Homework SourseSuppose that oil forward prices for 1 year 2 years and 3 yea
Suppose that oil forward prices for 1 year, 2 years, and 3 years are $57, $68, and $73 per barrel. The 1-year effective annual interest rate is 5.7%, the 2-year interest rate is 6.0%, and the 3-year interest rate is 6.6%. What is the fixed per-barrel price in a 3-year swap that calls for delivery of 4 barrels of oil at the end of the first year, 2 barrels the second year, and 2 barrels the third year?
a. $65.64
b. $63.37
c. $58.24
d. $57.16
e. $74.40
Suppose a dealer is paying the fixed rate and receiving the floating rate in a 2-year commodity swap. The dealer could best hedge this position by taking..
a. a long position in the 2-year forward contract only.
b. short positions in the 1-year and 2-year forward contracts on this commodity.
c. a short position in the 1-year forward contract, and a long position in the 2-year forward contract.
d. long positions in the 1-year and 2-year forward contracts on this commodity.
e. a long position in the 1-year forward contract, and a short position in the 2-year forward contract.
Solution
The swap demands delivery of 4 barrels at the end of Year 1, 2 barrels at the end of Year 2 and 2 barrels at the end of Year 3.
Cash Outflows would be (4 x 57) = $ 228 at the end of Year 1, (2 x 68) = $ 136 at the end of Year 2 and (2 x 73) = $ 146 at the end of Year 3.
The total PV of the aforementioned cash flows discounted at the time specific interest rates should be equal to the cash flow when the fixed oil rate prevails.
Let the fixed rate of oil be $ K per barrel.
Therefore, PV of Cash Flows under the fixed rate = P1 = (4 x K) / (1.057) + (2 x K) / (1.06)^(2) + (2 x K) / (1.066)^(3) = K x 7.21533
PV of Cash Flows under variable rate = P1 = (4 x 57) / 1.057 + (2 x 68) / (1.06)^(2) + (2 x 73) / (1.066)^(3) = $ 457.27
P1 = P2
K x 7.21533 = 457.27, K = $ 63.375 or $ 63.37 approximately.
Hence, the correct option is (b).
NOTE: Please raise a separate query for the solution to the remaining unrelated question.
