You have recently been hired as a consultant for a personal financial planning firm. One of your first projects is creating a retirement plan for a couple, Larry and Stacy Hendrickson. They have just celebrated their 45th birthdays and after paying for their children's education, they have decided to get serious about saving for retirement.
Larry and Stacy hope to retire 20 years from now (on their 65th birthdays), and they expect to live until age 80. Their hope is to be able to withdraw $125,000 a year from their retirement account - the first withdrawal will occur on their 65th birthdays, and the 15th and final withdrawal will occur on their 79th birthdays. On their 80th birthdays, the account is expected to have a zero value (i.e., they don't expect to have any remaining funds left for their children's inheritance).
Larry and Stacy currently have $100,000 saved in a retirement account, which consists of a portfolio of mutual funds that is expected to produce an annual return of 7%. In order to accomplish their goals, they would like to deposit an equal annual amount into their account starting one year from today (on their 46th birthdays) and continue to make those deposits through age 65. (Again, the account has an expected annual return of 7%.) Thus, they will make 20 annual end-of-year deposits to this account.
a. How much do Larry and Stacy need to contribute to the account at the end of each of the next 20 years in order to accomplish their goals?
b. If they wanted to have $1.5 million available for inheritance at age 80, how much would they need to contribute to the account at the end of each of the next 20 years? (Assume everything else stays the same.)
c. If they instead expected to earn only 5% a year from their mutual funds, how much would they need to contribute to the account at the end of each of the next 20 years? (Continue to assume that they want to have $1.5 million available for inheritance at age 80.)
d. Larry and Stacy realize that there are a lot of variables in their retirement plan. The two variables that they are particularly interested in are the expected return of their mutual funds and the amount they have available for inheritance at age 80. Create in Excel a two-input Data Table that tests the sensitivity of their annual deposit amount by varying the expected returns from 2% to 10% in 1% increments and varying the inheritance level from 0 to $4 million in $0.5 million increments. The data table should be constructed with the expected returns shown on the side of the table and the amount available for inheritance shown across the table. [Hint: An Excel file (in xlsx format) explaining how to create a Data Table is contained in the Calculator Tutorials & Excel Tools folder on the class web page.] You MUST set up and submit an Excel data table using Excel's Data Table feature to receive credit.
e. Larry and Stacy have one last concern. They recognize that the value of their $125,000 annual withdrawals during retirement will steadily decline because of expected inflation. Assume that they want to have the value of these withdrawals increase by 3% a year during retirement to account for expected inflation. In other words, they want to withdraw $125,000 at age 65, $128,750 at age 66, and 128,750 × 1.03 at age 67, and etc. Going back to the other original assumptions (7% return and no expected inheritance), how much would they need to contribute to the account at the end of each of the next 20 years in order to meet this revised goal which protects them against rising inflation? Set up this problem using Excel, refer to the Growing Annuity Example spreadsheet in the Files Page in the Other Classroom Materials folder.