Calculated: Own a home or stay a tenant?

Part 2

In Part 1, we looked at the theory behind the financial aspects of buying and owning vs. renting. If you haven't read that part yet, bookmark this post here and read Part 1 first, you can find Part 1 here: https://app.getquin.com/activity/FoLdCxttXY

In the 2nd part, we will use these basics and theoretical principles to go through a practical example. It will help you to better apply the calculations in your individual situation. In addition, it shows impressively what gigantic sums are involved in the end:

• Detailed calculation of an example (scenario 1)
• Step-by-step adjustment of this example to make it gradually more realistic (Scenario 2 to 6)

tl;dr

I compare the financial burden of a tenant and a buyer in Regensburg over a period of 60 years. For this purpose, two similar houses - one for rent and one for purchase - were selected on immoscout and used as a basis. The variables (increase in rents, development of a world portfolio, maintenance reserves, ...) were chosen as they can be assumed as probable based on the explanations in the 1st part (in the 3rd part we look at what effects the adjustments of these variables have: https://app.getquin.com/activity/GEBmMewkKS). This scenario will be adjusted in the course of the paper so that it corresponds more closely to reality. This includes, for example, an optimization of the follow-up financing and the assumption that a tenant lives more in line with demand than a buyer, i.e. moves more often into a property that suits the respective life situation.

In the most likely scenarios 5 and 6, the tenant's assets are several million euros higher than the buyer's assets at the end of the period under consideration. Buying such a property is thus a very expensive decision in Regensburg and comparable cities. From a financial point of view, a purchase is therefore not to be recommended - as long as the general conditions do not clearly turn in favor of the buyer. We will look at what has to happen for this recommendation to be overturned in Part 3.

Real estate selection

The search is on for a house in Regensburg with enough space for a couple with two children due to see the light of day in the next few years. An office is additionally needed. The two are not gifted craftsmen, so the cottage should be relatively new. Since the two earn well, a young building is financially viable. In addition, a gas or oil heating system should be avoided if possible. Found actually two comparable offers - once for rent and once to buy (see pictures at the end of the post). The rental house is a bit more centrally located, offers an extra room, an extra parking space for a car and a larger living space (131m² vs. 115m²). The house for sale is 4 years younger for that and brings a larger lot. Both houses are mid-terrace houses, heated with district heating and bring a fitted kitchen. Overall, the couple likes the rental house a little better and would be willing to spend more money on it. However, the two properties are similar enough for this comparison. To avoid making this detailed example too complex, we assume that the couple will live for another 60 years and stay in the same property until then (this assumption is removed in scenarios 5 and 6). Retrieved data from Immoscout on 6/15/22 - yes, I've been writing this post for a while.

Scenario 1 - a simple calculation example

The cold rent is 1,880 euros plus 80 euros for two parking spaces, for a total of 1,970 euros. The deposit amounts to 4,400 euros. The house for sale was advertised for 789,800 euros. In addition, there are costs of 30,000 euros for the garage, for a total of 819,900 euros. The couple manages to bargain the seller down to 750,000 euros. They saved 200,000 euros of their own capital.

Calculation of the purchase and loan costs

The house is located in Bavaria, which is why the following incidental purchase costs apply:

- Real estate transfer tax 3.5%

- Notary fees 1,5%

- land register entry 0,5%

- Brokerage fee 3,57%

For an appraiser 2,000 euros are due. The complete purchase costs therefore amount to 750,000 euros * (1 + 0.035 + 0.015 + 0.005 + 0.0357) + 2,000 euros = 820,025 euros. After deducting the equity, a loan of 820,025 euros - 200,000 euros = 620,025 euros must be taken out.

The couple obtains a loan with a nominal interest rate of 2.65% and can afford 2.5% for repayment. The initial monthly interest to be paid thus amounts to 620,025 euros * 0.0265 / 12 = 1,369.22 euros. The initial repayment equals 620,025 euros * 0.025 / 12 = 1,291.72 euros. In total, therefore, a monthly installment of 1,291.72 euros + 1,369.22 euros = 2,660.94 euros is due. The loan has a fixed interest rate of 15 years.

Calculation of the costs for maintenance and modernization

The simple, but in practice probably significantly underestimated calculation of provisions for maintenance, would be in this case 1 euro / sqm / month * 115 sqm = 115 euros / month. Since I do not know the actual production costs per square meter, I estimate 2,000 euros / sqm. According to Peters' formula, this results in maintenance costs of 2,000 euros * 1.5 / 80 / 12 * 115 = 359.38 euros per month. Based on Gerd Kommer's assumption, maintenance costs would range between 287.50 euros and 479.17 euros. Since the house was built in 2020 and is not detached, we orient ourselves to the lower end and calculate maintenance costs of 287.50 euros per month. Necessary modernizations are not expected in the next few years, which is why we only set aside 12.50 euros for this and thus round the amount up to 300 euros.

Monthly burden on the buyer and residual debt after 15 years

The buyers have to transfer 2,660.94 euros per month to the bank during the first 15 years. To this must be added 300 euros for provisions, which increase annually with an assumed inflation of 2%. In the first year, the total charge is therefore 2,660.94 euros + 300 euros = 2,960.94 euros. In the last year of the term of the first loan, maintenance costs amount to 300 euros * 1.02^14 = 395.84 euros. So in the last year of the loan, the buyers pay 2,660.94 euros + 395.84 euros = 3,056.78 euros. The remaining debt, as it can be calculated e.g. with https://www.zinsen-berechnen.de/kreditrechner.php or Excel, amounts to 334,902.69 euros after these 15 years.

Development of the tenant's assets in the first 15 years

At the beginning, the tenant invests his equity (200,000 euros) minus the deposit (4,400 euros) amounting to 195,600 euros in his world portfolio. We assume that a share costs 10 euros at this point and that the tenant thus acquires 19,560 shares. This is important for the subsequent determination of profits upon withdrawal. The difference between the cold rent and the purchase cost in the first year is 2,960.94 euros - 1,970 euros = 990.94 euros. This is also paid into the world portfolio every month at the rate of 10 euros. After one year, 195,600 Euro + 12 * 990.94 Euro = 207,491.28 Euro have been accumulated. We assume an average performance of 6% per year, which means that after one year the value of the portfolio increases to 207,491.28 Euro * 1.06 = 219,940.76 Euro.

The tenants calculate with annual rent increases of 2.2%. The rent in the 2nd year is thus 1,970 euros * 1.022 = 2,013.34 euros. Since the buyer at the same time adjusts his provisions in the amount of inflation by 2%, in the 2nd year per month only 2,660.94 euros + 300 euros * 1.02 - 2,013.34 euros = 953.60 euros can be invested by the tenant. At the same time, of course, the price of a share in the world portfolio has risen from 10 euros to 10.60 euros. For the 953.60 euros, the tenant thus receives 90.82 shares per month. Including the 6% performance, the tenant's assets will increase to (219,940.67 Euro + 953.60 Euro * 12) * 1.06 = 245,266.90 Euro at the end of this 2nd year.

Continuing the calculations, in the 15th year the rent amounts to 1,970 euros * 1.022^14 = 2,671.65 euros, which still allows the tenant a monthly investment of 3,056.78 euros - 2,671.65 euros = 385.13 euros. At the end of these first 15 years, the tenant's assets in the World Portfolio increase to approximately 690,435 euros. How is it possible to generate such a high level of wealth with only 195,600 euros in starting capital? The compound interest effect helps. The 195,600 euros alone have become 195,600*1.06^15 = 468,766.78 euros in the 15 years. In addition, there are the monthly deposits totaling over 125,000 euros, which of course also earned interest.

Monthly burden of the buyers and residual debt in the years 16 to 30

In order to repay the remaining debt of 334,902.69 euros, the buyer takes out another loan with a 15-year fixed interest rate after 15 years. The nominal interest rate has meanwhile risen from 2.65% to 4%. In order for the loan to be paid off after 15 years, the buyer must repay at 4.876%. Initially, 334,902.69 * 0.04 / 12 = 1,116.34 euros in interest must be paid, while 334,902.69 * 0.04876 / 12 = 1,360.82 euros are repaid. The monthly installment is therefore 2,477.16 euros. Costs for maintenance and modernization are calculated unchanged and amount to 395.84 euros * 1.02 = 403.76 euros per month in the 16th year, resulting in a total monthly burden for the buyer of 2,880.92 euros.

Over the course of the next 15 years, the provisions to be made increase to 403.76 euros * 1.02^14 = 532.75 euros, resulting in a total burden of 532.75 euros + 2,477.16 euros = 3,009.91 euros in the final year of the credit period. After these 15 years, there is a residual debt of 18.40 euros. The buyer settles this debt by drinking one less beer on his weekly pub night (inflation sends its regards).

Development of the tenant's assets in years 16 to 30

In the 16th year, the rent increases - as in the years before - by 2.2% to 2,671.65 euros * 1.022 = 2,730.43 euros. Since this is still less than the 2,880.92 euros that the buyer would have to pay in the 16th year, the tenant can continue to save. However, only 2,880.92 euros - 2,730.43 euros = 150.49 euros. In the 17th and 18th year, the tenant can still pay money into his world portfolio. After 18 years, the value amounts to approx. 826,376 euros. In the meantime, the increase in value is almost exclusively due to the return on the portfolio, while the deposits have only a minor impact. Even without further deposits, the portfolio value would have grown to 690,435 euros * 1.06^3 = 822,319.32 euros in these 3 years.

Things get interesting in the 19th year. In this year, the rental costs of 2,730.43 Euro * 1.022^3 = 2,914.63 Euro exceed the expenses of the buyer of 2,477.16 Euro + 403.76 Euro * 1.02^3 = 2,905.63 Euro for the first time by 9 Euro per month. So now money has to be taken out of the depot month after month. A share of our ETF is now worth 10 euros * 1.06^18 = 28.54 euros. In order not to make the calculation even more complicated and because tax matters can change significantly in the years until the withdrawal, we have to estimate the taxes and choose the currently valid tax rate for capital gains of 26.375% (incl. solidarity surcharge). We assume that the tenant is not subject to church tax and has already exhausted his annual exemption amount through other capital investments. We also ignore the possible partial exemption to 30% of the gain. The shares are sold according to the FiFo principle.

Since a share is now worth 28.54 euros, we have to sell a share to settle the 9 euros. In the first year, we were able to buy a lot of shares for 10 euros, which is why the profit per share is 28.54 euros - 10 euros = 18.54 euros. After taxes, 10 euros + 18.54 euros * (1 - 0.26375) = 23.65 euros are paid out. Of this amount, 9 euros are paid, leaving 23.65 euros - 9 euros = 14.65 euros. Of course, these 14.65 euros are reinvested and increase the ETF's portfolio by 14.65 euros / 28.54 euros / share = 0.513 shares. The value of the deposit has therefore decreased in the first month of the 19th year to 826,376 euros - 28.54 euros + 14.65 euros = 826,362.11 euros. The 9 Euro withdrawal has cost the tenant 13.89 Euro in real terms. Accordingly, the deposit value is reduced during the year to 826,376 euros - 13.89 euros * 12 = 826,209.32 euros. However, since returns are of course also earned this year, a significant plus is recorded at the end of the year, namely 826,209.32 euros * 1.06 = 875,781.88 euros.

The tenant must continue to withdraw a steadily increasing sum from his global portfolio in the remaining years. In the 30th year, the rent burden rises to 3,702.90 euros and is thus 692.99 euros higher than the buyer's burden. To settle this value, 17 shares must be sold each month at 54.18 euros each. The remaining good 30 euros are reinvested, of course. Nevertheless, the tenant's assets increase to approx. 1,582,372 euros by the end of the 30th year.

Interim balance sheet

Before we take a look at the next 30 years, let's take a look at the development of the two assets:

1) Value of the property

The property has always been nicely maintained, which is what the reserves were set aside for. We can therefore assume an increase in value, which we estimate at 2.6% per year: 750,000 euros * 1.026^30 = 1,619,877.18 euros. Of course, we also carried out modernizations. For this, we had saved an initial 300 euros - 287.50 euros = 12.50 euros per month. These were - just like the maintenance costs - increased by 2% every year. For simplicity's sake, we assume that the modernization reserves went directly into modernization projects and subsequently also led to an increase in value of 2.6% per year. That is, after 30 years, the value of the property has increased by 12.5 euros * 12 * 1.026^30 = 323.98 euros due to the modernizations in the first year. The modernizations in the second year resulted in an increase in value of 12.5 euros * 1.02 * 12 * 1.026^29 = 322.08 euros. In total, this results in an increase in value of 8,938.37 euros with investments of 6,085.21 euros. The value of the property after 30 years is therefore 1,619,877.18 euros + 6,085.21 euros = 1,625,962.39 euros.

If the buyer wants to sell the property, there are of course additional fees. Since the property has already been paid off in full, no early repayment penalty is due, nor does the land charge have to be cancelled. With the sales the broker commission at a value of 3,57% results, thus 1.625.962,39 euro * 0,0357 = 58.046,86 euro. In addition, a valuation report is prepared for which 0.5% of the market value is charged, i.e. 1,625,962.39 Euro * 0.005 = 8,129.81 Euro. Since the property was used by the owner throughout, no taxes are due on the sale. The "odds and ends" (energy certificate, etc.) will be a lump sum of 500 euros. The buyer can therefore achieve 1,625,962.39 euros - 58,046.86 euros - 8,129.81 euros - 500 euros = 1,559,285.72 euros through a sale.

2) Value of the deposit

As already calculated, during the same period the tenant could build up a deposit of 1,582,372 euros, the sale of which would of course still incur taxes.

3) Does the value of the deposit increase or decrease?

In fact, the value of the deposit increases continuously and in the 30th year from approximately 1,503,493 euros to 1,582,372 euros.

After 30 years and full payment of the property, the tenant and the buyer are left with similar assets, even if the buyer is slightly ahead.

Comparison after 60 years

In the 31st year, the buyer's costs drop significantly. The loan is paid off, only reserves for maintenance and modernization have to be set aside. Initially, these costs amount to 543.41 euros / month and rise to 965.01 euros / month by the 60th year of consideration. The rent to be paid increases in the same period up to 7,133.27 euros and is thus 6,148.26 euros above the monthly costs of the buyer.

1) Value of the property

The value of the property increases to 3,534,165 euros within 60 years, including modernizations carried out. At this point, the property will probably no longer be sold, but only inherited. Therefore, selling costs are not taken into account at this point.

2) Value of the deposit

The value of the securities account in the 60th year is 3,609,298 euros. Here, too, a sale is probably no longer on the cards. Only an inheritance seems to make sense.

3rd) Is the value of the portfolio rising or falling?

Even if the monthly costs of the tenant are more than 7 times as high as those of the purchaser, the value of the securities account actually increases even in the 60th year by a good 100,000 euros from 3,504,517 euros to 3,609,298 euros.

Although the tenant is slightly ahead after 60 years, the difference is nevertheless negligible. By slightly different parameters, the property owner could also take the lead. So in this respect, it's actually a draw. However, by buying a property, the buyer takes on a considerable cluster risk and can only use his assets in a very inflexible way. In addition, the high value of the tenant's portfolio stands out, which continues to develop positively and thus flexibly enables additional consumption. Accordingly, things are better for the tenant in this scenario.

Incidentally, the 3.5 million euros in 60 years correspond to a present-day purchasing power of just over a million euros, assuming inflation.

Scenario 2: Longer fixed interest rate, but higher interest rate

What happens if we assume a 30-year fixed interest rate and full repayment instead of a fixed interest rate with only 15 years and follow-up financing? In this case, we would probably be offered a loan with an interest rate of 3.5% today. The repayment would be approx. 1.889% and amount to approx. 2,784.43 euros per month - significantly higher than the monthly rate in scenario 1.

The value of the property remains unchanged in this scenario, of course. However, the tenant's deposit value increases to approximately 4.7 million euros. In scenario 2, therefore, the tenant again comes out the winner.

Since this scenario makes less economic sense (at least if we assume a loan interest rate above about 4% for follow-up financing), the idea of a longer fixed interest rate is again discarded in the subsequent scenarios.

Scenario 3: Faster repayment of follow-up financing

Since income is also very likely to increase over time, it may be possible for the buyer to repay the loan in as little as 10 years instead of 15. For a repayment in 10 years, at an interest rate of unchanged 4%, 8.149% must be repaid, which corresponds to a monthly installment of 3,390.61 euros.

In this scenario, the closing value of the deposit would decrease to a good 3.5 million euros, but would grow until the 60th year. Since the value of the property and that of the deposit do not differ significantly, but the deposit value continues to grow and offers the greater flexibility with less risk, the tenant also wins the comparison in scenario 3.

Since scenario 3 is more likely than scenario 1, it will serve as the basis for the subsequent scenarios.

Scenario 4: No annual rent increases, reduction of provisions in old age.

Many tenants do not receive annual rent increases. In this scenario, we therefore assume that the rent is only increased every 4 years, but then directly by 1.022^4 ~ 9.09% - i.e. the value that would have resulted after 4 years if the rent had been increased annually by the assumed 2.2%. So the rent in the 4th year is 1,970 Euro * 1.022^4=2,149.17 Euro - the same value as in the previous scenarios. Only in the years before only 1,970 Euro are calculated.

At the same time, some buyers will certainly not extensively renovate their property in the last years, but only repair the most necessary. Accordingly, we reduce the reserves for maintenance and modernization 10 years before the end of the period under consideration to 50 euros / month. This 50 euros / month will of course continue to be adjusted for inflation. Since the property loses value due to insufficient maintenance, I assume an annual increase in value of 0.5% for the last 10 years instead of the 2.6% in the first 50 years.

After 60 years, the value of the property amounts to approx. 2.9 million euros, that of the deposit to approx. 4 million euros with a continuous increase in value. Scenario 4 thus also goes - very clearly - to the tenant. In the following scenarios, we continue to assume that the purchaser reduces his provisions in recent years and that rent increases are only enforced every 4 years or upon relocation.

Scenario 5: The tenants occupy a property that is suitable for them

A tenant will continue to increase or decrease the size of the rental property over the course of his or her lifetime, adapting it to life circumstances. The buyer, on the other hand, will tend to stay in the property once purchased and choose a size at the time of purchase that suits the maximum number of people who will live in the property. So, in this scenario, nothing changes for the buyer. The tenants, on the other hand, stay in their old rental apartment with 4 rooms and 100sqm for the first 5 years before renting the big house. After the children - 20 years later - leave the house in their early 20s and move to another city, the tenants again decide to move into a perfectly adequate 3 room apartment with 90sqm.

I recalculate, for simplicity, the price per square meter of the rental house to the 4- and 3-room apartments. Moving from the 4-room apartment to the house will cost 2,000 euros and from the house to the 3-room apartment 3,000 euros. In addition, the rental apartments incur apportionable costs of 25 euros / month initially for the maintenance of an elevator and the like. These 25 euros are of course adjusted upwards over time with the rest of the rent.

So the rent for the first 4-room apartment is 1,970 euros / 131 sqm * 100 sqm + 25 euros = 1,528.82 euros and after 4 years it will increase to 1,528.82 euros * 1.022^4 = 1,667.86 euros. The deposit is 4,000 euros. After 5 years the move into the house takes place, the rent of which has meanwhile increased to 1,970 Euro * 1.022^5 = 2,196.45 Euro. In addition, there are one-time moving costs of 2,000 euros. The deposit for the house now amounts to 5,500 euros, which means that an additional 1,500 euros must be withdrawn from the tenant's deposit. Again, the rent is increased by 9.09% every 4 years. After the house has been occupied for 20 years, the tenant moves into the 3-room apartment at a rent of (1,970 Euro / 131 sqm * 90 sqm + 25 Euro) * 1.022^25 = 2,374.97 Euro plus one-time moving costs of 3,000 Euro. The deposit for this 3-room apartment amounts to 5,500 euros and is financed entirely from the previously recovered deposit.

The value of the purchased property remains unchanged at approximately 2.9 million euros. The value of the deposit amounts to approx. 7 million euros and is of course growing inexorably. A clear victory for the tenant.

Scenario 5 is - in my view - the most realistic scenario so far and therefore serves as the basis for scenario 6.

Scenario 6: The buyer also moves

If the buyer is able to part with his beloved property, he will also look for a property better suited to his life situation in the course of time. The buyer therefore also sells his house after 25 years and buys a better fitting 3 room apartment with 90 sqm. Again, for the sake of simplicity, we calculate the price per square meter of the house down to the 3-room apartment and multiply by the expected increase in value to determine the price of the apartment. 750,000 euros / 115 square meters * 90 square meters * 1.026^25 = 1,115,038.73 euros. Due to the buyer's negotiating skills, the apartment changes hands for 1 million euros. There are still 3.57% brokerage fee, 1.5% notary costs, 0.5% for the land register entry, 3.5% land transfer tax and 2,000 euros for an appraiser. In total 1.092.700 Euro

On the other hand, the value of the house for sale is 750,000 euros * 1.026^25 = 1,424,771.71 euros. Since the buyer has regularly invested money in modernizations, the sales price increases by another 6,891.74 euros to 1,431,663.45 euros. From this, brokerage fees of 3.57%, costs for an appraisal of 0.5% and "odds and ends" of 500 euros are to be deducted. 1.431.663,45 Euro * (1-0,0357-0,005) - 500 Euro = 1.372.894,75 Euro.

The buyer, after buying his new apartment and moving costs of 3,000 euros, still has a plus of 277,194.75 euros, which he invests in a world portfolio at the same conditions as the tenant. The monthly maintenance costs for the buyer decrease of course, but have to be paid to the WEG until the end of the considered period. In addition, there is an initial 20 euros for non-apportionable costs such as property management. Instead of 482 euros that the buyer last set aside for the house, the costs drop to 300 euros + 20 euros = 320 euros.

Since both the tenant and the buyer live in an apartment after 25 years, we can simplify the calculation somewhat and dispense with the consideration of apportionable incidental costs that are only incurred for apartments (e.g., the operating costs for an elevator). The relevant incidental rental costs for the 3-room apartment are therefore reduced accordingly.

In this scenario, the tenant has access to a good 6.9 million euros in the deposit at the end of the period under consideration, which of course grows significantly into the final year. The buyer's deposit has grown to a good 2.1 million euros over the same period. His apartment is now worth around 2.5 million euros. However, even in this scenario, the buyer's total assets of around 4.6 million euros are significantly lower than those of the tenant.

End of Part 2

From my point of view, scenarios 5 and 6 are the most likely. At least that's how I would behave as a buyer or tenant. Accordingly, the tenant wins more than clearly. Under the current conditions and the assumptions made, it makes no sense to buy a property in Regensburg or comparable regions from a financial point of view. In the next part, we will look at how these general conditions and assumptions would have to change so that the buyer would still make the better decision financially.

Are the assumptions unrealistic for you? Is the housing situation different in your region? That is quite likely. Feel free to share more realistic assumptions and conditions in the comments. I will then calculate this for you in part 3. You can find the 3rd part here: https://app.getquin.com/activity/GEBmMewkKS

You think scenarios 5 and 6 are unlikely? Feel free to let me know in the comments what seems more realistic to you!

Even if I have checked my calculations several times, there can always be a mistake. If you have found one, can't understand a calculation step or simply have a question about the calculation => Post it in the comments!

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