Question

A BBB-rated corporate bond has a yield to maturity of 7.1 %. A U.S. treasury security has a yield to maturity of 5.2 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay semi-annual coupons at a rate of 5.8 % 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)Treasury bonds
face value =	100
yield to maturity=	5.20%
semi Annual rate 7.1%/2=	2.60%
Coupon rate =	5.8%
Semiannual coupon rate = 5.8%/2=	2.90%
Coupon Amount = 100*2.9%=	2.9
Years to maturity (n)=	5
Semiannual periods (n) =5*2=	10
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
2.9*(1-(1/(1+2.60%)^10))/2.60%+ 100/(1+2.60%)^10
102.61
Price in % = Price/Face value*100
Bond price of Treasury bonds in % is 102.61/100*100 = 102.61%

b) BBB rated corporate bonds
face value =	100
yield to maturity=	7.10%
semi Annual rate 7.1%/2=	3.55%
Coupon rate =	5.8%
Semiannual coupon rate = 5.8%/2=	2.90%
Coupon Amount = 100*2.9%=	2.9
Years to maturity (n)=	5
Semiannual periods (n) =5*2=	10
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
2.9*(1-(1/(1+3.55%)^10))/3.55%+ 100/(1+3.55%)^10
94.61
Price in % = Price/Face value*100
Bond price of BBB rated corporate bonds in % is 94.61/100*100 = 94.61%

c.

Credit spread formula = Yield of corporate bonds - Yield of Treasury bonds

7.1%-5.2%

1.90%

So credit spread on BBB rated bonds is 1.90%