Every day more than a thousand houses are sold in Spain and about 20% of those properties are bought/sold by an expat.

Once signed the contract of sale is exactly when doubts assail both those who have sold their home and those who have made the purchase. "Have I sold too cheap?" "Have I bought for too much?" Should I have raised the price a little more?" Should I have asked for a bigger discount?

In this article I will try to explain with the aid of simple mathematical used by the Bankinter bank if you have bought your house too expensive or cheap.

It is virtually impossible for either party to be really satisfied with the amount obtained by the sale or the price paid for the property. Psychologically this question will daunt for some time, but there are very simple mathematical formulas that can help the bargain hunter sleep more peacefully. Formulas that go beyond whether we can afford to buy and pay for that house, and that will tell us if we have bought or sold expensive or cheap and, in case of investment, if it is a profitable operation.

Bankinter, for example, has designed an interesting table that allows anyone to know the fair price of a home. For its elaboration, the entity takes into account two variables. The gross return per rental and the Price Earnings Ratio (PER). But what do these variables refer to?

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**A) Gross rent for letting**

It is the percentage that results from dividing the annual money we get for a rental property between its selling prices. Thus, for example, a house that rents for 900 Euros per month (10,800 Euros a year) and that is worth 250,000 Euros is said to offer a gross profitability of 4.3% according to this formula:

(10,800 / 250,000) x 100 = 4.3%

**B) The PER**

The PER, on the other hand, equals the number of times the rental price is contained in the sale price or the number of years it would take to pay the price of a home through rent under current conditions. It is a universally accepted ratio for valuing assets such as companies, housing, etc. Basically it is the reverse operation; divide the selling price between the rental prices.

Thus, following the example above, the PER of that dwelling would be 23.1 and the calculation by which that would have been reached would be:

(250,000 / 10,800) = 23.1

**C) The GPR**

The GPR speaks of a gross profitability of rent of 4.6%, a percentage that serves as reference to know if we are buying cheap or expensive

Now, in what range should the GPR move to know if we have made a good purchase or investment? Or what should be the profitability obtained? To give us an idea, according to the Bank of Spain, the gross profitability of renting a home in Spain at the end of the first quarter of 2016 was 4.6% - a percentage that the Idealista real estate portal places in the 5 , 9% in the third quarter - well above the 1.9% offered by the state's 10-year bonds.

This percentage would correspond, according to Bankinter, to a GPR of 21.7 years or what is the same, 260 months. That percentage and these data give us a first reference to know if we are buying expensive or cheap. Based on these data, this entity has drawn up a table in which it establishes the relationship between rental price and purchase price for these numbers to come out.

Simply divide the purchase price between the rental prices to get the said GPR: 260 months.

**Let’s see this in a practical example.**

First we must locate the house we want to buy. Once we have found the house of our dreams, the next step is to look for a property of similar characteristics
(location, size, age ...) __but for rent__. Let's imagine that a very similar house is offered to be rented for 800 Euros. If we multiply this figure by 260 months (GPR), we would obtain that
__the sale price__ of the house we want to buy which should be around 208,000 Euros under current market conditions, which, in turn, represents a return of 4.7%.

If our intention, on the other hand, is to buy a house as an investment, the GPR helps us to know, for example, that if the house in which we are interested has an asking price of 180,000 Euros, we could charge a rent close to 700 Euros or what is the same, 8,400 Euros per year (180,000 / 260 = 692). At these prices, the gross return per rental would be at 4.6%: (8,400 / 180,000) x 100. Percentage in line with data from the Bank of Spain.

However, if we make a search and find that the rents in that area hardly exceed 500 euros (6,000 euros per year), we should rethink the operation or demand a price reduction. In this case, about 50,000 euros (500 x 260 = 130,000) for the numbers to come out. Since, if we finally rent to 500 euros, the profitability would be significantly reduced to 3.3% (6,000 / 180,000) x 100.

I hope you found this information useful.

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