Question

Selling bonds. Lunar Vacations needs to raise $6,400,000 for its new project​ (a golf course on the​ moon). Astro Investment Bank will sell the bond for a commission of 2.7%. The market yield is currently 7.8% 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 $6,400,000​?

Assume that all bonds are issued at a par value of $1,000. How many bonds will Lunar need to sell to raise the $6,400,000​?

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 + 7.8/200)^k]     +   1000/(1 + 7.8/200)^20x2

k=1

Bond Price = 768.96

Number of bonds to sell = capital to raise/(bond price*(1-commission %))

=6400000/(768.96*(1-0.027))=8553.88