A surcharge of 13k seems high for Pinneberg, but of course compared to gas, not compared to an air-water heat pump (which is usually the decision that builders face). Are these 13k the surcharge that Kage wants? Then subtract the costs for the gas house connection, which you save. BAFA also pays a subsidy for brine heat pumps depending on the specific design of about 5k, which you also have to deduct. And (if you are not planning a stove) the chimney sweep does not have to come, which is not only a financial point but also a gain in comfort. The difference is not as big as initially thought when you consider everything. However, projecting the running costs into the future always remains a matter of belief, especially because you have different energy sources to choose from.