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 9 percent, which is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 25 years to maturity. Compute the price of the bonds based on semiannual analysis.

To compute the price of the bonds, we will use the **present value (PV)** formula for bonds, which is the sum of the present value of coupon payments and the present value of the face value at maturity.

Here’s a breakdown of the information given:

- **Par value (Face value)**: $1,000
- **Coupon rate**: 9% annually, paid semiannually, so each payment is $ \frac{9\% \times 1,000}{2} = 45 $ dollars.
- **Yield to maturity (YTM)**: 10% annually, but since we are using semiannual analysis, the semiannual YTM is $ \frac{10\%}{2} = 5\% $.
- **Years to maturity**: 25 years, which means $ 25 \times 2 = 50 $ semiannual periods.

### Formula to calculate bond price:

The bond price $ P $ is the sum of the present value of coupon payments (an annuity) and the present value of the face value (a lump sum). The formula is:

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

Where:
- $ C $ is the semiannual coupon payment = 45
- $ r $ is the semiannual yield to maturity = 0.05
- $ F $ is the face value of the bond = 1,000
- $ n $ is the total number of semiannual periods = 50

We’ll calculate both the present value of the coupon payments and the present value of the face value.

Let me calculate this for you.The price of Olsen’s Clothing Stores' bond, based on semiannual analysis, is approximately **$908.72**.

Would you like further details or have any questions?

Here are five related questions that expand on this topic:
1. How does the bond price change if the yield to maturity increases?
2. What happens to the bond price if the time to maturity decreases?
3. How does the coupon rate impact the bond’s price relative to its par value?
4. What is the relationship between bond prices and market interest rates?
5. How would you calculate the yield to maturity if the bond price were given?

**Tip**: A bond's price and yield to maturity are inversely related—when one goes up, the other typically goes down.

Calculate the price of Olsen’s Clothing Stores' bonds using a detailed semiannual analysis. Learn how to apply bond pricing formulas, including present value calculations for coupon payments and face value, with a 10% yield to maturity. Suitable for finance students and professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation