The Bureau of Reclamation is studying a stretch of the leaky Coachella Canal in California with
a view to lining the presently unlined canal.
The new plastic lining will cost $170 million. Yaerly maintenance will cost $1 million for the first
year of operation and will increase by $1,2 million per year for each succeeding year. Thus, the
cost for year 2 will be $2,2 million, for year 3, $3,4 million, and so on. The life of lining is 25
years, with no salvage value.
The original canal cost $800 million 30 years ago. It will last in its present unlined condition for
another 20 years at minimum, but with an increasing water loss each year. Water loss is
estimated at $20 million for next year. For each succeeding year, the water loss will increase
by $5 million per year. The cost of water loss for year 2 will thus be $25 million, for year 3, $30
million, and so on.
The opportunity cost of capital in constant dollars is 8 percent; all estimates are made in
constant dollars. Assume that, for the purpose of a preliminary calculation, the new lining can
be installed at time 0, that is, immediately. For the public enterprise, no income taxes need be
considered.
(a) What is the economic life of challenger?
(b) At what year from now, time 0, should the new lining be installed, or should it not be
installed at all?