Kasey Corporation has a bond outstanding with a coupon rate of 5.96 percent and semiannual payments. The bond has a yield to maturity of 5.3 percent, a par value of $2,000, and matures in 19 years. What is the quoted price of the bond?

Multiple Choice

2,372.56

107.84

108.15

110.00

2,156.87

To find the quoted price of the bond, we need to use the **present value formula** for bond pricing, which involves calculating the present value of the bond's coupon payments and the present value of the par value (face value) at maturity.

Here's the step-by-step breakdown:

1. **Coupon Rate and Payments**:
   - The annual coupon rate is 5.96%, so the annual coupon payment is:
     \[
     \text{Coupon Payment} = 5.96\% \times 2000 = 119.20 \text{ annually}
     \]
   - Since payments are **semiannual**, the coupon payment per period is:
     \[
     \text{Semiannual Coupon Payment} = \frac{119.20}{2} = 59.60
     \]

2. **Yield to Maturity (YTM)**:
   - The **semiannual yield** is half of the annual YTM:
     \[
     \text{Semiannual YTM} = \frac{5.3\%}{2} = 2.65\%
     \]
   - In decimal form:
     \[
     \text{Semiannual YTM} = 0.0265
     \]

3. **Number of Periods (N)**:
   - Since the bond matures in 19 years and payments are semiannual, the total number of periods is:
     \[
     N = 19 \times 2 = 38 \text{ semiannual periods}
     \]

4. **Present Value of Coupon Payments**:
   The present value of the coupon payments is calculated using the annuity formula:
   \[
   PV_{\text{coupons}} = C \times \left( 1 - \frac{1}{(1 + r)^N} \right) \div r
   \]
   Where:
   - $C = 59.60$ (semiannual coupon payment)
   - $r = 0.0265$ (semiannual yield)
   - $N = 38$ (semiannual periods)

5. **Present Value of Par Value**:
   The present value of the par value (face value) is calculated using the present value of a lump sum formula:
   \[
   PV_{\text{par}} = \frac{F}{(1 + r)^N}
   \]
   Where:
   - $F = 2000$ (face value)
   - $r = 0.0265$ (semiannual yield)
   - $N = 38$ (semiannual periods)

Let's compute these values.The quoted price of the bond is approximately **$2,156.87**.

Thus, the correct answer from the multiple choice options is:

**2,156.87**

Would you like further details or have any questions? Here are five related questions to explore further:

1. How does the yield to maturity affect the price of a bond?
2. What is the difference between the coupon rate and yield to maturity?
3. How do bond prices change as interest rates fluctuate?
4. What are the implications of bonds with semiannual vs annual coupon payments?
5. How would the price change if the bond matures in 10 years instead of 19?

**Tip**: A bond trades at a premium if its price is above par value, which happens when the coupon rate is higher than the yield to maturity.

Kasey Corporation has a bond outstanding with a coupon rate of 5.96 percent and semiannual payments. The bond has a yield to maturity of 5.3 percent, a par value of $2,000, and matures in 19 years. What is the quoted price of the bond?

Learn how to calculate the quoted price of a bond for Kasey Corporation with a coupon rate of 5.96%, yield to maturity of 5.3%, and a 19-year maturity. The detailed solution involves key concepts like the present value of coupon payments and the present value of par value. Suitable for college-level finance or advanced high school economics students.

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