You 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 $ 1 million per annum. The interest rate is 10%. You plan to fully fund the obligation using five-year and 20-year maturity zero-coupon bonds. a. how much market value of each of the zeros will be necessary to fund the plan if you desire an immunised position?
Question
You 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 $ 1 million per annum. The interest rate is 10%. You plan to fully fund the obligation using five-year and 20-year maturity zero-coupon bonds. a. how much market value of each of the zeros will be necessary to fund the plan if you desire an immunised position?
Solution
To fund the plan with an immunised position, we need to match the duration of the assets (bonds) with the duration of the liabilities (annuities).
First, we need to calculate the duration of the annuity. The formula for the duration of a perpetuity is D = (1 + r) / r, where r is the interest rate. Substituting the given values, we get D = (1 + 0.10) / 0.10 = 11 years.
Next, we need to determine the proportions of the 5-year and 20-year bonds to match this duration. Let's denote the proportion of the 5-year bond as x and the 20-year bond as (1 - x). The equation to solve is 5x + 20(1 - x) = 11.
Solving for x, we get x = 0.45. Therefore, 45% of the fund should be invested in the 5-year bond and 55% in the 20-year bond.
Finally, we need to calculate the market value of each bond. The present value of a 1,000,000 / 0.10 = $10,000,000.
Therefore, the market value of the 5-year bond is 4,500,000 and the 20-year bond is 5,500,000.
Similar Questions
A pension plan is obligated to make disbursements of $1 million, $2 million, $5 million, and $1 million at the end of each of the next four years, respectively. If the plan wants to fully fund and immunise 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? Assume the interest rate is 10% annually. Group of answer choicesDuration is 2.6019Duration is 2.7329Duration is 2.6873Duration is 2.5871
Suppose we are in 2022. An insurer has to make a guaranteed payment to a policyholder in five years (2027) of $1,469, a lump-sum policy payout on retirement, equivalent to investing $1,000 at an annually compounded rate of 8 percent over five years. To protect itself, the insurer has bought a six-year maturity bond paying 8% annual coupons with an 8% YTM that has a duration of 4.993 or approximately 5 years. The face value of this bond is $1000. If the interest rates fall to 7%. At the end of fifth year, which of the following statements is FALSE?A.The insurer receives the proceeds from selling the bond at the end of fifth year of $1,009B.The insurer receives an reinvestment income of $60.C.The insurer has matched the maturity of its liabilties with that of its assets. D.The insurer receives coupons of $400.E.The insurer is immunized from interest rate risk.
You plan to retire in 20 years and want to have a retirement fund that pays you $50,000 per year for 25 years after your retirement. If the interest rate is 6%, what lump sum do you need to deposit today to achieve this goal?
b. what must be the face value of the two zeros to fund the plan?
How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume an interest rate of 10% and cash flows at the end of each period
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.