Question

Draiman Corporation has bonds on the market with 14.5 years to maturity, a YTM of 5.3 percent, a par value of $1,000, and a current price of $987. The bonds make semiannual payments. What must the coupon rate be on the bonds?

Answer 1

We can use the formula for the present value of a bond to solve for the coupon rate:

PV = (C / 2) * [1 - 1 / (1 + r/2)^(2n)] + 1000 / (1 + r/2)^(2n)

where PV is the current price of the bond, C is the semiannual coupon payment, r is the semiannual yield to maturity (YTM), and n is the number of semiannual periods remaining until maturity.

Substituting the given values:

PV = $987

r = 0.053 / 2 = 0.0265 (semiannual YTM)

n = 14.5 years * 2 = 29 semiannual periods

We can solve for C:

C = [PV - 1000 / (1 + r/2)^(2n)] / [1 - 1 / (1 + r/2)^(2n)]

C = [$987 - $552.62] / [1 - 1 / (1 + 0.0265)^(2*29)]

C = $434.38

Therefore, the semiannual coupon payment is $434.38, and the annual coupon rate is:

Coupon rate = 2 * $434.38 / $1000 = 0.8688 or 86.88% (rounded to two decimal places)

Note that the high coupon rate reflects the fact that the bond's YTM is lower than the coupon rate, indicating that the bond is selling at a premium.

Step-by-step explanation: