1.You own a piece of raw land in an up-and-coming area in Gotham City. The costs to construct a building increase disproportionately with the size of the building. A building of q square feet costs 0.1 × q2 to build. After you construct a building on the lot, it will last forever but you are committed to it: You cannot put another building on the lot. Buildings currently rent at $100 per square foot per month. Rents in this area are expected to increase in five years. There is a 50% chance that they will rise to $200 per square foot per month and stay there forever, and a 50% chance that they will stay at $100 per square foot per month forever. The cost of capital is fixed at 12% per year.
a. Should you construct a building on the lot right away? If so, how large should the building be?
b. If you choose to delay the decision, how large a building will you construct in each possible state in five years?
2.Genenco is developing a new drug that will slow the aging process. In order to succeed, two breakthroughs are needed, one to increase the potency of the drug, and the second to eliminate toxic side effects. Research to improve the drug’s potency is expected to require an upfront investment of $10 million and take 2 years; the drug has a 5% chance of success. Reducing the drug’s toxicity will require a $30 million up-front investment, take 4 years, and has a 20% chance of success. If both efforts are successful, Genenco can sell the patent for the drug to a major drug company for $2 billion. All risk is idiosyncratic, and the risk-free rate is 6%.
a. What is the NPV of launching both research efforts simultaneously?
b. What is the optimal order to stage the investments?
c. What is the NPV with the optimal staging?
3.Your engineers are developing a new product to launch next year that will require both software and hardware innovations. The software team requests a budget of $5 million and forecasts an 80% chance of success. The hardware team requests a $10 million budget and forecasts a 50% chance of success. Both teams will need 6 months to work on the product, and the risk-free interest rate is 4% APR with semiannual compounding.
a. Which team should work on the project first?
b. Suppose that before anyone has worked on the project, the hardware team comes back and revises their proposal, changing the estimated chance of success to 75% based on new information. Will this affect your decision in (a)?
4.Your firm is thinking of expanding. If you invest today, the expansion will generate $10 million in FCF at the end of the year, and will have a continuation value of either $150 million (if the economy improves) or $50 million (if the economy does not improve). If you wait until next year to invest, you will lose the opportunity to make $10 million in FCF, but you will know the continuation value of the investment in the following year (that is, in a year from now, you will know what the investment continuation value will be in the following year). Suppose the risk-free rate is 5%, and the risk-neutral probability that the economy improves is 45%. Assume the cost of expanding is the same this year or next year.
a. If the cost of expanding is $80 million, should you do so today, or wait until next year to decide?
b. At what cost of expanding would there be no difference between expanding now and waiting? To what profitability index does this correspond?
5.Assume that the project in Example 22.5 pays an annual cash flow of $100,000 (instead of $90,000).
a. What is the NPV of investing today?
b. What is the NPV of waiting and investing tomorrow?
c. Verify that the hurdle rate rule of thumb gives the correct time to invest in this case.
6.Assume that the project in Example 22.5 pays an annual cash flow of $80,000 (instead of $90,000).
a. What is the NPV of investing today?
b. What is the NPV of waiting and investing tomorrow?
c. Verify that the hurdle rate rule of thumb gives the correct time to invest in this case.