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Example 8
Chloe and Madison enter into a two year interest rate swap. Under the swap, Chloe will pay a
fixed rate on a notional amount of 500,000 while receiving payments based on a floating interest
rate. The swap rate is 3.5% with annual settlement periods. The floating rate is LIBOR plus 25
basis points. The LIBOR rate for the first year is 3.1% and for the second year it turns out to be
3.7%. Determine the net swap payment that will occur between Chloe and Madison at the end of
the first year and at the end of the second year.
At the end of the first year, Chloe will pay the fixed rate while Madison will pay the floating
rate. Therefore, Chloe would pay (500,000)(0.035) = 17,500. Since Madison is paying the
floating rate, she will pay (500,000)(0.031 + 0.0025) = 16,750. These two payments would be
netted so the net swap payment would be 17,500 – 16,750 = 750 from Chloe to Madison.
At the end of the second year, Chloe would again pay (500,000)(0.035) = 17,500 as the fixed rate
has not changed. Since Madison is paying the floating rate, she will pay (500,000)(0.037 +
0.0025) = 19,750. These two payments would be netted so the net swap payment would be
19,750 – 17,500 = 2,250. This time the net swap payment would be paid by Madison to Chloe.
If one of the counterparties to the swap has a loan, then the net swap payment combined with the
interest that the counterparty must make on the loan results in a net interest payment on the
loan. The net interest payment is the interest paid on the loan plus any net swap payment made
by the loan holder less any net swap payment received by the loan holder.
Example 9
We extend Example 8, so that in addition to the swap, Chloe also has a 500,000 loan from
Anderson Bank, which charges a floating interest rate of LIBOR plus 25 basis points. Calculate
the net interest payment required by Chloe at the end of each of the two years.
At the end of the first year, Chloe must pay Anderson Bank the interest based on the floating
rate. Therefore, Chloe must pay Anderson Bank (500,000)(0.031 + 0.0025) = 16,750. We also
know from Example 8 that Chloe must pay 750 to Madison at the end of the first year. Therefore,
Chloe’s net interest payment is 16,750 + 750 = 17,500.
At the end of the second year, Chloe must again pay Anderson Bank the interest based on the
floating rate, which would be (500,000)(0.037 + 0.0025) = 19,750. We also know from Example
8 that Chloe will receive a payment of 2,250 from Madison at the end of the second year.
Therefore, Chloe’s net interest payment is 19,750 – 2,250 = 17,500.
We note that in both years, Chloe’s net interest payment is 17,500. Since Chloe has swapped the
floating interest rate on the loan with Anderson Bank for a fixed interest rate, we should expect
the interest paid to be the same in both years. Also, note that the net interest payment is equal to
(500,000)(0.035) = 17,500. That is, the net interest payment is just the amount of the loan
multiplied by the fixed interest rate. This will be true as long as the notional amount of the swap
is equal to the amount of the loan and the floating rate on the loan is the same as the floating rate
being swapped.