Say that we plan to make a new computer product. We have already spent a total of ˆ I = $5M. The project will require an additional investment of I =$3M at t = 0 (now). This investment must be made now, or the project cannot proceed. Also, the product will require us to acquire some intellectual property (IP) to defend ourselves from potential lawsuits from competitors. Suppose that the cost of the IP will be 0.1St (in millions), where St is the stock price for Google Google (GOOG). That is, if Google becomes more successful, the intellectual property will be more expensive to buy. Although we must invest I at t = 0, we may choose to wait one year to acquire the IP and sell the product. Whether we choose to acquire the IP at t = 0 or t = 1, the product will go to market at t = 1 and will produce revenues of R = $65M with no additional costs.

Suppose the risk free rate is r = 2% (EAR). Also say that Google’s current stock price is $600. Suppose also that Google’s stock at t = 1 will either rise to $740 (60% chance actual probability) or fall to $580 (40% chance actual probability).

Consider the following options:

O1. Invest now (t = 0), acquire the IP now (t = 0), and produce the product at t = 1.

O2. Invest now (t = 0), but wait until t = 1 and, if conditions are favorable, acquire the IP and produce the product.

1. Compute the NPV of O1.

2. Write a formula for the NPV of O2 in terms of ˆI,I,R,S1, and r. Write your answer using the risk neutral expected value, Eq.

3. Compute the NPV of O2.

4. What do you recommend to do? Explain why.

5. Suppose that you are very bullish on Google and believe that the price is very likely to go up. Thus, you feel that waiting will result in a very high cost for buying the IP. Does this a?ect your decision making process?

6. Suppose now that you are very risk averse. Option O1 is a sure thing. Does you risk aversion cause you to favor option O1?