Plains States Manufacturing has just signed a contract to sell agricultural equipment to Boschin, a German firm, for euro $1,000,000.$ The sale was made in June with payment due six months later in December. Because this is a sizable contract for the firm and because the contract is in euros rather than dollars, Plains States is considering several hedging alternatives to reduce the exchange rate risk arising from the sale. To help the firm make a hedging decision you have gathered the following information.

$$ The spot exchange rate is $$1\mathrm{.}40/$euro

$$ The six month forward rate is $$1\mathrm{.}38/$euro

$$ Plains States' cost of capital is $11\%$ p$.$a$.$

$$ The Euro zone $6-$month borrowing rate is $9\%$ p$.$a$.$

$$ The Euro zone $6-$month lending rate is $7\%$ p$.$a$.$

$$ The U$.$S$.6-$month borrowing rate is $8\%$ p$.$a$.$

$$ The U$.$S$.6-$month lending rate is $6\%$ p$.$a$.$

$$ December put options on euro: strike price $$1\mathrm{.}39/$euro$,$ premium is $1\mathrm{.}5\%$

$.$ December call options on euro: strike price $$1\mathrm{.}42/$euro$,$ premium is $2\mathrm{.}0\%$

$$ Plains States' forecast for $6-$month spot rates is $$1\mathrm{.}43/$euro

$$ The budget rate, or the lowest acceptable sales price for this project, is $$1,350,000$ or $$1\mathrm{.}35/$euro

a$)$ Suppose the spot rate in six months is as the Plains States$$ expectation. If Plains States chooses not to hedge their euro receivable, what is the amount they receive in six months?

b$)$ If Plains States chooses to hedge its transaction exposure in the forward market at the available forward rate, what is the payoff in $6$ months? If the expected $6$ month spot rate is $$1\mathrm{.}43/$euro$,$ how do you compare your payoff hedged in the forward market with the unhedged alternative from part a$)?$ Please show your work in details.

c$)$ If Plains States chooses to hedge its transaction exposure in the money market as the above given rates, what is the payoff in $6$ months? Compare your payoff from the money market hedge in $6$ months with the payoff from the forward market hedge in $6$ months? What is the break$-$even investment rate between forward hedge and money market hedge? Please show your work in details.

d$)$ If Plains States chooses to hedge its transaction exposure in the option market as the above given information, what is the payoff in $6$ months? Suppose the spot rate in $6$ months is $$1\mathrm{.}43/$euro$,$ would Plains States exercise its option? What is the break$-$even price on the option compared with the other strategies? What is the upper bound of the range? What is the lower bound of the range?

e$)$ Which alternative should Plains States choose if it is willing to take a reasonable risk and has a directional view that the euro may be appreciating versus the dollar during the next six months? If a figure$/$diagram can be used to help me understand this concept, it will be greatly appreciated.