Six months ago you entered a forward contract for delivery of 100M barrels of crude oil. Under the term of the contract you will receive $70 per barrel at delivery 2 years from now. Today, the spot price of the same grade of crude oil is $76. Assuming that the risk free rate is 3% per year, what is the value of the forward? Assume a zero storage cost and a zero convenience yield.
Please shows steps and calculations.
Spot Price of Crude oil = $76 per barrel | Risk-free rate = 3% | Time to delivery = 2 years
Contract Price = $70 per barrel to be received at delivery
No storage cost and zero convenience yield.
First using the Spot price, we will calculate the Forward Price of Crude oil after 2 years.
Forward Price = Spot Price * eRT
Putting values of Spot price, R and T
Forward Price of Crude at 2 years = 76 * e3% * 2
Forward Price of Crude at 2 years = 76 * 1.061837
Forward Price of Crude at 2 years = $80.70 per barrel
Now both Contract Price to be received and Forward Price are at 2 years. We can calculate the Payoff of the contract at the time of delivery
Payoff of the Contract = Contract Price to be received at Deivery - Forward Price at 2 years
Payoff of the Contract = $ 70 - $ 80.70
Payoff of the Contract at Delivery in 2 years = $ - 10.70
Now we will discount the payoff to Today for two years using the risk-free rate to calculate the Value of the Forward Contract.
Value of the contract = Payoff at Delivery after 2 years * e-RT
Value of the contract = - 10.70 * e-3% * 2
Value of the contract = - 10.70 * 0.94176
Value of the Forward contract = $ - 10.08 per barrel
Hence, The Value of the Forward contract is $ - 10.08 per barrel, which is Option 2nd among the given choices.