Heat pumps have exterior units, use a separate measure of efficiency, and don’t have an AFUE rating. However, most heat pumps have a back-up heat source, usually a gas or electric furnace ...

So, a furnace with a 97 rating is 97% efficient ... expect to pay $6,000 to $14,000 for a high-efficiency gas furnace, which is one that has an AFUE of 90 percent or better.