You are managing a pension plan that is due to pay $11 million a year for 15 years with the first payment one year from today and $8 million a year for 10 years with the first payment 5 years from today. You can use a zero coupon bond with 4 years to maturity and a 20 year coupon bond with a duration of 12.31 years to immunize your portfolio. The interest rate is 7 percent for all maturities. How many zero coupon bonds will you have to purchase? Assume annual cash flows and compounding in your calculations.
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You are managing a pension plan that is due to pay $11 million a year for 15 years with the first payment one year from today and $8 million a year for 10 years with the first payment 5 years from today. You can use a zero coupon bond with 4 years to maturity and a 20 year coupon bond with a duration of 12.31 years to immunize your portfolio. The interest rate is 7 percent for all maturities. How many zero coupon bonds will you have to purchase? Assume annual cash flows and compounding in your calculations.
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- 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 millionYou 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 millionYou manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are essentially going to resemble level perpetuities of $2.24 million per year. The yield to maturity on all bonds is 14%. (a). Assume the duration of six-year maturity bonds with coupon rates of 10% (paid annually) is 5 years, and the duration of 22-year maturity bonds with coupon rates of 7% (paid annually) is 11 years. Calculate how much of each of these two coupon bonds (in market value) you will want to hold in order to both fully fund and immunize your obligation. (b). Calculate the total par value of your holdings in the six-year maturity coupon bond. Please show working
- 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? (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 millionYou 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 ___ MillionYou 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 $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 are considering the purchase of a perpetual bond that pays you $174 per year for the foreseeable future. If you require a 5.85% rate of return on this bond investment, what is a fair price for the bond that you would be willing to pay today? To nearest $0.01You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.a. What is the present value and duration of your obligation?b. What maturity zero-coupon bond would immunize your obligation? c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 9%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation?d. What if rates fall immediately to 7%?
- A portfolio for a pension fund that you manage has payments resembling a perpetuity. You want to immunize the pension fund liability by purchasing 2 bonds: a zero coupon bond maturing in 6 years & a 10% coupon bond with a duration of 25 years. Assume the yield on both bonds & the pension fund is 7%. What percent of your portfolio should you invest in the zero-coupon bonds?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 $2 million per year to beneficiaries. The yield to maturity on all bonds is 16%.a. If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is four years and the duration of 20-year maturity bonds with coupon rates of 6% (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?b. What will be the par value of your holdings in the 20-year coupon bond?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 $2 million per year to beneficiaries. the yield to maturity on all bonds is 15%. a. if the duration of 5-year maturity bonds with coupon rates of 11% (paid annually) is 4 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?