Q) A benefit-cost study of a proposed dam is conducted. The dam costs $75 million to construct. The study estimates a stream of social benefits of $9.5 million per year (from avoided flood damage, hydroelectric power, etc.) and annual costs of $4 million ($2 million from operation and $2 million in environmental damages). Note: Feel free to use Excel/etc. on this problem.
a) Assuming a social marginal rate of time preference (i.e. social discount rate) of 4% per year, how many years does it take for the dam to “break even” (i.e., the NPV of benefits just exceed the NPV of costs)?
b) Opponents of the study disagree with using a single discount rate of 4% for all of the benefits and costs. They argue that the $2 million in environmental costs should only be discounted at 1%. Develop a graph of the NPV as a function of the years of operation – from 0 to 300 years – for this group of opponents. Assume all benefits and costs are $0 after the end of operation of the dam. In which year would the opponents be in favor of closing the dam facility, and why?