A wheat farmer expects to harvest 60,000 bushels of wheat in September. In order to pay for the seed and equipment, the farmer had to draw $150,000 from his savings account on January 1 this year. He earns 4.8% p. a. on the savings account, and interest on the account accrues monthly in arrears. The farmer is worried about fluctuations in the wheat price and wishes to hedge the position. Wheat futures are currently quoted as:

September 341.0 cent/bu

December 355.0 cent/bu

Prices are in cents per bushel, and wheat futures contracts are per 5,000 bushels.

1. Construct the perfect hedge for the farmer, using futures contracts. How many contracts should he buy or sell?

2. Demonstrate that your hedge is indeed perfect by comparing different developments of the wheat price between January and September to 325, 335 and 345 cents per bushel of wheat.

3. What is the break-even exchange rate the farmer must obtain, if the farmer could work for a salary instead of growing wheat from January to September for $3,500 per month (paid in arrears) and lease the land for a total of $5,000 during this period, payable in September. In this case he would leave the capital in his savings account.

4. Suppose the farmer could actually store the wheat at a cost of $1,200 per month from September to January. Assume all the wheat is harvested at the end of September, and storage costs are paid at the end of the months October to December. Should the farmer still sell the wheat forward in September, or store it until December and sell it forward in December?

5. Suppose the farmer could store up to 100,000 bushels of wheat at the same price as we used in 4), i.e. the marginal costs of storage are zero. Is there an opportunity for making money in this case?

6. Harvests are usually not that predictable. The total amount harvested depends on the weather. Unfortunately, whenever the weather is good for one farmer, it is typically good for many and the price of wheat is accordingly lower. Suppose harvests are of only two types: they are either good or bad with the following outcomes:

Good Harvest : Quantity 70,000 bu. @Price (Spot, Sept) 320 cents/bu.

Bad Harvest Quantity 50,000 bu. @Price (Spot, Sept) 360 cents/bu.

Is the hedge you constructed under 1. still optimal? As personal financial advisor to the farmer, what other strategy might you recommend?