Question

A​ BBB-rated corporate bond has a yield to maturity of 11.6 %. A U.S. Treasury security has a yield to maturity of 9.8 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay semiannual coupons at an annual rate of 9.9 % 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

YTM of treasury bond = 9.80%
Rate half yearly = 9.80%/2 = 4.9%
Coupon =9.9%*1000/2 =49.50
Par Value = 1000
Number of Periods = 5*2 = 10
Price of Bond = PV of Coupons + PV of Par Value =49.50*((1-(1+4.90%)^-10)/4.90%+1000/(1+4.90%)^10 =1003.88
Price as percentage of face value = 100.39%

b) YTM of BBB-rated corporate bond = 11.6%
Rate half yearly = 11.6%/2 =5.8%
Coupon =9.9%*1000/2 =49.50
Par Value = 1000
Number of Periods = 5*2 = 10
Price of Bond = PV of Coupons + PV of Par Value =49.50*((1-(1+5.80%)^-10)/5.80%+1000/(1+5.80%)^10 =936.84
Price as percentage of face value = 93.68%

c) Credit spread of Treasury bill and BBB bond =11.6%-9.8% =1.8%