Should I buy, or should I rent? On the face of it it seems like a house would be a sort of savings account. All that money you would have otherwise lost to rent! Yet there are also big financial downsides to buying property, such as the interest payments you lose servicing your debt, or the opportunity cost of not investing in the stock market.

Let's build a simple model to investigate the trade-off, with the following parameters:

We are interested in comparative net worth. Specifically, is your net worth greater if you purchase rather than rent property? And if so, after how many years?

Our model says that your net worth is indeed greater if you buy, and that it is so after 25.1 years:

To understand why, let's have a look at the annual change in comparative net worth. Here is a graph breaking down the contributions when you buy:

Depending on your inputs, the biggest positive contribution to net worth is usually growth of the house value. Deducations are dominated by purchase costs in the first year, and annual interest payments get smaller as the loan is paid off.

The situation when renting is simpler. There are two main components: monthly rent, and the growth of the initial capital invested in the stock market:

Any difference in yearly cash expenditure between the two scenarios is called "spare cash" and is assumed to be dutifully invested in the stock market. If buying costs you €1,800 in one month but renting only €1,500, the renter is assumed to have invested the €300 difference in the stock market.

You can also download the results as a CSV file.

Which parameters have the biggest impact?

We now ask how sensitive the model is to variations in the input values. The key outcome is the number of years it takes for buying to be more financially advantageous than renting, if that even occurs. A simple way to test the sensitivity of the model is to take each parameter in turn, modify it by plus or minus twenty percent, and see how much the outcome changes.

For example: when a green bar (an increase of the parameter) goes to the left, it means that the increase caused buying to be even more attractive than renting.

Typically, the most important parameters are the amount of rent, house price, interest rate, and house purchase costs.

Limitations

This is a very simple model. All market parameters—the value of the house, the growth of the stock market and so on—are modelled with constant, year-on-year growth. That doesn't capture the true stochastic nature of these parameters and the risk exposure to them in each scenario.

¹ A study by InterHyp from 2020 reports an average downpayment of 26% of the house value. ↩

² DeStatis reports the consumer price index for rentals (table 61111-0004, variable CC13-0411) as 108.5 in June 2021 compared to 100 in June 2015, or a 1.4% increase per year. ↩

³ A survey by Reuters predicted 2% for 2024. ↩

⁴ We take the S&P 500 to be representative of the stock market. This index saw a growth of 40% over the last five years, or 7% per year. ↩

⁵ An article by Stiftung Warentest from November 2022 reports a fifteen-year fixed-rate interest of 3.89% for a loan of 80% of the house price. ↩

⁶ Typical purchase costs consist of 3.57% broker commission (Maklerprovision), 6% property transfer tax (Grunderwerbssteuer), 2% notary fees (Notarkosten), and 0.5% for the land registry entry (Grundbucheintrag). ↩

⁷ An article by Stiftung Warentest from November 2022 reports a typical amortisation rate of 2%. ↩

⁸ The Wikipedia article on property tax in Germany on contains details about the calculation. We combine this with municipal tax values for Berlin to arrive at a figure of 0.13%. ↩

⁹ A press release from DeStatis reports the average natural gas (the most common source of heating) price paid by households in the first half of 2023 as 12.26 ct/kWh. According to the German ministry of the environment an average energy consumption for heating is 125 kWh/m² per year. ↩

¹⁰ A long view of the price index for imports of natural gas is provided by DeStatis. It reports a price index of 170.1 in July 2023 compared to 71.1 in January 2023, or 4.8% per year. ↩

¹¹ An article by Wüstenrot recommends a value of 17.18 €/m² per year for properties older than thirty-two years, 13.45 €/m² per year for properties between thirty-two and twenty-two years old, and 10.61 €/m² per year for properties newer than twenty-two years. We take the middle value. ↩

¹² DeStatis reports the consumer price index (table 61111-0004) for maintenance and repair of the dwelling (variable CC13-043) as 118.1 in July 2021 compared to 100.1) in July 2015, or 2.8% per year. ↩

¹³ The Berlin Senate Department for Urban Development and Housing published average utilities figures from 2017, indicating a monthly sum of 2.29 €/m², if we exclude property tax. To this number we apply a rough inflation figure (table 61111-0004, variable CC13-04) of 22% from October 2017 to October 2022. ↩

¹⁴ Tax on capital gains in Germany is approximately 26%. There is a tax-free allowance, but for simplicity we do not include this. ↩