Final answer:
To issue new 10-year coupon bonds at par, the coupon rate should be set at the yield to maturity (YTM) of the existing 7% coupon bond that is currently priced at $1,079. Calculating YTM involves finding the rate that discounts future cash flows of the bond to match its current price. The new coupon rate will be adjusted based on semi-annual payments to equate YTM with the current market rates.
Step-by-step explanation:
The student's question involves calculating the bond yield needed to price new 10-year coupon bonds at par, based on the yield of an existing bond. The existing 7% coupon bond is priced at $1,079, which is above its $1,000 par value, implying that the yield to maturity (YTM) on this bond is less than 7%. This is because investors are willing to accept a lower yield due to the bond's higher coupon rate compared to current market rates. To calculate the coupon rate needed for the new bond to be issued at par, we should equate its YTM to that of the existing bond.
Firstly, we calculate the annual coupon payment for the existing bond, which is 7% of $1,000, equating to $70. To find the YTM, we solve for the interest rate that sets the present value of the bond's future cash flows (the annual coupon payments and the par value at maturity) to the current price of $1,079. However, for the purpose of issuing new bonds at par value, we are interested in the coupon rate that will make the new bond's YTM equal to this calculated YTM. Therefore, the new coupon rate must be set to the same level as this YTM.
Given that the next coupon payment is due in six months, we would annualize this yield to determine the actual coupon rate for the new bond.