Question

Selling bonds.  Lunar Vacations needs to raise $5,900,000 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 7.7% on​ twenty-year semiannual bonds. If Lunar wants to issue a 5.6% semiannual coupon​ bond, how many bonds will it need to sell to raise the $5,900,000​?

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 =∑ [(5.6*1000/200)/(1 + 7.7/200)^k]     +   1000/(1 + 7.7/200)^20x2

k=1

Bond Price = 787.45

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

=5900000/(787.45*(1-0.022))=7661.083