Retirement Planning

Retirement Planning

Your 30 year old client wants to retire when
Subject: Business    / Finance   
Question
Fall 721
Mini case II: Retirement Planning
Due date 10/06/2013, 5:00 PM
Email me an excel file saved with the “Mini case II xxxx” name. Where xxxx is your
team name.
Your 30 year old client wants to retire when he is 65 years old, and have a retirement
income equivalent to $5,000 per month in today’s dollars. We cannot be sure of how long
we live after retirement, but the client wants to be extra careful and save for 25 years of
after retirement life. Market expectation for average annual inflation for the future is
2.15%. Because of inflation, he will need substantially higher retirement monthly income
to maintain the same purchasing power. He plans to purchase a lifetime annuity from an
insurance company one month before he retires, where the retirement annuity will begin
in exactly 34 years (420 months). The insurance company will add a 2.00 percent
premium to the pure premium cost of the purchase price of the annuity. The pure
premium is actuarial cost of his anticipated lifetime annuity. He has just learned the
concept of time value of money and never saved anything earlier. He will make the first
payment in a month from now and the last payment one month before he retires (a total
of 419 monthly payments).
1) Given a rate of return of 5% for the foreseeable future, how much does he need to
save each month until the month before he retires?
2) What if he already has a saving of $35,000?
3) Are there any non-quantifiable factors that he should be aware of?

Hints/Clarifications:
1. All the calculations should be done with monthly numbers and rates to take care of the
compounding.
2. Find out what should be the starting income for your client given the current inflation
rate.
3. Use answer from step 2 as the payment (or as C in the growing annuity formula) to
find out how much he will need at the time of retirement to buy the insurance plan.
4. Use answer from step 3 and add 2% premium.
5. Use answer from step 4 as the FV for which your client will be saving, and solve for
PMT.
In the step 5 above when you are solving for PMT, there will be no PV in part 1) and it
will be 35,000 in part 2) Interest rate clarification:
The interest rate on investment is annual rate with monthly compounding. So it is okay to
divide that rate by 12 for all calculations.
However, inflation is usually annual rate without any monthly compounding. Thus, you
have rate in annual terms and payments in monthly terms. You need to find out what
monthly period rate will make the effective annual rate equal to the rate of inflation. You
have EAR, so the formula on slide number 6-48 can be rearranged to solve for the period
rate (i.e. APR/m).