Case: The Time Value of Money

It is December31, 2010 and 35 year old Camille is reviewing her retirement savings and planning for her retirement at age 60. She currently has $55,000 saved (which includes the deposit she just made today) and invests $2,000/year (at the end of the year) in a retirement account that earns 10% annually. She has decided that she is comfortable living on $40,000/year (in today’s dollars) and believes she can continue to live on that amount as long as it is adjusted for inflation. Inflation is expected to average 2.86%/year for the foreseeable future. After researching information on average life expectancy for females of her background, her plan will assume she lives to age 88. She will withdraw the amount needed each year during retirement at the beginning of the year. So, on December 31 at age 60, she will make her last deposit of $2,000 and the following day (January 1st) she will withdraw her first installment for retirement.

1) If Camille continues on her current plan, will she be able to accomplish it?

2) How would the situation change if Camille were to start placing the $2,000 annual savings into her account on January 1st rather than December 31 of each year? Assume that the investment still pays interest at the end of the year.

3) If Camille resumes making her deposits at the end of the year, how much would she have to save to accomplish her objective?

4) Assume Camille continues with her current plan. What interest rate would she have to earn on her investment to make it work?

5) If Camille wishes to leave $50,000 perpetuity to her alma mater, starting one year from the year she turns 88, then how much extra money would she need to have on December 31 of the year she turns 88? Assume the investment will earn 10%.

6) Rework the previous question for the case where Camille wants the university investment to grow by 5% per year.

From Corporate Finance by Graham, Smart and Megginson, 2010 (3rd Edition)