Question

Selling bonds.??Rawlings needs to raise ?$41,800,000 for its new manufacturing plant in Jamaica. Berkman Investment Bank will sell the bond for a commission of 2.2 %. 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 ?$41,800,000?? Assume that the bond is semiannual and issued at a par value of $ 1000. How many bonds will Rawlings need to sell to raise the ?$41,800,000??

Answer 1

First, we need to compute the price of the bonds.

A zero - coupon bond does not pay coupon payments so, bond price is the present value of cash inflows from the zero - coupon bond, i.e., present value of maturity value using YTM as the discount rate. Since we are given semi - annual bond, we need semi - annual rates and time periods.

Semi - annual YTM = 7.7% / 2 = 3.85%, No. of semi - annual periods till maturity = 20 x 2 = 40

Bond price = $1000 / (1 + r)ⁿ = $1000 / (1 + 0.0385)⁴⁰ = $220.668308088

The investment bank will sell the bonds at the above price but will charge a 2.2% commission out of above price.

Net proceeds to Rawlings = $220.668308088 - [ $220.668308088 x 2.2% ] = $215.813605311

Therefore, No. of bonds required = Amount required / Net proceeds to Rawlings = $41,800,000 / $215.813605311 = 193,685.657 or 193,686 bonds