Where a Heat Pump Doesn't Pay Back, and Why
Two different ways to fail
A heat pump can fail to pay back in two different ways, and the model keeps them apart. The first is costing more to run every year, so there is nothing to pay the extra cost back with. The second is saving money, but so slowly that the equipment wears out first. Against a gas furnace, the first happens in 1,214 of the 3,206 cities covered here and the second in 1,467.
When it costs more every year
New York, NY is the largest city in this group: at $17.58 per Mcf for gas and 29.22¢ per kWh for electricity, a heat pump there would cost about $15 a year more to run than the existing furnace and AC. Chicago, IL and Indianapolis, IN show the same pattern. The cause is the price of electricity relative to gas, not the price of either alone. A heat pump is two to three times as efficient as a furnace, but where a unit of heat from electricity costs more than two to three times a unit of heat from gas, and especially where cold winters pull the heat pump's seasonal efficiency down, the furnace is cheaper to run. No change to the upfront price can fix a running cost that is higher every year.
When it pays back, just not in time
Los Angeles, CA saves about $41 a year by switching, a real saving, but recovering the $3,000 extra cost at that rate takes 72.9 years, beyond the 15-year equipment life this site uses. Philadelphia, PA and San Diego, CA land in the same place. In these cities the decision usually comes down to things the model does not price: wanting one system for heating and cooling, avoiding a gas connection, or a rebate that cuts the upfront cost.
What can change the answer
Three things move a city out of these groups. A home that heats with electric resistance rather than gas usually saves a great deal, as the electric-resistance guide shows. A local rebate shortens a slow payback, though it cannot fix a higher running cost. And a home without central air conditioning compares differently again, since the heat pump then adds cooling rather than replacing an old air conditioner. Your own gas and electricity rates matter too: check them against the state averages on your city's page.