$($CHAPTERS $22-23)$

You and your brothers have just had a great

idea for a new product, and you would like to

try to bring it to life. You would need to

immediately spend $$35,000.$ Your pro$-$forma

calculations show that an estimated $$5,000$

would be coming in each year in after$-$tax profits for the next

$8$ years. You believe $10\%$ is appropriate to use for the discount

rate.

Unfortunately, according to these numbers the NPV of this pilot

project is negative $($which can be verified$).$ Fortunately, though,

you and your brothers completely disagree on how much profit

may be coming in each year. The volatility of these annual profits

is $54\%.$ What this means is that if for this pilot project the profits

turn out much higher, then you all agree that expanding this

business might make a lot of sense. The expansion would involve

adding $10$ more of such products to your production line and this

would take place when the first $8-$year pilot product project is

over.

In general, a lower volatility $($see given$)$

makes it less worth it to do

the project expansion.

In order to calculate the value of the possibility of this

expansion one can use the Black$-$Scholes formula. In this

formula, the equivalent of the "current stock price" equals

$,$ which is nothing but

HINT: You will not need to use some numbers that are given in

this problem!