Question

Selling bonds.  Lunar Vacations needs to raise $ 5,700,000 for its new project​ (a golf course on the​ moon). Astro Investment Bank will sell the bond for a commission of 2.2 %. The market yield is currently 7.9 % on​ twenty-year semiannual bonds. If Lunar wants to issue a 5.5 % semiannual coupon​ bond, how many bonds will it need to sell to raise the $ 5,700,000​? Assume that all bonds are 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 =∑ [(5.5*1000/200)/(1 + 7.9/200)^k]     +   1000/(1 + 7.9/200)^20x2

k=1

Bond Price = 760.71

Number of bonds to issue = amount to raise/(price*(1-commission%))

=5700000/(760.71*(1-0.022))=7661.55 ~ 7662