Answer the following questions based on the table below. Use the Table of the Standard Normal Cumulative Distribution Function at the last page to answer question (b).

a) The 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) 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 5th 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 0.50. Risk free interest rate is 3.5% (0.035). This implies that the present value of

opening 30 restaurants at the end of year 4 equals 24,000,000/1.035^4. If he considers this option to

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.Homer Simpson plans to open a restaurant and makes the following forecast.

\begin{tabular}{l|c|c|c|c|c|} & Year 1 & Year 2 & Year 3 & Year 4 & \begin{tabular}{l} All future years \\ forever (per \\ year) \end{tabular} \\ \hline Sales & 300,000 & 600,000 & 900,000 & 1,000,000 & 1,000,000 \\ \hline Capital Expenditure & 0 & 0 & 0 & 0 & 0 \\ \hline \begin{tabular}{l} Unlevered Net \\ Income+Depreciation \end{tabular} & 130,000 & 50,000 & 80,000 & 300,000 & 300,000 \\ \hline \begin{tabular}{l} Increase in Working \\ Capital \end{tabular} & 40,000 & 30,000 & 20,000 & 20,000 & 0 \\ \hline Free Cash Flow & & & & & \end{tabular}