Question

A farmer currently holds 6,000 bushels of corn. The local mill is offering a price of $3.25 per bushel. Currently, a three-month futures contract is trading at $3.45. The farmer is considering selling to the local mill or holding the corn in inventory and selling a futures contract now. The farmer can store and insure the corn at a cost of 18 cents per bushel per annum to be paid monthly in advance at the beginning of each month. Interest rates are 9%, continuously compounded.

             (a)       Calculate total carrying cost of 6,000 bushels of corn.

(b)       What is the theoretical price for a three-month futures contract.

(c)       What is the best strategy for the farmer to minimize risk and maximize gain? Explain why.

(d)      What is the basis today?

Answer 1

Solution

From the data we find that Total Corn Bushels = 6000 Price at Local Mill - $ 3.25 per bushel Store and insure cost = 18 cents per bushel per annum Price of three-month future Contract = $ 3.45 per bushel Interest Rate = 9% per annum (continuously compounded) a). Carrying Cost of 6000 bushels Duration - 3 months = 1/4 year = 25 year carrying cost for 6000 bushels is computed as Carrying cost per bushel * Duration * 6000 = 18 cent *.25 * 6000 = 27000 cents Carrying Cost of 6000 bushels = $ 270 (for three Months) b). Theoretical Price of the three-month future contract = (Current price * No of bushels) + Interest Earned on the amount for 3 months = (3.25 * 6000) + ((19500 *(1+0.09)^1/4) - 19500) = 19500 + ((19500(1.09) -0.25) - 19500) = 19500 + 424 = 19924 = 19924/6000 Theoretical Price of the three-month future contract = 3.32 per bushel c). Best Strategy If Sells today and earn interest on the amount for 3 months He/she will get 19924 (from B) If holds and sells the futures contract for three months = 3.45 * 6000 - 270 (holding/carrying cost) He/she will get = 20430 The best Strategy is to Hold the corn and sell 3-moth futures contract @ 3.45 Because it will give us additional profit of $ 506 d). Basis Today is 1. Interest Rate - if it increases then Holding become more expensive and if it decreases it more favourable to hold 2. Holding/carrying Cost - If increase it is more expensive to hold and if it decreases holding become cheaper