Final answer:
The price of the Treasury and BBB-rated corporate bonds is calculated using their respective yields to maturity and coupon rates. The Treasury bond is priced considering a 6.5% yield and the corporate bond at an 8.2% yield, both with 7% semiannual coupons and 5 years to maturity. The credit spread is the difference in yields, which in this case is 1.7%.
Step-by-step explanation:
To calculate the price of the bonds as a percentage of the face value, we must first determine the present value of each bond's cash flows, which include the semiannual coupon payments and the face value returned at maturity. The calculation takes into account the yield to maturity (YTM), coupon rate, and the number of periods until maturity. The U.S. Treasury bond has a YTM of 6.5%. With semiannual coupon payments of 3.5% (half of the annual 7%), there will be 10 periods (5 years at 2 periods per year) to maturity.
The BBB-rated corporate bond has a YTM of 8.2%. We utilize the same method of calculation as with the Treasury bond, taking into account the different YTM. The credit spread is the difference in yield between the corporate bond and the similar Treasury bond. In this case, it would be the yield on the BBB-rated bond (8.2%) minus the yield on the Treasury bond (6.5%), amounting to a 1.7% credit spread.