I've worked through this problem already and was hoping for some feedback on my approach. The problem description is:
You have a notional amount of 100 million paying fixed coupons of 8% annually for 5 years. You bough the bonds at a discount for 92.418, implying a YTM of 10%. You want to enter an agreement to repackage these bonds. The agreement you will enter is to provide $100 for each bond purchased and will receive receive LIBOR plus a 40 basis point spread as the floating rate for 5 years. You will also receive a repayment of the 100 principal at maturity. These floating rate payments will take place at the end of each year (i.e. annually) to match the payments on the bond and up to and including the final maturity in year 5.
The par swaps curve is given as:
Maturity 1 Yr 2 yr 3 yr 4 yr 5 yr
Par swaps rate against LIBOR 9.50% 9.59% 9.62% 9.69% 9.70%
Now I'm slightly confused by the wording in the question. it says {you} will provide $100 for each bond purchased
meaning I pay an initial cash outflow of 100, while I will receive LIBOR plus 40 basis point(s)
. So it doesn't seem to be a true interest rate swap, but more of an intitial payment by me to receive floating coupons over the 5 years.
I've structured my cash flow calculation accordingly.
Years 0 1 2 3 4 5
Par Swap Rate 9.50% 9.59% 9.62% 9.69% 9.70%
Pmt -100 9.5 9.59 9.62 9.69 109.7
PV(Pmt) -100 8.636 7.926 7.228 6.618 68.115
PV(bond) -1.477
The PV(Pmt)
is calculated as $\frac{1}{(1+YTM)^{i}}$ and the Pv(bond)
is the sum of the Pv(Pmt)
. The part I'm most unsure on is my discount factor being the 10%. I don't believe this is correct. Could someone confirm or deny if this is correct, and if I'm wrong provide some feedback on the correct approach?