Author Topic: Help with Calculations  (Read 2161 times)

bray

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Help with Calculations
« on: June 15, 2019, 02:50:49 PM »
Hello!

My wife and I currently have $200k in taxable investments (VTSAX), and $170k in IRAs/401(k)s.  We're 36 and 35, and would like to retire in 12 years.  For example purposes, say we want to withdraw $80k / year once we retire.

I'm getting inconsistent results when I try to figure out how much we'll need to have in 12 years (so we know how much we need to invest per month), so I'd appreciate if you could tell me where I'm going wrong.


Simple Calculation

4% rule: $80,000 * 25 = $2,000,000 required to retire

This shows, to get to $2,000,000 in 12 years, we have to invest $7,700/mo for 12 years (I entered 7% return - 3% inflation = 4% return):

https://www.calculator.net/investment-calculator.html?ctype=endamount&ctargetamountv=36500&cstartingprinciplev=370000&cyearsv=12&cinterestratev=4&ccontributeamountv=7700&ciadditionat1=monthly&printit=0&x=0&y=0


Slightly Less Simple Calculation

We need our VTSAX withdrawals to last from my age 48 till 59.5 = 11.5 years (for simplicity, assume we don't plan to withdraw from retirement accounts early).

So, working backwards, this shows if we withdraw $6,666/mo ($80k / year) in today's dollars and we have $742k in VTSAX, it'll last 11.5 years (I entered 7% return - 3% inflation = 4% return):

https://www.calculator.net/retirement-calculator.html?cneededamount=742000&cmonthlywithdraw=6666&cinterestrate=4&ctype=4&x=0&y=0#howlongtowithdraw

Is that right though?  If we say a 7% return rate, but take out 3% for inflation, does that mean we'll be withdrawing $80k / year in today's dollars, i.e. we'll actually increase the withdrawals each year by inflation, assuming that's 3% each year?


If that is correct, then to get $742k in VTSAX, we need to invest $2,300/mo for the next 12 years into VTSAX, assuming a 4% return rate (7% return - 3% inflation):

https://www.calculator.net/investment-calculator.html?ctype=endamount&ctargetamountv=36500&cstartingprinciplev=200000&cyearsv=12&cinterestratev=4&ccontributeamountv=2300&ciadditionat1=monthly&printit=0&x=0&y=0


So that gets us to age 59.5.  Then we'll tap retirement accounts.

Now, to see how long our retirement accounts will last, we'll invest the remaining amount from the Simple Calculation to retirement accounts.  That said that we need to invest $7,700/mo, so $7,700 - $2,300 to VTSAX = $5,400/mo should go to retirement accounts.

If we do that for 12 years, we'll have $1,200,000 in retirement accounts:

https://www.calculator.net/investment-calculator.html?ctype=endamount&ctargetamountv=36500&cstartingprinciplev=170000&cyearsv=12&cinterestratev=4&ccontributeamountv=5400&ciadditionat1=monthly&printit=0&x=0&y=0

Then that sits another 12 years (to take me to age 60), and becomes $2,000,000:

https://www.calculator.net/investment-calculator.html?ctype=endamount&ctargetamountv=36500&cstartingprinciplev=1263000&cyearsv=12&cinterestratev=4&ccontributeamountv=0&ciadditionat1=monthly&printit=0&x=99&y=22


This shows $2,000,000 with an $80k / year (today's dollars) withdrawal rate would last *102 years*:

https://www.calculator.net/retirement-calculator.html?cneededamount=2000000&cmonthlywithdraw=6666&cinterestrate=4&ctype=4&x=71&y=20#howlongtowithdraw


I'm not ruling it out, but I don't think we'll live to 162 years old.

So my main question is why does a $7,700/mo investment until ER in 12 years, as the 4% rule seems to suggest we need, seem like overkill?  I know this doesn't take into account taxes, and I know I shouldn't count on 7%, but I'd be fine if our retirement accounts lasted ~30 years, not 102 years.

Or it's entirely possible some of my calculations are wrong.  I just feel like I'm going in circles here.

Thank you!

secondcor521

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Re: Help with Calculations
« Reply #1 on: June 16, 2019, 09:24:18 AM »
I see several things.

First, your very first link has a starting amount of $370,000.  Everywhere else you use $200,000.

Second, the 4% rule is more conservative because it accounts for variation in returns.  This conservative approach is thought necessary because if returns in the market are low or negative and you continue to make withdrawals, then you're taking a bigger percentage of the stash while it's down, which leaves less to recover for the years after that.  Read the description on the first page at http://www.firecalc.com.

Third, I think your link after "If we do that for 12 years, we'll have $1,200,000 in retirement accounts:" should have a starting value of $0, not $170,000.

Fourth, in your second set of calculations, you're assuming you're contributing $5,400 a month towards retirement from age 48 to age 59.5.  How are you doing that if you're retiring at 48?  In the first set of calculations, you're retiring at 48 and not contributing any more money.

There may be more, but that's what I see on first review.

bray

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Re: Help with Calculations
« Reply #2 on: June 16, 2019, 05:40:02 PM »
Thanks for the reply!

First, your very first link has a starting amount of $370,000.  Everywhere else you use $200,000.

The $370k is our total taxable + retirement investments. So for the 4% rule, to be able to withdraw $80k/year, we'd need $2,000,000. To get there in 12 years, this shows we'd need to invest $7,700/mo for 12 years (plus our initial $370k total) to get to $2,000,000.

Third, I think your link after "If we do that for 12 years, we'll have $1,200,000 in retirement accounts:" should have a starting value of $0, not $170,000.

I used $170k here because in this Slightly Less Simple Calculation, I first used the $200k taxable balance to get us from age 48 to 59.5.  At age 59.5, the taxable balance would be essentially gone.  But we also have the $170k in retirement accounts.  So, in addition to the $2,300/mo we'll invest to VTSAX from now till age 48, we'll also invest $5,400/mo to retirement accounts from now till age 48.  This calculation shows doing that will net $1,263,000 in retirement accounts by age 48.

Fourth, in your second set of calculations, you're assuming you're contributing $5,400 a month towards retirement from age 48 to age 59.5.  How are you doing that if you're retiring at 48?  In the first set of calculations, you're retiring at 48 and not contributing any more money.

I'm not contributing anything from age 48 to 59.5.  This shows contributing to retirement accounts from age 36 to 48:

If we do that for 12 years, we'll have $1,200,000 in retirement accounts:

https://www.calculator.net/investment-calculator.html?ctype=endamount&ctargetamountv=36500&cstartingprinciplev=170000&cyearsv=12&cinterestratev=4&ccontributeamountv=5400&ciadditionat1=monthly&printit=0&x=0&y=0

And then this shows, that balance of $1,263,000 growing for another 12 years (48 to 59.5) with no additional contributions:

Then that sits another 12 years (to take me to age 60), and becomes $2,000,000:

https://www.calculator.net/investment-calculator.html?ctype=endamount&ctargetamountv=36500&cstartingprinciplev=1263000&cyearsv=12&cinterestratev=4&ccontributeamountv=0&ciadditionat1=monthly&printit=0&x=99&y=22

Let me know if that makes sense.

secondcor521

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Re: Help with Calculations
« Reply #3 on: June 16, 2019, 08:03:01 PM »
I had a reading comprehension failure where I didn't notice the $170K number.  I also didn't understand what your plan was when you were doing the more complicated calculation.

After reading your second post and re-reading your original post, yes, it all makes sense to me.

The answer to the main question in your original post is in the second point of my first reply.  All of your math is using a simple calculator which adds 4% real rate of return year in and year out.  As you well know, VTSAX doesn't return 4% real every year.  This variability helps when you're adding to the stash but hurts when you're living off of it.

As a side note, VTSAX has historically done more like 10% nominal, 7% real.  So you can either back off your contributions to ~$5,268:

https://www.calculator.net/investment-calculator.html?ctype=contributeamount&ctargetamountv=2000000&cstartingprinciplev=370000&cyearsv=12&cinterestratev=7&ccontributeamountv=7700&ciadditionat1=monthly&printit=0

Or shorten your timeline from 12 years (age 48) to 10 years (age 46):

https://www.calculator.net/investment-calculator.html?ctype=investlength&ctargetamountv=2000000&cstartingprinciplev=370000&cyearsv=12&cinterestratev=7&ccontributeamountv=7700&ciadditionat1=monthly&printit=0

Also, as a practical matter if you've got any chance of succeeding at FIRE, you're probably either a good businessperson or a good employee, so you'll probably be able to increase the amount you're investing over the next 10-12 years.

HTH.

RWD

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Re: Help with Calculations
« Reply #4 on: June 16, 2019, 09:06:08 PM »
So you're expecting to need to spend $80k per year in today's dollars? That's quite a lot. You can cut quite a few working years if you can reduce that.

Anyway, the median return for the SP500 over a 12 year period is 6.951% (after inflation). If you want $2 million twelve years from now in 2019 dollars starting at $370k then you'll need to save ~$5,300 per month (increasing with inflation). With that you'll exceed your target number about 50% of the time. For an 80% chance you'll need to save ~$9,600 per month.

bray

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Re: Help with Calculations
« Reply #5 on: June 17, 2019, 08:57:52 AM »
So you're expecting to need to spend $80k per year in today's dollars? That's quite a lot. You can cut quite a few working years if you can reduce that.

That's just an example, for now.  We haven't nailed down that number yet. Just wanted to make sure I'm doing rough calculations correctly first.

Anyway, the median return for the SP500 over a 12 year period is 6.951% (after inflation). If you want $2 million twelve years from now in 2019 dollars starting at $370k then you'll need to save ~$5,300 per month (increasing with inflation). With that you'll exceed your target number about 50% of the time. For an 80% chance you'll need to save ~$9,600 per month.

Can you explain how you got those numbers? FIRECalc?

RWD

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Re: Help with Calculations
« Reply #6 on: June 17, 2019, 09:02:44 AM »
Anyway, the median return for the SP500 over a 12 year period is 6.951% (after inflation). If you want $2 million twelve years from now in 2019 dollars starting at $370k then you'll need to save ~$5,300 per month (increasing with inflation). With that you'll exceed your target number about 50% of the time. For an 80% chance you'll need to save ~$9,600 per month.

Can you explain how you got those numbers? FIRECalc?

The investment returns come from:
https://dqydj.com/sp-500-historical-return-calculator/

Then I used the following calculator for monthly additions:
https://financialmentor.com/calculator/compound-interest-calculator