1 Replacing an old furnace with a high-efficiency new one can also require installing a chimney liner for about $300 -$700 for a gas furnace or $700 -$1,800 for a fuel oil model.2  If needed, make sure this is included in all estimates. A building/mechanical permit is usually required to replace a furnace. 2  Permit and inspection fees are typically about $50-$300, but can cost more in some locations.