Consider a manufacturing project (e.g., colored bowling balls). In the first year, if demand is high (probability 60%), the expected cash flow will be 100, if demand is low (probability 40%), the expected cash flow will be 50. If demand is high in the first year, there is an 80% probability that it will also be high in year 2, with an expected cash flow of 410, and a 20% probability it will be low in year 2, with an expected cash flow of 180. On the other hand, if demand is low in the first year, there is only a 40% probability that it will be high in year 2, with an expected cash flow of 220, and a 60% probability that it will be low in year 2, with an expected cash flow of 100. This decision tree, with cash flows and probabilities is given in the Excel spreadsheet. Also, think of the year 2 cash flows as including the value, at time 2, of all subsequent expected cash flows.

a. What is the expected cash flow at time 2, if demand is high in year 1? What is the expected cash flow at time 2, if demand is low in year 1? (Note that these are just expected cash flows. No discounting is necessary, yet.)

b. What are the time 1 and 2 expected cash flows before knowing whether demand will be high or low in years 1 or 2?

c. If the project requires an initial investment of 250 at time 0, what is its NPV of this project at a discount rate of 10%?

d. Now assume that there is an expansion option embedded in the project. At time 1, the firm can invest an additional 250 to scale up the project. This expansion will only make sense if demand is high in the first year. If demand is high in the first year, and the firm decides to expand, the expected cash flows in year 2 are 800 if demand is high in year 2 (probability 80%) and 100 if demand is low (probability 20%). These time 2 numbers are 2 total expected cash flows in year 2, i.e., they include the cash flows generated from the initial investment (given above) and those from the expansion. In other words, if they dont expand, they receive 410 or 180 at time 2, if they do expand, they receive 800 or 100, assuming demand is high in year 1. What is the total expected cash flow in year 2, if demand is high in year 1 and they undertake the expansion? What is the incremental expected cash flow in year 2 associated with exercising this expansion option, assuming demand was high in year 1, i.e., the expected cash flow over and above what would have been expected had they not expanded?

e. Assuming demand in year 1 is high, what is the incremental expected cash flow at time 1 associated with undertaking the expansion option?

f. What is the value at time 1, when the decision must be made, of this expansion option, assuming demand is high in year 1? (Use the same 10% discount rate.)

g. What are the total expected cash flows on the project, assuming this expansion option is exercised at time 1 if demand is high in year 1? (Note that the expansion option should be exercised if the value in part f is positive, which it should be if you have done the calculations correctly.) What is the NPV of these expected cash flows at a discount rate of 10%?

h. What is the value at time 0 of the expansion option, before you know what demand will look like in year 1? (Use the same 10% discount rate.)