Question

Problem 11-20

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 $2 million per year. The interest rate is 20%. You plan to fully fund the obligation using 5-year and 15-year maturity zero-coupon bonds.

Requirement 1:

How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? (Enter your answer in millions. Round your answers to 2 decimal places.)

	Market value
Five-year		million
Twenty-year		million

Requirement 2:

What must be the face value of the two zeros to fund the plan? (Enter your answer in millions. Round your answers to 2 decimal places.)

	Face value
Five-year		million
Twenty-year		million

Answer 1

The question does not clearly specifies whether both the bonds are used together or seperately (either of one is used).For the former option,the mix (proportion of each type of bond is not given).Hence we are assuming that either of the bond is to be used and we are analyzing both the bonds.

Amount required in fund = 2,000,000/0.2 =$10,000,000

A) Market value of 5 year ZCB = 10,000,000/(1.2)⁵ = 10,000,000/2.4883=$4,018,775

Market value of 20 year ZCB =10,000,000/(1.2)²⁰ =$260,840

B)FV of both the bonds will be $10,000,000.

This is the amount we need in fund at the end of period & ZCB always matures at FV.