[1.] A pension plan is obligated to make disbursements of $1.7 million, $2.7 million, and $1.7 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.)

Portfolio

Investment in one-year zero-Coupon bonds ______________%

Investment in perpetuity ______________%

[2.] You will be paying $12,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 9%.

a.What is the present value and duration of your obligation?(Do not round intermediate calculations. Round "Present value" to 2 decimal places and "Duration" to 4 decimal places.)

Present Value $ _________

Duration _______ _ Years

b.What is the duration of a zero-coupon bond that would immunize your obligation and its future redemption value?(Do not round intermediate calculations. Round "Duration" to 4 decimal places and "Future redemption value" to 2 decimal places.)

Duration _________Years

Future redemption value _________

c.Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 10%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation?(Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Net position changes by: ____________

d.What if rates fall to 8%?(Enter your answer as a positive value. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Net Position Changes by: ___________

[3.] You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are going to closely resemble level perpetuities of $1.4 million per year. The interest rate is 8%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds.

a.How muchmarket valueof each of the zeros will be necessary to fund the plan if you desire an immunized position?(Do not round intermediate calculations. Enter your answers in millions. Round your answers to 1 decimal place.)

Market Value

Five -Year _____________ Million

Twenty- Year _____________ Million

b.What must be theface valueof each of the two zeros to fund the plan?(Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places.)

Face Value

Five-Year ___________ Million

Twenty- Year ___________ Million