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%

Please Discuss in case of Doubt

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