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Project Alpha has two phases. You may invest in the first, in both, or in neither. The first phase requires an investment of $100 today. One year later, Alpha will deliver either $120 or $80, with equal probability. At that time, (after the phase 1 payout has been received) you can invest an additional $100 for phase 2. One year later phase 2 pays out either 20% more cash than phase 1 actually delivered, or (equally likely) 20% less. For investments in this business, your company normally applies a 10% hurdle rate.

a. Assuming you can wait to decide about phase 2, what is the total value of Project Alpha? Should you invest the first $100?

b. Project Omega has exactly the same structure as Project Alpha, and the same systematic risk, but somewhat different cash flows. For $100 invested today, Omega delivers in phase 1 either $140 or $60, with equal probability. Phase 2 requires an additional $100 investment and delivers either 40% more or 40% less than phase 1 did. What is the total value of Project Omega? Should you invest the first $100?

c. Compare these two projects. Which is riskier? Which is more valuable? Which has a higher fraction of its value accounted for by "growth options," i.e., the phase 2 opportunity? Assuming both were undertaken, would you finance Alpha and Omega differently? How and why?

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