Question

ABCD Company plans to raise $80,000,000 by issuing 23-year semiannual coupon bonds with coupon rate of 5.60%, yield to maturity of 6.10%, and face value of $1,000. How many bonds should ABCD sell in order to raise the $80,000,000 it needs?

Answer 1

Face Value = $1,000

C = Semi annual Coupon = $1,000 * 5.6%/2 = $28

r = Semi annual yeild to maturity = 6.10%/2 = 3.05%

n = 23*2 = 46 months

Bond Price Today = [C * [1 - (1+r)^-n] / r] + [Face Value / (1+r)^n]

= [$28 * [1 - (1+3.05%)^-46] / 3.05%] + [$1,000 / (1+3.05%)^46]

= [$28 * 0.748931528 / 0.0305] + [$1,000 / 3.98297721]

= $687.543698 + $251.068471

= $938.612169

= $938.61

Amount need to raise = $80,000,000

Number of bonds need to sell = Amount need to raise / Bonds Price

= $80,000,000 / $938.61

= 85,232.4182

Therefore, number of bonds need to sell to raise the amount is 85,232.