Question

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Growth Option: Option Analysis

Fethe's 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. Fethe's cost of capital is 10%.

1. What is the expected NPV of the project? Round your answer to the nearest dollar.

   $  

2. 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 additional payment 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 the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 0.3718 and that the risk-free rate is 6%. Do not round intermediate calculations. Round your answers to the nearest dollar.

   Use computer software packages, such as Minitab or Excel, to solve this problem.

   Value of the growth option: $  

   Value of the entire project: $  

Answer 1

Part 1

Cash outflow at 0 period = $ 20,000 × 1 = $ 20,000

Cash Inflow

Year 1 = ( 0.4 × $ 25,000 + 0.6 × $ 5,000 ) × 0.909 = $11,817

Year 2 = ( 0.4 x $ 25,000 + 0.6 × $ 5,000 ) × 0.826 = $10,738

Total Cash Inflow = $ 22,555

Expected NPV = cash inflow- cash outflow = $ 2,555

Part II

Cash Outflow = $ 20,000 × 1 + $ 20,000 × 0.826 = $ 36,520

Cash Inflow = $ 22,555 ( as calculated above) + $ 13,000 × 0.751 + $ 13,000 × 0.683 = $ 41,197

Expected NPV = cash inflow - cash outflow = $ 41,197 - $ 36,520 = $4,677