I once looked up an expensive hot water heat pump from Stiebel Eltron for calculation purposes. I found the technical data for the cheapest heat pump (unfortunately also with significantly the worst performance factors; there are certainly better providers; but it’s better to calculate conservatively): 200l hot water storage tank, performance factor about 3.5, cost 2000€, if you don’t heat the hot water to maximum about 1kWh heat amount (! not to be confused with electricity amount) per day distribution loss. (If you can heat with photovoltaics, obviously less relevant). This results in X € electricity costs and an annual hot water energy demand of Y costs of: X*((Y+365)/3.5) In contrast, the instantaneous water heater simply tries to produce costs of: X*Y The difference between the two costs thus shows how much cheaper/more expensive the heat pump is compared to the instantaneous heater: X*Y - X*((Y+365)/3.5) If the value is positive, heating with the heat pump is cheaper (and the number is the amount per year). Special features such as pipes/other losses/efficiency of the instantaneous water heater (less than 1 for short durations), which may possibly balance out in certain cases, are not taken into account. Example: X = 0.2 (20C electricity costs), Y = 600 (kWh hot water demand) 0.2*600 - 0.2*((600+365)/3.5) = 120 - 55.14 = 65€. So you save 65€ per year, but have to invest 2000 euros. In this example, it would not be worthwhile. However, if you find a cheaper heat pump, or have more demand, it can look completely different. Incidentally, you can also perform the same calculation here with a gas boiler, since the ratio of costs per kWh is comparable to that of a heat pump.