Replacing an old furnace may reduce yearly energy bills by $115 or more, according to Energy Star as of 2015. The specific amount depends on the climate, which affects how often the furnace is used. The age and energy efficiency of the old furnace also affects the savings.
Furnaces manufactured before 1992 run at only about 55 to 78 percent efficiency, with an average of about 60 percent, according to Today Money. Replacing a model that is only 60 percent efficient with a new model that is 97 percent efficient may save up to 30 percent on energy bills. The older and less efficient the old model, the more savings the homeowner sees on utilities.