Question

Find the duration of a 7.4% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6.0%. What is the duration if the yield to maturity is 9.4%? Note: The face value of the bond is $100. (Do not round intermediate calculations. Round your answers to 4 decimal places.) 6% YTM Years 9.4% YTM Years

Answer 1

Answer: (a) Coupon Rote = 7.4%p.a. Coupon Payment - Semi- Annual face value = $100 YTM (kd) = 67. ; years to Moturity a 3 yeon Since the Coupon Payments are semi- Annual , Hence total payments shell be 6 ie Speriod of Adjusted Kd = 6% +2 = 3%. Value of Bond tody (Bo) = Interest (1+ Kd) & Interest (it kd) Interest interest interest (1+xd)3 . (1+ (dd)" interest t Redemption Amount) (1+ Adjo 3.7 (1+0.03) 3.7 3.7 +3.7 +3.7 & 103.7. (+0.03) (10.03) (120.03(1+003) 5 (H0.03) $ 103.792 Duration of Bond I/1x Interest) + Bo 112 l+ke / 1 x Interest 12 (1+kd) ² + (3x Interest 12 (1+ kd) (1 + Kdo 1 1. 85 311. + 3.7 ts.55 27.9 9.25 T + 103.792 / (1+0.031 0.03)? +0.03) . = 2.75 yoors

Now, in Cose Vield to Maturity (ka) is 9.4% & all other particulos remains Similar to the previous situation. Adjusted Kd = 9.4 -2 = 4.7% Value og Boud today : 3.7 (Bo) u (1+0.047) & 3.7 (1+0.047)² 3.7 t 37 (1+0.047)3 (1+0.047)" + 3.7 + + (1+0.047) 103.7 (1+0.047) (+ Bo=$94.87 Duration & of Bond = L / 1.85 & 3.7 94.87 / (1+0.047)' (1+0.047] 5.55 & 7.4 (1+0.04%)(1+0.047)4 + 9.25 + 311.1 (1+0.04755 (1+0.047) 3487* [ 259.554] 2.73 years