Question

A​ BBB-rated corporate bond has a yield to maturity of 9.4%.A U.S. treasury security has a yield to maturity of

7.5%. These yields are quoted as

APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 8.2% and have five years to maturity.    

a. What is the price​ (expressed as a percentage of the face​ value) of the treasury​ bond?

b. What is the price​ (expressed as a percentage of the face​ value) of the​ BBB-rated corporate​ bond?

c. What is the credit spread on the BBB​ bonds?

Answer 1

Par Value =1000
Semi Annual Coupons =8.2%*1000/2 =41
Number of Periods =5*2 =10
a. Semi annual YTM of treasury bond =7.5%/2 =3.75%
Price of the treasury bond =PV of Coupons + PV of Par Value =41*((1-(1+3.75%)^-10)/3.75%)+1000/(1+3.75%)^10 =1028.74
Percentage of face value =102.87%

b. Semi annual BBB rated bond =9.4%/2 =4.7%
Price of the BBB rated bond =PV of Coupons + PV of Par Value =41*((1-(1+4.7%)^-10)/4.7%)+1000/(1+4.7%)^10 =952.99
Percentage of face value =95.30%

c. Credit Spread on the BBB bonds =9.4%-7.5% =1.9%