Problem 11-11 (Algo) Required: A pension plan is obligated to make disbursements of $2.6 million, $3.6 million, and $2.6 million at the end of each of the next three years, respectively. The annual interest rate is 7%. If the plan wants to fully fund and immunize its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Investment in one-year zero-coupon bonds Investment in perpetuity Portfolio % %

Problem 11-11 (Algo) Required: A pension plan is obligated to make disbursements of $2.6 million, $3.6 million, and $2.6 million at the end of each of the next three years, respectively. The annual interest rate is 7%. If the plan wants to fully fund and immunize its position, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Investment in one-year zero-coupon bonds Investment in perpetuity Portfolio % %

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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A pension plan is obligated to make disbursements of $1.9 million, $2.9 million, and $1.9 million at the end of each of the next three years, respectively. The annual interest rate is 11%. If the plan wants to fully fund and immunize its position, how much of its portfolio should it allocate to one - year zero - coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan?
A pension fund has a liability of £65000 to be paid precisely in 4 years time. It wants to Reddington immunise this liability with P 3-year zero coupon bonds and Q 5-year zero coupon bonds, where P and Q are to be determined. Interest is compounded continuously with rate 2%. What is the present value, effective duration and convexity of the liability?
You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $1.4 million per year. The interest rate is 8%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds.Required: a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position?
You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $1.8 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds. Required: a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? (Do not round intermediate calculations. Enter your answers in millions. Round your answers to 1 decimal place.) Five-year Twenty-year Market Value million million b. What must be the face value of each of the two zeros to fund the plan? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places.) Five-year Twenty-year Face Value million million
You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $1.8 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds.Required: a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? (Do not round intermediate calculations. Enter your answers in millions. Round your answers to 1 decimal place.) Market Value Five-Year ___ Million Twenty-Five Year ___ Million b. What must be the face value of each of the two zeros to fund the plan? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places.) Face Value Five-Year ___ Million Twenty-Five Year ___ Million
You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $2.3 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds. Required: a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position?. Five-year Twenty-year Market Value Five-year Twenty-year million million b. What must be the face value of each of the two zeros to fund the plan? Face Value million million
You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $2.1 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds.Required: a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? (Do not round intermediate calculations. Enter your answers in millions. Round your answers to 1 decimal place.) Market Value Five year: Twenty year: b. What must be the face value of each of the two zeros to fund the plan? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places.) Face Value Five year: Twenty year:
You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $2.0 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds. Required: a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? (Do not round intermediate calculations. Enter your answers in millions. Round your answers to 1 decimal place.) Five-year Twenty-year Market Value Five-year Twenty-year million million b. What must be the face value of each of the two zeros to fund the plan? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places.) Face Value million million
A pension fund faces a promised outflow of $5 million in 6 years. Its managers plan to dedicate a portfolio comprised of the following two bonds to meet this obligation. d. Suppose that it is now 3 years later and that there has been a parallel increase in interest rates of 2%. Explain how immunization at least partially protects this portfolio. That is, what are the sources of losses and gains associated with each of the bonds caused by the increase in interest rates? How do they offset each other?
Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $3.0 million per year to beneficiaries. The yield to maturity on all bonds is 20%. Required: a. If the duration of 5-year maturity bonds with coupon rates of 16% (paid annually) is 3.7 years and the duration of 20-year maturity bonds with coupon rates of 7% (paid annually) is 6.5 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? (Do not round intermediate calculations. Enter your answers in millions rounded to 5 decimal places.) > Answer is complete but not entirely correct. Holdings 5-year bond 20-year bond $ 1.60000 million $ 22.20000 million b. What will be the par value of your holdings in the 20-year coupon bond? (Enter your answer in dollars not in…
Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $1.9 million per year to beneficiaries. The yield to maturity on all bonds is 19.0%. Required: a. If the duration of 5-year-maturity bonds with coupon rates of 11.8% (paid annually) is four years and the duration of 20-year-maturity bonds with coupon rates of 7% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? Note: Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places. b. What will be the par value of your holdings in the 20-year coupon bond? Note: Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places. a. 5 year bond a. 20 year bond b. Par…
Suppose that a pension fund manager anticipates the purchase of a 20-year 8 percent coupon T-bond at the end of two years. Interest rates are assumed to change only once every year at year end. At that time, it is equally probable that interest rates will increase or decrease 1 percent. When purchased in two years, the T-bond will pay interest semiannually. Currently, it is selling at par a. What is the pension fund manager’s interest rate risk exposure? b. How can the pension fund manager use options to hedge that interest rate risk exposure?

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