Question

A BBE-rated comporate bond has a yield to maturity of 13.5%. A U.S. Treasury securly has a yield to maturity of 12 . OW. These yibids are quotod as APRa wh semiarrival conpounding. Boh bonde pay semi-annual coupons at a rate of 12.2% and have five years to maturily.

a. What is the price (exgressed as a percentage of the face value) of the Treasury bond?
b. What is the price (expressed as a percentage of the tace value) of the BeB-rated corporate bond?
c. What is the cregt spread on the 808 bonds?

Answer 1

The price of the Treasury bond is approximately 107.12% of the face value, while the price of the BBB-rated corporate bond is approximately 93.845% of the face value. The credit spread on the corporate bond is 1.5%.

Step-by-step explanation:

To calculate the price of a bond, you can use the present value formula. For the Treasury bond, the semi-annual coupon payment is 12.2% of the face value, or $122. The yield to maturity is 12% APR with semi-annual compounding, and the bond has 10 years to maturity. Plugging these values into the present value formula, the price of the Treasury bond is approximately $1,071.20, expressed as a percentage of the face value, which is 107.12%.

For the BBB-rated corporate bond, the same process can be followed. The only difference is that the yield to maturity is 13.5% APR. Plugging in the values, the price of the corporate bond is approximately $938.45, expressed as a percentage of the face value, which is 93.845%.

To calculate the credit spread, subtract the yield on the Treasury bond from the yield on the corporate bond. The credit spread is 1.5% (13.5% - 12%).