Question

XYZ Corporation’s $1,000 par value bond sells for $940, matures in four years, and has a 7% coupon rate paid semiannually. What is the bond’s yield to maturity? Show full working.

(Answer 8.81%)

Answer 1

Given:

Maturity value= $1,000

Market value of the bond= $940

Time period= 8 years (since it is a semiannual bond, 4*2=8)

Interest rate= 3.5% (7/2=3.5%)

Formula for calculating the bond’s YTM:

Bond price= Cash flow1/(1+YTM)^1+Cash flow 2/(1+YTM)^2+Cash flow 3/(1+YTM)^4………………+Cash flow 8/(1+YTM)^8+Maturity value/(1+YTM)^8

940=35/(1+YTM^1+35/(1+YTM)^2+35/(1+YTM)^3+35/(1+YTM)^4+35/(1+YTM)^5+35/(1+YTM)^6+35/(1+YTM)^7+35/(1+YTM)^8+1000/(1+YTM)^8

YTM is calculated using a trial and error method.

Through trial and error, it is found that the bond’s YTM is 4.406. Therefore, the YTM is 4.406*2= 8.81.

YTM can also be calculated using a financial calculator.

Calculator solution is:

N=8; PMT= 35; FV=1,000; PV= -940

CPTI/Y=4.4062

The YTM is 4.4.62*2= 8.8123.

I hope that was helpful :)