Question

The answer i am looking for is 7.4786% but i have no idea what to do. Any help would be great, also please show work so i can follow what to do. Thank you.

Exercise (9.11) Suppose that ZYX's loan in Example (9.10) is 400 million at time 0, and that ZYX has agreed to pay interest at the 1-year spot rate and also repay 100 million of principal at the end of each of the 4 years. ZYX enters into an interest rate swap (as the "payer") that covers years 2, 3, and 4 of this loan. Because the principal decreases over the term of the swap, this is an "amortizing" swap. Based on the spot rates in Example (9.10), what is the swap rate for this deferred amortizing swap? Answer: 7.4786%

Answer 1

In this case, 100 million principal is paid off, at the end of each year so outstanding principal at the end of year 1 will be 400 million; at the end of year 2 will be 300 million; at the end of year 3 will be 200 million; and, at the end of year 4 will be 100 million.

PV factors are already provided. It is a one-year deferred swap so year 1 will not be included in the calculations.

Using formula (9.9), we have

{Year 2 principal*(P2-P1) + Year 3 principal*(P3-P2) + Year 4 principal*(P4-P3)}/{Year 2 principal*P2 + Year 3 principal*P3 + Year 4 principal*P4}

= {300*(0.88166-0.9434) + 200*(0.8163-0.88166) + 100*(0.75581-0.8163)}/{(300*0.88166) + (200*0.8163) + (100*0.75581)}

= 7.4786% (swap rate for the swap)