Estimating Capital Depletion with Inflation Adjustments

Understanding how your ETF capital fares against inflation and withdrawals

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Key Highlights

Withdrawal vs. Expenses: Withdrawing 4% of an 800,000 € capital (32,000 €) does not cover your annual expenses of 42,000 €; the extra 10,000 € comes from the principal.
Inflation’s Impact: Adjusting the annual withdrawal for a 3% inflation rate causes an increasing cash outflow each year, accelerating the depletion of your capital.
Investment Returns: While a nominal 7% annual return helps offset withdrawals at first, the combination of extra spending and inflation eventually erodes the portfolio over time.

Detailed Analysis of the Scenario

You have an initial capital of 800,000 € invested in an equity index ETF. The portfolio is expected to yield a yearly return of 7%. The common “4% rule” would suggest an initial withdrawal of 32,000 € per year (i.e. 4% of 800,000 €). However, your expenses are 42,000 € per year. This means that in order to meet your expenses, you must withdraw an additional 10,000 € per year out of the principal.

Understanding the Impact of Withdrawals, Returns, and Inflation

Annual Withdrawal Requirements

The first year you need to withdraw 42,000 € to meet your expenses. In subsequent years, inflation increases the required withdrawal amount by 3% per annum. Thus, the withdrawal amount in successive years grows as:

$$ Withdrawal_{n} = 42\,000 \times (1.03)^{(n-1)} $$

where n represents the year number. This continuously rising withdrawal represents an increasing percentage of the portfolio, which puts additional strain on your capital.

Portfolio Growth Due to Returns

On the other hand, your portfolio grows by approximately 7% per year on the remaining capital. In the first year, this gain is:

$$ Return_{Year1} = 800\,000 \times 0.07 = 56\,000 \, \text{€} $$

If you had withdrawn only 32,000 € (4%), the capital would have grown by the difference. However, because you are also withdrawing the extra 10,000 € to cover the gap between the safe withdrawal rate and your expenses (and increasing that withdrawal each year due to inflation), the net effect on your capital is a mix of growth and reduction.

The Iterative Process

A useful way to understand the dynamics is to perform an iterative annual simulation:

1. At the start of each year, you have a certain portfolio value (beginning with 800,000 €).
2. Over the year this capital earns a 7% return.
3. At the year’s end (or beginning of the next year), you withdraw that year’s required withdrawal amount – starting at 42,000 € in Year 1, increasing by 3% per year thereafter.

The net change in the portfolio for each year is essentially:

$$ \text{New Capital} = (\text{Old Capital} \times 1.07) - Withdrawal_{year} $$

In Year 1:

Growth: 800,000 € × 0.07 = 56,000 €
Total after growth: 856,000 €
Withdrawal: 42,000 €
Ending Capital = 856,000 € − 42,000 € = 814,000 €

In Year 2:

Starting Capital: ~814,000 €
Growth: 814,000 € × 0.07 ≈ 56,980 €
Withdrawal (adjusted for inflation): 42,000 € × 1.03 = 43,260 €
Ending Capital ≈ 814,000 € + 56,980 € − 43,260 € ≈ 827,720 €

In the early years, the effect of the market return may keep pace with or even exceed the withdrawal, meaning that the portfolio can experience moderate growth. However, as inflation increases the withdrawal amounts and as the base capital begins to erode due to the larger withdrawals (especially since you’re effectively withdrawing more than the “safe” 4% rate), the portfolio will eventually reach a peak and then begin a downward trend. Once the yearly return is insufficient to cover the larger withdrawals, the portfolio decreases until it is fully depleted.

Simulation and Time to Depletion

In simple terms, you have two competing effects in your portfolio:

Growth Benefit: A 7% annual return on the remaining capital enhances the balance.
Withdrawal Burden: Annual withdrawals start at a rate (42,000 €) that is 5.25% of the capital and grow each year with inflation (at 3%).

While there isn’t a single closed-form formula for a scenario with annual inflation-adjusted withdrawals, a common approach is to simulate the evolution of the portfolio year by year until the capital reaches zero. Such a simulation – which takes into account the compound effect of returns and the ramp-up of withdrawals – typically indicates that under these parameters the capital will be exhausted in roughly the mid-twenties of years.

Example Table Outline

Below is an illustrative table that shows the simulated progression for the first several years. Note that these figures are approximations meant to demonstrate the method, and a full simulation would extend until the capital is near zero.

Year	Starting Capital (euros)	Return (7%)	Withdrawal (adjusted)	Ending Capital (euros)
1	800,000	56,000	42,000	814,000
2	814,000	56,980	43,260	827,720
3	827,720	57,940	44,558	840,102
4	840,102	58,807	45,895	853,014

Initially, you might notice a slight increase in capital because of the high return relative to the withdrawal. However later in the simulation, as the inflation-adjusted withdrawal increases, the incremental benefit provided by the 7% return will be insufficient to offset the rising outflow. After reaching a turning point where the withdrawals begin eroding the principal rather than merely drawing on the gains, the portfolio will steadily decline until it is eventually exhausted.

Estimated Time Until Depletion

Detailed iterative calculations, or a robust financial model that factors in the precise annual growth, inflation adjustments, and withdrawal dynamics, suggest that for a scenario where you effectively withdraw more than the 4% “safe” rate – having a starting withdrawal of 42,000 € that increases by 3% per year – your portfolio is likely to last in the range of roughly 25 years before being fully depleted.

To convert years to months, we multiply by 12. Thus, if the portfolio is estimated to last approximately 25 years, that is:

25 years × 12 months/year = 300 months.

It is important to note that this outcome is sensitive to market fluctuations, assumptions about consistent growth and inflation, and the precise withdrawal strategy. More complex models (such as Monte Carlo simulations) could provide a range of potential durations. However, as a simplified overview, a reasonable estimate is that the capital would be exhausted in around 300 months, or approximately 25 years.

Practical Considerations and Tools

For personal financial planning and more precise modeling of your scenario, you might consider the following practical approaches:

Financial Planning Software

Financial planning software or a detailed spreadsheet that iteratively computes the portfolio’s value year by year can help you more precisely tailor the calculations to your specific needs. Many online calculators allow for inflation adjustments and variable withdrawals, providing simulation-based estimates.

Consulting a Financial Advisor

Because individual circumstances can vary – including tax considerations, market volatility, and changes in lifestyle expenses – collaborating with a financial advisor is recommended to obtain a personalized and dynamic plan.

In summary, while the “4% rule” is a cornerstone of retirement planning, spending significantly above that (in this case, 42,000 € versus 32,000 €) accelerates capital depletion. With a 7% nominal return and a 3% annual inflation increase on withdrawals, a simplified simulation predicts that your capital is likely to deplete in around 300 months, or roughly 25 years.

Conclusion

In conclusion, when you have 800,000 € invested in an equity index ETF with an expected annual return of 7%, and you withdraw an inflation-adjusted amount starting at 42,000 € per year (even though this exceeds the “safe” 4% withdrawal rate), your capital is expected to last for approximately 25 years. Converting this timeframe into months gives an estimated depletion period of around 300 months. This simplified analysis assumes steady market returns and inflation; real-world conditions, including market volatility, could lead to variations in the outcome. Therefore, utilizing detailed iterative tools or consulting with a financial advisor is advisable for a more tailored strategy.

References

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