You manage a pension fund that will provide retired workers with lifetime annuit

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 $1.8 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.

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.)

What must be the face value of the two zeros to fund the plan? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places.)

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 $1.8 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.

Explanation / Answer

Now the total value of the money required to pay annual installments will be 1.8 M/0.10 = 18 Million

Duration is 1.10/0.10 = 11 years

y is the weight of 5 year zeros and

1-y is the weight of 20 year zeros

Hence 5y + 20(1-y) =11

y = 5 year zeros = 0.6
1-y = 20 year zeros = 0.4

Market Value of 5 year zeros = 18 M * 0.6 = 10.8M

Market Value of 20 yaers zeros = 18M * 0.4 = 7.2 M

Part B

Face Value value of 5 year zeros = 10.8 Million * (1.10)^ 5 = 10.8 M *1.10^5 = 17.39 Million

Face Value of 20 year zeros = 7.2 Million * (1.10)^20 = 48.48 Milliom

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