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Maximizing Profits of Corn Production and Sale and Hedging Against Adverse Fluctuations in Corn Pric

## Price of Corn for Maximum Profits

For illustrative purposes, assume that all cash flows occur at the end of the year (i.e. assume that all corn is purchased and ethanal produced and sold at the end of the year).  This way, there is no adjustment for time value of money required to calculate profit.
a)If all of the above assumptions hold, what is the price of corn for which profits are maximized?  Calculate the maximum profit you can earn. [8 Marks]

Suppose that the price of corn will follow the following distribution one year from now:
Corn Price    Probability
1.00                   0.25
2.00                   0.25
3.00                   0.25
4.50                   0.25

The following one-year call options are available on the price of corn.  The risk free rate is 5% compounded continuously:

Strike Price    Call Premium
1.50                        1.24
2.00                        0.85
2.50                        0.55

The one year forward price of corn is 2.79 per bushel.
b)Given the information above, list at least 7 of the possible hedging strategies that you can use to hedge against adverse fluctuations the price of corn (i.e. possible combinations of derivatives above that apply).  No calculations are required for this question, you’re answer should be a list. HINT: there are 10 in total.
c)Calculate the expected unhedged after-tax profit on the production and sale of corn.

d)Calculate the expected after-tax profit for all possible hedging strategies that you listed in part b. State which hedging strategy results in the highest expected profit.
e)Explain why reducing earnings volatility in a progressive tax environment can improve expected after-tax profit.
Question 2
The expected rate of return on the stock index S is 12%.  The continuously compounded risk-free rate of return is 5%.  The continuously compounded dividend yield on the stock index is 2%.  The current price of S is 100.  You are considering two different options to purchase this stock: 1) an outright purchase, and 2) a long forward contract with a maturity date 1 year from today.
a)Calculate the expected stock price one year from today.
b)Calculate the expected profit on the long forward one year from today, assuming the forward is currently priced at the no-arbitrage level.

Explain why the expected profit on the long forward (at maturity, which is one year from today) is different than the expected change in stock price (i.e. the expected price of S one year from now minus the current price of S).