What can we finance?

Object costs 100,000 EUR
Rent 6.8%, i.e. 6,800 EUR

Equity 20,000 EUR
Capital market also brings me 6.8% guaranteed
Interest rate is 2%

one period
Beginning and end

Tenant
20,000 EUR
6.8% capital market return = 1,360 EUR return
6,800 EUR rent payment
Final amount: 20,000 + 1,360 - 6,800 = 14,560

Buyer
20,000 EUR equity + 80,000 EUR borrowed
2% interest on 80,000 EUR borrowed: -1,600 EUR
Final amount: 18,400 EUR equity + 80,000 EUR borrowed

2nd period

Tenant
14,560 x 0.068 = 990 EUR return
6,800 EUR rent payment
Final amount: 14,560 + 990 - 6,800 = 8,750 EUR

Buyer
18,400 EUR equity + 80,000 EUR borrowed
2% interest on 80,000 EUR borrowed: -1,600 EUR
Final amount: 16,800 EUR equity + 80,000 EUR borrowed

3rd period

Tenant
8,750 x 0.068 = 595 EUR return
6,800 EUR rent payment
Final amount: 8,750 + 990 - 6,800 = 2,545 EUR

Buyer
16,800 EUR equity + 80,000 EUR borrowed
2% interest on 80,000 EUR borrowed: -1,600 EUR
Final amount: 15,200 EUR equity + 80,000 EUR borrowed

4th period

Tenant
2,545 x 0.068 = 173 EUR return
6,800 EUR rent payment
Final amount: 2,545 + 173 - 6,800 = -4,082 EUR

Buyer
15,200 EUR equity + 80,000 EUR borrowed
2% interest on 80,000 EUR borrowed: -1,600 EUR
Final amount: 13,600 EUR equity + 80,000 EUR borrowed

From here on, the compound interest effect on the equity has said goodbye and now works for the buyer and no longer for the tenant.

One central counterargument of mine is that the savings phase in the owner-occupied property (installment) does not produce a compound interest effect, but the savings phase in, for example, the stock market does, if you invest accumulating. However, you ignore that. What is the reason for that?

Explanation: What you count as rent savings = return is invested in wealth building over the entire repayment period of the house (paid-off house).
Comparable on the stock market would be to always reinvest dividends in order to build wealth in the form of the value of the portfolio.

Mathematically, with the house you pay back a portion of the unchanging (!) loan amount every year, so linear growth.
With stocks you pay back a portion of the changing(!) (=increasing) amount every year, so exponential growth.

Of course, as a renter you can pay less per year into stocks because you don’t have the rent savings. On the other hand, you start the exponential effect with your equity that you would have otherwise invested in house construction.

While the shareholder slowly builds up a portfolio value, yes with compound interest (1.5% real over the last 20 years), the owner already has the full value that generates value. Even if you finance your house 20/80, you get the return of 100.

Just completely forget about living, renting, etc.

There is a market with a 6.8% eternal return. Shareholder A invests his 20k there. Shareholder B borrows 80k at 2% and invests 100k.

In this case, shareholder A corresponds to the renter and shareholder B to the buyer. Mathematically, it is nothing else.

Both benefit from the 6.8% on the 20k. Shareholder B additionally benefits from the spread 6.8%-2.0% = 4.8% on 80k. That is also the lion’s share of the profit.

You simply do not address any arguments, but only repeat your familiar calculations.

You even managed, in both cases, to have less equity in every period than in the previous period – only with the buyer the reduction is slower than with the renter. But the loan does not amortize. You must realize yourself how absurd your approach is because of that?

Additionally, in your example, the renter never invested the delta compared to the buyer’s payment into the capital market.

One last time, as simply as I can. Our two cases to consider:

1)
You buy a house with 100k equity and pay it off over 20 years until full repayment. It cost you 580k – including all interest, reserves, investments, and the land.

You have received a dividend for 20 years in the form of saved rent. Converted over 20 years, X% per year of 580k. In absolute numbers, 20*X*580k.

This dividend flowed into your amortization. You now have equity equal to the property value and continue to collect per year X*580k.

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2)
You rent. Your rent is lower than the loan payment. The delta is Y. Your equity is 100k.

You invest the 100k at Z% in the stock market. You also invest the delta Y every year there. You also reinvest the annual dividend of Z% there. You do this for 20 years.

Your equity after 20 years corresponds to the value of the portfolio.

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These two cases are to be compared. And mathematically, you simply cannot do it the way you do:

Just completely forget about living, renting, etc.

There is a market with 6.8% eternal return. Shareholder A invests his 20k there. Shareholder B borrows 80k at 2% and invests 100k.

In this case, shareholder A corresponds to the renter and shareholder B to the buyer. Mathematically, it is nothing else.

Both benefit from the 6.8% on the 20k. Shareholder B additionally benefits from the spread 6.8%-2.0% = 4.8% on 80k. That is also the lion’s share of the profit.

Here you have just turned the property into a compound interest object, which it is not and never can be. Reason see above! The stock market investment, however, is one.

How this turns out depends on the assumptions with which you assign X, Y, and Z. Then you can run it through a spreadsheet and simply compare the final numbers.

Your assumption of 6.8% dividend through the saving of cold rent is, for example, extremely high. You can hardly rent out condominiums today, let alone houses.

And in case there are any readers who are unsure: Extremely unreliable numbers are also being used here.

For example, price index is confused with performance index. The former only measures price gains, the latter also the constant reinvestment of dividends (compound interest effect).

As performance indices, ETFs from MSCI World and S&P 500 have averaged 7.7% and 9% gross over the last 25 years, respectively. The DAX has been at 8.8% since 1987. Etc. After all deductions and inflation, it should be between 4 - 5 % real net. This matches my experience and that of everyone I know who is invested in the stock market. We all certainly do not just get lucky that we easily surpass the 1 - 1.5 % given here. The numbers are simply not correct.

The 4,x% constantly thrown around here are: pure price gains, without reinvestment of dividends. And thus the wrong numbers for the intended comparison.

Whether one considers a 6.8% rental yield on a single-family house a realistic approach is up to each homeowner to evaluate.

I want those who are undecided to be clear that ignoring the difference between linear (real estate loan) and exponential (stock portfolio with dividend reinvestment) developments as well as using wrong numbers about the development of stock portfolios (far too low) are used to make an owner-occupied property look better in comparison. However, I do not assume any intent!

Whether one considers a 6.8% rental yield on a single-family home to be a realistic approach is something every builder can assess for themselves.

Even though I calculated the numbers myself, I want to emphasize once again that this is certainly not standard.

Even though I came up with the numbers myself, I want to emphasize once again that this is definitely not standard.

I’m not blaming you at all. Your #70 shows how to calculate it correctly from the approach.

And you yourself calculate that despite your enormous 6.8%, a performance of the alternative investment of 5% over 15 years comes out roughly equal. And 5% are realistically achievable in the accumulating portfolio.
And now calculate a repayment period of 20-25 years and much more frequent standard rental yields. That’s what I want to get at.

Edit: And really, no one rents the standard that they would afford to own. But you can hardly factor that in, comparing apples to oranges...