You are the manager of the MegaFoods flourmill. You need $1000$ tonnes of wheat in three months time to fulfill existing orders, but you have no room to store the wheat at the current time. Since you have already agreed upon a selling price of flour to your customers, you are concerned about potential changes in your input costs of wheat. The current spot price for wheat is $$127\mathrm{.}50$ per tonne. Three$-$month futures contracts on wheat have a current price of $$130$ per tonne $($assume each futures contract is for one tonne of wheat$).$ Margin requirements are as follows:

Initial Margin: $10\%$ of total value of the underlying position

Maintenance Margin: $5\%$ of total value of the underlying position $($marked$-$to$-$market daily$)$

a$.$ What strategy should you adopt to hedge your risk $($briefly describe strategy $($i$.$e$.$ long or short$)?$

b$.$ Given the amount of wheat you want to hedge, what is the total amount you have to deposit into your margin account at time $0($beginning of day $1)$ to establish your hedge position?

c$.$ At the end of Day $1,$ the futures price has changed to $$120$ per ton $($closing price on day $1$ is $$120).$ Based on the end of day marking to market, by how much will the value of your margin account change $($state the closing balance$)?$

d$.$ Based on the information from part b and c$,$ will you be subject to a margin call $($explain why$)$ and, if so$,$ how much money will you have to deposit into your margin account?

e$.$ At the end of Day $2,$ the futures price has changed to $$125$ per ton. What is your new closing balance?