Question

a bond traded on march 30, 2015, and matures on march 30, 2028 and may be called anytime after march 30, 2018 at a call price of 110. the bond pays a 5.75 coupon semiannually and currently trades at 98. what are the YTM and YTC for this bond?

Answer 1

(a) YTM determination:

Coupon Rate = 5.75 % per annum payable semi-annually, Par Value = $ 100, Current Value = $ 98, Bond Tenure = 13 years or 26 half-years

Semi-Annual Coupon = 0.0575 x 0.5 x 100 = $ 2.875

Let the YTM be 2R

Therefore, 98 = 2.875 x (1/R) x [1-{1/(1+R)^(26)}] + 100 / (1+R)^(26)

Using the EXCEL's Goal Seek Function to solve the above equation we get:

R = 2.99% approximately per half-year

Therefore, YTM = 2 X R = 2.99 x 2 = 5.98% per annum

(b) YTC determination:

Call Price = $ 110, Tenure to Call = 3 years or 6 half - years

Let the YTC be 2R

98 = 2.875 x (1/R) x [1-{1/(1+R)^(6)}] + 110/(1+R)^(6)

Using EXCEL's Goal Seek Function to solve the above equation we get:

R = 4.75 % approximately per half-year

Therefore, YTC = 2 X R = 2 x 4.75 = 9.5% per annum approximately