New City is considering building a recreation center. The estimated construction cost is $12 million with annual staffing and maintenance costs of $750,000 over the twenty year life of the project. At the end of the life of the project, New City expects to be able to sell the land for $4 million, though the amount could be as low as $2 million and as high as $5 million. Analysts estimate the first year benefits (accruing at the end of the year of the first year) to be $1.2 million. They expect the annual benefit to grow in real terms due to increases in population and income. Their prediction is a growth rate of 4 percent, but it could be as low as 1 percent and as high as 6 percent. Analysts estimate the real discount rate for New City to be 6 percent, though they acknowledge that it could be a percentage point higher or lower.
a. Calculate the present value of net benefits for the project using the analysts’ predictions.
b. Investigate the sensitivity of the present value of net benefits to alternative predictions within the ranges given by the analysts.