Enterprises has bonds on the market making annual payments, with 15 years to maturity, a par value of $1,000, and selling for $971. At this price, the bonds yield 8.3 percent. What must the coupon rate be on the bonds? 32.16. Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., Coupon rate
Enterprises has bonds on the market making annual payments, with 15 years to maturity, a par value of $1,000, and selling for $971. At this price, the bonds yield 8.3 percent. What must the coupon rate be on the bonds? 32.16. Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., Coupon rate
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
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Kk.173.
![### Problem Statement
Nikita Enterprises has bonds on the market making annual payments, with 15 years to maturity, a par value of $1,000, and selling for $971. At this price, the bonds yield 8.3 percent. What must the coupon rate be on the bonds?
**Note:** Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.
**Answer:**
Coupon rate: [Input Box] %
Please input your answer in the designated box above.
---
### Explanation & Formulas
To determine the coupon rate on the bonds, we need to use the formula for the present value of a bond, which includes the annual coupon payment. The bond's price, par value, yield (interest rate), and number of years to maturity are given. The formula is expressed as follows:
\[ P = \left( C \times \frac{1 - (1 + r)^{-n}}{r} \right) + \left( \frac{F}{(1 + r)^n} \right) \]
Where:
- \( P \) = Price of the bond ($971)
- \( C \) = Annual coupon payment (which we need to find)
- \( r \) = Yield or interest rate (8.3% or 0.083)
- \( n \) = Number of years to maturity (15)
- \( F \) = Par value of the bond ($1,000)
Rearranging the formula to solve for \( C \), the annual coupon payment:
1. Calculate the present value of the par value:
\[ \frac{F}{(1 + r)^n} = \frac{1000}{(1 + 0.083)^{15}} \]
2. Substitute back to find \( C \):
\[ 971 = \left( C \times \frac{1 - (1 + r)^{-n}}{r} \right) + \left( \frac{1000}{(1 + 0.083)^{15}} \right) \]
By solving the above equation step-by-step, we can determine \( C \).
3. Finally, calculate the coupon rate:
\[ \text{Coupon Rate} = \left( \frac{C}{F} \right) \times 100 \]
Enter your answer as a percentage rounded to two decimal places in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ef2e86f-df5b-40a3-8009-016cf0671dd4%2Fb1f5455d-e037-42e0-b8f8-c8a7856857e2%2F8pgtjb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Nikita Enterprises has bonds on the market making annual payments, with 15 years to maturity, a par value of $1,000, and selling for $971. At this price, the bonds yield 8.3 percent. What must the coupon rate be on the bonds?
**Note:** Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.
**Answer:**
Coupon rate: [Input Box] %
Please input your answer in the designated box above.
---
### Explanation & Formulas
To determine the coupon rate on the bonds, we need to use the formula for the present value of a bond, which includes the annual coupon payment. The bond's price, par value, yield (interest rate), and number of years to maturity are given. The formula is expressed as follows:
\[ P = \left( C \times \frac{1 - (1 + r)^{-n}}{r} \right) + \left( \frac{F}{(1 + r)^n} \right) \]
Where:
- \( P \) = Price of the bond ($971)
- \( C \) = Annual coupon payment (which we need to find)
- \( r \) = Yield or interest rate (8.3% or 0.083)
- \( n \) = Number of years to maturity (15)
- \( F \) = Par value of the bond ($1,000)
Rearranging the formula to solve for \( C \), the annual coupon payment:
1. Calculate the present value of the par value:
\[ \frac{F}{(1 + r)^n} = \frac{1000}{(1 + 0.083)^{15}} \]
2. Substitute back to find \( C \):
\[ 971 = \left( C \times \frac{1 - (1 + r)^{-n}}{r} \right) + \left( \frac{1000}{(1 + 0.083)^{15}} \right) \]
By solving the above equation step-by-step, we can determine \( C \).
3. Finally, calculate the coupon rate:
\[ \text{Coupon Rate} = \left( \frac{C}{F} \right) \times 100 \]
Enter your answer as a percentage rounded to two decimal places in
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