Homer Simpson plans to open a restaurant and makes the following forecast. a$)$ Discount rate is $20\%.$ Building cost at Year $0$ is $800,000.$ What is the net present value of the project? Should Homer undertake the business or not?

b$)(15\%)$ Now, he thinks of another possibility. Instead of just opening a restaurant, he considers an option to expand. If his first restaurant $($a pilot restaurant$)$ turns out to be successful at the end of year $4,$ he will open $30$ more restaurants at the end of year $4.$ Each of these restaurants will create cashflow from $5$th year $($from now$)$ to all future years forever. Cashflow estimate of these restaurants are exactly the same as described in the table above. Homer Simpson estimates the standard deviation of the $30$ restaurants$$ aggregate cashflow total to be $0\mathrm{.}50.$ Risk free interest rate is $3\mathrm{.}5\%(0\mathrm{.}035).$ This implies that the present value of

opening $30$ restaurants at the end of year $4$ equals $24,000,000.$ If he considers this option to $1\mathrm{.}0354$

expand, should he undertake his first restaurant or not? $($Assume that if he does not start his pilot restaurant, he cannot have an option to expand at the end of year $4).$ Use the Black Sholes Model of the lecture note $7$ and the table $1$ at the end of this problem set.