Pension funds pay lifetime annuities to recipients. If a firm remains in business indefi- nitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments. Your task is to immunize the value of your portfolio, using two bonds. The yield curve is flat at 9% and data on the coupons and maturities of the two bonds as well as the size of the obligation are given in Table 3.

Table 3: Data for solving Question 5. Bond maturities are expressed in years and the obligation is expressed in millions of e, paid yearly to beneficiaries

Bond 1: Coupon 2% Maturity 25

Bond 2: Coupon 8% Maturity 10

Obligations: 3.5

Face Value: 1000

• The duration of your obligations, Bond 1, and Bond 2.

• The present value of your obligations (in mill e).

• The weights and market values (in mill e) of the two bonds that fully immunize your portfolio. Note: The solution to this problem involves solving a linear equation with one unknown. Do not use excels solver to find the solution, because the solver does not do well with solving linear problems.

• The market value of the portfolio cash flows in the subsequent 15 years, stemming jointly from the two bonds.