A state government has the option of damming a major river to generate energy an

Question

A state government has the option of damming a major river to generate energy and divert water to local agriculture. The cost of constructing the dam and associated infrastructure is 100 million. The value of the energy generated and the water is 10 million per year forever. There are, however, losses to ecosystem services associated with damming. These environmental costs amount to 6 million a year forever. The interest rate: i=0.05. What is the present value of the returns to building the dam? What is the present value of the costs (construction and environmental) to building the dam? Should the state government build the dam?

Explanation / Answer

(a) PV of returns = annual returns / interest rate (Since it is perpetuity)

= $10 million / 0.05

= $200 million

(b) PV of total costs = $100 million + ($6 million / 0.05)

= $220 million

(c) Net present value = PV of returns - PV of costs

= $(200 - 220) million

= - $20 million

Since Net present value is negative, government should not build the dam.

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