Final answer:
To calculate the market value of the bond, semi-annual coupons and the face value must be discounted using the current market yield, resulting in a bond that is priced above face value due to the lower current interest rates compared to the coupon rate.
Step-by-step explanation:
The question is asking to calculate the market value of a 10-year bond with a face value of $1,000 and a 7% annual coupon rate when similar bonds are yielding 4%. To find the market value using semi-annual analysis, we consider the semi-annual coupon payments of $35 ($1,000 * 7% / 2) and discount them along with the face value using the current market yield of 4% semi-annually (2% per period). The bond's price is the present value of these cash flows.
The calculation involves two parts: present value of the annuity (coupon payments) and the present value of the face value. To get the present value of the annuity, we would use the formula for the present value of an ordinary annuity. The present value of the face value is calculated by discounting the $1,000 back using the current market yield for the number of semi-annual periods remaining until the bond's maturity.
Since interest rates have fallen from the coupon rate to the current yield, we expect the bond to sell for more than its face value. As interest rates fall, bonds with higher coupon rates become more valuable, leading to a price above the face value.