Question

1. A $1,000 face value corporate bond with a 6.5 percent coupon (paid semiannually) has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.2 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 8.5 percent. What will be the change in the bond's price in dollars and percentage terms? (LG 6-2)

17. A $1,000 face value corporate bond with a 6.75 percent coupon (paid semiannually) has 10 years left to maturity. It has had a credit rating of BB and a yield to maturity of 8.2 percent. The firm recently became more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 7.1 percent. What will be the change in the bond's price in dollars and percentage terms? (LG 6-2)

Answer 1

1. Face Value =1000
Coupon =6.5%*1000/2 =32.50
Number of Periods =15*2 =30
Semi annual rate of BBB bond =7.2%/2 =3.6%
Price of BBB Bond =PV of Coupons + PV of Par Value =32.50*(((1-(1+3.6%)^-30)/3.6%)+1000/(1+3.6%)^30 =936.43

Semiannual Discount Rate for BB bond =8.5%/2 =4.25%
Price of BB Bond =PV of Coupons + PV of Par Value =32.50*(((1-(1+4.25%)^-30)/4.25%)+1000/(1+4.25%)^30 =832.21

Price change in dollars =936.43-832.21 =104.22
Percentage decrease in price of dollars =104.22/936.43 =11.13%

2.  Face Value =1000
Coupon =6.75%*1000/2 =33.75
Number of Periods =10*2 =20
Semi annual rate of BBB bond =8.2%/2 =4.1%
Price of BBB Bond =PV of Coupons + PV of Par Value =33.75*(((1-(1+4.1%)^-20)/4.1%)+1000/(1+4.1%)^20 =902.34

Semiannual Discount Rate for BB bond =7.1%/2 =3.55%
Price of BB Bond =PV of Coupons + PV of Par Value =32.50*(((1-(1+3.55%)^-20)/3.55%)+1000/(1+3.55%)^20 =975.24

Price change in dollars =975.24-902.34 =72.90
Percentage decrease in price of dollars =72.90/902.34  =8.08%