhh....

Income generating assets must = 25x to 33x your desired passive income level at retirement.

Simple.
Title: Re: Simplify the Shockingly Simple Math?
Post by: MDM on December 16, 2014, 02:37:03 PM
Nords has the most detailed explanation I've seen: http://the-military-guide.com/2011/01/03/how-many-years-does-it-take-to-become-financially-independent-2/.

Probably best if you read the whole thing, but here's a short version:
Expenses * 25 = (Savings rate) * [(1 + compounding rate)^^Time – 1] / (compounding rate)

One can express both "Expenses" and "Savings rate" in dollars per year, or divide both sides by the same income - it's algebra - and the equation is still true.  If you use the same income base for "expenses as a percent of income" and "savings rate as a percent of income" you can use any income you choose.

Or, yes, you can divide both sides by savings rate and go from there.
Title: Re: Simplify the Shockingly Simple Math?
Post by: shuffler on December 16, 2014, 03:22:53 PM
It seems like a lot of people have trouble coming up with an accurate "net". I just thought the spending number might be a bit more concrete.
Hmm.  I hadn't thought that'd be a problem.  Just look at last year's tax return.
But maybe people do have a problem with that?  Meh.

Plus I think it makes more sense because income has no bearing on the retirement numbers, but expenses do.
Ah, well, *improving* the SSM is an entirely different beast than just trying to *simplify* it.

The SSM is just an easy calculation with the intent of opening people's eyes to the idea of reducing spending and increasing savings.
Sure, "income has no bearing", but as other have pointed out "expenses during your working years may have little bearing on expenses in retirement years".  And if you accept that, then why stop at using a constant rate of expenses rather than a model for expenses that takes into account people's natural tendency to spend less as they age (modulo healthcare, which is a whole 'nuther ball of wax).  ... And suddenly you're competing with Bo_Knows's newly open-sourced CFireSim.  ;^)
Title: Re: Simplify the Shockingly Simple Math?
Post by: arebelspy on December 16, 2014, 04:44:53 PM
That seems like a weird way to do it to me, but do whatever works for you!  :)

I think as a whole this metric is likely less useful for the average person because most people know what they net (can easily look at paystubs) and what they saved (can easily look at account statements/contributions), but less know what they spent (would have to track their spending, which most don't do - or could look at account statements, but there's a lot more adding to do on all the little expenses).

In other words, the inputs that go into the normal calculation are easier to obtain than your suggested inputs, for most people.
Title: Re: Simplify the Shockingly Simple Math?
Post by: gecko10x on December 16, 2014, 06:35:01 PM
All good points :-)

Thanks for the discussion!
Title: Re: Simplify the Shockingly Simple Math?
Post by: arebelspy on December 16, 2014, 08:51:38 PM
Thanks for the discussion!

(https://media.giphy.com/media/6PopYBwOlKS8o/giphy.gif)
Title: Re: Simplify the Shockingly Simple Math?
Post by: Bob W on December 16, 2014, 08:59:35 PM
You're forgetting to factor in SS and pensions. Totally messes with numbers and can allow for FI at as low as 5 times expenses depending on age.
Title: Re: Simplify the Shockingly Simple Math?
Post by: SwordGuy on December 16, 2014, 10:40:22 PM
You're forgetting to factor in SS and pensions. Totally messes with numbers and can allow for FI at as low as 5 times expenses depending on age.

Yep.  You need 25 times (Expected expenses minus expected social security minus expected pension).

Except that doesn't account for the years that you'll be too young to collect either social security or the pension...

If that's not to long a gap, the simplest way is to add # years before pension times expected expenses to the above number and assume you'll spend this additional amount by the time you collect your first SS or pension money.

If it's long enough for compounding to kick in, then it's not so simple again.

Title: Re: Simplify the Shockingly Simple Math?
Post by: nereo on December 17, 2014, 06:26:05 AM
Thanks for the discussion!

(https://media.giphy.com/media/6PopYBwOlKS8o/giphy.gif)
gulp, gulp....ahhhhh, refreshing!  When was the last time I had a Flaming Moe?
Title: Re: Simplify the Shockingly Simple Math?
Post by: Thegoblinchief on December 17, 2014, 06:27:55 AM
I just use the FI Laboratory created by Mad Fientist.  It's especially useful if, like many people, your expenses are going to be very different post FI.

I forgot about that one. Maybe I'll give it a spin after our holiday.
Title: Re: Simplify the Shockingly Simple Math?
Post by: Workinghard on December 17, 2014, 10:35:07 AM
I like this formula that I saw posted on Bogleheads.  I can't remember who posted it and unfortunately I didn't copy and paste the name. Here's what he said.

Nest Egg = (( Non Discretionary Budget * 2) - Annual Pension Amts and or S.S.) * 25

There has to be some flexibility in your budget to cut back if necessary. My formula for having 'Enough' \$\$\$ to retire. (The constant of '2' is there to cut expenses by 50%, if need be)
Title: Re: Simplify the Shockingly Simple Math?
Post by: nereo on December 17, 2014, 11:08:10 AM
Nest Egg = (( Non Discretionary Budget * 2) - Annual Pension Amts and or S.S.) * 25

There has to be some flexibility in your budget to cut back if necessary. My formula for having 'Enough' \$\$\$ to retire. (The constant of '2' is there to cut expenses by 50%, if need be)
Holy Cow (!)  Correct me if I'm wrong, but wouldn't that give you a SWR of 2%?!  Way too rich for my blood...

Title: Re: Simplify the Shockingly Simple Math?
Post by: arebelspy on December 17, 2014, 11:23:23 AM
Nest Egg = (( Non Discretionary Budget * 2) - Annual Pension Amts and or S.S.) * 25

There has to be some flexibility in your budget to cut back if necessary. My formula for having 'Enough' \$\$\$ to retire. (The constant of '2' is there to cut expenses by 50%, if need be)
Holy Cow (!)  Correct me if I'm wrong, but wouldn't that give you a SWR of 2%?!  Way too rich for my blood...

Depends on what fraction of your budget is discretionary.  It might give you a 50% WR if you have a huge discretionary budget!

Seems like an odd way to do it to me, to only count some of your expenses, and double those, and...

/shrug
Title: Re: Simplify the Shockingly Simple Math?
Post by: nereo on December 17, 2014, 11:28:07 AM
Depends on what fraction of your budget is discretionary.  It might give you a 50% WR if you have a huge discretionary budget!

Seems like an odd way to do it to me, to only count some of your expenses, and double those, and...

/shrug
but...but..but... the only other inputs are for pensions or SS.  which makes me question what 'non-discretionary' is supposed to mean in this scenario.  the overwhelming majority of workers won't have a pension, so ER pre 62/65/67 would basically all be nest egg = ('spending' x 2) x 25.

(shrug).  Whatever make s people happy.
Title: Re: Simplify the Shockingly Simple Math?
Post by: Dan_at_Home on December 17, 2014, 12:20:18 PM
The original blog article is meant to be a general guide to (1) see the relationship between your savings rate and time to FI and (2) to get a ballpark figure as to how long it takes to reach FI.

To get more accurate information, I believe you just have to sit down and list out all your expenses in FI making the estimates as close as possible, then lay out all your passive income sources and work out the numbers, i.e. by using an excel spreadsheet or similar software.

Title: Re: Simplify the Shockingly Simple Math?
Post by: sirdoug007 on December 17, 2014, 02:58:16 PM
I've been messing around with the spreadsheet Nords links to.  One of my issues with it is it only gives you a time from zero savings.  Once you have anything significant in the bank you're not really sure where you are along the FI path.

I also think the expense/savings ratios are awkward (mostly in that you have to do some other math outside the spreadsheet and the implicit assumption that they should add to 1).  Using dollar amounts seems much more straightforward.

My revisions are attached.

The beauty in the Nords equation is income does not matter at all.  Current expenses don't matter either (only to the extend that they allow you to achieve the annual savings).  Only annual savings and FIRE expenses find their way into the math.

It took a bit of derivation to get current savings into the equation but it seems to work.

Just input:
-Expected rate of return
-Annual savings
-Annual FIRE expenses
-SWR
-Current savings

Let me know what you folks think.  Cheers!
Title: Re: Simplify the Shockingly Simple Math?
Post by: Workinghard on December 17, 2014, 03:56:55 PM
Nest Egg = (( Non Discretionary Budget * 2) - Annual Pension Amts and or S.S.) * 25

There has to be some flexibility in your budget to cut back if necessary. My formula for having 'Enough' \$\$\$ to retire. (The constant of '2' is there to cut expenses by 50%, if need be)
Holy Cow (!)  Correct me if I'm wrong, but wouldn't that give you a SWR of 2%?!  Way too rich for my blood...

Depends on what fraction of your budget is discretionary.  It might give you a 50% WR if you have a huge discretionary budget!

Seems like an odd way to do it to me, to only count some of your expenses, and double those, and...

/shrug

I look at the discretionary budget for things that aren't necessary such as travel, etc. it's just another way of padding. Really it's no different than when Vanguard ran a financial plan that showed our spending outlook. At that time, increasing our spending 23k a year still gave us a 100% success rate. That's a huge increase!
Title: Re: Simplify the Shockingly Simple Math?
Post by: MDM on December 17, 2014, 08:41:23 PM
I've been messing around with the spreadsheet Nords links to.  One of my issues with it is it only gives you a time from zero savings.  Once you have anything significant in the bank you're not really sure where you are along the FI path.

I also think the expense/savings ratios are awkward (mostly in that you have to do some other math outside the spreadsheet and the implicit assumption that they should add to 1).  Using dollar amounts seems much more straightforward.

My revisions are attached.

The beauty in the Nords equation is income does not matter at all.  Current expenses don't matter either (only to the extend that they allow you to achieve the annual savings).  Only annual savings and FIRE expenses find their way into the math.

It took a bit of derivation to get current savings into the equation but it seems to work.

Just input:
-Expected rate of return
-Annual savings
-Annual FIRE expenses
-SWR
-Current savings

Let me know what you folks think.  Cheers!
Looks good.

Yours and the one in How To Write a Reader Case Study (http://forum.mrmoneymustache.com/ask-a-mustachian/how-to-write-a-'case-study'-topic/msg274228/#msg274228) seem to get the same answer if one uses the "taxable" cells in the case study spreadsheet.

E.g., see results from the 4% case:
(http://s23.postimg.org/5r3p9m65n/screenshot_41.png) (http://postimage.org/)
Title: Re: Simplify the Shockingly Simple Math?
Post by: Cressida on December 17, 2014, 10:02:17 PM
I've been messing around with the spreadsheet Nords links to.  One of my issues with it is it only gives you a time from zero savings.  Once you have anything significant in the bank you're not really sure where you are along the FI path.

I also think the expense/savings ratios are awkward (mostly in that you have to do some other math outside the spreadsheet and the implicit assumption that they should add to 1).  Using dollar amounts seems much more straightforward.

My revisions are attached.

The beauty in the Nords equation is income does not matter at all.  Current expenses don't matter either (only to the extend that they allow you to achieve the annual savings).  Only annual savings and FIRE expenses find their way into the math.

It took a bit of derivation to get current savings into the equation but it seems to work.

Just input:
-Expected rate of return
-Annual savings
-Annual FIRE expenses
-SWR
-Current savings

Let me know what you folks think.  Cheers!

I like it! Just simple enough that I should be able to explain it to DH. :)

(this is at least as much of a knock on my comprehension as on his)
Title: Simplify the Shockingly Simple Math?
Post by: arebelspy on December 17, 2014, 10:54:38 PM

IDK, you may not want to trust the author of that spreadsheet...

There's some much better ones around now. I'll see if I can post a good one next time I'm on the computer.
Title: Re: Simplify the Shockingly Simple Math?
Post by: sirdoug007 on December 18, 2014, 10:51:39 AM

I like it! Just simple enough that I should be able to explain it to DH. :)

(this is at least as much of a knock on my comprehension as on his)

Just stay away from the natural logs and you'll be good :)

An important part of this stuff for me is the rate of return sensitivity.  Obviously if you are getting to FI on a really small budget in under 10 years it is less of a concern, but in my case I like seeing how different market outcomes affect the results.
Title: Re: Simplify the Shockingly Simple Math?
Post by: RapmasterD on December 18, 2014, 04:43:15 PM
I think the original "shockingly simple" post was indeed shockingly simple. And let me tell you something else, since you didn't ask for my advice.

If you find, post-FIRE, that you're burning at too high a rate, then just turn down the heat...and eat...some...CHICKEN FEET!

http://www.simplyrecipes.com/recipes/how_to_make_stock_from_chicken_feet/
Title: Re: Simplify the Shockingly Simple Math?
Post by: NinetyFour on December 19, 2014, 08:10:28 AM