### Author Topic: Question on savings rate calculation. (Math question!)  (Read 7052 times)

#### Vitai Slade

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##### Question on savings rate calculation. (Math question!)
« on: April 17, 2014, 01:24:22 PM »
Alright, so I know that there are a thousand ways to calculate your savings rate. To include mortgage principal or not to include? Include investment gains or no? Etc. etc. and on and on. My question doesn't really pertain too much to those things as I already have a way of calculating mine. HOWEVER, what I need advice on is if the math I am using is technically correct or not. It's a switch between Gross and Net. Let me show you how I calculated January, for example:

Math:

Total NET income:     \$4,265.51
Total Expenses:       -\$2,393.28

=\$1,872.23
Mortgage Principle: +\$509.89

=\$2,382.12
Total Net income:    /\$4,265.51

=55.85%
401k Deferral:         +15.00%

=70.85%

Summary: So I started by subtracting my expenses from my income, then adding back in the principal portion of the mortgage that I subtracted. I do this because, while it is an expense, it is an asset that remains mine just as a stock when I purchase it. The principal acts just like a stock (once I get it paid off) in that it pays dividends forever in the form of free rent (not including property tax, of course). Afterwards, I divided my net income from the total to come up with 55.85%. Then I added in my 401k deferral percentage. That is gross savings that are not included in the NET number included above.

Question: So this is where it gets tricky. I'm adding a straight 15% gross savings to the 55.85% calculation of my net savings. I look at it as... whatever the number is, whether it be \$200 before tax of \$150 after tax, it is still 15% gross or net, therefore, it can just be added on top to account for my 401k savings that I don't see in my net savings rate. I want to include my 401k savings in my savings rate as it IS savings, but I'm not sure if I did the math correctly or not. Is this the right way of adding that in? Or is there another way that I'm not seeing?

#### bikebum

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #1 on: April 17, 2014, 01:42:26 PM »
I think it is not correct to add the percentages, as one is based on net income and the other is based on gross, if I follow what you did. I would include the 401K contribution in your net income right from the start. I think you will get a lower, and more real, savings rate.

#### matchewed

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #2 on: April 17, 2014, 01:52:50 PM »
Agreed.

For example to use your numbers and the assumption that you're putting the maximum amount allowed for someone under the catch up age (17,500). You add your monthly contribution to your 401k to your income

Math:

Total NET income:     \$4,265.51
401k Contribution:   +\$1,458
Total Expenses:       -\$2,393.28

=\$3,330.23
Mortgage Principle: +\$509.89

Savings:                  =\$3,840.12
/Total Net income:   /(\$4,265.51+\$1,458)

Savings Rate           =67.09%

#### Vitai Slade

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #3 on: April 17, 2014, 02:00:27 PM »
I think it is not correct to add the percentages, as one is based on net income and the other is based on gross, if I follow what you did. I would include the 401K contribution in your net income right from the start. I think you will get a lower, and more real, savings rate.
Agreed.

For example to use your numbers and the assumption that you're putting the maximum amount allowed for someone under the catch up age (17,500). You add your monthly contribution to your 401k to your income

Math:

Total NET income:     \$4,265.51
401k Contribution:   +\$1,458
Total Expenses:       -\$2,393.28

=\$3,330.23
Mortgage Principle: +\$509.89

Savings:                  =\$3,840.12
/Total Net income:   /(\$4,265.51+\$1,458)

Savings Rate           =67.09%

So how would you recommend going about adding in the 401k deductions without having to manually input the exact numbers each month? Or is that how I'm supposed to go about it? And then how to you account for the change from gross to net? Do I add up all the deductions and then hack off 25%?

#### NewStachian

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #4 on: April 17, 2014, 02:55:27 PM »
What I'm about to say isn't THE way to do it - it's my 2 cents on how I do it.

Bottom line is it doesn't matter how you do it as long as you keep it consistent over time so you can compare the rates against each other and see what progress you're making.

Personally, I convert everything to post-tax dollars and compute everything off that. I assume a 20% tax bracket and make my 401(k) contribution what it would be after tax by multiplying it by .8.

I also take my single money dumps to my investment account and divide that all by 12. so when I do my roth, that gets added in to my monthly rate as \$5500/12. this will obviously make my savings rate grow throughout the year and reset to its lower value in January when I copy my spreadsheet template and make a new one. This method isn't for everyone, obviously.

So my numerator is: money i automatically invest + 401(k)*.8 + house principal + random additions to my investments / 12
denominator is: after-tax revenue for that month

#### Spork

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #5 on: April 17, 2014, 03:03:04 PM »

Bottom line is it doesn't matter how you do it as long as you keep it consistent over time so you can compare the rates against each other and see what progress you're making.

This.

Now: if we all want to compare to each other... we all should use a consistent method.... but if you're tracking over time, you're just comparing yourself to yourself.  Pick a way that works and stick with it.

Personally:  I do it the way I think is "correct accounting".   I enter all the numbers.  All of them.  I enter all my expenses (which would include interest, taxes, etc) and all of my income (salary, the employer 401k contribution, dividends, etc).
Then: income-expenses=savings

Yes, I put every stinking value in... down to the piddly dollar amounts per check that go to insurance (expense) and FICA (expense).  The software I use (gnucash) understands scheduled deposits and I really only update that template once a year when costs/salaries/expenses change.

#### matchewed

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #6 on: April 17, 2014, 05:55:55 PM »
I think it is not correct to add the percentages, as one is based on net income and the other is based on gross, if I follow what you did. I would include the 401K contribution in your net income right from the start. I think you will get a lower, and more real, savings rate.
Agreed.

For example to use your numbers and the assumption that you're putting the maximum amount allowed for someone under the catch up age (17,500). You add your monthly contribution to your 401k to your income

Math:

Total NET income:     \$4,265.51
401k Contribution:   +\$1,458
Total Expenses:       -\$2,393.28

=\$3,330.23
Mortgage Principle: +\$509.89

Savings:                  =\$3,840.12
/Total Net income:   /(\$4,265.51+\$1,458)

Savings Rate           =67.09%

So how would you recommend going about adding in the 401k deductions without having to manually input the exact numbers each month? Or is that how I'm supposed to go about it? And then how to you account for the change from gross to net? Do I add up all the deductions and then hack off 25%?

The how depends on what sort of software you are using for your calculations. If you're using something like excel your 401k contribution should be a flat amount each month unless you're manually adjusting it for some reason or another. My income fluctuated by small amounts so I used a flat amount that I knew wouldn't be exact but it wouldn't be off by much.

What do you mean account for the change from gross to net? Given your calculation above we're talking net. When did gross get involved? Much like Spork said calculate it any way you want. As long as you're consistent you will get apples to apples. You can even do it the way you outlined previously. I wouldn't personally do it that way but if it works for you, cool.

#### bikebum

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #7 on: April 17, 2014, 06:04:29 PM »
Here's a way to think about it that highlights the error: If your expenses were 0, your method would calculate a savings rate of 115%.

#### arebelspy

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #8 on: April 17, 2014, 06:35:30 PM »
Here's a way to think about it that highlights the error: If your expenses were 0, your method would calculate a savings rate of 115%.

I don't see that as a problem.

I'm okay with someone saving more than they make because of a certain way they're counting it (percentage of net, counting investment income, counting percent of main job saved, but living on side gig, etc.)

As others have said, as long as you're consistent, who cares.

I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### bikebum

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #9 on: April 17, 2014, 06:49:39 PM »
Here's a way to think about it that highlights the error: If your expenses were 0, your method would calculate a savings rate of 115%.

I don't see that as a problem.

I'm okay with someone saving more than they make because of a certain way they're counting it (percentage of net, counting investment income, counting percent of main job saved, but living on side gig, etc.)

As others have said, as long as you're consistent, who cares.

Hey I guess you're right. The way I think about it, I would not want to see a savings rate over 100%. But others may not mind.

I think there is still a problem with the original calculation though since the percentages are based on different totals. But if OP is consistent and just compares to him/herself, that's fine.

Although if you want to use the savings rate to estimate your working years, don't you have to be careful to do it correctly?

#### arebelspy

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #10 on: April 17, 2014, 06:55:01 PM »
Although if you want to use the savings rate to estimate your working years, don't you have to be careful to do it correctly?

Therein lies the rub.  What is "correctly"?

(I'm genuinely asking that, not being facetious.)

What savings rate calculation is the most accurate for time to retirement formulas like this one: http://the-military-guide.com/2011/01/03/how-many-years-does-it-take-to-become-financially-independent-2/

I actually don't know the answer to that.  Do you?
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### bikebum

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #11 on: April 17, 2014, 07:40:22 PM »
Although if you want to use the savings rate to estimate your working years, don't you have to be careful to do it correctly?

Therein lies the rub.  What is "correctly"?

(I'm genuinely asking that, not being facetious.)

What savings rate calculation is the most accurate for time to retirement formulas like this one: http://the-military-guide.com/2011/01/03/how-many-years-does-it-take-to-become-financially-independent-2/

I actually don't know the answer to that.  Do you?

That's a good question. All the formulas and charts I've seen ignore taxes. If you use your net savings rate, it ignores the future taxes you will pay and gives you too few working years. If you use the gross savings rate, it assumes you have to keep paying all those taxes forever and gives you too many working years. I think the net savings rate would get you pretty close on the charts, since the future taxes will probably be pretty small.

I don't actually use a savings rate to figure out how much longer I have. I have my estimated expenses which include future taxes, and use a spreadsheet to keep track of the stash and project it out to see when I hit my "number." I would guess this is how most do it. So maybe my comment about the savings rate needing to be correct doesn't matter either, haha. Did you set me up?

#### arebelspy

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #12 on: April 17, 2014, 07:45:57 PM »
lol.  It wasn't intended to be a setup, but I did laugh at your conclusion.

Yeah, I think savings rate as time to FIRE is useful for those with quite a ways to go (5-15 years).  And however you calculate it, it's probably "close enough."  Once you start getting closer, you'll hone in more on specifics and not just use a rough "savings rate" tool.
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### Spork

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #13 on: April 18, 2014, 10:03:28 AM »
Re: estimating working years... I do it a few ways...

1. take last year's expenses/income and current "financial assets" and sort out how many years at the current rate to hit 25x
2. same as #1 but with last 5 years
3. brute force the firecalc web app.   Use current expenses/income for last year and current "financial assets" to see if I hit a target success percentage.  If not, do it another year.  Repeat until done.
4. same as #3 but with last 5 years data

Obviously none of these are fool proof.

#### bikebum

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #14 on: April 18, 2014, 01:31:18 PM »
Although if you want to use the savings rate to estimate your working years, don't you have to be careful to do it correctly?

Therein lies the rub.  What is "correctly"?

(I'm genuinely asking that, not being facetious.)

What savings rate calculation is the most accurate for time to retirement formulas like this one: http://the-military-guide.com/2011/01/03/how-many-years-does-it-take-to-become-financially-independent-2/

I actually don't know the answer to that.  Do you?

That's a good question. All the formulas and charts I've seen ignore taxes. If you use your net savings rate, it ignores the future taxes you will pay and gives you too few working years. If you use the gross savings rate, it assumes you have to keep paying all those taxes forever and gives you too many working years. I think the net savings rate would get you pretty close on the charts, since the future taxes will probably be pretty small.

I don't actually use a savings rate to figure out how much longer I have. I have my estimated expenses which include future taxes, and use a spreadsheet to keep track of the stash and project it out to see when I hit my "number." I would guess this is how most do it. So maybe my comment about the savings rate needing to be correct doesn't matter either, haha. Did you set me up?

Here's an old spreadsheet that I just updated to add a future tax rate into the working years calculation. You input your expected rate of return and future tax rate and it gives you working years for different net savings rates and SWR. There's two tables so you can compare to the case where you ignore the future taxes. And I put a table at the bottom so you can see how many working years are added when you include future taxes. It also has replicas of those really neat graphs that have working years on the y-axis, savings rate on the x-axis, and lines of different SWR.

I'm pretty certain the equations are correct, but if anyone wants to check that'd be cool.
« Last Edit: April 18, 2014, 01:43:26 PM by bikebum »

#### warfreak2

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #15 on: April 19, 2014, 05:52:54 AM »
It's up to you to define what "savings rate" means for you, but if you want to apply the formula from Shockingly Simple Math to determine your FI date, you should use the definition used therein, which is (almost) as described by Spork: 100% - (income/expenses) where your mortgage principal is not an expense.

Spork counts investment income in his calculation, which is correct in terms of double-entry accounting. However, expected investment returns are baked into in the SSM, so should not also be included as "income" for that purpose.

#### Spork

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #16 on: April 19, 2014, 06:56:49 AM »
It's up to you to define what "savings rate" means for you, but if you want to apply the formula from Shockingly Simple Math to determine your FI date, you should use the definition used therein, which is (almost) as described by Spork: 100% - (income/expenses) where your mortgage principal is not an expense.

Spork counts investment income in his calculation, which is correct in terms of double-entry accounting. However, expected investment returns are baked into in the SSM, so should not also be included as "income" for that purpose.

Yeah, I was being terse I guess.  But yes... I don't consider principal an expense.  It is an asset transfer/liability reduction.

#### warfreak2

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #17 on: April 19, 2014, 07:57:20 AM »
But yes... I don't consider principal an expense.  It is an asset transfer/liability reduction.
Indeed, using double-entry accounting, your mortgage is a liability so money transferred to it from your bank account (an asset) is not an expense. Profit = income - expenses, savings rate = 100% - (expenses / income), neither of these formulae include assets or liabilities.

#### NewStachian

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##### Re: Question on savings rate calculation. (Math question!)
« Reply #18 on: April 19, 2014, 07:58:35 AM »

Although if you want to use the savings rate to estimate your working years, don't you have to be careful to do it correctly?

The math model is a thumbrule which makes wild assumptions that will not be true over your number of years. The market will not return the exact number you expect and your savings rate will fluctuate over time. The margin for error is beyond the method you are using.

Don't just use the thumbrule table, do the math yourself! I ran the numbers for the percent of your income graph in excel to see how i liked them. Doing this will teach you a bunch about how it all works.

I have a formula that calculates the DAY I can FIRE. The accuracy is probably +/- 20% (which can be years) but it's a baseline that works for me. Here's what I do:

=today() + (log((Yearly Spending*25)/Net Worth Today)/log(1+Annualized Net Worth Appreciation))*365

My net worth appreciation over the last 11 years has been 19% which means the sum of my additions plus stock returns has averaged 19%. I assumed this would go down over time, but it's been 24% the last few years. Obviously the stock  market has been doing much,  much better which is most of it, but I'm also shoveling large amounts of money into the market. If I put .24 instead of .19 in, it knocks 2 years off my FIRE time. You can make the numbers do whatever you want. At the end of the day you have to look yourself in the mirror and know your math is legit.
« Last Edit: April 19, 2014, 08:02:01 AM by NewStachian »