Question

LKM, Inc. wants to issue new 20-year bonds for some much-needed expansion projects. The company currently has 6.5 percent coupon bonds on the market that sell for $972.78, make semiannual payments, and mature in 20 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?

Answer 1

6.75%

Step-by-step explanation:

Price of bonds is equal to their par value when coupon rates match with yields to maturity. The 20-year bond with semiannual coupon payments is going to have 40 coupons payment plus 1 par value payment. Let formulate the price of this bond as below:

Bond price = [Par value x (Coupon rate/2)]/[1 + (YTM/2)] + [Par value x (Coupon rate/2)]/[1 + (YTM/2)]^2 + ...+ [Par value x (Coupon rate/2) + Par value]/[1 + (YTM/2)]^40, or:

972.78 = [1,000 x (6.5%/2)]/[1 + (YTM/2)] + [1,000 x (6.5%/2)]/[1 + (YTM/2)]^2 + ...+ [1,000 x (6.5%/2) + 1,000]/[1 + (YTM/2)]^40

Solve the equation we get YTM = 6.75%.

So, the company should set 6.75% coupon rate on its new bonds if it wants to sell them at par.