Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
![**Understanding Bond Valuation: An Analysis of Bond A**
Bond A is an example of a financial instrument that illustrates the concept of bond valuation. This bond has the following characteristics:
- **Coupon Rate**: 10.04 percent
- **Annual Yield to Maturity (YTM)**: 4.79 percent
- **Face Value**: $1,000.00
- **Maturity**: 8 years
The bond pays coupon payments annually, with the next payment expected in 1 year. To understand more about this bond’s valuation, we need to determine the present value components of its coupon payments and face value. The question arises: What is the value represented by \( X + Y + Z \), given that:
- **X** is the present value of any coupon payments expected to be made in 3 years
- **Y** is the present value of any coupon payments expected to be made in 6 years
- **Z** is the present value of any coupon payments expected to be made in 9 years
### Multiple Choice Options for the Present Value Calculation:
1. **An amount equal to or greater than $82.70 but less than $124.77**
2. **An amount equal to or greater than $124.77 but less than $141.42**
3. **An amount equal to or greater than $141.42 but less than $172.16**
4. **An amount equal to or greater than $172.16 but less than $229.36**
5. **An amount less than $82.70 or a rate greater than $229.36**
Each of these options represents a range within which the calculated present value of the bond’s future coupon payments could fall. Determining the correct answer would involve using present value formulas and discounting the future coupon payments and face value by the bond’s YTM of 4.79 percent.
### Detailed Analysis:
1. **Understanding Coupon Payments**: Calculate the yearly coupon amount by applying the coupon rate to the face value.
\[
\text{Coupon Payment} = \frac{10.04}{100} \times 1000 = \$100.40
\]
2. **Present Value Calculations**:
- For a coupon payment expected in 3 years (X):
\[
X = \frac{100.40}{(1 + 0.0479)^3}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfbc4ba1-e0ed-49af-a997-602aa39b0c1c%2Fc27fc907-18e6-4130-ac38-363da31e2e96%2Fwxzg0n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Bond Valuation: An Analysis of Bond A**
Bond A is an example of a financial instrument that illustrates the concept of bond valuation. This bond has the following characteristics:
- **Coupon Rate**: 10.04 percent
- **Annual Yield to Maturity (YTM)**: 4.79 percent
- **Face Value**: $1,000.00
- **Maturity**: 8 years
The bond pays coupon payments annually, with the next payment expected in 1 year. To understand more about this bond’s valuation, we need to determine the present value components of its coupon payments and face value. The question arises: What is the value represented by \( X + Y + Z \), given that:
- **X** is the present value of any coupon payments expected to be made in 3 years
- **Y** is the present value of any coupon payments expected to be made in 6 years
- **Z** is the present value of any coupon payments expected to be made in 9 years
### Multiple Choice Options for the Present Value Calculation:
1. **An amount equal to or greater than $82.70 but less than $124.77**
2. **An amount equal to or greater than $124.77 but less than $141.42**
3. **An amount equal to or greater than $141.42 but less than $172.16**
4. **An amount equal to or greater than $172.16 but less than $229.36**
5. **An amount less than $82.70 or a rate greater than $229.36**
Each of these options represents a range within which the calculated present value of the bond’s future coupon payments could fall. Determining the correct answer would involve using present value formulas and discounting the future coupon payments and face value by the bond’s YTM of 4.79 percent.
### Detailed Analysis:
1. **Understanding Coupon Payments**: Calculate the yearly coupon amount by applying the coupon rate to the face value.
\[
\text{Coupon Payment} = \frac{10.04}{100} \times 1000 = \$100.40
\]
2. **Present Value Calculations**:
- For a coupon payment expected in 3 years (X):
\[
X = \frac{100.40}{(1 + 0.0479)^3}
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