You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 12 percent, which is paid semiannually. The yield to maturity on the bonds is 12 percent annual interest. There are 10 years to maturity. Compute the price of the bonds based on semiannual analysis.

To compute the price of the bond based on semiannual analysis, we'll apply the bond pricing formula. Given the semiannual nature of the bond, we'll adjust the interest payments and the yield to maturity for a semiannual period.

The formula for the price of a bond is:

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

Where:
- $ P $ = price of the bond
- $ C $ = coupon payment
- $ r $ = semiannual yield (half of the annual yield)
- $ F $ = face value of the bond (par value)
- $ n $ = total number of periods (semiannual periods)

### Given dataTo compute the price of the bond based on semiannual analysis, we'll apply the bond pricing formula. Given the semiannual nature of the bond, we'll adjust the interest payments and the yield to maturity for a semiannual period.

The formula for the price of a bond is:

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

Where:
- $ P $ = price of the bond
- $ C $ = coupon payment
- $ r $ = semiannual yield (half of the annual yield)
- $ F $ = face value of the bond (par value)
- $ n $ = total number of periods (semiannual periods)

### Given 
- Par value ($ F $) = \$1,000
- Annual coupon rate = 12%
- Semiannual coupon payment ($ C $) = $ \frac{12\% \times 1,000}{2} = 60 $ dollars
- Yield to maturity = 12% annual (so semiannual yield $ r = \frac{12\%}{2} = 6\% = 0.06 $)
- Time to maturity = 10 years = $ 10 \times 2 = 20 $ semiannual periods

### Calculation:
Now, we can plug these values into the formula. The price of the bond is the present value of the semiannual coupon payments plus the present value of the par value at maturity.

Let's compute this.

\[
P = 60 \times \sum_{t=1}^{20} \frac{1}{(1 + 0.06)^t} + \frac{1000}{(1 + 0.06)^{20}}
\]

I will calculate this step-by-step.The computed price of the bond is approximately \$1,000. This makes sense, as the yield to maturity (YTM) equals the coupon rate, indicating that the bond is priced at par.

Would you like further details or explanations on any aspect of this calculation?

Here are 5 related questions for further exploration:
1. How would the bond price change if the yield to maturity were higher than the coupon rate?
2. What is the impact of a longer maturity period on bond prices?
3. How does semiannual compounding affect bond yields?
4. How would the bond price change if interest were paid annually instead of semiannually?
5. What is the relationship between bond price and interest rate changes?

**Tip:** When yield to maturity equals the coupon rate, a bond will typically trade at par value.

Learn how to compute the bond price for Olsen's Clothing Stores using semiannual analysis. This finance problem covers key concepts like bond valuation, semiannual compounding, and present value. The bond has a par value of $1,000, an annual coupon rate of 12%, and a yield to maturity of 12%. Suitable for undergraduate finance students.

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