Math Behind ERE

[youngsaver]

Trying to wrap my head around the math behind ERE...

If your annual expenses are $25,000 and you'd like to stop working entirely with no expected future income, the portfolio size needed to support the expenses would be $25,000/.03 = $833,333 or, as jacob points out, approx $25,000 x 33 = $825,000.

For illustrative purposes, if we assume a 5% return then that would require 15 years of contributing $38,000 to your portfolio. 15 years is much sooner that your typical 40 year working for income career but makes it difficult to do while still in your thirties.

Of course, the annual expenses could be cut to shorten the length of time. Just looking to see if this is the sort of simple arithmetic that ERE'ers think about.

[Seppia]

Some say 3% is too conservative, 4% being a popular alternative.
Regardless, it’s a good gauge: if you are very far from it you should not consider pulling the trigger, if you’re close... start looking at other variables ie general market valuations (different to have 25x in 2009 ve having 25x today), what your asset allocation is (different having X$ in cash or X$ in a brokerage account) etc etc.

It’s not a video game where you hit a number and you “win” imho

[jacob]

Some say 3% is prudent and 4% is foolhardy ;-P

Basic math:
https://wiki.earlyretirementextreme.com ... _retire%3F
https://wiki.earlyretirementextreme.com ... Retirement

Advanced math:
Final chapter in the ERE book.

Ultimately, it comes down to an interplay between savings rate and compound rate. In general, you'd focus on the former for ER and the latter for R.

[Chris]

That looks ok as a simple case. There are some other accelerating factors to consider:

1. It's unlikely you will be earning a flat salary over your accumulation period. By keeping expenses flat while income increases, each additional dollar will fall straight into savings. Factoring in a 5% annual increase will knock 3-4 years off.
2. Saving in tax-advantaged accounts can provide a boost of 20-30% over post-tax saving.
3. Lowering expenses has the double affect of increasing savings and lowering your future required withdrawal rate.

[sky]

Lowering your annual expenses increases your savings rate while decreasing your target investment. That is the magic of ere.

[jacob]

http://earlyretirementextreme.com/what- ... ate-b.html

[Fish]

For modeling the accumulation phase, I use the simple math all the time just to get an idea of what’s possible. At this level it is common to do the calculations in terms of savings rate and years of expenses. Your example is equivalent to a 60% savings rate (=38/(25+38)) which accumulates 1.5 years of expenses annually (=38/25) toward a FI target of 33x expenses (=833/25). By thinking in these terms it is much easier to develop an intuition for how time to FI/RE is affected as parameters are varied.

There definitely is value in knowing how to run a more precise calculation, for purposes of 1) understanding the benefits of tax optimization, and 2) assessing robustness of FI/RE plans to sequence of return risk. But if you’re more than 5 years away from retirement, the simple calculation is what you want to use most of the time.

The “advanced math” in the ERE book is not technically difficult... you can construct the relevant equation(*) from the compound interest and annuity formulas. (The annuity formula is simply a partial sum of the geometric series, which is high school math, perhaps undergrad for millenials. ) What makes it “advanced” is that it used to be very uncommon to think about personal finance in relative terms such as savings rate and years of expenses. Jacob’s FI/RE math, now ubiquitous in 2018, was a novelty in 2010 because everyone else at the time was performing dimensional calculations and shooting themselves in the wallet by assuming expenses approximately equal to income.

(*) Future NW = FV of principal + FV of periodic payments

Use the compound interest formula for FV of principal, and annuity formula to get the FV of periodic payments. Once you have the RHS of the equation, you can set NW = 1/SWR (to calculate time to FI), or NW = 0 (to see how long a portfolio will last). Check your work by comparing to the equations and results presented in the last chapter of the ERE book.

[2Birds1Stone]

Yes, $25k @ 3% will take some time.

You will cut many years off that timeline by getting your expenses much lower than that! If you can manage some passive or part time income then you need even less of a nest egg.

[Seppia]

Some say 3% is prudent and 4% is foolhardy ;-P

Definitely agree, I was just presenting the alternatives
I personally think retiring @4% in today’s environment is a bit... uh... adventurous, but I’m definitely biased towards prudence.

This said, too many variables are in play, but 3% is a ballpark: if one is close, he/she may want to look at the other variables.
If one is very far... he/she is probably not ready to ere