5. Cosmic Communications Inc. is planning two new issues of 25-year bonds. Bond

Question

5. Cosmic Communications Inc. is planning two new issues of 25-year bonds. Bond Par will be sold at its $1,000 par value, and it will have a 10% semiannual coupon. Bond OID will be an Original Issue Discount bond, and it will also have a 25-year maturity and a $1,000 par value, but its semiannual coupon will be only 6.25%. If both bonds are to provide investors with the same effective yield, how many of the OID bonds must Cosmic issue to raise $3,000,000? Disregard flotation costs, and round your final answer up to a whole number of bonds.

Explanation / Answer

Solution:
price of OID bond:
Total yield of Bond Par:


-=25 years with 10% semiannually = 25 * 2 * 0.1 * 1 000 (bond nominal) = 5 000
-returning the bond = 1 000
=> total yield = 1 000 + 5 000 = 6 000
Yield effectiveness of Bond Par

= total yield / bond price (for Bond Par bond price is equal to bond nominal),

for Bond Par i=

6 000 / 1 000 = 6
Total yield of OID bond:
-25 years with 6.25% semiannually

= 25 * 2 * 0.0625 * 1 000

= 3 125
returning the bond = 1 000
so Total yield

= 1 000 + 3 125

= 4 125
Now Yield effectiveness of OID bond

= 4 125 / OID bond price

, the effectiveness of Bond Par and OID bond are equal,

so 4 125 / OID bond price

= 6, OID bond price = 687.5
Now to raise 3 000 000 Cosmic must issue:

3 000 000 / 687.5 = 4 337 bonds Ans

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