## Retirement Withdrawal Math Verification Needed

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Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Retirement Withdrawal Math Verification Needed

Can someone check my calculations? I am trying to calculate how long my theoretical retirement account would last into retirement. The scenario I created:

Retire at 65 (33 years from now)
Account value when first withdrawal made \$2.5MM
Withdrawal rate of \$50,000/year present value
Assume retirement account earns 3% annually
Assume inflation is 2.1% annually

This scenario has me running out of money at 94 years old. Does that seem correct?

I have created a retirement sheet and I am running different scenarios such as fixed salary, fixed withdrawal rate (i.e. 4% per year), etc. and want to ensure I am not missing something in my withdrawals.

Also, is 3% growth a reasonable assumption considering I will likely be 80%/90% bonds during retirement?

Lastly, is a 2.1% annual inflation rate reasonable as well?
Last edited by NBKCF on Tue Jul 09, 2019 10:20 am, edited 1 time in total.

luminous
Posts: 196
Joined: Sat Dec 30, 2017 10:28 pm

### Re: Retirement Withdrawal Math Verification Needed

Is 2.5M also future value?
Is 3% annual return nominal or real?
50/20/30 US stock/international stock/bonds. Hope to semi-retire in 2022.

HomeStretch
Posts: 4780
Joined: Thu Dec 27, 2018 3:06 pm

### Re: Retirement Withdrawal Math Verification Needed

At retirement age 65, you will have 50x saved if you have a retirement portfolio of \$2.5 million (future value) and withdrawals of \$50k (future value). With your projected annual earnings (modestly) exceeding projected annual inflation, at a high level review it doesn’t make sense that your portfolio is depleted at age 94 after only 29 years.

user9532
Posts: 34
Joined: Sun Dec 18, 2016 10:08 pm

### Re: Retirement Withdrawal Math Verification Needed

Your portfolio will last roughly 68 years assuming

- Portfolio value when you start your withdrawal is \$2.5M
- The first year you will withdraw \$50,000, thereafter 50K adjusted for inflation at 2.1%/year
- Your portfolio balance grows at 3% annually.

Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Re: Retirement Withdrawal Math Verification Needed

luminous wrote:
Tue Jul 09, 2019 9:52 am
Is 2.5M also future value?
Is 3% annual return nominal or real?
2.5MM is future (I think). That is the value I get after contributing until 65 years old assuming a 5% annual return.

3% is real. My calculations take \$50K and convert it to a future value and withdrawal that amount from the portfolio. It recalculates every year so the 3% incorporates that year’s inflation.

Hope this helps.

soccerrules
Posts: 1033
Joined: Mon Nov 14, 2016 4:01 pm

### Re: Retirement Withdrawal Math Verification Needed

\$2.5M is cash gives your 50 years of \$50K withdrawals -- you are good to 115! (not factoring increased withdrawals due match inflation)

in general 2% inflation adjusted withdrawal rate of portfolio assuming at least a 30-40% stock position -- is widely considered bullet proof to not run out of money over 30 years

Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Re: Retirement Withdrawal Math Verification Needed

HomeStretch wrote:
Tue Jul 09, 2019 9:57 am
At retirement age 65, you will have 50x saved if you have a retirement portfolio of \$2.5 million (future value) and withdrawals of \$50k (future value). With your projected annual earnings (modestly) exceeding projected annual inflation, at a high level review it doesn’t make sense that your portfolio is depleted at age 94 after only 29 years.

Future value of 50k in 33 years is \$99,270. So to have 50k I have to withdrawal \$99,270 in future dollars. That value increases every year to maintain an equivalent \$50k salary. Am I doing something wrong?

Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Re: Retirement Withdrawal Math Verification Needed

Sorry folks! I meant a present value of \$50k! So a future equivalent to that value. I will edit my initial post.

Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Re: Retirement Withdrawal Math Verification Needed

user9532 wrote:
Tue Jul 09, 2019 10:12 am
Your portfolio will last roughly 68 years assuming

- Portfolio value when you start your withdrawal is \$2.5M
- The first year you will withdraw \$50,000, thereafter 50K adjusted for inflation at 2.1%/year
- Your portfolio balance grows at 3% annually.
Sorry for the confusion, \$50k present value.

user9532
Posts: 34
Joined: Sun Dec 18, 2016 10:08 pm

### Re: Retirement Withdrawal Math Verification Needed

NBKCF wrote:
Tue Jul 09, 2019 10:21 am
user9532 wrote:
Tue Jul 09, 2019 10:12 am
Your portfolio will last roughly 68 years assuming

- Portfolio value when you start your withdrawal is \$2.5M
- The first year you will withdraw \$50,000, thereafter 50K adjusted for inflation at 2.1%/year
- Your portfolio balance grows at 3% annually.
Sorry for the confusion, \$50k present value.
Yes, you are right. It will last until you are 94 years old.

Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Re: Retirement Withdrawal Math Verification Needed

soccerrules wrote:
Tue Jul 09, 2019 10:16 am
\$2.5M is cash gives your 50 years of \$50K withdrawals -- you are good to 115! (not factoring increased withdrawals due match inflation)

in general 2% inflation adjusted withdrawal rate of portfolio assuming at least a 30-40% stock position -- is widely considered bullet proof to not run out of money over 30 years
Excellent information. I will add to me sheet. If I understand, you’re saying a 2% withdrawal rate incorporates account growth with 30-40% bonds and inflation, right? Effectively, a 4% growth and 2% inflation.

soccerrules
Posts: 1033
Joined: Mon Nov 14, 2016 4:01 pm

### Re: Retirement Withdrawal Math Verification Needed

NBKCF wrote:
Tue Jul 09, 2019 10:27 am
soccerrules wrote:
Tue Jul 09, 2019 10:16 am
\$2.5M is cash gives your 50 years of \$50K withdrawals -- you are good to 115! (not factoring increased withdrawals due match inflation)

in general 2% inflation adjusted withdrawal rate of portfolio assuming at least a 30-40% stock position -- is widely considered bullet proof to not run out of money over 30 years
Excellent information. I will add to me sheet. If I understand, you’re saying a 2% withdrawal rate incorporates account growth with 30-40% bonds and inflation, right? Effectively, a 4% growth and 2% inflation.
the 4% SWR is a commonly acceptable safe withdrawal rate. That you can withdrawal 4% adjusted for inflation each year for 30 years and not run out of money. This also means having an AA of 40-50% stocks and the rest in bonds. If you are looking at withdrawals starting at \$50K on \$2.5M that is 2% SWR. if 4% is considered safe for 30 years --then what is withdrawing 50% of what is considered safe ? -- #bullettproof.

dbr
Posts: 33194
Joined: Sun Mar 04, 2007 9:50 am

### Re: Retirement Withdrawal Math Verification Needed

NBKCF wrote:
Tue Jul 09, 2019 9:49 am

Assume retirement account earns 3% annually
Assume inflation is 2.1% annually

These two assumptions are fundamentally flawed unless you have investments that have no variability. In the real world both returns and inflation vary from year to year and the average return does not predict what your actual experience will be. That is before one discusses whether the estimate of the average is accurate.

You should look at a model such as FireCalc and others of that nature that take this into account. The previous mention of 4% SWR is a reference to that approach.

Note the effects of variability of returns and inflation on portfolio support of withdrawals was an area that began to be explored in the early 1990's by Bengen, by the Trinity Study, and so on. That is background a person can read if interested. I would be surprised if they were the first people to be aware of the issue either.

Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Re: Retirement Withdrawal Math Verification Needed

dbr wrote:
Tue Jul 09, 2019 12:08 pm
NBKCF wrote:
Tue Jul 09, 2019 9:49 am

Assume retirement account earns 3% annually
Assume inflation is 2.1% annually

These two assumptions are fundamentally flawed unless you have investments that have no variability. In the real world both returns and inflation vary from year to year and the average return does not predict what your actual experience will be. That is before one discusses whether the estimate of the average is accurate.

You should look at a model such as FireCalc and others of that nature that take this into account. The previous mention of 4% SWR is a reference to that approach.

Note the effects of variability of returns and inflation on portfolio support of withdrawals was an area that began to be explored in the early 1990's by Bengen, by the Trinity Study, and so on. That is background a person can read if interested. I would be surprised if they were the first people to be aware of the issue either.
Thank you for the reply. I am creating a simplified sheet to project where certain savings rates will land me, so I am not expecting complete accuracy. My plan is to update the sheet annually to reflect real growth for that year to see how it affects the retirement account. After all, we can only assume what our returns will be so I am remaining conservative. I was most curious if I was calculating my account depletion correctly with certain withdrawal rates.

Great recommendation on FireCalc - I have not seen that site. It appears that my plans has zero indications of failure unless I am inputting something wrong.

longinvest
Posts: 4329
Joined: Sat Aug 11, 2012 8:44 am

### Re: Retirement Withdrawal Math Verification Needed

NBKCF wrote:
Tue Jul 09, 2019 8:02 pm
I am creating a simplified sheet to project where certain savings rates will land me, so I am not expecting complete accuracy. My plan is to update the sheet annually to reflect real growth for that year to see how it affects the retirement account. After all, we can only assume what our returns will be so I am remaining conservative. I was most curious if I was calculating my account depletion correctly with certain withdrawal rates.
If you're looking for inspiration, you might be interested to look at the Bogleheads wiki's VPW Accumulation And Retirement Worksheet. It takes a lifelong investing view, across accumulation and retirement. Here's a screenshot of its Accumulation sheet:

It uses the investor's current age, salary, portfolio balance and allocation, target retirement age, and future pension promises to calculate a suggested retirement savings amount for the current year. It also informs the investor about the impact of a 50% stock loss on the plan.

It aims at balancing, across accumulation and retirement, the amount of money available to pay for taxes and expenses, excluding retirement savings. In the illustrated example, salary minus retirement savings is \$32,380, and projected retirement income is \$23,735 from Social Security and \$8,645 from portfolio withdrawals, for a total of \$32,380.

As future returns are variable and unpredictable, the method is based on the idea of successive approximations. At least once a year, the investor must update input data (new age, new salary, new portfolio balance, new Social Security estimates, etc.) to get a new retirement savings amount suggestion.

This Social Security Estimator could be useful for finding the information to appropriately fill the pension section. I suggest delaying Social Security to age 70.

Here's a link to a post (followed by a few additional posts) showing backtests of the method, along with some discussion.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

decapod10
Posts: 656
Joined: Thu Dec 28, 2017 6:46 pm

### Re: Retirement Withdrawal Math Verification Needed

NBKCF wrote:
Tue Jul 09, 2019 8:02 pm
dbr wrote:
Tue Jul 09, 2019 12:08 pm
NBKCF wrote:
Tue Jul 09, 2019 9:49 am

Assume retirement account earns 3% annually
Assume inflation is 2.1% annually

These two assumptions are fundamentally flawed unless you have investments that have no variability. In the real world both returns and inflation vary from year to year and the average return does not predict what your actual experience will be. That is before one discusses whether the estimate of the average is accurate.

You should look at a model such as FireCalc and others of that nature that take this into account. The previous mention of 4% SWR is a reference to that approach.

Note the effects of variability of returns and inflation on portfolio support of withdrawals was an area that began to be explored in the early 1990's by Bengen, by the Trinity Study, and so on. That is background a person can read if interested. I would be surprised if they were the first people to be aware of the issue either.
Thank you for the reply. I am creating a simplified sheet to project where certain savings rates will land me, so I am not expecting complete accuracy. My plan is to update the sheet annually to reflect real growth for that year to see how it affects the retirement account. After all, we can only assume what our returns will be so I am remaining conservative. I was most curious if I was calculating my account depletion correctly with certain withdrawal rates.

Great recommendation on FireCalc - I have not seen that site. It appears that my plans has zero indications of failure unless I am inputting something wrong.
If you are using the default mode, FireCalc uses historical data for its projections, which means the return is much higher than your assumption of 3% annual return.

onthecusp
Posts: 803
Joined: Mon Aug 29, 2016 3:25 pm

### Re: Retirement Withdrawal Math Verification Needed

In the original post NBKCF mentions "80-90%" bonds in retirement. Not sure where you are at right now in asset allocation, but you have 20 years or so to get to terms with the idea that a higher allocation to equity might be a good idea, even in retirement. Posters here seem to top out at about 70% bonds, but most would not go for more bonds than 50/50 stocks/bonds.

That should support substantially higher safe withdrawals.

balbrec2
Posts: 290
Joined: Mon Nov 13, 2017 3:03 pm

### Re: Retirement Withdrawal Math Verification Needed

IMHO at your age you are far from needing to think about the question you have asked.
You can't even know you will have that much capital by that age let alone how long it will last.
Right now just think about stashing as much as you can into various retirement plans and an
appropriate asset allocation. See what you come out with at the other end and go from there.

Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Re: Retirement Withdrawal Math Verification Needed

onthecusp wrote:
Wed Jul 10, 2019 1:44 pm
In the original post NBKCF mentions "80-90%" bonds in retirement. Not sure where you are at right now in asset allocation, but you have 20 years or so to get to terms with the idea that a higher allocation to equity might be a good idea, even in retirement. Posters here seem to top out at about 70% bonds, but most would not go for more bonds than 50/50 stocks/bonds.

That should support substantially higher safe withdrawals.
Noted. I was curious how long the funds would last with "safe" investing in retirement, but I will certainly reevaluate my plan with your recommendation.

Topic Author
NBKCF
Posts: 141
Joined: Wed Aug 01, 2018 6:14 pm

### Re: Retirement Withdrawal Math Verification Needed

balbrec2 wrote:
Wed Jul 10, 2019 5:26 pm
IMHO at your age you are far from needing to think about the question you have asked.
You can't even know you will have that much capital by that age let alone how long it will last.
Right now just think about stashing as much as you can into various retirement plans and an
appropriate asset allocation. See what you come out with at the other end and go from there.
Well said and received. I sometimes go down these rabbit holes to the nitty gritty when I should just save and worry about it 10ish years out from retirement.

onthecusp
Posts: 803
Joined: Mon Aug 29, 2016 3:25 pm

### Re: Retirement Withdrawal Math Verification Needed

NBKCF wrote:
Wed Jul 10, 2019 8:57 pm
onthecusp wrote:
Wed Jul 10, 2019 1:44 pm
In the original post NBKCF mentions "80-90%" bonds in retirement. Not sure where you are at right now in asset allocation, but you have 20 years or so to get to terms with the idea that a higher allocation to equity might be a good idea, even in retirement. Posters here seem to top out at about 70% bonds, but most would not go for more bonds than 50/50 stocks/bonds.

That should support substantially higher safe withdrawals.
Noted. I was curious how long the funds would last with "safe" investing in retirement, but I will certainly reevaluate my plan with your recommendation.
You found a great site here to go down many rabbit holes.
As a start on this question the WIKI has a page on "safe withdrawal rates"