Suppose that the City of Old York is considering building a recreation center. Its estimated construction cost is $12 million, and there will be annual staffing and maintenance costs of $750,000 over the 20-year life of the project. At the end of the life of the project, Old York expects to be able to sell the property for $4 million. However, given the vicissitudes of the real estate market, the sale amount could be as low as $2 million or as high as $5 million. Analysts estimate that the first year benefits will be $1.2 million. They expect that the annual benefits will grow in real terms as the neighborhood’s population and income increase. Specifically, they estimate that benefits will grow at a rate of 4 percent per year. However, given the uncertainty surrounding this, the benefits could grow by as little as 1 percent per year or as much as 6 percent per year. The analysts recommend using a discount rate of 6 percent in valuing the project. NOTE: ALL THE CALCULATIONS NEEDED TO ANSWER THE QUESTIONS BELOW CAN BEST BE DONE USING A SPREADSHEET.
a. Calculate the net present value of the project using the analysts’ baseline estimates.
b. Discuss the sensitivity of the result you calculated in (a) to the alternative estimates of market value and annual benefits noted above. Do the alternative calculations change your conclusion in (a)?
c. Using the baseline estimates, at what discount rate would this project have a zero net present value?
d. The nature of the benefits in this example is not specified. Would you agree that the following should be included as benefits in this example: (1) the increase in residential property values caused by the construction of the recreation center; (2) the salaries paid to the construction workers; (3) the revenue derived from residents paying to use the facility. Explain.