$(6$ points$)$ IBM US Commercial Computer Operations sold a state$-$of$-$the$-$art mainframe computer system to the Institute of Molecular Pathology and Immunology of the University of Porto in Portugal on credit and invoiced $10$ million payable in six months. Currently, the six$-$month forward exchange rate is $$\frac{1\mathrm{.}10}{}$ and the Treasury Department's foreign exchange analyst for IBM predicts that the spot rate is likely to be $$\frac{1\mathrm{.}05}{}$ in six months a$.$ What is the expected gain$/$loss from the forward hedging? Show all calculations as part of your response.

b$.$ If you were the financial manager of IBM, would you recommend hedging this euro receivable? Why or why not?

c$.($Graduate only$)$ Suppose the foreign exchange analyst predicts that the future spot rate will be the same as the forward exchange rate quoted today. Would you recommend hedging in this case? Why or why not?