A private company is considering whether to retire an irrigation canal it built 50 years ago at a cost of $2 million. The original estimated life of the canal was 75 years. The construction of an interstate highway has reduced the water discharge in the canal. Revenue collection from irrigation

Question

A private company is considering whether to retire an irrigation canal it built 50 years ago at a cost of $2 million. The original estimated life of the canal was 75 years. The construction of an interstate highway has reduced the water discharge in the canal. Revenue collection from irrigation fees is estimated to be $120,000 per year. The cost to maintain the canal is $80,000 per year, which is likely to increase each year by $5,000. Assuming zero salvage value for the canal, should it be retired (abandoned!) if the applicable annual compound interest rate is 6%?

Accepted Answer

The initial construction cost of $2 million being sunk cost is irrelevant. Since a decision criterion is not specified, we can choose to use any of the six discussed in the text. Let us use the PW-criterion under which we abandon the canal if its PW is negative.

Noting that the canal’s remaining life is 25 years, n = 25. As given, [latex]i = \%6 [/latex]. For the given cashflow data (sketch a diagram if necessary),

[latex] PW =PW_{benefits} - PW_{costs}[/latex]

[latex]=120,000({P}/{A},6\%,25)-\left\{80,000({P}/{A},6\%,25)+5,000({P}/{G},6\%,25) ight\}[/latex]

[latex]=(120,000-80,000)({P}/{A},6\%,25)-5,000({P}/{G},6\%,25) [/latex]

[latex]=40,000 imes 12.783-5,000 imes 115.9732[/latex]

[latex]=511,320-579,866[/latex]

[latex]=-\$68.546[/latex]

Since its present worth is negative, the canal should be retired.

Question 12.10: A private company is considering whether to retire an irriga...

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