Question

Lunar Vacations needs to raise

$ 5 comma 500 comma 000$5,500,000

for its new project (a golf course on the moon). Astro Investment Bank will sell the bond for a commission of

2.5 %2.5%.

The market yield is currently

7.9 %7.9%

on twenty-year semiannual bonds. If Lunar wants to issue a

5.6 %5.6%

semiannual coupon bond, how many bonds will it need to sell to raise the

$ 5 comma 500 comma 000$5,500,000?

Assume that all bonds are issued at a par value of

$ 1 comma 000$1,000.

How many bonds will Lunar need to sell to raise the

$5 comma 500 comma 0005,500,000?

Answer 1

K = Nx2

Bond Price =∑ [(1000 Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =20x2

Bond Price =∑ [(5.6*1000/200)/(1 + 7.9/200)^k]     +   1000/(1 + 7.9/200)^20x2

k=1

Bond Price = 770.68

Number of bonds to issue = capital to be raised/(bond price*(1-commission %))

Number of bonds to issue = 5500000/(770.68*(1-0.025)) =7319.54