21st Century Educational Products (21st Century) is a rapidly growing software company; and consistent with its growth, it has a relatively large capital budget. While most of the company€™s projects are fairly easy to evaluate, a handful of projects involve more complex evaluations.
John Keller, a senior member of the company€™s finance staff, coordinates the evaluation of these more complex projects. His group brings their recommendations directly to the company€™s CFO and CEO, Kristin Riley and Bob Stevens, respectively.
a. In recent months, Keller€™s group has begun to focus on real option analysis.
(1) What is real option analysis?
(2) What are some examples of projects with real options?
b. Considering real options, one of Keller€™s colleagues, Barbara Hudson, has suggested that instead of investing in Project X today, it might make sense to wait a year because 21st Century would learn more about market conditions and would be better able to forecast the project€™s cash flows. Right now 21st Century forecasts that Project X will generate expected annual net cash flows of $33,500 for 4 years. However, if the company waits a year, it will learn more about market conditions. There is a 50% chance that the market will be strong and a 50% chance that it will be weak. If the market is strong, the annual cash flows will be $43,500. If the market is weak, the annual cash flows will be only $23,500. If 21st Century chooses to wait a year, the initial investment will remain $100,000 and cash flows will continue for 4 years after the initial investment is made. Assume that all cash flows are discounted at 10%. Should 21st Century invest in Project X today, or should it wait a year before deciding whether to invest in the project?
c. Now assume that there is more uncertainty about the future cash flows. More specifically, assume that the annual cash flows are $53,500 if the market is strong and $13,500 if the market is weak. Assume that the upfront cost is still $100,000 and that the WACC is still 10%. Will this increased uncertainty make the firm more or less willing to invest in the project today? Explain.
d. 21st Century is considering another project, Project Y. Project Y has an up-front cost of $200,000 and an economic life of three years. If the company develops the project, its after-tax operating costs will be $100,000 a year; however, the project is expected to produce after-tax cash inflows of $180,000 a year. Thus, the project€™s estimated cash flows are as follows:

(1) The project has an estimated WACC of 10%. What is the project€™s NPV?
(2) While the project€™s operating costs are fairly certain at $100,000 per year, the estimated cash inflows depend critically on whether 21st Century€™s largest customer uses the product. Keller estimates that there is a 60% chance that the customer will use the product, in which case the project will produce after tax cash inflows of $250,000. Thus, its net cash flows will be $150,000 per year. However, there is a 40% chance that the customer will not use the product, in which case the project will produce after-tax cash inflows of only $75,000. Thus, its net cash flows will be -$25,000. Write out the estimated cash flows and calculate the project€™s NPV under each of the two scenarios.
(3) While 21st Century does not have the option to delay the project, it will know one year from now whether the key customer has selected the product. If the customer chooses not to adopt the product, 21st Century has the option to abandon the project. If 21st Century abandons the project, it will not receive any cash flows after Year 1 and it will not incur any operating costs after Year 1. Thus, if the company chooses to abandon the project, its estimated cash flows will be as follows:

Again, assuming a WACC of 10%, what is the project€™s expected NPV if it abandons the project? Should
21st Century invest in Project Y today, realizing it has the option to abandon the project at t ¼ 1?
(4) Up until now, we have assumed that the abandonment option has not affected the project€™s WACC. Is this assumption reasonable? How might the abandonment option affect the WACC?
e. Finally, 21st Century is also considering Project Z. Project Z has an up-front cost of $500,000, and it is expected to produce after-tax cash inflows of $100,000 at the end of each of the next five years (t = 1, 2, 3, 4, and 5). Because Project Z has a WACC of 12%, it clearly has a negative NPV. However, Keller and his group recognize that if 21st Century goes ahead with Project Z today, there is a 10% chance that this will lead to subsequent opportunities that have a net present value at t = 5 equal to $3,000,000. At the same time, there is a 90% chance that the subsequent opportunities will have a negative net present value (-$1,000,000) at t = 5. On the basis of their knowledge of real options, Keller and his group understand that the company will choose to develop these subsequent opportunities only if they appear to be profitable at t = 5. Given this information, should 21st Century invest in Project Z today? Explain your answer.

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Cash Outflows ($200,000) (100,000) (100,000) (100000) Year Cash Inflows Net Cash Flows 180,000 180,000 180,000 ($200,000) 80,000 80,000 80,000 0 2 60% probability 200,000 150,000 150,000 150,000 40% probability 200,000 -25,000