Can someone help me out with a CFA retirement planning question?
Here is the question: You are helping a friend plan for retirement. She expects to retire at the end of 15 years. She expects to receive annual retirement income for 25 years after she retires. Her first retirement withdrawal will be in the amount of $100,000 and will be taken at the end of the 15th year. For the first 5 years of retirement, she wishes her income to keep pace with inflation of 3% per year. After that, for the last 20 years, income will remain constant at the same level as income in the 5th year of retirement. She currently has $5,000 in a bank account and expects to receive a bequest of $5,000 at the end of 10 years from now. Assume an interest rate of 6.5% per year. How much will she have to save annually if she saves an equal amount from now (t=0) until the end of year 15? This seems to me like a simple PV calculation, but I don't know if I have to figure how to save for $100,000 at the beginning of retirement or sometihng else. All the information is pertinent
Public Comments
- Okay... I did the time value of money calculations on a spreadsheet... I know they can probably be done on a piece of scratch paper with an HP-12c type calculator, but it's late. I ended up with her needing to save $67,827.89 every year in between now and retirement. I assumed that all withdrawals and deposits were made at the beginning of periods, because it did not state otherwise. Here was my method: 1. I started by calculating the present value at "Day 1" of retirement of all her future withdrawals. This amount was $1,766,537.06 2. I then calculated the future value of her current savings account and the bequest at retirement "Day 1" as well. The savings account would be worth $12,859.21. The bequest would be worth $6,850.43. 3. I netted the present value of all her future cash withdrawals, with the future value of her current nd expected investment. 4. I then calculated the required payment, assuming beginning of the period deposits and 6.5% rate of return, to acquire the shortfall amount of $1,746.827.42. Hence the above answer. I ran it through year-by-year breakout in excel, and came within .59 cents of being dead broke at the end of her life. Hope that helps... let me know what you come up with! Ken Clark Certified Financial Planner
