Pump Replacement Under a 12% MARR
The existing pump has an annual operating cost of $48,000, a current salvage value of $10,000, five years of remaining life, and no salvage at retirement. A new pump costs $120,000, has an annual operating cost of $22,000, a 10-year life, and a $15,000 salvage value. The MARR is 12%. If the old pump is kept, assume it will be replaced at year 5 by an equivalent used pump for $10,000. The new pump, if bought, would be replaced identically at year 10. Use (A/P,12%,5) = 0.27741, (A/P,12%,10) = 0.17698, and (A/F,12%,10) = 0.05698.
1. Compare the alternatives on an annual-worth basis over a common 10-year horizon. Which pump should be selected?
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For the old pump, treat the $10,000 current salvage as an opportunity cost and replace it at year 5 with another $10,000 used pump:
- AW_old = 10,000(A/P,12%,5) + 48,000
- AW_old = 10,000(0.27741) + 48,000 = 2,774 + 48,000 = $50,774/yr
For the new pump:
- AW_new = 120,000(A/P,12%,10) − 15,000(A/F,12%,10) + 22,000
- AW_new = 21,238 − 855 + 22,000 = $42,383/yr
The new pump saves about $8,391/yr. Because the comparison is over a common 10-year horizon with identical replacement assumptions, the new pump is the economically better choice.
2. Compute the simple payback period on the incremental investment. How much weight should the decision-maker give it?
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The incremental first cost is $120,000 − $10,000 = $110,000. The annual operating savings are $48,000 − $22,000 = $26,000.
- Simple payback = 110,000 / 26,000 = 4.23 years
This is less than the old pump's five-year remaining life, so the project passes a quick screening test. But payback ignores the time value of money, the $15,000 salvage value, and cash flows after the payback date. It should be used only as a secondary check; the annual-worth comparison already provides the economically correct decision.
3. The new pump's annual operating cost is uncertain. At what operating cost would the old pump become the better choice, all else equal?
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The new pump's annual worth, excluding operating cost, is:
- 120,000(0.17698) − 15,000(0.05698) = 21,238 − 855 = $20,383/yr
So AW_new = 20,383 + OC_new. Set this equal to AW_old = $50,774:
- 20,383 + OC_new = 50,774
- OC_new = $30,391/yr
The new pump remains preferred as long as its annual operating cost is below about $30,400. That is a wide margin above the estimated $22,000, so the decision is fairly robust to operating-cost uncertainty. If the new pump were expected to run near continuous duty or energy prices were expected to rise sharply, this breakeven should be revisited.