# PS6Answers - Problem 1 Part 1 The farmer can hedge...

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Problem 1) Part 1 The farmer can hedge perfectly by selling the September wheat forward. For selling 60,000 bushels he Part 2 No matter what the exchange rate is, the revenue of the farmer is \$3.41*60,000=\$204,600 from the forward sale. Commodity contracts are typically not cash-settled, but you can compute notional gains/losses: Quantity 60000 Futures price \$3.41 Wheat spot price \$3.25 \$3.35 \$3.45 Notional gain on futures \$9,600 \$3,600 -\$2,400 Hypothetical revenue \$195,000 \$201,000 \$207,000 from spot sale Total \$204,600 \$204,600 \$204,600 Part 3 There are slightly different ways of doing this. First, compute the present value of the farmer's salary as of January 1st, using a monthly discount rate of 0.4% (4.8%/12): \$30,879.13 To this you have to add the \$150,000 the farmer can leave in his bank account in January. Then the total costs from these two items in January are: \$180,879.13 The future value as of September 30 is then: \$187,495.94 To this you have to add the opportunity costs of leasing the land, assuming the lease payment for the land would be due at the end of September: \$192,495.94 breakeven rate for the wheat price is found by dividing \$192,495.94 by 60,000 bushels to obtain the break even price per bushel: \$3.208 Hence, for a wheat price below \$3.208 the farmer does not break even anymore. Part 4 The farmer could also store the wheat and wait until December. Compute the gain from this as of September 30. Then you have to compare the \$204,600 the farmer makes from selling in September with the present value from selling in December, minus the present value of the storage costs. This gives: Present value of sale in December \$208,389.31 PV of storage costs \$3,571.39 Total \$204,817.92 Net (deduct opportunity costs) \$217.92 Hence, selling in December and storing in the months from September to December gives the farmer a small gain of \$217.92. Part 5 In this case the answer is clear without calculations from part 4: the farmer can store an addtional 40,000 bushels at no costs, hence the profit margin must be bigger than in part 4, where the storage costs where needs to sell 60,000/5,000 = 12 September wheat contracts. This is the total dollar amount the farmer could make from not growing wheat . Hence the

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factored in. In this case the farmer should buy 40,000 bushels of September wheat and sell forward in December. The total gain is: Costs from purchase \$136,400.00 Revenue from Sale \$140,600.00 PV(Revenue) \$138,926.21 Net gain (as of Sept) \$2,526.21 The net profits on this operation are \$2526.21. Part 6 Now the farmer is not hedged perfectly anymore. If he sold the 60,000 forward in September and the harvest turns out bad, he would have to buy 10,000 bushels because he is short this amount in the spot market at 360 cents per bushel. On these he would make a loss. Good harvest Bad harvest Revenues \$236,600.00 \$168,600.00 Other strategies may be available which involve options. These include: a) The farmer could stick to the futures hedge and buy call options on the 10000 bushels. This would hedge the downside in the bad harvest, he would still have price risk in the good harvest.
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