In: Finance
A BBB-rated corporate bond has a yield to maturity of 7.0 % 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 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?
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%