Keys being delivered - When to Buy a House

When to Buy a House? How to Answer It with Simple Math

Renting vs Owning a House: Compare it to Answer When to Buy a House

The question of when to buy a house is not alone among the few major decisions with the potential to change our paths.

  • When we are still teenagers or in the early 20s, picking careers and (if any) academic degrees.
  • When we decide to marry and have kids, or not.
  • If we will rely on public pensions (hint: don’t) or private savings for retirement.

It is difficult — it not impossible — to decide about the first two listed above based on calculations. But the answer to the dilemma between buying or renting a house is easier to get.

Don’t worry, it is not complicated math — I am not an engineer or a physicist myself, so even my own mathematical resources are limited.

In this article, however, I will approach the decision between renting and buying a house from a financial point. Of course, there are other advantages and disadvantages on both sides. Eg: in the case of an invasion by a foreign power, the renter can escape without caring if insurance covers mortar explosion. Sorry for the weird example. I live in Poland.

In ordinary times, people praise real estate ownership as an investment that may build equity and tax deductions. To rent, on the other side, gives flexibility with no maintenance headaches. To learn more about investments, I prepared this list of audio books about the subject and this other list with the books recommended by the legendary investor Warren Buffett.

Still, there is a common belief that buying a house is a more financially sound decision. Not always this is true, and here you will learn how to discover if this is your case.

The Costs of Buying A House

The first step is to gather all the costs from both sides (buying and renting).

We will not consider some expenses, like furnishing for two reasons: first, because they often exist regardless if you are a renter or a homeowner. Second, because onetime costs are diluted over the years and are of little significance over long periods of time.

So what are a homeowner’s yearly, recurring costs?

  • Loan interests (L)
  • The opportunity cost of the money spent(O)
  • Property taxes (P)
  • Maintenance costs (M)
Picture to illustrate When to Buy a House How to Answer It with Simple Math
When to Buy a House? How to Answer It with Simple Math

Loan Interest (Mortgage) Costs of Buying a House

First of all, the loan costs are not the same as the total mortgage, but only the interests. Most of the value of your mortgages will add to your equity (meaning, the house), except for the interest you pay to the bank.

To calculate the loan costs, we use the effective APR (annual percentage rate). It includes fees and compound interests. Be aware that the effective APR is always equal to or higher than the nominal interest rate, and not everywhere banks disclose these values — here in Poland a law obligates them to do so.

During this exercise, I will use two countries: Poland, where I live, and Brazil, which is where I came from.

The effective rate for a mortgage contracted by a middle-class couple with no dependents in Poland is somewhere around 2% to 4%. To make it simple, let’s consider an effective rate of 3% per year. In Brazil, it is between 6% to 12%, so we will consider 9%.

In both cases, the values are net of inflation — remember that mortgage rates often have a variable, indexed component, so they may fluctuate over time. By the way, If you want to know how to be prepared for an inflationary spiral, here is a useful guide.

The Opportunity Cost of the Money Used

In most mortgage loan contracts, the bank demands a down payment from the buyer. Usually around 20%.

Some loans don’t demand this 20%, but they have higher interest rates. It is a matter of calculated risk for the bank: your down payment reduces their exposure, therefore the higher the down payment, the lower the interest rates.

Imagine if you invested this 20% in high-yield fixed-income in your country. How much it would pay you per year? In Poland, around 1%. In Brazil, somewhere near 5%. Again: both are net of inflation.

But when you buy a house, you will not earn this 1% or 5% over your down payment because you spent the money to buy a house. This money you don’t earn is the opportunity cost. As defined by Investopedia:

Opportunity costs represent the potential benefits an individual, investor, or business misses out on when choosing one alternative over another.

Since your down payment is only 20% of the total house value, this means that the opportunity cost in Brazil is 1% and in Poland is 0.2% of the total house value.

If the house value is $200 000, the 20% down payment is $40000. In Brazil your cost of opportunity is 5% of 40000, meaning $200 per year. In Poland, it is 1% of 40000, resulting in $400.

One crucial thing to consider: if the house you bought appreciates more than the inflation, you should subtract this extra appreciation from the opportunity cost. But if your house appreciated less than the inflation, or even depreciated, this increases the opportunity cost.

In most situations, real estate prices will not depreciate but also not spike, except in rare cases like someone finding oil in his backyard. In our exercise, we consider that real estate prices just follow inflation.

Property Taxes and the Maintenance Costs of Buying A House

Except for unusual rental contracts, the responsibility to pay the property tax is from the landlord or homeowner, not from the renter.

In Europe, property taxes vary drastically. From 0.09% in Austria to a painful 1.93% in Great Britain. In Poland, it is 0.91%. In Brazil, 1%.

There are also maintenance costs. Things that homeowners pay, but renters don’t.

  • Roof, pipes, and other structural repairs
  • Pest control
  • Air-condition or heating filters
  • Leaky faucets
  • Lender-required insurances (flood, fire, earthquake, etc.)
  • Period inspections and permits, when and if required by the local authorities

According to the expert Maurie Backman, writing for MillionAcres, you should expect to spend between 1% and 4% of your home’s value each year for maintenance. Newer homes usually are in the lower range of this interval. In our exercise, we will consider maintenance costs representing 1.5% per year of the total home value.

Explained all the annual costs, here is a summary of them for both countries (Poland and Brazil) we will use in our exercise of when to buy a house:

  • Loan interests (L): Poland = 3%, Brazil = 9% of the total house value per year.
  • The opportunity cost of the money used (O): Poland = 1%, Brazil = 5% of the value used as down payment OR Poland = 0.2% and Brazil = 1% of the 20% used as down payment, per year.
  • Property taxes (P): Poland = 0.9%, Brazil = 1% of the total house value per year.
  • Maintenance costs (M): For Both Countries, 1.5% of the total house value per year.

The Costs of Renting A House

The monthly cost of renting a home is simple. It is:

Expenses like utilities are not considered because we need to pay them regardless if we are renting or buying.

One could also argue that renters have the additional cost of contracts adjusted annually by an inflation index. However, most mortgage loan contracts also have inflation adjustments — at least mine has. Since these things affect both sides almost equally, it does not make sense to consider them, unless you managed to rent a house or take a mortgage with no inflation adjustment (if this is the case, congratulations).

There are double-edged benefits to renting a house. From one side, it allows you to move without penalty each time your contract finishes. However, it also means your landlord may not accept to renew your contract.

A renter also may face unpredictable rent increases every time he needs to renew his contract. In districts with rising popularity, rent hikes can be steep. In contrast, the only increase in mortgage payments will be due to inflation.

The “Buying a House” Equation (Please don’t be scared, it is easier than it looks)

The decision if renting is better or worse than buying a house will come from a simple calculation:

If the annual cost of buying a house (ACB) is bigger than the annual cost of renting a house (ACR), for the same house value (HV).

ACB = (HV*L) + (HV*O) + (HV*P)+(HV*M)

ACR = (HV*R), or ACR = Annual Rent

If ACB > ACR, it is better to rent a house. If ACB < ACR, it is better to buy a house.

I know it still may look complicated, but it is not. Just look at the two examples below, both considering house values (HV) of $200 000.

Is It a Good Idea to Buy a House In Poland?

HV = $200 000

Loan interests (L): 3% * 200 000 = $6000 per year

Opportunity cost of the money used: 0.2% of 200 000=$400 per year

Property Taxes: 0.9% of 200 000= $1800 per year

Maintenance Costs: 1.5% of 200 000 = $3000 per year

The total cost of buying a house: 6000+400+1800+3000 = $11 200 per year.

The total cost of renting a house = Annual Rent: 6% of 200 000 = $12 000 per year.

Therefore, considering the parameters we used, buying a house will save you $1000 per year in Poland. That is almost a monthly average salary in Poland. In this case, it is a good idea to buy a house there.

Is It a Good Idea to Buy a House In Brazil?

HV = $200 000

Loan interests (L): 9% * 200 000 = $18000 per year

Opportunity cost of the money used: 1% of 200 000=$2000 per year

Property Taxes: 1% of 200 000= $2000 per year

Maintenance Costs: 1.5% of 200 000 = $3000 per year

The total cost of buying a house: 18000+2000+2000+3000 = $25 000 per year.

The total cost of renting a house = Annual Rent: 6% of 200 000 = $12 000 per year.

Therefore, considering the parameters we used, buying a house will make you spend an additional $13 000. In this case, it is a bad idea to buy a house in Brazil.

Shocked by the result? There are a few things that are cheap in Brazil, but that does not include mortgage loans. The lack of Brazilian legal stability adds to the high costs.

If, in My Case, It Is a Bad Idea to Buy a House, What Should I Do?

A better alternative (from the financial point of view) is to do what a friend of mine — head economist of a local bank — does: he saves his money and invests it in high-yield fixed-income titles. The risk of these titles is mitigated by the FGC (a device that covers any loss caused by banks defaulting until a certain value).

The interest paid by his investments covers his rent.

Remember, however, that all these are purely financial calculations.

Not always the decision of buying a house is about the money. It may also depend on your life plans or family requirements. Just avoid point-blank statements like X or Y is always better.

Instead, do the math.

The formula I already gave you, so all you need is to change the numbers I used (taxes, cost of opportunity, etc) for the figures of your circumstance and location.

All the Hows of a First-Time Business Owner: There is a thin line between bankruptcy and the freedom to be an entrepreneur: An idea for a present for yourself (or to any entrepreneur).
An idea of a present for yourself (or to any entrepreneur).

If you liked this article about when to buy a house, check also:

3 Financial Rules for Buying a House, a Car, or a Smartphone.

What is the Velocity of Money: Signals of Grim Times for the S&P 500

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Levi Borba is the founder of, creator of the channel Small Business Hacks and the same website for Small Business Owners, and best-selling author. Subscribe to my articles (for free) and receive (also for free) the ebook “The Blueprint for First-Time Business Owners”.

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