Hi,

Please could someone clarify what is meant by the bit in bold below? What is meant by the “second floating rate payment combined with 1”?

Question:

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)** $15,633. **C)** $12,465.

Answer:

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. T**he 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.