Nico has a 20-year-old oil-fired hot air furnace in his house. He is considering replacing it with a new high-efficiency natural gas furnace. The oil-fired furnace has a scrap value of $500, which it will retain indefinitely. A maintenance contract costs $300 per year, plus parts. Nico estimates that parts will cost $200 this year, increasing by $100 per year in subsequent years. The new gas furnace will cost $4500 to buy and $500 to install. It will save $500 per year in energy costs. The maintenance costs for the gas furnace are covered under guarantee for the first five years. The market value of the gas furnace can be estimated from straight-line depreciation with a salvage value of $500 after 10 years. Using a MARR of 10 percent, should the oil furnace be replaced?
| Net Investment | |
| Cost of new gas furnace | $ 4,500 |
| Add: Installation Cost | $ 500 |
| Less: Scrap value of oil-fired furnace | $ (500) |
| Net Investment | $ 4,500 |
| (Hint for parts cost: Nico estimates that parts will cost $200 this year, increasing by $100 per year in subsequent years.) (Hint for Maintenance cost = he maintenance costs for the gas furnace are covered under guarantee for the first five years.) | |||
| Year | Maintenance Cost | Parts Cost | Annual Cost |
| 1 | $ 300 | $ 200 | $ 500 |
| 2 | $ 300 | $ 300 | $ 600 |
| 3 | $ 300 | $ 400 | $ 700 |
| 4 | $ 300 | $ 500 | $ 800 |
| 5 | $ 300 | $ 600 | $ 900 |
| 6 | $ 700 | $ 700 | |
| 7 | $ 800 | $ 800 | |
| 8 | $ 900 | $ 900 | |
| 9 | $ 1,000 | $ 1,000 | |
| 10 | $ 1,100 | $ 1,100 | |
| Year | Annual Cost Saving (As above) | Saving in energy costs | Total Savings |
| 1 | $ 500 | $ 500 | $ 1,000 |
| 2 | $ 600 | $ 500 | $ 1,100 |
| 3 | $ 700 | $ 500 | $ 1,200 |
| 4 | $ 800 | $ 500 | $ 1,300 |
| 5 | $ 900 | $ 500 | $ 1,400 |
| 6 | $ 700 | $ 500 | $ 1,200 |
| 7 | $ 800 | $ 500 | $ 1,300 |
| 8 | $ 900 | $ 500 | $ 1,400 |
| 9 | $ 1,000 | $ 500 | $ 1,500 |
| 10 | $ 1,100 | $ 500 | $ 1,600 |
| Year | Cash Flow | Discount Factor @ 10% | Present Value |
| 0 | $ (4,500) | 1.00000 | $ (4,500) |
| 1 | $ 1,000 | 0.90909 | $ 909 |
| 2 | $ 1,100 | 0.82645 | $ 909 |
| 3 | $ 1,200 | 0.75131 | $ 902 |
| 4 | $ 1,300 | 0.68301 | $ 888 |
| 5 | $ 1,400 | 0.62092 | $ 869 |
| 6 | $ 1,200 | 0.56447 | $ 677 |
| 7 | $ 1,300 | 0.51316 | $ 667 |
| 8 | $ 1,400 | 0.46651 | $ 653 |
| 9 | $ 1,500 | 0.42410 | $ 636 |
| 10 | $ 1,600 | 0.38554 | $ 617 |
| Incremental Net Present Value | $ 3,228 | ||
| Oil furnace should be replaced. Because Incremental Net Present Value of replacement is positive. | |||
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