Consider a commodity purely held for investment purposes. Today, a company enter

Question

Consider a commodity purely held for investment purposes. Today, a company enters into a long position in 50 forward contracts (each on 100 units of the commodity) to hedge the purchase of 5,000 units of the commodity in 9 months. The spot price of the commodity is $1,250 per unit. The risk-free rate of interest is 4% per annum with continuous compounding. The 9-month storage cost per unit of the commodity is $10, payable at the end of the contract. A. What is the 9-month forward price per unit of the commodity today? B. Note that the price in (A) is the delivery price of the forward contract. What is the value of the long position today? C. Three months later, the spot price per unit of the commodity is $1,275. What is the forward price per unit of the commodity? What is the value of the long position?

Explanation / Answer

Per unit Purchase price in spot market=$1,250=

Value of $1,250 after 9 months (0.75 years)at 4% continuous compounding=1250*(e^(0.04*0.75))= $ 1,288.0682

Cost of storage paid at the end of 9 months=$10

Delivery price of the forward contract per unit=(1288.0682+10)=$1,298.0682

.A. FORWARD PRICE PER UNIT TODAY=$1298.07

Total delivery price=5000*1298.0682= $ 6,490,341

.B. Value of the long position today=6490341/(e^(0.04*0.75))= $ 6,298,522

.C.Spot price after 3 months=$1,275

Number of months to settlement =6 months=0.5 years

Value of $1,275 at the time of settlement=1275*(e^(0.04*0.5))= $ 1,300.76

Assuming storage cost remains same =$10 per unit

Forward price per unit=$1300.76+$10=$1,310.76

Value of the long position =(5000*1310.76)/(e^(0.04*0.5))= $   6,424,026

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