Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual payments). The first payment will come in exactly 5 years (at the end of year 5) and the last payment in 9 years (at the end of year 9). a. What is the duration of the pension obligation? The current interest rate is 9% per year for all maturities. b. To generate the scheduled pension payments, the pension fund wants to invest the present value of the future payouts in bonds and match the duration of its obligation in part a). If the fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how much money (dollar amount) ought to be placed in each bond now? What should be the total face value (not current market value) of each zero coupon bond held? c. Right after the fund made its investment outlined in part b), market interest rates for all maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in part b) can still approximately fund the future payments by showing that the present values of the two after the drop in market interest rates are still roughly the same
Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual payments). The first payment will come in exactly 5 years (at the end of year 5) and the last payment in 9 years (at the end of year 9). a. What is the duration of the pension obligation? The current interest rate is 9% per year for all maturities. b. To generate the scheduled pension payments, the pension fund wants to invest the present value of the future payouts in bonds and match the duration of its obligation in part a). If the fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how much money (dollar amount) ought to be placed in each bond now? What should be the total face value (not current market value) of each zero coupon bond held? c. Right after the fund made its investment outlined in part b), market interest rates for all maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in part b) can still approximately fund the future payments by showing that the present values of the two after the drop in market interest rates are still roughly the same
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
![Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual
payments). The first payment will come in exactly 5 years (at the end of year 5) and the last
payment in 9 years (at the end of year 9).
a. What is the duration of the pension obligation? The current interest rate is 9% per year for all
maturities.
b. To generate the scheduled pension payments, the pension fund wants to invest the present
value of the future payouts in bonds and match the duration of its obligation in part a). If the
fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how
much money (dollar amount) ought to be placed in each bond now? What should be the total
face value (not current market value) of each zero coupon bond held?
c. Right after the fund made its investment outlined in part b), market interest rates for all
maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in
part b) can still approximately fund the future payments by showing that the present values of
the two after the drop in market interest rates are still roughly the same](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50d7c0d6-afc8-43bd-8c5e-2957d5c6574a%2Fedfb760c-1090-4003-aa7d-eeabb252589e%2F7p7t9h_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual
payments). The first payment will come in exactly 5 years (at the end of year 5) and the last
payment in 9 years (at the end of year 9).
a. What is the duration of the pension obligation? The current interest rate is 9% per year for all
maturities.
b. To generate the scheduled pension payments, the pension fund wants to invest the present
value of the future payouts in bonds and match the duration of its obligation in part a). If the
fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how
much money (dollar amount) ought to be placed in each bond now? What should be the total
face value (not current market value) of each zero coupon bond held?
c. Right after the fund made its investment outlined in part b), market interest rates for all
maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in
part b) can still approximately fund the future payments by showing that the present values of
the two after the drop in market interest rates are still roughly the same
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9781260013924/9781260013924_smallCoverImage.jpg)
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
![FUNDAMENTALS OF CORPORATE FINANCE](https://www.bartleby.com/isbn_cover_images/9781260013962/9781260013962_smallCoverImage.gif)
![Financial Management: Theory & Practice](https://www.bartleby.com/isbn_cover_images/9781337909730/9781337909730_smallCoverImage.gif)
![Essentials Of Investments](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9781260013924/9781260013924_smallCoverImage.jpg)
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
![FUNDAMENTALS OF CORPORATE FINANCE](https://www.bartleby.com/isbn_cover_images/9781260013962/9781260013962_smallCoverImage.gif)
![Financial Management: Theory & Practice](https://www.bartleby.com/isbn_cover_images/9781337909730/9781337909730_smallCoverImage.gif)
![Foundations Of Finance](https://www.bartleby.com/isbn_cover_images/9780134897264/9780134897264_smallCoverImage.gif)
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
![Fundamentals of Financial Management (MindTap Cou…](https://www.bartleby.com/isbn_cover_images/9781337395250/9781337395250_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9780077861759/9780077861759_smallCoverImage.gif)
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