Question

Problem #2 Consider a farmer who is scheduled to harvest wheat at time T. Imagine that the spot price of wheat at time T is equal to 100 per bushel. What is the total income of the farmer is she sells her wheat - 500 bushels in total - right after it is harvested? Imagine that at time t the farmer chooses to sell 5 futures contracts that stipulate that 100 bushels of wheat be delivered at time T per contract. What is the total income of the farmer if a futures contract costs 100 at time t and stipulates that 100 bushels be delivered at time T? Assume that the spot price of wheat at time T is equal to 150 per bushel. iii) Does the farmer gain from holding the futures contract from period t to T? iv) What is the payoff to a mill-operator who purchased 5 futures contracts at time and accepted delivery at time T?

Answer 1

(i) Spot price of wheat = $100 per bushel (Assuming transaction unit as USD)

Total quantity sold by the farmer = 500 bushels

Total income = 500 x 100 = $50,000

(ii) No. of future contracts taken by farmer at time t = 5

Quantity of wheat promised per contract at T time = 100 bushels

Cost of future contract = $100

Total income the farmer receives on delivery at time T = Value of wheat per contract x no. of

contracts

= (100 x 100) x 5

= $50,000  

(iii) From part (ii) we know that spot price of wheat is $150 per bushel at time T.

With 5 future contracts worth 100 bushels for $150 each, the total income of the farmer without a

future contract would be (100 x 150) x 5 = $75,000

Loss to the farmer = $75,000 - $50,000 = $25,000

Thus, by holding the future contract from t to T, the farmer lost $25,000 i.e. $50 per 100 bushels per contract.

(iv) The mill-operator purchased the futures contract and ends up paying $25,000 less at time T than she would have paid if the trade was taking place in a spot market.  Thus, her pay-off is

$75,000 -($50,000) = $25,000