# Course: ISyE 6308, Analysis of Production Operations, Spring 1995

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```							                                   Valuing a Real Estate Option
Introduction to Financial Engineering—ISyE 6227

The real-estate price for a one-unit condominium, P, is currently \$100 thousand. Next year the price
will, with equal probability, rise to either \$150 thousand, if the market moves favorably, or decline to \$90
thousand, if the market moves unfavorably. The construction cost (both now and next year) for a 6-unit
building is \$80 thousand per unit, and \$90 thousand for a 9-unit building. For simplicity, if a rented
condominium is assumed to just break even, i.e., the rent covers operating expenses, so no free cash flow is
generated now or next year. The risk-free rate is 10%.

QUESTIONS:

1. If the real estate is developed today:
a. What is the NPV of the construction project?
b. According to traditional NPV analysis should the company invest in the construction project?

2. Since the company has the option to delay construction for 1 year, what is the ROA value of this
construction project? Provide an economic justification for this market value.

3. Management realizes that it holds 2 delay options, one for each building option (6-unit or 9-unit). What
are the exercise prices? The times to maturity? The initial value of the underlying asset?

4.   For this delay option:
a. Graphically depict its final period’s payoffs as a function of the 1-unit condominium price P.
b. Express it as a sum of 2 call options with different strike prices.

```
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