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Should You Rent or Own Your Home? You Can Answer It with Simple Math…



Renting vs Owning a Home


There are a 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.

  • When we decide between renting or buying a house.

It is difficult — if 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 a REALTOR®, and not an engineer or a physicist myself, so even my own mathematical resources are limited.

In this post, 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.

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.

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:

  1. Loan interests (L)

  2. The opportunity cost of the money spent(O)

  3. Property taxes (P)

  4. Maintenance costs (M)

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 Portugal a law obligates them to do so.

The effective rate for a mortgage contracted by a middle-class couple with no dependents in Portugal is somewhere around 2% to 4%. To make it simple, let’s consider an effective rate of 3% per year.

The values are net of inflation — remember that mortgage rates often have a variable, indexed component, so they may fluctuate over time.

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. How much it would pay you per year? In Portugal, around 1%. Again it is net of inflation.

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

“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 is 0.2% of the total house value.

If the house value is $200 000, the 20% down payment is $40000. That 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 gold or diamonds 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. Here in Portugal, it is 0.91%.

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 INE (National Estatistics Institute), 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 my 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:

  1. Loan interests (L): = 3% of the total house value per year.

  2. The opportunity cost of the money used (O): = 0.2%… (1% of the 20% used as down payment, per year.)

  3. Property taxes (P): = 0.9% of the total house value per year.

  4. Maintenance costs (M): = 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:

The rent you pay (R). On average corresponds to 6% of the total house value.

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. 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*6% = 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?

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 this case, it is a good idea to buy a house.

If, in Any 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 FGB, Fundo Garantia Bancária, (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.

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