$6.$ A large food company in the U$.$S$.$ has forward contracted with a New Zealand firm to take delivery of $100,000$ pounds of frozen lamb for $1\mathrm{.}10$ New Zealand dollars $($NZD$)$ in three months. The company is concerned about potential changes in the exchange rate between the U$.$S$.$ dollar $($USD$)$ and the New Zealand dollar. To protect itself from exchange rate risks, the company decides to hedge its future exchange using NZD$/$USD futures. The current spot exchange rate between the NZD and the USD is $0\mathrm{.}8225($it takes $0\mathrm{.}82$ USDs to buy one NSD$).$ NZD$/$USD futures $($three months out$)$ are currently trading at $0\mathrm{.}8205.$ NZD$/$USD futures have a contract size equal to $100,000$ NZDs$.($a$)$ What position should the company take to hedge its future currency exchange? $($b$)$ If the company had to pay for the lamb today, how much would they have to pay in USDs in total for their purchase? $($c$)$ How many contracts should the company trade to fully hedge its exchange rate risk? Assume that three months have elapsed, and the lamb has been delivered to the food company. The New Zealand firm is waiting for payment. The spot exchange rate for NZD$/$USD is $0\mathrm{.}8471$ and the futures are trading at $0\mathrm{.}8469.($d$)$ Without the hedge how much would the company have to pay for the lamb in USDs? $($e$)$ How much will the company have to pay for the lamb considering that they hedge in the futures market? $($f$)$ Using the result from part $($d$)$ above, what is the realized exchange rate for NZDs$?($g$)$ If you use the formula S$2-($F$2-$ F$1)$ to calculate a "realized hedge price" what is the realized exchange rate? $($h$)$ Explain the difference between your answer in part $($f$)$ and part $($g$).$