You, the CFO of a large pension fund, are responsible for making sure that your fund is fully funded (i.e., that your fund has enough money to meet its obligations). You estimate that, in 10 years, your fund will need to pay out $5 billion. The market interest rate is 5.4%. You decide to fund the obligation using five-year zero-coupon bonds and perpetuities that make annual coupon payments.

1. How can you immunize the obligation? (Here, you need to construct an immunized portfolio that consists of the zero-coupon bonds and the perpetuities.) To begin, you need to find the present value of the obligation.

2. Now suppose that one year has passed and that the market rate is still 5.4%. You need to ensure that the obligation is still fully-funded and immunized. Is the obligation still fully-funded and immunized? If not, what do you need to do to fully fund and immunized the obligation?