Three mutually exclusive projects are being considered for a

Three mutually exclusive projects are being considered for a remote river valley: Project R, a recreational facility, has estimated benefits of $10million and costs of $8 million; project F, a forest preserve with some recreation facilities, has estimated benefits of $13 million and costs of $10 million; project W, a wilderness area with restricted public access, has estimated benefits of $5million and costs of $1million. In additional, a road could be built for a cost of $4 million that would increase the benefits of project R by $8 million, increase the benefits of project F by $5 million, and reduce the benefits of project W by $1 million. Even in the absence of any of the other projects, the road has estimated benefits of $2 million.

a. Calculate the benefit-cost ratio and net benefits for each possible alternative to the status quo. Note that there are seven possible alternatives to the status quo; R, F, and W, and both with and without the road, and the road alone.

b. If only one of the seven alternatives can be selected, which should be selected according to the CBA decision rule?

Solution

a. The seven possible alternatives to the status quo have the following costs (millions), benefits (millions), benefit/cost ratios, and net benefits (millions):

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b. Though Project W without the road has the largest benefit/cost ratio, Project R with the road offers the largest net benefits among the possible projects and therefore would be selected by the CBA decision rule.