Pump Replacement with Unequal Lives and a MARR Sensitivity
A plant is deciding whether to replace a cooling-water pump now or keep it for its remaining 6-year life. The old pump has a current salvage value of $5,000, annual operating cost of $18,000, and annual maintenance cost of $4,000; its salvage after 6 years is expected to be zero. A new pump costs $45,000 installed, has a 10-year life, annual operating cost of $8,000, annual maintenance of $2,000, and salvage of $4,000. The plant uses a 10% MARR. Production is not expected to change, and the new pump's capacity matches the old one. The finance group wants a present-worth comparison over 6 years; the maintenance group argues for annual worth because the lives differ. The old pump has no known immediate repair need, but its reliability has been declining. The decision must be defensible to a capital committee that is skeptical of 'soft' savings.
1. Compute the annual worth of keeping the old pump and of replacing it now at MARR 10%. Use the current salvage value of the old pump as an opportunity cost and state your replacement recommendation.
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Use annual worth because the lives differ. Old pump: keeping it forgoes the $5,000 salvage now; CR=(5,000−0)(A/P,10%,6)=5,000(0.2296)=$1,148/yr. Annual O&M=$18,000+$4,000=$22,000. AW_old=−$23,148/yr. New pump: CR=(45,000−4,000)(A/P,10%,10)+4,000(0.10)=41,000(0.16275)+400=$7,073/yr. Annual O&M=$8,000+$2,000=$10,000. AW_new=−$17,073/yr. The new pump has the lower annual cost by about $6,075/yr, so replace now, assuming the old pump really can last 6 years and the new pump's performance is as quoted.
2. Test the decision at MARR 15%. Does the recommendation change?
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At 15%, (A/P,15%,6)=0.26424 and (A/P,15%,10)=0.19925. AW_old=−22,000−5,000(0.26424)=−$23,321/yr. AW_new=−10,000−[41,000(0.19925)+4,000(0.15)]=−10,000−(8,169+600)=−$18,769/yr. The new pump is still better by about $4,552/yr. The recommendation does not change over this MARR range; the advantage is robust to the discount-rate assumption.
3. List the non-economic or risk factors that could override the annual-worth result, and describe one sensitivity that would change the decision.
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Non-economic factors include reliability and downtime risk, spare-parts availability, footprint and piping changes, permits, noise, maintenance skills, safety, and whether the old pump's remaining life is really 6 years. A sensitivity that could change the decision is a required immediate old-pump repair; if that repair costs more than roughly the present advantage of keeping it, replacement becomes even more attractive. Conversely, if new-pump installation has an extra $25,000 in unlisted costs or the old pump's operating cost drops because production falls, the annual-worth gap narrows. The analysis is a guide, not the whole decision.