Q $3($a$)$ Suppose you are the chief financial officer of Hotels International and you purchase $1,000,000$ pounds of coffee each month. You are concerned about the price of coffee three months from now. The spot price is now $$1\mathrm{.}8/$pound but it is likely to go up$.$ To protect yourself against the risk, you decide to use futures contracts. The futures contracts are for $1,000,000$ pounds of coffee, have a current price of $$2/$pound and expire in three months. Show the cash flows of the futures contracts, of the underlying transaction and of the hedge strategy if the spot price of coffee on the delivery date is $$1\mathrm{.}5/$pound$,$ $$2/$pound or $$2\mathrm{.}5/$pound$.$