Reinegar Corporation 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 Reinegar issue to raise $3,000,000

4500 bonds

Explanation:

In the given information:

Bond Life - 25 years

Sale value of bond - $1,000

Rate:

- Semi - annual bond - 10%

- second semi - annual bond - 6%

Original Issue Discount (OID) value of bond - $1,000

Bond value of OID - 25 years

First, we have to calculate total yield and its effectiveness for both type of bond:

rate = 10%

The yield of bond = $1000 * 25 * 2 * 10%

= $5000

Since the bond is sold, so it would be added while calculating total yield

So total yield = $5,000 + $1,000

= $6,000

Yield effectiveness = Total Yield / Bond price

= 6000 / 1000

= 6

So, the yield effectiveness for bond par is 6 for this type of bond.

Rate = 6%

The yield of bond = $1000 * 25 * 2 * 6%

= $3,000

Since the bond is sold,

So total yield = $3,000 + $1,000

= $4,000

Yield effectiveness = Total Yield / Bond price

= 4,000 / 6

= 666.67

So, the yield effectiveness for OID bond par is $666.67.

Now, after calculating the yield effectiveness of OID bond we can calculate the number of bonds for raising by the following formula

= amount issued / yield effectiveness of OID bond

= $3,000,000. / $666.67

= 4500 bonds

Thus, 4500 bonds is to raise for issuing $3,000,000.