Pump Replacement Economics with Energy Escalation
A cooling-water pump at a food plant runs 6,000 hours per year. The existing 75 kW motor has a measured wire-to-shaft efficiency of 70% and is beyond repair life. Option A is a premium-efficiency unit costing $28,000 installed, with 80% efficiency and a 12-year expected life. Option B is to repair the existing unit for $6,000, keep 70% efficiency, and plan replacement in 5 years. Electricity is $0.09/kWh now, and the plant uses an 8% minimum attractive rate of return. The maintenance manager argues that the repair has a 4.7-year simple payback and should be chosen because capital is tight. A vendor offers a forecast of 4% per year energy escalation, but it is not guaranteed. The plant has a 10-year planning horizon and no salvage value is expected for either option.
1. Compute the annual energy cost for each option and the incremental simple payback of Option A relative to Option B. State whether the manager's 4.7-year payback claim is consistent with these numbers.
Read the worked answer
Electrical input power = shaft power / efficiency.
Option A: 75 kW / 0.80 = 93.75 kW. Annual energy = 93.75 × 6,000 = 562,500 kWh. Annual cost = 562,500 × $0.09 = $50,625.
Option B: 75 kW / 0.70 = 107.14 kW. Annual energy = 107.14 × 6,000 = 642,857 kWh. Annual cost = 642,857 × $0.09 = $57,857.
Annual savings from A = $57,857 − $50,625 = $7,232.
Incremental capital cost = $28,000 − $6,000 = $22,000.
Incremental simple payback = $22,000 / $7,232 = 3.04 years.
The manager's 4.7-year figure is not consistent with these data. A 4.7-year payback would imply annual savings of about $4,680, or about 65% of the calculated savings. The manager may have used a different run time, a different electricity price, or compared the repair cost to doing nothing rather than comparing the two viable options. The correct incremental payback is about 3.0 years, which favors Option A even before considering the 12-year life.
2. Using an 8% MARR and a 12-year life for Option A, compute the present worth of the incremental savings and decide between the options. Then repeat for the plant's 10-year horizon.
Read the worked answer
The incremental savings are $7,232 per year. Use the present-worth factor for an annuity: (P/A, 8%, n) = [(1.08)^n − 1] / [0.08(1.08)^n].
For n = 12: 1.08^12 = 2.518; factor = 1.518 / 0.2014 = 7.536.
PW of savings = 7,232 × 7.536 = $54,500.
Net PW of choosing A over B = −$22,000 + $54,500 = +$32,500.
For n = 10: 1.08^10 = 2.159; factor = 1.159 / 0.1727 = 6.710.
PW of savings = 7,232 × 6.710 = $48,500.
Net PW = −$22,000 + $48,500 = +$26,500.
Under both horizons, Option A has a positive incremental present worth and is economically preferable. The 12-year life assumption is favorable but not necessary: even over 10 years, the premium unit recovers its extra capital and returns more than the MARR. The decision should be documented with the assumptions, and the plant should confirm that the pump will actually run 6,000 hours per year; a large drop in run time would weaken the case for A.
3. How should the engineer treat the 4% per year energy escalation forecast and the 5-year remaining life of the repaired unit? Give a recommendation that separates base-case facts from uncertain forecasts.
Read the worked answer
The 4% escalation is a forecast, not a contract, so it should be treated as a sensitivity case rather than folded into the base case without disclosure. Escalation increases the dollar savings each year, so it makes Option A more attractive, not less. A growing-annuity calculation would raise the PW of savings above the constant-dollar values computed earlier. Even if escalation is zero, Option A wins over both 10- and 12-year horizons.
The 5-year repair life means Option B is not a 10-year solution. At year 5 the plant would face another replacement decision, likely with less favorable capital timing. A fair comparison could include a second repair or a replacement at year 5, but that only strengthens Option A.
Recommendation: present the base case at the current $0.09/kWh with no escalation, show the 3.0-year incremental payback and positive PW, then show a sensitivity with 4% escalation and with a shorter 5-year horizon. Recommend Option A unless the plant expects to close or curtail cooling-water service within about three years. Do not let the unguaranteed escalation forecast be the sole justification; the efficiency difference alone supports the decision.