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?
6.25 percent
6.37 percent
6.50 percent
6.67 percent
6.75 percent

Answer 1

Coupon rate is annual payout as a percentage of the bond's par value.


Compounding = semi annually
Par Value = 1000
Market Rate = 6.5
Market Price = 972.78
N = 40


Coupon Rate Formula
Coupon Rate = 2[ (Market Price - Par Value x PVIF(ytm%, n) ) / ( Par Value x PVIFA(ytm%, n) ) ]
PVIFA(0.0325, 40) = 22.2084332365
PVIF(0.0325, 40) = 0.278225919814
Coupon Rate Calculation
Coupon Rate = 2[ (972.78 - 1000 x 0.278225919814 ) / ( 1000 x 22.2084332365 ) ]
Coupon Rate = 2[ 972.78 - 278.225919814 ] / 22208.4332365
Coupon Rate = 2[694.554080186 / 22208.4332365]
Coupon Rate = 2[0.0312743394723]
Coupon Rate = 6.25%