Suppose that the City of Old York is considering building a recreation center. I

Question

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.

Explanation / Answer

Given ,construction cost - $12,000,000

Annual staffing & maintenance costs - $750,000

Period - 20 years

Scrap value - $4,000,000 ( highest - $5m & lowest - $2m)

first year benefits - $1,200,000

after that growth rate - 4% ( highest - 6% & lowest -1%)

discount rate - 6%

Part a

Part B

Hence Best Case Scenerio -

where annual benefits have growth rate of 6% & also project has highest scrap value of $5m. But the dicount rate applied needs to be 5%

Worst Case Scenerio -

where Annual benefits have growth rate of 4%, having scrap value of $4m, & project discounted @ 6%

year particulars inflow $ outflow $ Net cashflow $ discount factor @ 6% present value $ 0 consturction cost 0 12000000 -12000000 1 -12000000 1 annual cash outflow 1200000 750000 450000 0.9434 424530 2 annual cash outflow 1248000 750000 498000 0.89 443220 3 annual cash outflow 1297920 750000 547920 0.8396 460034 4 annual cash outflow 1349837 750000 599837 0.7921 475131 5 annual cash outflow 1403830 750000 653830 0.7473 488607 6 annual cash outflow 1459983 750000 709983 0.705 500538 7 annual cash outflow 1518383 750000 768383 0.6651 511052 8 annual cash outflow 1579118 750000 829118 0.6274 520189 9 annual cash outflow 1642283 750000 892283 0.5919 528142 10 annual cash outflow 1707974 750000 957974 0.5584 534933 11 annual cash outflow 1776293 750000 1026293 0.5268 540651 12 annual cash outflow 1847345 750000 1097345 0.497 545380 13 annual cash outflow 1921239 750000 1171239 0.4688 549077 14 annual cash outflow 1998088 750000 1248088 0.4423 552029 15 annual cash outflow 2078012 750000 1328012 0.4173 554179 16 annual cash outflow 2161132 750000 1411132 0.3936 555422 17 annual cash outflow 2247577 750000 1497577 0.3714 556200 18 annual cash outflow 2337481 750000 1587481 0.3503 556095 19 annual cash outflow 2430980 750000 1680980 0.3305 555564 20 annual cash outflow 2528219 750000 1778219 0.3118 554449 20 Scrap value 0 0 4000000 0.3118 1247200 Net Present Value -347378

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