Navarro, Incorporated, plans to issue new zero coupon bonds with a par value of $1,000 to fund a new project. The bonds will have a YTM of 5.07 percent and mature in 30 years. If we assume semiannual compounding, at what price will the bonds sell?

Multiple Choice

$226.80

$217.11

$215.25

$213.77

$222.68

To find the price of a zero-coupon bond, we can use the following formula:

\[
P = \frac{F}{(1 + r)^n}
\]

Where:
- $P$ is the price of the bond.
- $F$ is the face value of the bond (par value), which is $1,000.
- $r$ is the semiannual yield to maturity (YTM) divided by 2.
- $n$ is the total number of semiannual periods (number of years multiplied by 2).

### Step-by-Step Calculation:
1. **Face Value (F):** $1,000.
2. **YTM (annual):** 5.07% = 0.0507.
3. **Semiannual YTM (r):** 5.07% / 2 = 0.0507 / 2 = 0.02535.
4. **Number of periods (n):** 30 years × 2 = 60 periods.

Now, we can plug these values into the formula:

\[
P = \frac{1,000}{(1 + 0.02535)^{60}}
\]

Let me compute this for you.The price of the zero-coupon bond will be approximately **$222.68**.

Therefore, the correct answer is:

**$222.68**.

Would you like further details or explanations on any part of this calculation? Here are some related questions you might find helpful:

1. How does compounding frequency affect bond prices?
2. What is the difference between zero-coupon bonds and regular bonds?
3. How does the yield to maturity (YTM) influence bond pricing?
4. What is the impact of changing interest rates on zero-coupon bonds?
5. Why is semiannual compounding commonly used in bond markets?

**Tip:** When dealing with bonds, always ensure that the compounding frequency used for YTM matches the frequency assumed in bond pricing models to avoid errors.

Navarro, Incorporated, plans to issue new zero coupon bonds with a par value of $1,000 to fund a new project. The bonds will have a YTM of 5.07 percent and mature in 30 years. If we assume semiannual compounding, at what price will the bonds sell?

Calculate the price of a zero coupon bond issued by Navarro, Inc. with a par value of $1,000, a YTM of 5.07%, and a 30-year maturity using semiannual compounding. This detailed solution covers bond pricing, the time value of money, and compounding interest concepts.

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