Question 4

A vacant lot is zoned for construction of a condo building. The lot is suitable for a building with either 10 or 20 condo units. We want to value the lot from the perspective of a real estate developer who owns the land and considers when to build (this year or next year) and what to build (10 units or 20 units).

Assume that:

• The risk free rate is 10%
• Per unit construction costs (this year or next year):
  • $95,000 for building with 10 units
  • $125,000 for building with 20 units

• Construction does not take time (i.e., the real estate developer can immediately sell the condos in the year in which she builds)
• Current price of each condo unit is $170,000
• Per year rental rate of a condo is $20,000 per unit (net of expenses, to be paid at the end of the year)
• Next year, if market conditions are:
  • Favorable, condos sell for $200,000
  • Unfavorable, condos sell for $125,000

4a) Suppose that the real estate developer has to build this year. Should she build 10 or 20 units? What is the value of the lot in this case?

4b) Suppose that the real estate developer can wait and make the construction decision next year, after learning whether market conditions are favorable or unfavorable. What is the value of the lot in this case?

4c) Suppose now that the real estate developer has the option to sell the lot to someone else who wants to build a house on the lot for his personal use and is willing to pay $450,000 for the lot. This offer is valid for one year; that is, the real estate developer can accept the offer and sell the lot now or can wait until next year, observe whether the market conditions are favorable or unfavorable, and then decide whether to accept the offer. What should the real estate developer do in this case (i.e., build now, sell now, or wait until next year to make the decision)? What is the value of the lot in this case?