d) If the pension fund you manage expects to have an inflow of $200 million 12 months from now, what forward contract would you seek to enter into to lock in current interest rates?
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- 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…Suppose that a life insurance company has guaranteed a payment of $14 million to a pension fund 4.5 years fromfund and can invest the entire premium for 4.5 years at an annual interest rate of 6.25%, how much will the life in$13.7 million$17.8 million$18.4 million$14.1 millionA corporate pension plan has to make the following payments over the next few years: Year 1 2 3 4 Amount ($ million) 29 33 39 47 NO CHAT GPT, HAND WRITTEN ONLY OTHERWISE WILL LEAVE A DOWNVOTE The appropriate interest rate is 8%. What is the present value of the liability (in $ million)? What is the duration 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 (approximately) level perpetuities of $1 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year maturity and 20-year maturity zero-coupon bonds. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? 4 million for 5 year bond and 6 million of 20-year bond. 6 million for 5 year bond and 4 million of 20-year bond. O 6.67 million for 5 year bond and 3.33 million of 20-year bond. O 3.33 million for 5 year bond and 6.67 million of 20-year bond. Question 9 Using the same information from question 8, suppose that one year has passed, and the interest rate remains at 10%. What actions are required to rebalance the portfolio? O buy additional 0.67 million 5-year bond and sell 0.67 million 20-year bond. Sell 0.67 million 5-year bond, purchase additional 0.67 million…12. If a financial contract promises you to pay $110 next year and $121 the year after that, and if you lend $200 today, what is its yield to maturity in this contract? Write down the appropriate formula, calculation procedure, and the answer.8) Special Retirement PlanYou set up a retirement plan where you will invest $20,000 per year in an account with a guaranteed rate of return of ? = 0.05. The plan requires that you start investing immediately at year t=0, and make fifteen (15) additional payments of $20,000 in years t=1, t=2, ..., t=10. You make 11 investments in total. a. What will be the value of this stream of investments in year t=50? b. What is the maximum you can withdraw per year over the twenty (20) year period from t=51, t=52, ..., t=70? You have to withdraw the same amount each year. c. What is the maximum that you can withdraw per year forever if you start to make withdrawals in year t=51. You have to withdraw the same amount each year. 19)
- A pension fund must pay out $1 million next year, $2 million the following year, and then $3 million the year after that. If the discount rate is 8%, what is the duration of this set of payments?NOTE: Provide a format and show your work (example: N = 6, PV = XXX, I = X%, etc.) It is now the year 2048 and you have amassed a retirement fund of $1.2 million. You want to retire in 13 years (year 2061). At the time, you plan to start withdrawing $20,000 per month.If your investment fund is invested at a 6.0 percent rate, how many months will it last you once you start to withdraw the money? (Assume monthly compounding. Do not round intermediate calculations and round your final answer to 2 decimal places.) Hint: draw a timeline to help visualize the problem.2. You intend to invest $3,000 per year in a mutual fund that averages a 9% return. If you start that the last day of 2021 and do it for 20 years, how much could you withdraw annually beginning the last day of 2041 and ending the last day of 2050, assuming the fund continues to earn 9%.
- You plan to invest $19,000 per year into a retirement account. If you earn a compound annual rate of return of 8%, how many years will it take you to reach a balance of $1,000,000? Question 10 options: 18.98 22.26 20.16 17.54 21.45You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the funds are going to closely resemble perpetuities of $1 million per year. The interest rate is 9% per year. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds. How much market value of each of the zero coupon bonds will be necessary to fund the plan if you desire an immunized position? Duration of a perpetuity is (1+y)/ya) At what annual interest rate would the following have to be invested? i) $500 to grow to $1,948.00 in 12 years ii) $300 to grow to $422.10 in 7 years iii) $50 to grow to $280.20 in 20 years iv) $200 to grow to $497.60 in 5 years b) You are considering invest ing in a security that will pay you $1,000 in 30 years. i) If the appropriate discount rate is 10 percent, what is the present value of this investment? ii) Assume these securities sell for $365, in return for which you receive $1,000 in 30 years. What is the rate of return investors earn on this security if they buy it for $365? USE EXCEL TO WORK THIS OUT AND SHOW THE FORMULA!
