It costs however much electricity is used to produce the heat. The concept of heat transfer from the outside air is a fairly efficent system , albeit that efficency decreases the colder the outside air becomes.
Generally the cost savings comes from not burning a fuel to produce heat, though that too changes when the outside air temperature decreases forcing a supplemental heat source needed for the heat pump.
So , as you see your heat is not *free*.
The one point that needs to considered is the heated ambient air is not lost unlike the use of a bathroom or kitchen exhaust fan.In this case the heat is not free! They are taking the heat from the ambient air which has been heated by the home's heating system and putting into the tank. This heat is not free, it has been paid for in the cost of your heating bill.
All they are doing here is ultimately just transferring some of the cost of heating the water from the hot water heater itself to your home's heating system. This is all in the name of going "green"? I would expect the total cost to actually be higher because of the cost of running the heat pump
It's true these water heaters use a heat pump type of system by intaking ambient air and transfering the exchanged heat to the water tank.The efficiency of heat transfer is what makes the concept of these systems an attractive alternative.
These systems generally are using the hybrid system for maintaining the water temperature in the tank ,offsetting the need to use the electric elements inside an electric water heater. Instead the elements would be mostly used only for high use .
I would have to say A. Spruce hit the nail on the head with some points. It's not likely that these water heaters will be anywhere that would be noticeable.
They are somewhat new and little detailed information is lacking at this point regarding real world savings. What the actual savings will be is yet to be determined, but I doubt they will be what the manufacturers publish.
Somewhere I had run across an article in which some folks that were involved in the intial trial run. I'll see if I can locate and post some feed back from those users.