Bonner Metals wants to issue new 20-year bonds. The company currently has 8.5 percent bonds on the market that sell for $994, make semiannual payments, and mature in 7 years. What should the coupon rate be on the new bonds if the firm wants to sell them at par?

Question

Quizplus · Accepted Answer

The current bonds have a 7-year maturity and make semiannual payments, so there are 2 * 7 = 14 coupon payments left. We can find the yield to maturity (YTM) for these bonds using the following formula:

PV = (C / (1 + r/2)^1) + (C / (1 + r/2)^2) + ... + (C + 1000 / (1 + r/2)^14)

where PV = 994 (the current bond price), C = 8.5% / 2 * 1000 = $42.50 (semiannual coupon payment), and r = YTM. Solving for YTM using trial and error or a financial calculator, we get a YTM of 10.11%.

To sell the new bonds at par (i.e. for $1000), we need to set the coupon rate such that the present value of the bond's cash flows is also $1000. Using the same formula as before, but with 20 * 2 = 40 coupon payments, we can solve for the required coupon rate:

1000 = (C / (1 + r/2)^1) + (C / (1 + r/2)^2) + ... + (C + 1000 / (1 + r/2)^40)

Setting PV = 1000 and solving for C, we get a required coupon rate of 8.62%. Therefore, the answer is D) 8.62 percent.

Bonner Metals Wants to Issue New 20-Year Bonds