A $1 000 face value corporate bond with a 6.75% coupon (paid s emiannually) has 10 years left to

QUESTION

A $1,000 face value corporate bond with a 6.75% coupon (paid semiannually) has 10 years leftto maturity. It has a credit rating of BB and a yield to maturity of 8.2%. The firm recentlybecame more financially stable and the rating agency is upgrading the bonds to BBB. Thenew appropriate discount rate will be 7.1%. What will be the change in the bonds price indollars and in percentage terms?
Solution: Price of bond = A*(1-(1+i)^-n)/i + FV/(1+i)^n A = 1000*6.75%/2 = 33.75 i = 8.2% / 2 = 4.1% n = 10*2 = 20 Existing price = 33.75*(1-(1+.041)^-20)/.041+ 1000/(1+.041)^20 = 902.34 Price after change in rating: i = 7.1% / 2 = 3.55%

rice =33.75*(1-(1+.0355)^-20)/.0355 + 1000/(1+.0355)^20 = 975.24 Change in price in dollars = 975.24 902.34 = 72.90 Change in % terms = 72.90 / 902.34 = 8.08%

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