Calculating bond YTM

CFA General
#1

Hi!

I am calculating the YTM of a 2-year bond with the following structure:

(1) It paid fixed coupon of 10% for the first year. Coupon paid semi-annually.

(2) It paid float rate + 4% spread for the next year. Coupon paid semi-annually.

Please help me calculating the YTM. I have no remaining knowledge on bond valuation and such.

#2

Recall that YTM is simply an IRR.

Whip out your calculator and put in the cash flows:

  • C0 = initial price of the bond; make sure that it’s negative
  • C1 = 50 (assuming a 1,000 par)
  • C2 = 50 (assuming a 1,000 par)
  • C3 = whatever (based on rrf + 400 bp)
  • C4 = 1,000 + whatever (based on rrf + 400 bp and assuming a 1,000 par)

Hit the IRR button to get the semiannual YTM. Double it to get the annual YTM (BEY).

Voilà!

#3

Thanks for this. But isn’t the whatever (float) rate unknown at the present? How can I calculate such IRR?

#4

There are two methods for that.

Method 1 (Simplistic approach):

Assume the floating rate is flat (e.g. 6 month floating rate held constant for the entire duration of the bond)

Method 2 (More appropriate):

Use the current yield curve relevant to the bond and calculate the implied 6-month forward rates. Use the forward rates as the floating rates for future coupon payments.

#5

You had written the question as if the bond had already matured.

For a bond maturing in the future, use the yield curve: the first payment will be based on the 6-month spot rate, the second on the 6-month forward rate starting 6 months from today, the third on the 6-month forward rate starting 12 months from today, and the fourth on the 6-month forward rate starting 18 months from today.