I need a step by step explanation for the following problem involving basic hedg

Question

I need a step by step explanation for the following problem involving basic hedging. A refiner, Ref Inc., needs to buy 100,000 barrels of oil 1 year from today and again 2 years from today. The forward prices for delivery of oil in 1 year and 2 years are $91.40 and $81.41 1- and 2-year ‘default risk free’ zero-coupon bond yields are .10% and .50% A bond paying $1 at the end of yr. 1 and which matures at that date has an annual yield of .10% A bond which pays nothing at the end of yr. 1, but which pays $1 at the end of yr. 2 at which date it matures has an annual compound yield of .50% Compute the fixed swap price you would agree to pay for a 2-year swap agreement with a bank (assume all cash flows occur at the end of the year). Suppose the spot price of oil at the end of the second year equals $92. How much do you receive or pay to the bank (the counterparty). What is the effective price you pay for one barrel under the swap agreement?

Explanation / Answer

Let P be the  fixed swap price per barrel you would agree to pay for a 2-year swap agreement with a bank to buy 100,000 barrels of oil,

P/1.0011 + P/1.0052 =91.40/1.0011 + 81.41/1.0052

P(0.999 +0.990 )=91.31 + 80.60

P(1.989 )=171.91 =>P=171.91 /1.989 =86.43 $/barrel

At end of  second year if price equals $92,

Net receive from bank=$(92-86.43)*100,000 =$557,000

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