Answer to Question #6025 in Economics of Enterprise for LaMarcus Streeter

Question

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.

a. 4,228
b. 4,337
c. 4,448
d. 4,562
e. 4,676

Answer 1

Answer: b) 4 337

Explanation:

We need to find the price of OID bond:

1) Calculate 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
- so we have total yield = 1 000 + 5 000 = 6 000

2) yield effectiveness of Bond Par = total yield / bond price (for Bond Par bond price is equal to bond nominal), for Bond Par it equals
6 000 / 1 000 = 6

3) 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 we have total yield = 1 000 + 3 125 = 4 125

4) 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

5) to raise 3 000 000 Cosmic must issue 3 000 000 / 687.5 = 4 337 bonds