Question

A​ BBB-rated corporate bond has a yield to maturity of 10.6 %. A U.S. treasury security has a yield to maturity of 9.3 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 9.8 % 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) Let the face value of both bonds be $1000 (without loss of generality)

For Treasury bond

Semiannual coupon = $1000*9.8%/2 = $49

No. of coupons = 5*2 = 10

Semiannual yield = 9.3%/2 = 0.0465

So,

Price of bond = 49/0.0465*(1-1/1.0465^10)+1000/1.0465^10

=$1019.637

So, price of the bond (expressed as % of Face value ) = 1019.637/1000 = 1.019637

b)

For BBB rated corporate bond

Semiannual coupon = $1000*9.8%/2 = $49

No. of coupons = 5*2 = 10

Semiannual yield = 10.6%/2 = 0.053

So,

Price of bond = 49/0.053*(1-1/1.053^10)+1000/1.053^10

=$969.55814

So, price of the bond (expressed as % of Face value ) = 969.558/1000 = 0.969558

c) Credit Spread on BBB bonds = 10.6% -9.3% = 1.3% or 130 basis points