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 $\backslash (\backslash$$ $20,000\backslash ).$ If demand is good $(\backslash (40\backslash \%\backslash )$ probability$),$ then the net cash flows will be $\backslash (\backslash$$ $25,000\backslash )$ per year for $2$ years. If demand is bad $(\backslash (60\backslash \%\backslash )$ probability$),$ then the net cash flows will be $\backslash (\backslash$$ $5,000\backslash )$ per year for $2$ years. Fethe's cost of capital is $\backslash (10\backslash \%\backslash ).$

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

$\backslash (\backslash$$ $\backslash )$

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 $\backslash (\backslash$$ $20,000\backslash ).$ 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 $0\mathrm{.}3153$ and that the risk$-$free rate is $\backslash (8\backslash \%\backslash ).$ 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: $\backslash (\backslash$$ $\backslash )$

Value of the entire project: $\backslash (\backslash$$ $\backslash )$