Economic efficiency of geothermal heat pump

We are currently building a single-family house (Pinneberg, construction company Kage, 119 sqm, 40-degree gable roof, without basement) and I am considering a ground source heat pump. The construction advisor advised us against it because it is too expensive: 13,000 euros more than a normal gas heating system.

At the moment we are renting (semi-detached house, 3 people, built in 2008, 130 sqm, gas heating) and we consume gas about 60 euros/month = 720 euros/year.
If the heat from the ground source heat pump only costs half (so the advisor says, roughly estimated), then you calculate 13,000 / (0.5 * 720) = 36 annual performance factor !!!!
Is that correct?

What do you think about the economic efficiency of the ground source heat pump?

PS
I am sorry German is not my best language, please be patient... :-{

Can only tell you about our new building from just over four years ago - back then Kfw 70.

We heated 300 sqm with just under 400€ per year. Comfortable temperature at just under 22 degrees. We had a controlled residential ventilation system. I can't say what it would have cost in gas. But at the resale two years ago, it already paid off...

Totally uneconomical, you'll never manage to make it add up. I would definitely recommend gas to you! Especially with a small house of 120 m², it makes no sense at all.

OK thanks.

But 300 sqm and 119 sqm are very different. Of course, with 300 sqm you need a larger heating system, whether gas or heat pump, but I don't suppose much more expensive.
But the operating costs with 300 sqm are much higher than with 119 sqm.

The bigger the house, the better the economy of the heat pump.

Let's say, only theoretically, the heat pump consumes NO gas or electricity.
Then 13,000 EUR / 720 EUR/year = 18 years.
Although we do not know future gas prices, gas will probably become more expensive, but even with a heat pump we have to pay higher interest for the larger loan.

Uneconomical.

That's how it is and your heat pump also needs a lot of electricity.