$$ Cray Research sold a super computer to the Max Planck Institute in Germany on credit and invoiced $13\mathrm{.}20$ million payable in six months. Currently, the six$-$month forward exchange rate is $$1\mathrm{.}26/$ and the foreign exchange advisor for Cray Research predicts that the spot rate is likely to be $$1\mathrm{.}21/$ in six months.

$($a$)$ What is the expected gain$/$loss from the forward hedging?

$($b$)$ If you were the financial manager of Cray Research, would you recommend hedging this euro receivable? Why or why not?

$($c$)$ Suppose the foreign exchange advisor 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?

$($d$)$ Suppose now that the future spot exchange rate is forecast to be $$1\mathrm{.}33/.$ Would you recommend hedging? Why or why not?