> Our analysis finds that electric heat pumps generally use less energy in warm states and have moderately positive economics in these states if a heat pump can replace both the furnace and a central air conditioner.
> Based on our analysis, we find that electric heat pumps have higher equipment and installation costs than gas furnaces and that electricity is generally more expensive per Btu than natural gas. As a result, in all of the comparisons the gas furnace has a lower life cycle cost for homes without central air-conditioning. However, if a central air conditioner can be replaced with a heat pump, the high-efficiency heat pump has lower life cycle costs in climates from Virginia southward as well as in the Northwest. This is shown by an analysis that credits the avoided cost of a central air conditioner and also includes cooling-energy savings from replacing a central air conditioner meeting federal minimum efficiency standards—a seasonal energy efficiency ratio (SEER) of 13 in the North and a SEER of 14 in the South—with a higher-efficiency heat pump
> As discussed above, our analysis is only for existing homes. The results may be more positive toward heat pumps for new homes, as most new homes have air-conditioning and the cost of supplying gas to the home can be avoided by installing heat pumps.
Note that this is a few years old (2016), and more efficient heat pumps improve the economics.