Question

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.

1. $-1.57 per barrel
2. $-10.08 per barrel
3. $1.57 per barrel
4. $10.08 per barrel

Please shows steps and calculations.

Answer 1

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 * e^RT

Putting values of Spot price, R and T

Forward Price of Crude at 2 years = 76 * e^{3% * 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.