In an existing (not new) interest rate swap, your company receives 3.50% (fixed)

Question

In an existing (not new) interest rate swap, your company receives 3.50% (fixed) per annum and pays 3-month LIBOR in return on a notional principal of $100 million with cash payments being exchanged every 3 months. The swap contract has a remaining life of 14 months so the next cash exchanges will happen in 2 months, 5 months, 8 months, 11 months and 14 months. The last cash exchange happened 1 month ago and the 3-month LIBOR was 3.00% per annum with quarterly compounding. The current LIBOR rates for different maturities are given as follows.

What is the current value of this swap to your company?

Maturity LIBOR per annum with continuous compounding 2 months 2.75% 5 months 3.00% 8 months 3.25% 11 months 3.50% 14 months 3.75%

Explanation / Answer

notional value = 100M

fixed rate annual = 3.5 %

fixed rate quarterly = (1+3.5%)^1/4 - 1 = > 0.864%

so quarterly payment received = 0.8637M

discounting

2months = 0.8637^(-2.75%x2/12) => 1.000672

similarly

5 months => 1.001833

8 months => 1.00318

11 months => 1.004712

14 months => 1.006431

TOTAL VALUE OF SWAP = 5.01683M

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