You are considering replacing your aging propane furnace for a natural gas model. The propane model originally cost $2,200, will last 6 more years, and will have no salvage value. The gas model costs $2,200 and offers a $400 trade-in on the old furnace. It lasts 13 years and can be salvaged for $500 at the end of year 13. Annual fuel costs are $800 for the propane furnace and $600 for the gas furnace. The real interest rate is 9% per year. Using cash-flow replacement and annual worth analysis, should the propane furnace be replaced with the gas model?

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.

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