An electric heat pump water heater was featured on a recent "Ask This Old House". The claim was made that this water heater was much more efficient than a regular (resistance) electric water heater. That may be true for the water heater all by itself. But when you consider the total heating costs of the house, the savings is not so clear.
When you run a heat pump like that in the house, it heats the water by cooling the ambient air. That ambient air eventually has to be heated by the house's space heating system (at least in winter). The house in question had electric space heating as well as electric water heating. So the cost of heating the water just gets transferred to the space heating cost, and the total remains the same.
If the house had been heated by a cheaper fuel, like natural gas, then there might have been some savings in switching to the heat pump for water heating. Or, if the heat pump had extracted its heat from the outside, then again it might have been a winner. But extracting heat from inside an electrically heating house is not.
About the only advantage I can see in the featured installation is that in the summer, when there is free heat in the ambient air, then the heat pump water heater will indeed save money. But it is certainly not a year-round money saver. That point should have been explained. It may help people making their cost-effectiveness decisions.