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 $10\%.$

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

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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 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 $0\mathrm{.}3936$ and that the risk$-$free rate is $7\%.$ 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: $ $q,$

Value of the entire project: $