Question

A bond with 10 years left to maturity currently sells for 75% of par value. If the bond makes a $90 annual coupon payment, then the bond must have a YTM greater than what percentage rate?

Answer 1

Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. It has some restrictive assumptions which are as follows –

1. The bond is held to maturity.

2. All cash flows will be recovered on time

3. All intermediate cash flows shall be reinvested at the YTM itself.

Here for this question we let the par value of the bond be $1000.

Current Price of the bond= 75% of 1000 = $750

Annual Coupon payment = $90.

Remaining life of the bond = 10 years

Therefore YTM =

750 = 90/(1+r) + 90/(1+r)² + 90/(1+r)³ + 90/(1+r)⁴ + 90/(1+r)⁵ + 90/(1+r)⁶ +

90/(1+r)⁷ + 90/(1+r)⁸ +90/(1+r)⁹ +(1000+90)/(1+r)¹⁰

Therefore YTM i.e. r = 13.7453%

The following answer can also be computed in this manner.

PLEASE LIKE THE ANSWER IF YOU FIND IT HELPFUL OR YOU CAN COMMENT IF YOU NEED CLARITY / EXPLANATION ON ANY POINT.

Thanks.