Question

You manage a pension fund that will provide retired workers with lifetime annuities. You determine that...

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 \$600.000 per year. The interest rate is 8%. 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?

Homework Answers

Answer #1

Solution

The present value of the annuities is \$0.6 million / 0.08 = \$7.5M

The duration is 1.08 / 0.08 =13.5 years

Let x = Weight of 5 years Zeros and

1-x = Weight of 20 years Zeros

13.5= 5x+20(1-x)

13.5 = -15x +20

x = 6.5/15

and so x = 0.4333(in 5 year zeros) and 1-x = 0.56667 (in 20 year zeros)

5 year zeros : \$7.5 M *0.4333 = \$3.25M market value

20 year zeros : \$7.5 M *0.56667 = \$4.25 M market value

Face value of 5 year zeros : \$3.25 M *(1.08)5 = 4.78 M

Face value of 20 year Zeros : \$4.25 M * (1.08)20 = 19.81 M

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