Fethes Funny Hats is considering selling trademarked, orange-haired curly wigs for University of Tennessee football games. The purchase cost for a 2-year franchise to sell the wigs is $20,000. If demand is good (40% probability), then the net cash flows will be $25,000 per year for 2 years. If demand is bad (60% probability), then the net cash flows will be $5,000 per year for 2 years. Fethes cost of capital is 10%.

a. What is the expected NPV of the project?

b. If Fethe makes the investment today, then it will have the option to renew the franchise fee for 2 more years at the end of Year 2 for an investment of $20,000. In this case, the cash flows that occurred in Years 1 and 2 will be repeated (so if demand was good in Years 1 and 2, it will continue to be good in Years 3 and 4). Use decision-tree analysis to calculate the expected NPV of this project, including the option to continue for an additional 2 years. What is the value of the option to grow itself using decision tree analysis?

c. Using the Black-Scholes model to estimate the value of the option. Assume that the variance of the projects rate of return is 0.2025 and that the risk-free rate is 6%.

d. If the variance of the projects rate of return was not given, how would you estimate?