Question

Funding Retirement The long-run goal of many is enjoying a long, gratifying retirement without financial worries. This is the case for Andrew Potts. He is attempting to manage Garcia Energy in such a way that it provides for his retirement through the accumulation of funds during his working years. Mr. Potts is expecting to retire in 20 years, at the age of 70. Upon retirement, he is seeking an annual beginning-of-the year payment of $60,000 ($5,000/month) for 16 years. For ease of computation, assume that if Andrew dies prior to the end of the 16-year period, annual payments will pass to his wife and/or heirs. During the 20-year “accumulation period” Garcia Energy wishes to fund the annuity by making equal, annual, end-of-year deposits into a mutual fund historically earning 8% interest. Once the 16-year “disbursement period” begins, Garcia Energy plans to move the accumulated monies into an account earning a guaranteed 4% per year. At the end of the distribution period, the account balance will be zero. Note that the first deposit will be made at the end of Year 1 and that the first distribution payment will be received at the end of Year 20 (which is the beginning of year 21).

Hints:

a. Report inputs: N, I, PV, PMT, FV, when used, in order to earn partial credit despite wrong final solutions

b. Draw a timeline depicting all of the cash flows associated with Garcia Energy’s view of the retirement annuity. Be sure to identify the accumulation period, disbursement period, interest rates, known cash flows, annuity cash flows, and timing of each.

2. Identify the size of the sum Garcia Energy must accumulate by the end of year 20 to provide the 16-year, $60,000 annuity due. (4 points)

3. Identify the size of Garcia Energy’s equal, annual, end-of-year deposits into the account over the 20-year accumulation period. (4 points)

4. Redo #2 and #3 assuming that payments made to Ms. Garza in retirement would be made at the beginning of each month. Furthermore, assume that Garcia Energy is going to take more risk in order to accommodate this earlier payment and could earn 9 percent during the accumulation period, while keeping the assumption that Garcia Energy’s ordinary annuity payments to a retirement account would be on an end-of month basis.

Report: a. Size of the accumulated amount (3 points)

b. Size of the “accumulation period” end-of-year annuity (4 points)

5. If the payments made to Mr. Potts (or his descendants) is a perpetuity of $60,000 annually beginning one year after Andrew’s retirement, how much would Garcia Energy need at the beginning of the distribution period. Assume that the applicable interest rates are 9 percent and 6 percent, during the accumulation and distribution period, respectively. Report:

a. Size of the amount available when Mr. Potts retires. (3 points)

b. Size of the “accumulation period” end-of-month annuity needed (3 points)

6. Think back to the financial statements of Part A. Does it seem as though Garcia Energy will be able to afford this sort of retirement for Andrew? Would you be more included or less inclined to urge Andrew to accept the inventory expansion project discussed in Part B. In 300 words present a written report regarding retirement funding to Mr. Potts, including retirement age and annuity payments. (4 points)

Answer 1

The answer with description for first 4 points is as follows -

In this case the first important thing is that " Mutual Fund" historical returns are 8%, so we can assume that it will give the same % of returns in future.

a) The inputs are as follows -

*Total Investment Time - 20 years ( yearly accumulation at the end of year)

*Estimated annual returns on investment (i) = 8% Per Annum.

*Post retirement requirement = 16 years ( $60000 /year ; $5000 / month).

*The Total $ 960000 required to settle all 16 years claim.

For first 20 years, the interest rate is annual 8 % and after that for the rest of 16 years the fixed rate will be 4 % on the reducing amount.

Please feel free to ask any doubts.

Thank You.