You are a financial analyst at Global Conglomerate and are considering entering the shoe business. You believe that you have a very narrow window for entering this market. Because of Christmas$$ demand, the time is right today and you believe that exactly a year from now would also be a good opportunity. Other than these two$$ windows, you do not think another opportunity will exist to break into this business. It will cost you $$35\mathrm{.}2$ million to enter the market. Because other shoe manufacturers exist and are public$$ companies, you can construct a perfectly comparable company.$$ Hence, you have decided to use the$$ Black$-$Scholes formula to decide when and if you should enter the shoe business. Your analysis implies that the current value of an operating shoe company is $$39\mathrm{.}7$ million and it has a beta of $1\mathrm{.}2.$However$,$ the flow of customers is$$ uncertain, so the value of the company is$$ volatile$-$your analysis indicates that the volatility is $23\%$ per year.$$Twenty percent of the value of the company is attributable to the value of the free cash flows$($cash available to you to spend how you$$ wish$)$ expected in the first year. If the$$ one$-$year risk$-$free rate of interest is $3\mathrm{.}9\%$:

a$.$ Should Global enter this business$$ and, if$$ so$,$ when?

b$.$ How will the decision change if the current value of a shoe company is $$35\mathrm{.}6$ million instead of $$39\mathrm{.}7$million$?$

c$.$ Plot the value of your investment opportunity as a function of the current value of a shoe company.

d$.$ Plot the beta of the investment opportunity as a function of the current value of a shoe company.