Katie Watkins, an entrepreneur, believes that consolidation is the key to profit in the fragmented recreational equine industry. In particular, she is considering starting a business that will develop and sell franchises to other owner-operators, who will then board and train hunter-jumper horses. The initial cost to develop and implement the franchise concept is $8 million. She estimates a 25% probability of high demand for the concept, in which case she will receive cash flows of $13 million at the end of each year for the next 2 years. She estimates a 50% probability of medium demand, with annual cash flows of $7 million for 2 years, and a 25% probability of low demand, with annual cash flows of $1 million for 2 years. She estimates the appropriate cost of capital is 15%. The risk-free rate is 6%.

a. Find the NPV of each scenario, and then find the expected NPV.

b. Now assume that the expertise gained by taking on the project will lead to an opportunity at the end of Year 2 to undertake a similar venture that will have the same cost as the original project. The new projects cash flows would follow whichever branch resulted for the original project. In other words, there would be an $8 million cost at the end of Year 2 and then cash flows of $13 million, $7 million, or $1 million for Years 3 and 4. Use decision-tree analysis to estimate the combined value of the original project and the additional project (but implement the additional project only if it is optimal to do so). Assume that the $8 million cost at Year 2 is known with certainty and should be discounted at the risk-free rate of 6%. (Hint: Do one decision tree that discounts the operating cash flows at the 15% cost of capital and another decision tree that discounts the costs of the projectsthat is, the costs at Year 0 and Year 2at the risk-free rate of 6%; then sum the two decision trees to find the total NPV.)

c. Instead of using decision-tree analysis, use the Black-Scholes model to estimate the value of the growth option. Assume that the variance of the projects rate of return is 0.15. Find the total value of the project with the option to expandthat is, the sum of the original expected value and the growth option. (Hint: You will need to find the expected present value of the additional projects operating cash flows in order to estimate the current price of the options underlying asset.)