1. Suppose a project is dependent on whether there is a good economy and whether a com- petitor enters the market. If there is no competitor, the project will produce $50 million in a good economy and $15 million in a poor economy. If there is a competitor, the project will produce $30 million in a good economy and $10 million in a poor economy. The probability of a good economy is 60%, versus 40% for a poor economy; and the probability for a competitor to enter the market is 30%, versus 70% for no competitor.
a) Find the expected value of the cash flow from the project.
b) Assume the project cannot begin for three years and has a risk-adjusted dis- count rate of 18%. Calculate the present value of the project’s expected cash flow.
c) Using the calculation from part b, calculate the expected three-year holding- period return, the variance of the three-year holding-period return, and the standard deviation of the three-year holding-period return.
d) Adjust the variance and the standard deviation in part c to annual terms.
2. Assume that the project in Problem 5 is valuable if it can generate a cash flow above $25 million. A decision on whether to develop the project at a cost of $6.5 million needs to be made today if the project is to be implemented in three years. Given a 5% annual risk-free rate and the calculations from Problem 5, generate a binomial tree (each stage of the tree being one year) to value the development option and make a decision.