4. Last year Arman purchased a $3028 face value corporate bond with an 8% annual coupon rate and a 15-year maturity. At the time of the purchase, it had an expected yield to maturity of 10.45%. If Arman sold the bond today for $3000, what rate of return would she have earned for the past year?
4. Last year Arman purchased a $3028 face value corporate bond with an 8% annual coupon rate and a 15-year maturity. At the time of the purchase, it had an expected yield to maturity of 10.45%. If Arman sold the bond today for $3000, what rate of return would she have earned for the past year?
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
Related questions
Question
![**Problem Statement:**
_Last year Arman purchased a $3028 face value corporate bond with an 8% annual coupon rate and a 15-year maturity. At the time of the purchase, it had an expected yield to maturity of 10.45%. If Arman sold the bond today for $3000, what rate of return would she have earned for the past year?_
**Detailed Breakdown:**
1. **Face Value and Coupon Rate**:
- The face value of the bond is $3028.
- The bond has an 8% annual coupon rate.
2. **Maturity**:
- The bond was set to mature in 15 years from the purchase date.
3. **Yield to Maturity at Purchase**:
- When Arman purchased the bond, the yield to maturity was expected to be 10.45%.
4. **Selling Price After One Year**:
- Arman sold the bond today for $3000.
**Objective**:
Calculate the rate of return Arman earned for the past year.
**Calculation Steps**:
1. **Coupon Payment**:
- The annual coupon payment is calculated as:
\[
\text{Coupon Payment} = \text{Face Value} \times \text{Coupon Rate} = 3028 \times 0.08 = 242.24
\]
2. **Purchase Price**:
- Given the yield to maturity and coupon rate, the purchase price when bought can be calculated using bond pricing formulas (not provided in the problem but relevant for deeper financial understanding).
3. **Total Earnings**:
- Total earnings in one year include the coupon payment and the difference between the selling price and the purchase price if bought at a different price.
4. **Rate of Return Calculation**:
\[
\text{Rate of Return} = \frac{\text{Coupon Payment} + (\text{Selling Price} - \text{Buying Price})}{\text{Buying Price}}
\]
For simplification:
- Assuming the bond was bought at par value ($3028), consider the following:
\[
\text{Rate of Return} = \frac{242.24 + (3000 - 3028)}{3028} = \frac{242.24 - 28}{3028} = \frac{214.24}{3028} \approx 0.0707 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffeeb79a1-23ea-4f54-b610-a8910f30c066%2F68333ad6-6010-4b96-9e81-92363bb6e96a%2F7zplr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
_Last year Arman purchased a $3028 face value corporate bond with an 8% annual coupon rate and a 15-year maturity. At the time of the purchase, it had an expected yield to maturity of 10.45%. If Arman sold the bond today for $3000, what rate of return would she have earned for the past year?_
**Detailed Breakdown:**
1. **Face Value and Coupon Rate**:
- The face value of the bond is $3028.
- The bond has an 8% annual coupon rate.
2. **Maturity**:
- The bond was set to mature in 15 years from the purchase date.
3. **Yield to Maturity at Purchase**:
- When Arman purchased the bond, the yield to maturity was expected to be 10.45%.
4. **Selling Price After One Year**:
- Arman sold the bond today for $3000.
**Objective**:
Calculate the rate of return Arman earned for the past year.
**Calculation Steps**:
1. **Coupon Payment**:
- The annual coupon payment is calculated as:
\[
\text{Coupon Payment} = \text{Face Value} \times \text{Coupon Rate} = 3028 \times 0.08 = 242.24
\]
2. **Purchase Price**:
- Given the yield to maturity and coupon rate, the purchase price when bought can be calculated using bond pricing formulas (not provided in the problem but relevant for deeper financial understanding).
3. **Total Earnings**:
- Total earnings in one year include the coupon payment and the difference between the selling price and the purchase price if bought at a different price.
4. **Rate of Return Calculation**:
\[
\text{Rate of Return} = \frac{\text{Coupon Payment} + (\text{Selling Price} - \text{Buying Price})}{\text{Buying Price}}
\]
For simplification:
- Assuming the bond was bought at par value ($3028), consider the following:
\[
\text{Rate of Return} = \frac{242.24 + (3000 - 3028)}{3028} = \frac{242.24 - 28}{3028} = \frac{214.24}{3028} \approx 0.0707 \
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Accounting
Accounting
ISBN:
9781337272094
Author:
WARREN, Carl S., Reeve, James M., Duchac, Jonathan E.
Publisher:
Cengage Learning,
Accounting Information Systems
Accounting
ISBN:
9781337619202
Author:
Hall, James A.
Publisher:
Cengage Learning,
Accounting
Accounting
ISBN:
9781337272094
Author:
WARREN, Carl S., Reeve, James M., Duchac, Jonathan E.
Publisher:
Cengage Learning,
Accounting Information Systems
Accounting
ISBN:
9781337619202
Author:
Hall, James A.
Publisher:
Cengage Learning,
Horngren's Cost Accounting: A Managerial Emphasis…
Accounting
ISBN:
9780134475585
Author:
Srikant M. Datar, Madhav V. Rajan
Publisher:
PEARSON
Intermediate Accounting
Accounting
ISBN:
9781259722660
Author:
J. David Spiceland, Mark W. Nelson, Wayne M Thomas
Publisher:
McGraw-Hill Education
Financial and Managerial Accounting
Accounting
ISBN:
9781259726705
Author:
John J Wild, Ken W. Shaw, Barbara Chiappetta Fundamental Accounting Principles
Publisher:
McGraw-Hill Education