Q1 (DECISION TREE). You have located a piece of property that you would like to buy to build a factory on. It is currently zoned for multi-family housing but you are planning to request new zoning.

You are given the following information: Cost of land, $2 Million, Probability of rezoning = 0.60, and if land is rezoned there will be an additional cost of $1 million for new roads, lighting, and so on.

If the land is rezoned, you must decide whether to: 1) build a large factory at a construction cost of $10M that can produce 150,000 units/year and, depending on the market, has a 70% chance of making $4M/year profit, and a 30% chance of making $5M/year profit; or 2) a smaller factory at a construction cost of $9M that can produce 100,000 units/year and, depending on the market, has a 60% chance of making $4.5M/year profit, and a 40% chance of making $3M/year profit. However, if the land is not rezoned, you must comply with the existing zoning. You do not need to spend $1M on site prep but now you will build 600 apartments at a construction cost of $5M and rent each one at a $3,000 profit/year.

Part A.) Draw the decision tree with the probabilities on each branch:

Part B.) If the land is rezoned, what is the expected 1-year return on investment (ROI) for each of the two factory options? Would you build the large or small factory?

Part C.) If the land is not rezoned, what is the expected 1-year return on investment (ROI) for building the apartments?

Part D.) Since you don't know the zoning outcome at the time of purchase, what is the overall expected 1-year ROI for this project? Do you think it's a good investment?