Question

1) Rawlings needs to raise $37,100,000 for its new manufacturing plant in Jamaica. Berkman Investment Bank will sell the bond for a commission of 2.4%. The market yield is currently 7.7% on​ twenty-year zero-coupon bonds. If Rawlings wants to issue a​ zero-coupon bond, how many bonds will it need to sell to raise the $37,100,000​? Assume that the bond is semiannual and issued at a par value of $1,000.

Answer 1

Price of the Bond

The Price of the Zero-Coupon Bond is the Present Value of the Par Value of the Bond

Par Value = $1,000

Semi-annual Yield to Maturity (YTM) = 3.85% [7.70% x ½]

Maturity Period = 40 Years [20 Years x 2]

Therefore, the Price of Zero-Coupon Bond = Par Value / (1 + YTM)ⁿ

= $1,000 / (1 + 0.0385)⁴⁰

= $1,000 / 4.53169

= $220.67 per Bond

Net Price of the Bond = Price per Bond – Selling commission

= $220.67 – [$220.67 x 2.40%]

= $220.67 - $5.30

= $215.37 per Bond

Number of bonds needs to sell to raise the $37,100,000​

Number of Bonds to be sold = Amount raised / Net price of the Bond

= $37,100,000 / $215.37 per Bond

= 172,262 Bonds

“Therefore, Rawlings needs to sell 172,262 Bonds to raise $37,100,000”