Question

Selling bonds.  Rawlings needs to raise $43,200,000 for its new manufacturing plant in Jamaica. Berkman Investment Bank will sell the bond for a commission of 2.7%.

The market yield is currently 7.9% 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 $43,200,000​?

Assume that the bond is semiannual and issued at a par value of $1,000.

Answer 1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =20x2

Bond Price =∑ [(0*1000/200)/(1 + 7.9/200)^k]     +   1000/(1 + 7.9/200)^20x2

k=1

Bond Price = 212.33

Number of bonds required = amount to raise/(bond price*(1-commission rate))

=43200000/(212.33*(1-0.027))= 209102.655