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Selling with Forward Contract or on the Spot Market

A farmer faces two uncertainties regarding the revenue from selling his crop. First, the yield of the crop is uncertain: the harvest could produce a large crop of 10,000 tons or a small crop of 6,000 tons, with equal probability. Second, the spot market price at the time the crop will be sold could be high at $180 per ton, or low at $120 per ton. If the crop is large, the probability of a high market price is 50%; if the crop is small, there is a 70% probability that the market price will be high.

To manage the future price risk, the farmer can choose to sell all or part of the crop in advance with a forward contract at a price of $150/ton.

a) Construct a decision tree for the decision to sell all the crop forward, all on the spot market, or sell half forward and half on the spot market. Based on expected value, what is the best alternative?

For the remaining questions, assume that the farmers utility function for money is exponential with a risk tolerance coefficient of $200,000.

b) Based on this risk tolerance, what is the best alternative?

c) What is the lowest forward contract price acceptable to the farmer?

d) Still assuming a forward contract price of $150/ton, what percentage of the crop should the farmer sell forward?

Instructions.

Prepare an Excel file with two worksheets: one for part (a), another for parts (b), (c) and (d). For each question, type text in cells or text boxes to explain how you obtained your answer. Putting a formula in a cell that returns a numerical value is not sufficient, you need to briefly explain the logic. Clearly identify your answers by question number, so that we do not have to guess where to find them in your Excel sheet.

To incorporate the risk tolerance in question (b), you can duplicate the decision tree you built for (a). To do this, remember that you need to duplicate the entire worksheet: right-click the sheet tab, select Move or Copy and check the small box Create a copy. Copying and pasting a decision tree from one sheet into a new blank sheet will not work; you need to duplicate the entire worksheet containing the decision tree.

Inspect your file before submission to ensure everything is in order and visible. Remember to include the honor code statement at the beginning of your file.

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