Final answer:
To find the coupon rate of Draiman Corporation's bonds, calculate the semiannual coupon payment that makes the present value of the bond's future cash flows equal to the current market price, using the bond's YTM as the discount rate.
Step-by-step explanation:
The coupon rate of Draiman Corporation's bonds can be calculated using the present value formula for bonds. Given that the bonds have a current price of $1,039, a yield to maturity (YTM) of 6.2%, and they make semiannual payments, we can determine the semiannual coupon payment that makes the present value of the bond's remaining cash flows equal to its current price. To do this, we will find the present value of the bond's cash flows, which include semiannual interest payments and the face value repayment at maturity, discounted at the bond's YTM.
A bond's price is the present value of its future cash flows, which include periodic coupon payments and the repayment of the bond's face value at maturity. The coupon rate can be found by determining what fixed semiannual payment (the coupon payment) will make the present value of these cash flows equal to the bond's current market price, using the YTM as the discount rate.
Without the use of financial calculators or software, we need to set up the following equation for the present value of an annuity to find the coupon payment (C):
$1,039 = C * ((1 - (1 / (1 + 0.031)^31) / 0.031 + $1,000 / (1 + 0.031)^31)
Here, 0.031 is the semiannual YTM (6.2% / 2), and 31 is the number of semiannual periods left until maturity (15.5 years * 2). Solving for C will give us the semiannual coupon payment, and multiplying C by 2 will provide the annual coupon rate (in percentage) when we set this equation equal to the bond's current price.