Question

Suppose a small hydro dam is planned for the Trinity River in northern California. Up front construction costs (initial costs in year 0) are $20 million. After that (beginning in year 1), electricity benefits of $2 million/yr, and operating costs of $0.2 million/yr, are expected into perpetuity (the dam is very durable). Also, construction of the dam implies the loss of wilderness and recreation values known to be $1 million/yr, (starting in year 1) into perpetuity. At what interest rate are we -as economists - indifferent between constructing the dam and leaving the river wild? In other words, at what interest rate does the conclusion of the CBA for the dam flip from "Don't build the dam" to "Build the dam"? (You see, I hope, the effect of the discount rate in economic analysis). Clearly show your work. Highlight (or box) your answers.

Answer 1

$ 20 million is the initial cost of the dam

$ 2 million will be income every year

$1 million is loss of recreational value

$0.2 million is operating cost

Benefit after all costs would be $ 0.8 million

So now we have to calculate at what interest rate the project is feasible.

For this dam we can take Simple interest P*R*T/100

800,000= 20,000,000*R*1/100

R = 800000*100/20,000 = 4

As we have not specified time in years and we clearly mentioned perpetuity, we just need to calculate rate of interst

R = 4%.

At 4% rate of interest the project is feasible, any higher it would be not feasible