We have an old gentleman who belongs to the VFW who has limited funds. He replaced his central A/C in 2009 and was told his 23 year old furnace doesn't have much life left in it. The folks who want to replace the furnace for him now want him to replace the 2009 central A/C. Doesn't quite make sense to me since he has no problems with it. Can one pair a new furnace with an old coil and A/C system? Thanks.