Interest rate Swap

Dear All:

For the present value of this calculation (250,000/(1 + 0.05 × (90/360)) + 10,250,000/(1+ 0.054 × (270/360)) = $10,097,947, why not discount back 6 months for the first cash flow and 1 year for the second cash flow becuase it is semi annualy?

thank you so much for your time

A $10 million 1-year semi-annual-pay LIBOR-based interest-rate swap was initiated 90 days ago when LIBOR was 4.8%. The fixed rate on the swap is 5%, current 90-day LIBOR is 5% and 270-day LIBOR is 5.4%. The value of the swap to the fixed-rate payer is closest to:

A) $19,229. B) $12,465. C) $15,633.

Your answer: C was correct!

The fixed rate payments are 0.05 × (180/360) × 10,000,000 = 250,000. The present value of the remaining payments are 250,000/(1 + 0.05 × (90/360)) + 10,250,000/(1+ 0.054 × (270/360)) = $10,097,947.

The floating payment in 90 days is 0.048 × (180/360) = 240,000 and the present value is 240,000/(1 + 0.05/4) = $237,037. The second floating-rate payment combined with 1 at the end of the swap has a present value of 1 on the first payment date. The present value of 1 is 1/(1 + 0.05 × (90/360)) = 0.987654321 so the present value of the second floating rate payment combined with the principal amount is $9,876,543. The total value is 9,876,543 + 237,037 = $10,113,580.

The value of the swap to the fixed-rate payer is 10,113,580 – 10,097,947 = $15,633

It’s because you are already 90days in to the SWAP. As you can read in the first statement of the question - " was initiated 90 days ago".

So since it being semi-annual payments on 180th day and 360th day payments are made, but we are 90 days in to the swap meaning, we have (180-90) = 90 days before the 1st payment and (360-90) = 270 days before the second payment. That is why you are seeing the discount factors of 90/360 and 270/360 in the above calculations.

ganeshrpl, you seem to have a good understanding of swaps. Can you give me any tips on how to best solve for swaps. It’s not intuitive to me. I’ve been trying to understand this concept for a week, but I’m still hitting a wall on how to solve these easily.

well i am not sure how to suggest you. I aint too good in all topics of Swap but, my suggestion would be to go through the CFA level 1 book ( not schweser, the CFAI material) on swaps. Just read the first few pages. They explain you with actual world scenarios. That might help you digest the information bit by bit. That is how i learnt it. But i can surely give it a shot in explaining you. Over the weekend probably, if you can email me your contact # we can have a chat …

Ganeshrpl @

hey swt326,maybe this will help gain a different perspective…somtimes it helps