A pension plan is obligated to make disbursements of $1.1 million, $2.1 million,

Question

A pension plan is obligated to make disbursements of $1.1 million, $2.1 million, and $1.1 million at the end of each of the next three years, respectively. The annual interest rate is 11%. 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.)

Portfolio Investment in one-year zero-coupon bonds % Investment in perpetuity %

Explanation / Answer

Assume w - weight of zero coupon bonds and 1 - w - weight of perpetuity

w x 1 + (1 - w) x (1 + 11%) / 11% = 1.9467

=> w + 10.0909 x (1 - w) = 1.9467

=> w = 89.59% is weight in zero-coupon

1 - w = 10.41% is weight in perpetuity

Year PMT PV of PMT Weight Year x Weight 1 $     1.10 $   0.9910 28.32% 0.2832 2 $     2.10 $   1.7044 48.70% 0.9740 3 $     1.10 $   0.8043 22.98% 0.6895 $   3.4997 100.00% 1.9467

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