4. A farmer grows and sells wheat, while a food manufacture purchases and uses w
ID: 2820795 • Letter: 4
Question
4. A farmer grows and sells wheat, while a food manufacture purchases and uses wheat to make its products. The sale and purchase of wheat by the respective parties is scheduled to occur six months from now. The following six-month-maturity options are available in the marketplace (all figures are dollars per bushel): Strike Price 4.80 4.90 5.00 5.10 5.20 5.30 Call Premium 0.56 0.50 0.44 0.39 0.35 0.30 Put Premium 0.18 0.21 0.25 0.30 0.35 0.40 Additional information; The current spot price of wheat is S5.00 per bushel. The six-month forward price of wheat is S 5.20 per bushel. The cost of production for the farmer is $4.50 per bushel (evaluated and paid at time of sale of the wheat.) The farmer produces 50,000 bushels of wheat The normal annual interest rate is 4% semi-annually a. What is the profit or loss for the farmer if he does not enter any derivative positions, and the spot price of wheat six months from now is $5.10 per bushel? Suppose the farmer buys a six-month $5.20-S5.30 strike collar on his entire crop. What's the maximum possible profit? Suppose the food manufacture needs to buy 50,000 bushels of wheat from the farmer, and wants to spend exactly $260,000 (exclusive of the derivatives price) in making this purchase. Name two different ways that will guarantee this purchase price and explain your answer b. c.Explanation / Answer
a) The cost of production for the farmer is = $4.50
The spot price of wheat 6 months from now is = $5.10
Therefore, profit made by farmer is = $5.10 - $4.50 = $0.60
The profit made by farmer by selling 50,000 bushels of wheat is
= 50000 x 0.60 = $30,000
b) Farmer buys a 6 month $5.20-$5.30 strike collar indicates that farmer buys $5.20 strike price put option for premium $0.35 and sell $5.30 strike price call option for premium $0.30.
The effective price the farmer paid on one strike collar option is
= $0.35 - $0.30 = $0.05
The maximum profit is realized by farmer when the wheat price reaches $5.30.
The cost of production for the farmer is = $4.50
The cost including the collar strategy is = $4.50 + $0.05 = $4.55
The maximum profit earned on $5.20-$5.30 strike collar is
= 5.30 – 4.55 = $0.75
The profit made by farmer on 50,000 contracts is
= 50000 x 0.75 = $37,500
C) One way in which the food manufacturer can buy 50,000 bushels of wheat from farmer by spending exactly $260,000 is by entering into 6 months forward contract to purchase wheat for $5.20 per bushels.
= 5.2 x 50000 = 260,000
Another way is by purchasing 50,000 call options contract with $5.20 strike price (since they have mentioned exclusive of derivative price).
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