Question

Coccia Co. wants to issue new 20-year bonds for some much-needed expansion projects. The company currently has 7 percent coupon bonds on the market that sell for $1,085, 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

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%