Respuesta :
The question is incomplete. The complete question is :
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 $41,800,000?
Solution :
We know that a zero compound bond does not pay any coupon payments, so the bond price is present value for the cash inflow from a zero coupon bond.
The present value of a maturity value uses a YTM as a discount rate.
We will find the semi annual rates and the time periods as the semi annual bond is given.
The semi annual YTM is = [tex]$\frac{7.7 \%}{2}$[/tex]
                    = 3.85 %
Number of the semi annual periods till maturity = 20 x 2
                                        = 40
The bond price = [tex]$\frac{\$ \ 1000}{(1+r)^n}$[/tex]
             [tex]$=\frac{\$ \ 1000}{(1+0.0385)^{40}}$[/tex]
             = $ 220.668308088
The investment bank will then sell the bonds at a price above but the charge will be2.2% commission on the above price.
The net proceeds to Rawlings  [tex]$= 220.668308088 - (220.668308088 \times 2.2 \%)$[/tex]
                          = $ 215.813605311
∴ The number of bonds required :
 [tex]$=\frac{\text{amount required}}{\text{net proceeds to Rawlings}}$[/tex]
 [tex]$=\frac{\$ 41,800,000}{\$ 215.813605311}$[/tex]
 = 193,685.657
 ≈ 193,686 bonds
