What is the swap rate? (the fixed rate that will make the interest rate swap zero NPY at the beginning) Select one: a 1.99% b 2.09% c1.89% d 2.19%
What is the swap rate? (the fixed rate that will make the interest rate swap zero NPY at the beginning) Select one: a 1.99% b 2.09% c1.89% d 2.19%
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
![### Interest Rate Swaps: Understanding the Calculation
#### Example Problem:
**Q20:** Company ABC enters a 50 million notional principal interest rate swap. The swap requires ABC to pay a fixed rate and receive a floating rate equal to LIBOR. The swap contract specifies that payments are made every twelve months with the floating payments determined by LIBOR at the beginning of the twelve months. The period of the swap is four years.
The following zero coupon curve prevails in the market (annual compounding):
| Time (years) | 1 | 2 | 3 | 4 |
|--------------|------|------|------|------|
| Rate | 0.015| 0.018| 0.020| 0.022|
**Question:** What is the swap rate? (The fixed rate that will make the interest rate swap zero NPV at the beginning)
**Options:**
a) 1.99%
b) 2.09%
c) 1.89%
d) 2.19%
#### Detailed Explanation:
Interest rate swaps are a fundamental financial instrument used by companies to manage interest rate exposure. In this problem, Company ABC has entered into a swap to exchange floating rate payments for fixed rate payments. To determine what the fixed rate should be, we need to ensure the net present value (NPV) of the swap is zero at the start.
The zero coupon curve provided in the problem indicates the discount rates over different periods. Here's how to use this data:
1. **Understand the Zero Coupon Curve:** A zero coupon rate is the yield on a bond that pays no interest and is initially sold at a discount. The rates are given for 1 to 4 years.
2. **Calculate the Present Value Factors:** The present value factor (`PVF`) for each year can be calculated using the formula:
\[
\text{PVF} = \frac{1}{(1 + \text{Rate})^{\text{Year}}}
\]
3. **Determine Cash Flows:** For the fixed rate, the cash flows will be the same every year. For the floating rate, the cash flows will adjust based on LIBOR each year.
4. **Formulate the Equation:** We need to balance the present value of fixed rate payments with the present value of floating rate receipts. The general formula for the swap rate `S` in a fixed](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F933b2e7c-bcb1-4a47-8bd3-8f81e6e7ee8a%2F46cf88df-df97-4edc-837c-0b35f154434a%2Fc4r54rk_processed.png&w=3840&q=75)
Transcribed Image Text:### Interest Rate Swaps: Understanding the Calculation
#### Example Problem:
**Q20:** Company ABC enters a 50 million notional principal interest rate swap. The swap requires ABC to pay a fixed rate and receive a floating rate equal to LIBOR. The swap contract specifies that payments are made every twelve months with the floating payments determined by LIBOR at the beginning of the twelve months. The period of the swap is four years.
The following zero coupon curve prevails in the market (annual compounding):
| Time (years) | 1 | 2 | 3 | 4 |
|--------------|------|------|------|------|
| Rate | 0.015| 0.018| 0.020| 0.022|
**Question:** What is the swap rate? (The fixed rate that will make the interest rate swap zero NPV at the beginning)
**Options:**
a) 1.99%
b) 2.09%
c) 1.89%
d) 2.19%
#### Detailed Explanation:
Interest rate swaps are a fundamental financial instrument used by companies to manage interest rate exposure. In this problem, Company ABC has entered into a swap to exchange floating rate payments for fixed rate payments. To determine what the fixed rate should be, we need to ensure the net present value (NPV) of the swap is zero at the start.
The zero coupon curve provided in the problem indicates the discount rates over different periods. Here's how to use this data:
1. **Understand the Zero Coupon Curve:** A zero coupon rate is the yield on a bond that pays no interest and is initially sold at a discount. The rates are given for 1 to 4 years.
2. **Calculate the Present Value Factors:** The present value factor (`PVF`) for each year can be calculated using the formula:
\[
\text{PVF} = \frac{1}{(1 + \text{Rate})^{\text{Year}}}
\]
3. **Determine Cash Flows:** For the fixed rate, the cash flows will be the same every year. For the floating rate, the cash flows will adjust based on LIBOR each year.
4. **Formulate the Equation:** We need to balance the present value of fixed rate payments with the present value of floating rate receipts. The general formula for the swap rate `S` in a fixed
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 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Recommended textbooks for you
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
ISBN:
9780077861759
Author:
Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:
McGraw-Hill Education