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.

Recall that YTM is simply an IRR.

Whip out your calculator and put in the cash flows:

- C
_{0} = initial price of the bond; make sure that it’s negative
- C
_{1} = 50 (assuming a 1,000 par)
- C
_{2} = 50 (assuming a 1,000 par)
- C
_{3} = whatever (based on *r*_{rf} + 400 bp)
- C
_{4} = 1,000 + whatever (based on *r*_{rf} + 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!

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

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.

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.