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

Question #6025

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

a. 4,228

b. 4,337

c. 4,448

d. 4,562

e. 4,676

Expert's answer

**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__
## Comments

Assignment Expert10.04.14, 16:03Assignment Expert10.04.14, 15:32D P17.07.13, 07:14I worked with a tutor and came up with D. The required rate of return, or effective yield is the same as the coupon rate only if (as in this case) the bond is selling at par.

Effective Yield 0.05

NPER 50

Coupon 31.25

FV 1000

Present Value of OID 657.7

3000000/657.70= 4561.34

It appears that the "expert" made the mistake of not dividing coupon payments by two for the semiannual periods.

No Thanks27.01.13, 07:02Answer 4337 is wrong. The answer is 4562

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