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 $115 million now. Alternatively, a smaller pipeline can be constructed now for $65 million and enlarged 16 years from now for another $100 million. The pumping cost will be $25,000 per year higher for the smaller pipeline during the first 16 years, but it will be approximately the same thereafter. Both pipelines are expected to have the same useful life with no salvage value.
Required:
1. At an interest rate of 8% per year, which alternative is more economical?

smaller pipe

Explanation: for the first alternative that is constructing with bid size pipe which cost total of $115 million throughout the 50 years and a pumping cost which cost $25000 less than the smaller pipe for the next 16 years of which after those years, it will be equal.

While the smaller pipe cost $65million + $100million = $165million then plus the pumping cost which is equally higher than the big pipe cost . Already there is a difference in cost(minus pumping cost)= $165-115= $50million.

And then $25,000 *16 years= $400000 .

So the total difference in cost for the first 16 years is $50.4 million.

So now with interest rate of 8% you'll see that much capital is used in the smaller pipe , so if both pipe system receive interest rate of 8%, the smaller pipe will have more interest than the bigger.