Question

A​ BBB-rated corporate bond has a yield to maturity of

7.0 %7.0%.

A U.S. treasury security has a yield to maturity of

5.1 %5.1%.

These yields are quoted as

APRs

with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of

5.6 %5.6%

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

1

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

Effective Annual Rate = ((1+5.1/2*100)^2-1)*100

Effective Annual Rate% = 5.17

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

Bond Price =∑ [(5.6*100/200)/(1 + 5.17/200)^k]     +   100/(1 + 5.17/200)^5x2

k=1

Bond Price = 101.87

2

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

Effective Annual Rate = ((1+7/2*100)^2-1)*100

Effective Annual Rate% = 7.12

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

Bond Price =∑ [(5.6*100/200)/(1 + 7.12/200)^k]     +   100/(1 + 7.12/200)^5x2

k=1

Bond Price = 93.7

3

credit spread = BBB yield - treasury yield = 7.12-5.17 = 1.95%