A U$.$S$.$ firm expects an outflow of $300,000,000$ Bangladeshi Taka $($BDT$)$ in six months. Today's spot exchange rate is $0\mathrm{.}013$ US$$/$BDT$.$ The firm decides to hedge using options. The US $ interest rate is $4\mathrm{.}50\%$ and the BDT interest rate is $5\mathrm{.}75\%.$ The firm contacts JPMorgan Chase, which offers the following options on the BDT:

American call option on the BDT with $T=9$ months, $K=0\mathrm{.}014$ US $\frac{\text{\$}}{B}DT,$ and a price $C=0\mathrm{.}0003$ US$$/$BDT

American put option on the BDT with $T=9$ months, $K=0\mathrm{.}014$ US$$/$BDT$,$ and a price $P=0\mathrm{.}0020$ US$$/$BDT

American call option on the BDT with $T=6$ months, $K=0\mathrm{.}014$ US$$/$BDT$,$ and a price $C=0\mathrm{.}00025$ US$$/$BDT

American put option on the BDT with $T=6$ months, $K=0\mathrm{.}014$ US$$/$BDT$,$ and a price $P=0\mathrm{.}0018$ US$$/$BDT

Answer the following questions, assuming that these options have no resale value, and ignoring transaction costs.

A$.$ Which option should the firm choose and why?

B$.$ What is the maximum value in US$$/$BDT that the firm can establish in this hedge?

C$.$ Suppose that six months later $($i$.$e$.,$ at the time when the firm pays $300$ million BDT$)$ the spot exchange rate is $0\mathrm{.}013$ US $\frac{\text{\$}}{B}DT.$ What should the firm do$?$ How many US $ will the firm pay for the $300$ million BDT$,$ after considering the initial cost of buying the option?

D$.$ Now suppose that at the time $($six months later$)$ the firm pays $300$ million BDT the spot exchange rate is $0\mathrm{.}015$ US $\frac{\text{\$}}{B}DT.$ What should the firm do$?$ How many US $ will the firm pay for the $300$ million BDT$,$ after considering the initial cost of buying the option?