Answer to Question #138189 in Financial Math for Md.Mobarak Hossain

Question

A 12 percent coupon bond has 10years to maturity and discounted semi annually. Its current market price is Tk. 995, and 1st call price is Tk. 1065, calculate the YTC of the bond (trial & error approach) and interpret your findings focusing on bond pricing.

Answer 1

Then let the face value be 900, than:

$PM=\sum[\frac{Ct}{1+YTC}t+\frac{TV}{1+YTC}^n]$

we must find the value of YTC, which makes the right side of the equation 995

calculate the YTC of the bond by method trial & error approach)

YTC=12

$\sum[\frac{54}{1+\frac{0.12}{2}}t+\frac{1065}{(1+\frac{0.12}{2})}^n]=\sum[\frac{54}{1+\frac{0.12}{2}}+\frac{54}{(1+\frac{0.12}{2})^2}+...+\frac{54}{(1+\frac{0.12}{2})^{10}}+\frac{1065}{(1+\frac{0.12}{2})^{10}}]=992.14$

the resulting value is less than 995, so we try with a higher and lower bid

at 13 percent, it will be

$\sum[\frac{54}{1+\frac{0.13}{2}}+\frac{54}{(1+\frac{0.13}{2})^2}+...+\frac{54}{(1+\frac{0.13}{2})^{10}}+\frac{1065}{(1+\frac{0.13}{2})^{10}}]=955.55$

at 11 percent, it will be

$\sum[\frac{54}{1+\frac{0.11}{2}}+\frac{54}{(1+\frac{0.11}{2})^2}+...+\frac{54}{(1+\frac{0.11}{2})^{10}}+\frac{1065}{(1+\frac{0.11}{2})^{10}}]=1030.52$

995 is in the range between 992 and 1030, so the YTC rate is in the range from 11%-12%

YTC is between 11% and 12%