The existing system changes the answer
A heat pump moves heat rather than creating it directly, and one system can provide both heating and cooling. The Department of Energy says modern air-source heat pumps can use substantially less electricity than electric resistance heating. That makes the economics especially attractive when the alternative is baseboard heat, an electric furnace, propane or oil.
The comparison can be closer when a home already has efficient natural-gas heat, particularly where gas is inexpensive and electricity is costly. The right calculation uses your utility rates and your current system—not a national savings claim.
Replacement timing matters
A $15,000 heat-pump project is a very different decision if your furnace and air conditioner both need replacement next year than if both systems are five years old and working well. Compare the heat pump's incremental cost with the equipment you would otherwise need to buy, not with zero.
If you need air conditioning anyway, count the avoided cost of a separate air conditioner. If ductwork needs major repair or electrical service needs upgrading, count those costs too.
Efficiency is only useful if the house can use it
Sizing and installation matter. Weatherization can matter too. DOE recommends considering air sealing and insulation because a leaky house can undermine the savings from efficient equipment.
Ask bidders for the exact equipment model, efficiency ratings, design temperature, load calculation, backup-heat strategy and expected electrical work. A proposal that simply replaces a furnace by tonnage without evaluating the house is not giving you much basis for comparison.
A better payback test
Calculate annual heating and cooling cost under the existing system, then estimate the new system using local energy prices and realistic efficiency assumptions. Add maintenance differences and incentives you actually qualify for. Divide the extra upfront cost—not the entire project cost—by the expected annual savings.
That gives you a payback period worth discussing. It will not capture comfort, quieter operation or avoiding two separate systems, but it keeps those benefits from being disguised as energy savings.