Answer
He should buy the conventional model
Work Step by Step
First we calculate the cost of useful heat now:
$Cost_{usefulheat}=0.55*1200\frac{dollars}{year}=660\frac{dollars}{year}$
The costs of heating are:
$Cost_{82}=\frac{660660\frac{dollars}{year}}{0.82}=804.88\frac{dollars}{year}$
$Cost_{95}=\frac{660\frac{dollars}{year}}{0.95}=694.74\frac{dollars}{year}$
The the anual cost saving is:
$Cost_{save}=804.88\frac{dollars}{year}-694.74\frac{dollars}{year}=110.14\frac{dollars}{year}$
And the excess initial cost is:
$Cost_{excess}=2700dollars-1600dollars=1100dollars$
The simple payback period is:
$SPP=\frac{1100dollars}{110.14\frac{dollars}{year}=9.99 years}$
As the simple payback period is greater than $8 years$ he should buy the conventional model.
