Boiler Replacement Under Fuel-Price Uncertainty
A 10-year-old fire-tube boiler supplies process steam. Its measured annual fuel cost is $900,000 at current prices and its seasonal efficiency is 80%. A new condensing boiler would cost $650,000 installed, achieve 94% efficiency, and reduce maintenance from $45,000 to $25,000 per year. The old boiler can be sold now for $30,000; the new unit is expected to have a $60,000 salvage value after 10 years. The old boiler also needs a $180,000 refractory repair within six months; without it, capacity must be derated during peak demand. The company uses a 12% minimum attractive rate of return and a 10-year study period. Its capital policy rejects projects with simple payback longer than three years. Management has calculated payback on the installed cost alone and rejected the replacement. Fuel prices are volatile, and the steam load is expected to remain steady.
1. Calculate simple payback for the replacement, both on the installed cost alone and on the incremental cost relative to repairing the old boiler. State your assumptions.
Read the worked answer
Fuel savings = 900,000 x (1 - 80/94) = 900,000 x 0.14894 = $134,043 per year. Add maintenance savings of $20,000, giving $154,043 per year. Net installed cost = 650,000 - 30,000 = $620,000, so simple payback = 620,000 / 154,043 = 4.0 years. If the old boiler must be repaired anyway, the incremental cost of choosing new is 620,000 - 180,000 = $440,000, so payback = 440,000 / 154,043 = 2.9 years. Both calculations omit time value and salvage. The 3-year policy therefore rejects the project on the first calculation but accepts it on the second, which shows that the accounting boundary changes the answer.
2. Compute NPV at 12% over 10 years and explain why it conflicts with the payback screen. Include the repair avoidance.
Read the worked answer
At 12% for 10 years, the annuity factor is 5.650 and the present-value factor for year 10 is 0.322. NPV = -620,000 + 154,043 x 5.650 + 60,000 x 0.322 + 180,000 = -620,000 + 870,343 + 19,320 + 180,000 = +$449,663. The repair avoidance is a real benefit because the old boiler cannot continue at full rating without it. Payback ignores all cash flow after the payback date, ignores timing, and treats the 3-year threshold as a rule rather than a risk-adjusted policy. A 10-year asset with positive NPV can fail a short payback screen. The correct comparison is incremental, over the study period, at the MARR.
3. At what annual fuel cost does the replacement break even in NPV terms? What recommendation do you make?
Read the worked answer
Set NPV to zero. Required annual savings = (620,000 - 19,320) / 5.650 = $106,315. Subtract the $20,000 maintenance saving: required fuel saving = $86,315. Break-even fuel cost F satisfies F x 0.14894 = 86,315, so F = $579,500 per year. Current fuel cost is $900,000, leaving about 36% headroom. Recommend proceeding, subject to verifying the 94% efficiency with a stack test and duty profile, confirming condensate and flue-gas treatment, obtaining firm installation quotes, and testing sensitivity to fuel price and load. Do not use the 3-year payback as the sole criterion.