Consider a U$.$S$.-$based company that exports goods to Switzerland. The U$.$S$.$ Company expects to receive payment on a shipment of goods in three months. Because the payment will be in Swiss francs, the U$.$S$.$ Company wants to hedge against a decline in the value of the Swiss franc over the next three months. The U$.$S$.$ risk$-$free rate is $2$ percent, and the Swiss risk$-$free rate is $5$ percent. Assume that interest rates are expected to remain fixed over the next six months. The current spot rate is $$0\mathrm{.}5974$

a$.$ Indicate whether the U$.$S$.$ Company should use a long or short forward contract to hedge currency risk.

b$.$ Calculate the no$-$arbitrage price at which the U$.$S$.$ Company could enter into a forward contract that expires in three months.

c$.$ It is now $30$ days since the U$.$S$.$ Company entered into the forward contract. The spot rate is $$0\mathrm{.}55.$ Interest rates are the same as before. Calculate the value of the U$.$S$.$ Company$$s forward position.