8. You are considering the purchase of an old fire station, which you plan to co

Question

8. You are considering the purchase of an old fire station, which you plan to convert to an indoor playground. The fire station can be purchased for $200,000, and the playground will generate lifetime profits (excluding the cost of the building) of $700,000. (Assume that those profits are all realized one year after opening.) However, there is a 20% chance that the city council will re-zone the district to exclude establishments such as yours; a hearing is scheduled for the coming year, and if your building is re-zoned, your profit will be zero. Assume that there is no other building currently under consideration. Assume an interest rate of 10%. Calculate the net present value of opening the playground today. Note that the cost of purchasing the building today is certain, but the benefits are uncertain a. b. Calculate the net present value today of opening the playground in one year, after the zoning issues have been decided. Note that the benefits of opening the playground are uncertain today but will be certain in one year. Based on your answers to (a) and (b), should you open the playground today, or should you wait until the zoning commission reaches its decision? c.

Explanation / Answer

a. Chance of rezoning=20% in which case profit will be zero. So chance of not rezoning=80% in which case profit will be $7,00,000.

So expected profit after 1 year=0*20%+7,00,000*80%=$5,60,000

Expected NPV today=5,60,000/1.1-2,00,000=$3,09,091

b NPV of opening playgroound after 1 year after decision of zoning= 7,00,000/1.1-2,00,000=$4,36,364

c. On the basis of our calculations in a and b, it is better to open the playground after zoning committee reaches its decision.

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