Final answer:
The price of the corporate bond can be determined by discounting its coupon payments and face value at its yield to maturity, which is a sum of the yield to maturity of a similar Treasury bond and the credit spread of AA bonds.
Step-by-step explanation:
To calculate the price of a corporate bond that matures in 2 years with semi-annual coupons, a coupon rate of 5.8%, and a credit rating of AA, we must consider the yield to maturity of equivalent Treasury bonds and the credit spread. The corporate bond will have a yield to maturity that is the sum of the Treasury bond yield and the credit spread specific to AA bonds. In this case, the Treasury bond yield is 1.9% and the credit spread is 0.88%, resulting in a corporate bond yield to maturity of 2.78% (1.9% + 0.88%).
To find the bond's price, we discount each of the coupon payments and the face value at the bond's yield to maturity, considering the semi-annual compounding. For this corporate bond, the semi-annual coupon payment would be ($1,000 * 5.8%/2), which is $29. The bond makes these coupon payments every six months for two years, and at the end of two years, it also pays back the face value of $1,000.
We can calculate the present value of each cash flow, sum them up, and that would give us the bond's price. The calculation would be an application of the formula for the present value of an annuity for the coupon payments, plus the present value of a single sum for the face value paid at maturity. Since interest rates for corporate bonds are typically higher to compensate for the greater risk of default compared to Treasury bonds, the price of the corporate bond will generally be lower than its face value when the yield on the bond is above the coupon rate.