Question

A pension plan is obligated to make disbursements of $2.5 million, $3.5 million, and $2.5 million at the end of each of the next three years, respectively. The annual interest rate is 8%. If the plan wants to fully fund and immunize 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? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

To allocate a pension plan's funds between one-year zero-coupon bonds and perpetuities, the present value of the plan's future liabilities is calculated using the annual interest rate. The one-year zero-coupon bond allocation is set to cover the first-year obligation's present value, while the rest is allocated to perpetuities to cover subsequent years' obligations.

Step-by-step explanation:

The student is asking how to allocate funds between one-year zero-coupon bonds and perpetuities to immunize a pension plan against interest rate risk while meeting the plan's obligations. To solve this, we must first calculate the present value of the plan's liabilities given the annual interest rate of 8%. This is done using the present value (PV) formula for each disbursement, discounting them accordingly.

For the first-year disbursement:

PV = $2.5M / (1 + 0.08)^1

For the second-year disbursement:

PV = $3.5M / (1 + 0.08)^2

For the third-year disbursement:

PV = $2.5M / (1 + 0.08)^3

Once the total present value of liabilities is calculated, the portfolio allocation to one-year zero-coupon bonds should match the present value of the first-year obligation, since zero-coupon bonds fully mature in one year. The remainder of the portfolio should be allocated to perpetuities, which are infinite-lived assets, to fund the obligations for the subsequent years.

Answer 2

Please see attachment

Step-by-step explanation:

Please see attachment