Question

Lunar Vacations needs to raise $ 6,100,000 for its new project? (a golf course on the? moon). Astro Investment Bank will sell the bond for a commission of 2.5 %. The market yield is currently 7.5 % on? twenty-year semiannal bonds. If Lunar wants to issue a 6.4 % semiannual coupon? bond, how many bonds will it need to sell to raise the $ 6,100,000?? Assume that all bonds are issued at a par value of $ 1 comma 000. How many bonds will Lunar need to sell to raise the ?$6,100,000??

Answer 1

Answer:

Coupon (R) = 6.4% x $1,000 = $64

Bond yield (kd) = 7.5% = 0.075

No of years (n) = 20 years

No of compounding periods (m) = 2

Po= R/m(1-(1+Kd/m)-nm/Kd/m + FV/(1+Kd/m)nm

Po = 64/2(1-(1+0.075/2)-20x2 + 1,000/(1+0.075/2)20x2

                0.075/2

Po = 32(1-(1+0.0375)-40 + 1,000/(1 + 0.0375)40

                 0.0375

Po = 32(1-0.2293) + 229.34

             0.0375

Po = 32(20.552) + 229.34

Po = $957

Current market price less commission

= $957 - 2.5% x $957

= $957 - $23.925

= $933.075

No of bonds to issue = $6,100,000/$933.075

= 6,538 units

Explanation:

In this case, we need to determine the current market price of the bond, which is a function of present value of coupon and present value of the face value of the bond. Thereafter, we will deduct the issuing commission from the current market price. Finally, we will divide the value of the bond raised by the current market price after adjusting for commission so as to obtain the number of bonds issued.