This morning, you arrived at your job as Head of Client Advisory Services for a major investment firm and saw only two items of your calendar. At 10:00 am you have an appointment with a major client, Mrs. Smith and at 2:00pm you have a tee time to play Golf with several colleagues. While at first you were happy, you then read the details of your first appointment. Mrs. Smith today is turning 65, it is the first day of her retirement and she wants to discuss multiple options regarding her investments. You may have to skip golf today.
Before Mrs. Smith arrives, you study her account file and notice she has six different investments:
A promissory note entitling her to receive a lump sum of $100,000 5 years from today. Similar notes today yield 5% per year.
A 10 year CD paying 8% interest per year that she opened exactly 10 years ago with a $35,000 deposit.
An insurance settlement that will pay her $1,200 per month for the next 40 months. A finance company, GJ Worthless, is willing to buy this settlement from her today as long it can obtain a yield of 0.85% per month on its investment.
A retirement account that has always paid an APR of 6% per year (0.5% per month) compounded monthly, into which she has deposited $310 at the end of every month for the last 10 years.
50 shares of a stock that will pay a $25 quarterly dividend (per share) three months from today and is expected to continue paying the same $25 per quarter forever. Similar investments today are priced to yield 1.25% per quarter.
250 shares of a stock that will pay a $15 annual dividend (per share) a year from today and has increased its dividend payout by 2% every single year. This sock is expected to continue increasing its dividend payout at the same rate forever. Similar investments today are priced to yield 5% per year.
After reviewing Mrs. Smith's file, you wonder how valuable her account really is. After all, if you miss golf, it better be for big bucks. To answer your question, you decide to calculate the sum of the value as of today for all of Mrs. Smith's investments combined. Your total equals:
$ (40 points / 6.66 points for each question above). (Please show your calculation of the value as of today for each investment, 1 through 6 above, individually).
When Mrs. Smith arrives, after wishing her a happy 65th birthday and congratulating her on the first day of her retirement, you ask her what she has in mind for her investments. Mrs. Smith has several ideas and wants you to help her figure out some numbers she is not very clear on. For starters, Mrs. Smith plans to buy a luxury car. After this, she expects to have $420,000 left over in her account.
Mrs. Smith's ideas and questions are the following:
(A) As one option, Mrs. Smith would like to leave her heirs $1,000,000 upon her death.
1. If she starts with $420,000 today and deposits the proceeds in an account paying 6% annual interest, in how many years from now will the balance reach $1million?
2. If she lives to age 88, what annual APR will result in the $420,000 reaching a balance of $1,000,000 upon her death, if she deposits them in an account that offers monthly compounding?
(B) As another option, Mrs. Smith is considering letting her heirs fend for themselves and using her $420,000 to generate $3,300 per month for the rest of her life.
1. If Mrs. Smith manages to deposit the $420,000 at a an APR of 8% per year (8% APR = 8% / 12 per month) and receives $3,300 per month, what age will she be when her funds run out?
2. If Mrs. Smith plans to live to age 93, at what monthly interest rate must she deposit the $420,000 to be able to receive $3,300 per month with no balance left in the account at her death?
(C) As her last option, Mrs. Smith is considering leaving an endowment to her Alma Mater that will produce $10,000 a year forever, starting a year from now.
1. If the current rate for such investment is 4%, how much money must Mrs. Smith deposit to generate $10,000 per year forever?
2. If the current rate for such an investment is 6% and inflation is expected to be 1.5% per year, how much money must Mrs. Smith deposit to generate the equivalent of $10,000 per year, after inflation, forever? (i.e. the $10,000 would need to grow by 1.5% every single year).