Question

A​ BBB-rated corporate bond has a yield to maturity of 11.8%. A U.S. treasury security has a yield to maturity of 10.2%. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 11.1% 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)Treasury bonds  
face value =   1000
yield to maturity=   10.20%
semi Annual rate =10.2%/2=   5.10%
Coupon rate =   11.1%
Semiannual coupon rate = 11.1%/2=   5.55%
Coupon Amount = 1000*5.55%=   55.5
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  
55.5*(1-(1/(1+5.1%)^10))/5.1%+ 1000/(1+5.1%)^10  
1034.58  

Price in % = Price/Face value*100  
Bond price of Treasury bonds in percentage is 1034.58/1000*100 =    103.46%

(b) BBB rated bonds  
face value =   1000
Yield to Maturity =   11.80%
semi Annual rate 11.8%/2=   5.90%
Coupon rate =   11.1%
Semiannual coupon rate= 11.1%/2=   5.55%
Coupon Amount = 1000*5.55%=   55.5
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  
55.5*(1-(1/(1+5.9%)^10))/5.9% + 1000/(1+5.9%)^10  
=974.12  

Bond price of Treasury bonds in percentage is 974.12/1000*100 = 97.41%

(C)

Credit spread formula = Yield of BBB rated bonds - Yield of Treasury bonds  
11.8%-10.2%  
1.60%  
So credit spread on BBB rated bonds is 1.60%  

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