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 $95 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.

Answer 1

I guess the question is what is the implied rate of return on building the full-sized pipeline as opposed to building teh smaller one now and then enlarging it later.

Pls see the table below for calculations and result. The IRR of the incremental investment of building the full-sized pipeline is about 10% so it makes sense to build the full-sized one right now.

Amounts in '000			(Full-sized minus Smaller)	9.997%
Time	Full-sized	Smaller	Incremental	PV (incremental)
0	-95,000	-75,000	-20,000	-20,000
1		-25	25	23
2		-25	25	21
3		-25	25	19
4		-25	25	17
5		-25	25	16
6		-25	25	14
7		-25	25	13
8		-25	25	12
9		-25	25	11
10		-25	25	10
11		-25	25	9
12		-25	25	8
13		-25	25	7
14		-25	25	7
15		-25	25	6
16		-25	25	5
17		-25	25	5
18		-1,10,025	1,10,025	19,799
				0