Answer:
The information is not complete (we do not know the useful life of the propane model), but the difference in costs between one project and the other is two large. The NPV of the savings for the gas model almost pays for the initial investment, plus the present value of the costs of using the gas model are much lower for future equivalent projects, we can assume that replacing the propane furnace with the gas model is a good investment.
We cannot determine exactly by how much the actual worth of the costs of the gas model are lower than the costs of the propane model, but there is no doubt that they are much lower. The only way that the propane model would have lower actual costs would that its useful life is much longer.
Explanation:
use propane model use gas model
initial investment $0 $1,800
operating costs $800 $600
useful life 6 years 13 years
present value of the costs for first product life cycle:
$3,559 (6 years) $6,129 (13 years)
Since the useful lives of the alternatives are not the same, we must find a common denominator for the useful life of the alternatives. Here we have a problem because we are not given the information.
But we can assume that the useful life of a propane furnace is also 13 years:
use propane model use gas model
initial investment $2,200 $2,200
operating costs $800 $600
useful life 13 years 13 years
residual value $0 $500
present value of total costs per life cycle:
$8,190 $6,529
Now we need to determine the NPV of the money saved by using gas propane = -$140 (-$1,800, 9%, $200 saved during 12 periods and $700 received at last period), so basically the gas model almost pays for itself with the money it saves.
