I offer a variety of simplified math that relates to the work of attic efficiency and safety, at this web page tab. Facing the need to close a ventilation chase to the attic in a pending job, I wondered whether the home owner should first replace an old gas furnace, that I thought might be 80% efficient. Here is the math I developed:
The existing furnace should be professionally evaluated for safety, at minimum.
Furnace replacement with efficiency increase from 80% to 95% efficiency, $1000 per year present operation:
Power consumed is proportional to demand times efficiency, if weather and comfort demanded are constant. In fact, cost is maintained to some extent, affording greater comfort.
$1000*0.8 = X*0.95
X = .8/.95 * $1000 = $842.
Savings per $1000 present cost are $158 per year.
A $4000 replacement furnace cost is repaid in 25 years, if present fuel cost is $1000 per year.
I have pressed HVAC contractors to offer payback studies several times, without success. They may have no more confidence than I, in stating efficiency of the found furnace. Present operation cost is subject to use variables. A new tenant or other change in living needs can cause a large shift, and more variables in a learning curve with fuel bills. Behavior after a replacement will be uncertain. Maybe the user will judge that he can afford to stay more comfortable with the same fuel budget.
If you make a few assumptions, the math is not impossible. I am so very happy with a comparable furnace upgrade in my home, but it wasn't over efficiency. Twenty-year old furnaces die shamefully sometimes.