Business Management

We are in early December 2020, and the current price of March 2021 corn futures is $4.25/bu. You manage a small ethanol plant that processes about 2m bushels of corn each month. You buy your main input (corn) on the cash market, and pay for that corn every two months. Precisely, you pay the local cash grain price on the Friday that precedes, by at least 2 business days, the last business day of February, of April, of June, etc. You sell your output (ethanol mostly) to local fuel marketers on the cash (spot) market. You are worried that corn prices will go up, and decide to hedge your first 6 months of production costs in 2021 using the following strategy:
(i) buy March 2021, May 2021, and July 2021 call options on same-month corn futures, all with the same exercise price of $4.75 per bushel in each case. You use 800 contracts in each case (equivalent to 4m bushels for each maturity).
(ii) simultaneously sell March 2021, May 2021, and July 2021 puts with an exercise price of $4.00 per bushel. All options are European.
(iii) each of those options expires on the Friday which precedes, by at least 2 business days, the last business day of the month prior to the futures contract month (for example, the option on March futures expires in late February).
(a) (7.5 points) Using a graph or a payoff table, plot or relate your expected February purchase cost per bushel to the price of corn at that time. Assume that the basis at the time is -20 cents. 4 4
(b) (2.5 points) If corn prices do go up, to what extent will this strategy provide a hedge against an increase in your production costs? Explain, possibly but not necessarily with the help of a graph.
(c) (2.5 points) If corn prices do go up, will this strategy protect the plant against catastrophic losses? Why/why not? Explain. 5 5
(d) (2.5 points) Would your answer to (c) change if you had entered into a swap to sell the ethanol at a fixed price to a local fuel marketing company? Explain.

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