In order to provide drinking water as part of its 50-year plan, a west coast city is considering constructing a pipeline for importing water from a nearby community that has a plentiful supply of brackish ground water. A full-sized pipeline can be constructed at a cost of $122 million now. Alternatively, a smaller pipeline can be constructed now for $80 million and enlarged 20 years from now for another $100 million. The pumping cost will be $25,000 per year higher for the smaller pipeline during the first 20 years, but will be approximately the same thereafter. Both pipelines are expected to have the same useful life with no salvage value. (a) At an interest rate of 6% per year, which alternative is more economical? (b) Write the spreadsheet function to display the PW for the
smaller pipeline alternative.
What will be an ideal response?
(a) PWFull = $-122,000,000
PWSmall = -80,000,000 -100,000,000(P/F,6%,20) - 25,000(P/A,6%,20)
= -80,000,000 -100,000,000(0.3118) - 25,000(11.4699)
= $-111,466,748
Smaller pipeline is more economical
(b) Spreadsheet function for PWSmall
= -PV(6%,20,-25000) - 80000000 - PV(6%,20,,-100000000) displays $-111,467,221
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