In: Finance

# Six months ago you entered a forward contract for delivery of 100M barrels of crude oil....

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

## Solutions

##### Expert Solution

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.

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