Suppose that a commoditys respective forward prices for 1 ye

Suppose that a commodity’s respective forward prices for 1 year and 2 years are $130 and $140. The 1-year effective annual interest rate is 6.3%, and the 2-year interest rate is 5.7%. You will pay a fixed rate of $134.87559 in a 2-year swap and receive the floating rate. At the time you enter the swap contract, its value to you is..

.Answers: a. $–0.0280 b. $0.0280 c. $0.0000 d. $0.0323 e. $–0.0323

Please show proper formulas and explanations. Thank you!

Solution

Value of Swap = PV of Fixed leg - PV of Floating leg

Fixed leg is given @$134.87559 and we just need to calculate its PV

Calculation of PV of fixed leg = Fixed rate * PV discounting factor (for each year)

Discount factor for Yr 1 = 1/(1+6.3%) = 0.940734

Discount factor for yr 2 = 1/(1+5.7%)^2 = 0.895056

therefore, PV of fixed leg = 134.87559 *0.940734 + 134.87559 * 0.895056

= 247.6032

Calculation of PV of Floating Leg = Forward rate * discount factor (for each year)

Discount factor is the same as above

PV of floating leg = 130 * 0.940734 + 150 * 0.895056

= 247.6032

Value of swap = 247.6032 - 247.6032 = 0

option C is correct

Please let me know in comments if you have any queries on this. Thanks!