Question

A​ BBB-rated corporate bond has a yield to maturity of 6.6 %. A U.S. treasury security has a yield to maturity of 5.1 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 6.1 % 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

a) YTM of treasury bond = 5.1%
Rate half yearly = 5.1%/2 = 2.55%
Coupon = 6.1%*1000/2 =30.50
Par Value = 1000
Number of Periods = 5*2 = 10
Price of Bond = PV of Coupons + PV of Par Value = 30.50*(1-(1+2.55%)^-10)/2.55% + 1000/(1+2.55%)¹⁰ = 1043.65
Price as percentage of face value = 104.36%

b) YTM of BBB-rated corporate bond = 6.6%
Rate half yearly = 6.6%/2 = 3.3%
Coupon = 6.1%*1000/2 =30.50
Par Value = 1000
Number of Periods = 5*2 = 10
Price of Bond = PV of Coupons + PV of Par Value = 30.50*(1-(1+3.3%)^-10)/3.3% + 1000/(1+3.3%)¹⁰ =978.9973
Price as percentage of face value = 97.90%

c) Credit spread of Treasury bill and BBB bond = 6.6% -5.1%= 1.5%

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