In a commentary written by Keith Yap published by Channel News Asia on 16 Aug 2022, he says it is increasingly common to hear millennials talking about FIRE – Financial Independence, Retire Early.

It is a movement which is supposedly able to help millennials retire by their 40s, or even 30s.

In the CNA article, it is stated that the adherents of FIRE (let’s call them FIREists) aim to save 70% of their income until they reach 25x of their annual expenses and make a 4% annual withdrawal for living expenses.

Is it possible to retire in 10 years using this formula?

To find out, I have reverse-engineered the math behind those claims.

**Contents**

The Math behind FIRE

The FIRE Extinguisher – Inflation

Is FIRE still Workable?

In Conclusion

**The Math behind FIRE**

Warning: Not suitable for those allergic to Algebra. Proceed with caution!

First, let’s define the variables.

Based on the FIRE framework, M = 25 since the target Retirement Sum is 25x of annual expenses.

If FIREists save 70% of their income*, *it means that Annual Expenses = 30% of income. Therefore, e = 0.3.

They also expect to draw down 4% of their Retirement Sum to pay for Annual Expenses. Thus, the Drawdown Rate, d = 0.04.

The FIREist generates an income by investing the Retirement Sum. In theory, this income must be at least equal to expenses. Otherwise, the Retirement Sum will go down over time, creating even less future income.

Therefore, the ROI (r) must be equal or more than the Drawdown Rate, which is 4%.

FIREists are thus banking on the assumption that they can get at least a 4% ROI from their investments.

Investment income from retirement sum must be at least equal to annual living expenses. Therefore,

Dividing both sides by (e * I),

This matches with FIRE framework. Since both r and d are 0.04, M = 1/0.04 = 25.

But can you really reach your retirement sum in 10 years? Based on the FIRE numbers, yes.

If you insert the FIRE values of d = 0.04, e = 0.3 and solve the equation, you’ll get N = 10.7.

Therefore, yes, you can reach retirement within 10.7 years.

If a millennial starts work at 21, theoretically he or she can retire by age 32, based on the FIRE framework.

Thus, the FIRE claim that retirement can be achieved by the 30s is, on the surface, achievable.

**The FIRE Extinguisher – Inflation**

However, there is one huge variable that has been left out, and that is Inflation.

Inflation will increase the FIREist’s expenses every year. Unless the rate of return is high enough to compensate for inflation, the FIREist will find that the Retirement Sum shrinks every year.

Let’s say the FIREist’s Retirement Sum = $1,000,000, Annual Expenses = $40,000.

In Year 1, the investment income at 4% of $1,000,000 is $40,000, which can be drawn down to pay for living expenses. Income equals expenses, and the Retirement Sum remains at $1,000,000.

But if inflation is 2%, in Year 2, his income is still $40,000. However, the expenses have increased 2% to $40,800. This leads to a net loss of $800, and the Retirement Sum is reduced to $992,200.

In Year 3, due to the reduced Retirement Sum, the income is reduced to $39,968. But expenses continue to climb to $41,616. This leads to an even bigger loss of $1,648.

The vicious cycle continues, with losses increasing every year.

If you extrapolate, assuming investment return and inflation both remain constant at 4% and 2%, respectively, by Year 37, the FIREist will be bankrupt.

If the FIREist started work at age 21, reached retirement age by 32 and stopped working, he or she will go bankrupt by age 69.

And after being out of the workforce for 37 years, at age 69, is the FIREist still employable?

That’s a pretty scary thought.

Let’s now introduce a new variable.

To avoid the death trap, the ROI needs to be higher.

The FIREist assumption that r = d is fundamentally incorrect. Variable r must in fact be much higher to compensate for inflation.

The rate of inflation (f)must be added to the target draw-down rate (d*)* to work out the target ROI (r).

Thus, the correct formula is:

ROI (r) can only be equal to the draw-down rate (d) if the inflation rate (f) is zero. But that is an unrealistic assumption.

Using the above example where d = 0.04 and f = 0.02, you will get r = 0.06, or ROI = 6%.

With these numbers, the Retirement Sum keeps pace with inflation because it also grows by 2% per year and NEVER hits zero.

The FIREist has thus achieved true financial freedom.

Now let’s look at how inflation (f) interacts with the formula. Let’s replace r with d + f.

As f increases, N also increases.

Let’s look at how N is affected with every 1% increase in inflation, assuming r = 0.04 and e = 0.3.

The higher the inflation rate, the longer it takes for the FIREist to reach retirement.

Once the inflation rate is the same or higher than the ROI, N is no longer meaningful. The FIREist will NEVER achieve financial freedom.

**Is FIRE still Workable?**

It is always possible, but far more difficult than what a lot of millennials imagine.

Firstly, the FIREist must achieve a much higher ROI (r)than just 4%. The ROI must be 4% PLUS inflation rate. Can he or she do it?

Between 1961 to 2021, the average inflation rate in Singapore was 2.5%. The highest was 22.4% in 1974 and lowest was -1.8% in 1976. Again,

If d = 0.04 and f = 0.025, then r= 0.04 + 0.025 = 0.065. Thus, the target ROI needs to be at least 6.5%.

However, we are also moving into an environment where higher inflation is expected to persist. It is better to buffer and work based on inflation being 5%. That means the ROI target should be 9% or more.

Thus, the big catch is whether the FIREist is able to hit the ROI target, consistently.

Secondly, Singaporeans are fortunate that they live in a country where inflation is generally low.

What if you live in a country that has high inflation?

You would need to have God-like investment powers to generate the ROI needed to make FIRE work.

Thirdly, has there been enough buffer planned for unforeseen situations?

You may need to add another 5% to the Expense Ratio and make it 35% instead of 30%.

This 5% goes into your emergency funds to make sure that you always have something put aside for a rainy day.

Lastly, it’s one thing for you to live a minimalist lifestyle, but it’s another to let your family go through it with you.

Once you get married and have a family, can you keep your expenses the same?

You will need a lot of extra money to raise children, and this will throw your FIRE formula out of whack.

I live a minimalist lifestyle too. But I always end up spending more money on my children then on myself.

**In Conclusion**

FIREists need a reality check.

It’s not as simple as saving 70% of your income to hit 25x of your annual expenses. You also need to achieve a consistent investment ROI well above 4%.

If you retire at 32 and try to live off the investment income, you will likely find yourself being drowned slowly by inflation.

And by the time you realize it, you are 69 years old, broke, and your employable skills are already obsolete.

However, there is a lot of merit to the idea of putting aside 70% of your income and pumping them into investments. This part of the FIRE framework is good. Certainly, I’d love for all my children to do the same in the early part of their working lives.

It is the idea of retiring early after hitting the Retirement Sum target that is dangerous.

If you hate your job, at least get another job that you love, even if it pays less.

That income and your investment income, will prevent inflation from eating you alive.

It will also keep you in touch with the job market and keep your skills employable.

Ultimately, the best defence against economic shocks is a high-income skill. It’s best to keep your skills up to date as a fail-safe.