1. You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 and your actuarial tables suggest that you will live to be 100. You want to move to the Bahamas when you retire. You estimate that it will cost you $ 300,000 to make the move (on your 65th birthday) and that your living expenses will be $30,000 a year (starting at the end of year 66 and continuing through the end of year 100) after that.
a. How much will you need to have saved by your retirement date to be able to afford this course of action?
b. You already have $50,000 in savings. If you can invest money, tax-free, at 8% a year, how much would you need to save each year for the next 30 years to be able to afford this retirement plan?
c. If you did not have any current savings and do not expect to be able to start saving money for the next 5 years, how much would you have to set aside each year after that to be able to afford this retirement plan?
2. You have been hired to run a pension fund for TelDet Inc, a small manufacturing firm. The firm currently has $5 million in the fund and expects to have cash inflows of $2 million a year for the first 5 years followed by cash outflows of $ 3 million a year for the next 5 years.
Assume that interest rates are at 8%.
a. How much money will be left in the fund at the end of the tenth year?
b. If you were required to pay a perpetuity after the tenth year (starting in year 11 and going through infinity) out of the balance left in the pension fund, how much could you afford to pay?
3. You have been asked to estimate the value of a 10-year bond with a coupon that will be low initially but it is expected to grow later in the bond's life. The coupon is expected to be 5% of the face value of the bond (which is $ 1000) for the first 5 years, and will increase by 1% every year for the next 5 years ñ the coupon rate will be 6% in year 6, 7% in year 7, 8% in year 8, 9% in year 9 and 10% in year 10. Estimate the value of this bond.