Engineering360: "The case for heat pump usage in Europe"

If the heat pump runs on electricity and your furnace heats with gas, you have to factor in the ratio of price of energy of gas versus electricity.

"The economics of heat pumps are driven by the ‘gain’, the amount of heat output per unit electricity input, and by the ratio between electricity and gas prices. New data from the Energy Systems Catapult reveals that the typical heat pump delivers a gain of 2.8, but the price ratio is 4. This means that the majority of people will find a heat pump more expensive to run than a new gas boiler."

https://www.thegwpf.org/publications/new-paper-reveals-governments-heat-pump-plan-as-uneconomic

If your electricity is hydroelectric, heat pumps are a good deal. If it is generated by burning fuel, the Carnot efficiency of converting heat into mechanical energy to drive a generator may well result in more fuel being burned at the power plant than would be burned heating your home.