$|$Chapter $26$: Growth option

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

$$23,000.$ If demand is good $(40\%$ probability$),$ then the net cash flows will be $$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?

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 $$23,000.$ Use the

Black$-$Scholes option pricing model to estimate the value of the growth option.

Calculate the variance of the project's rate of return using the indirect approach. The

risk$-$free rate is $6\%.$

c$.$ What is the value of the project, including the growth option?

$C=P^{**}N(d_1)-x{e}^{-r}{f}_f^{T}N(d_2)$

$d_1=\frac{ln(\frac{P}{x})+(r_f+\frac{{}^2}{2})(T)}{\sqrt[\phantom{2}]{{}^2}\sqrt[\phantom{2}]{T}}$

$d_2=d_1-\sqrt[\phantom{2}]{{}^2}\sqrt[\phantom{2}]{T}$

a$.-438$

b$.P=18,646,{}^2=0\mathrm{.}225d1=0\mathrm{.}201d2=-0\mathrm{.}47,C=4,290$

c$.3,852$