Question

Mazeltov Corporation issued $100,000 3-year,

6%
stated rate bonds on January 1, 2004. The bonds pay interest
semi-annually
and were sold when the market rate was 10%.
a.
Calculate the iss
2. (10 points) Mazeltov Corporation issued \( \$ 100,000 \) 3-year, \( 6 \% \) stated rate bonds on January 1, 2004. The bonds pay interest semi-annually and were sold when the market rate was \( 10 \

Answer 1

The issue price of the Mazeltov Corporation's
`\( \$100,000 \) 3-year, \( 6\% \)` stated rate bonds, sold on January 1, 2004, with semi-annual interest payments and a market rate of
`\( 10\% \)`, is approximately
`\( \$82,470.22 \).`

Step-by-step explanation:

Mazeltov Corporation's bond issuance involves calculating the present value of future cash flows, considering the stated rate of
`\( 6\% \)` and the market rate of
`\( 10\% \)`. The semi-annual interest payments result in a
`\( 3\% \)` interest rate per period
`(\( 6\% / 2 \)).` The formula for calculating the present value of a bond is:

`\[ P = (C * (1 - (1 + r)^(-nt)))/(r) + (F)/((1 + r)^(nt)) \]`

Where:

`\( P \)` is the issue price,

`\( C \)` is the semi-annual interest payment
`(\( \$100,000 * 6\% / 2 \)),`

`\( r \)` is the interest rate per period (\( 10\% / 2 \)),

`\( n \)` is the total number of periods (6 semi-annual periods per year for 3 years,
`\( n = 6 * 3 = 18 \))`, and

`\( F \)` is the face value of the bond (\$100,000).

Substituting these values into the formula, we find that the issue price is approximately
`\( \$82,470.22 \).`

In conclusion, the market rate being higher than the stated rate leads to a bond issued at a discount, resulting in an issue price lower than the face value. This discount compensates investors for the lower interest rate relative to the market rate over the bond's life.