Question

2) Suppose you have purchased a 30-year, 4.99% coupon bond pays interest annually. The bond has a face Sunce value of $1,000. What is the change in the price of this bond if the market yield to maturity declines to 5.15% from the current rate of 5.90%? Please show all the calculations by which you came up with the final answer Why did the 30-year bond price change? Please explain your reasoning. (5 Points) Answer:

Answer 1

Solution: given information face value of Bond Coupan rate (Annual) Coupon payment Current YTM changed YTM $1000 4.99% $ 49.90 5.90%. 5.15% 30 year Period Calculation of Present Value of Bonde - - ~ Cn PV = [TYTM) (+7 ) 2 Existing (1+yTM) Where i C = Coupan payment (Annually) YTM = Yield to Maturity or discount rate h = No. of years PV of Bond = $49.90 $49.90 --- $49.90+ $1000 (1.0590 * 1.059)2 (1.059330 Pr = $49.90 (P/A 5.9%, 30 years) +1000 (P/A 5.91, 30th year) = $49.90x 13.9134 + $1000x0.1791 - $ 873.38 Price of Bond at current YTM 5.9% is $873.39

Calculation of Price of Bond at YTM 5.15% PV - $49.9 + $49.9 + $49.9+$1000 (1.0575) (1.057532' (1.057530 PV - $49.90 (P/A 5.15), 30 years) + $1000 CPJA 557, 30 th Year) - $ 49.90X15:1130 + $1000X0.2017. - $ 975.84 Price of Bond at YTM 5.15% is $975.84 % Increase in Bond Price = $975-84 - 873.38 x 100 873.38 = 11•73 o). Since, a 0.75% (5.9-5.15) decrease in Yield to Maturity Results of 11.73% Increase in Bond Price, this is because Yield to Maturity and Price of Bond. has: Inverse relationship. As Yield Increase the price of the Bond. dereases and as Yield decreases, the Price of the Bond increases. The above relationship between Price and field is one of the most Important concept that is used for valuation of Bond.