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 $$40,000.$ Your pro$-$forma calculations show that an estimated $$6,000$ would be coming in each year in after$-$tax profits for the next $9$ 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 $65\%.$ 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 $8$ more of such products to your production line and this would take place when the first $9-$year pilot product project is over.

In general, a higher volatility $($see given$)$ the project expansion.

In order to calculate the value of the possibility of this expansion one can use the BlackScholes 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!