Question

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 $125 million now. Alternatively, a smaller pipeline can be constructed now for $75 million and enlarged 18 years from now for another $110 million. The pumping cost will be $25,000 per year higher for the smaller pipeline during the first 18 years, but it will be approximately the same thereafter. Both pipelines are expected to have the same useful life with no salvage value.

At an interest rate of 7% per year, which alternative is more economical?

The present worth of the full-sized pipeline is determined to be $_______ and that of the small-sized pipeline is $_________

Answer 1

initial cost of larger pipeline = 125m

Initial cost of smaller pipeline = 75m

upgrading the smaller pipeline will cost = 110m after 18 yrs

Annual additional cost in smaller pipeline = 25000 for 18 years

Salvage =0

i = 7%

Present worth of larger pipeline = -125m

Present worth of smaller pipeline = -75m-110m*(P/F, 7%,18) - 25000 *(P/A,7%,18)

= -75m-110m*0.295863916 - 25000 *10.059086

= -107,796,507.90

We should go with smaller pipeline as it has less present cost