# Real Estate Finance

A developer is interested in a parcel of land for a small mixed use development. Similar developments are worth \$15 million and require the following sequential investments to complete:
Phase Description
1 Purch. land, permitting, utilities
2 Build retail
3 build apartment

Cost Time to complete
3 million 1 year
10 million 2 years
7 million 2 years

The volatility of the development value is 25% and the risk-free rate of interest is 3%. Due to competition the developer knows that the project will have to be completed in the next 6 years or not at all.

1. If the developer has to make a decision today (ie. invest today or do not invest at all) and assuming that a suitable discount rate for the project is the risk free rate plus 3% premium, should the project be undertaken?

2. Using the data provided above, give the developer some advice on how to proceed with this opportunity?

3. What is the probability that the development will actually be completed?

4. Suppose that after a careful examination of the data, the volatility is though to be lower than first anticipated for this project. What level kills the optionality in the investment and will force the developer to walk away from this opportunity?

5. Explain why your answer to number 4 above makes sense. That is, what is the relationship between volatility and the value of an option in the context of this investment decision?

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