A $2,600 face value corporate bond with a 6.5 percent coupon (paid semiannually)

Question

A $2,600 face value corporate bond with a 6.5 percent coupon (paid semiannually) has 12 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.0 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate will be 8.3 percent. What will be the change in the bond’s price in dollars and percentage terms? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 3 decimal places. (e.g., 32.161))

Explanation / Answer

Coupons=2600*6.5%/2=84.5

N=12*2=24

YTM=7%

Price=84.5/1.035+84.5/1.035^2...............84.5/1.035^24+2600/1.035^24

=>Price=84.5/1.035*(1-1/1.035^24)/(1-1/1.035)+2600/1.035^24

=>Price=84.5/0.035*(1-1/1.035^24)+2600/1.035^24

hence, old price=$2495.621

New price=84.5/0.0415*(1-1/1.0415^24)+2600/1.0415^24

New price=$2248.638

So, Change in Bond's Price=2248.638-2495.621=-246.983

% change in bond's price=-246.983/2495.621=-0.09897=-9.897%

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