Question

III.   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:

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

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.  

a. A key aspect of this component B is the $60,000 Provide Andrew Potts for 16 years. Provide Andrew with some information regarding the anticipated purchasing power of this annuity. You can look anywhere on the Internet, but be sure to fully cite your sources. Your report should be between 350 and 450 words long.

b. 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.

c. Identify the size of Garcia Energy’s equal, annual, end-of-year deposits into the account over the 20-year accumulation period.

d.   Redo #3 assuming that Garcia Energy could earn 10% rather than 8% during the accumulation period.

e. Redo #2 and #3 assuming that payments made to Ms. Garza in retirement would be made at the end of each month and Garcia Energy’s ordinary annuity payments to a retirement account would also be on an end-of month basis. Report:

     a. Size of the accumulated amount

     b. Size of the “accumulation period” end-of-year annuity

f. 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 8 percent and 4 percent, as originally specified. Report:

     a. Size of the accumulated amount

     b. Size of the “accumulation period” end-of-month annuity

g.   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.

Answer 1

a. Purchasing power can be determined using the inflation index and the inflation growth rate. Sum of $60000 is a nominal sum and may not reflect the true purchasing power of the money. However, the sum is due to be received 20 years hence, we need to adjust the same using a long term inflation growth forecast. As per the Federal Bank monetary target, inflation should not exceed 2% (+- 1%) in the long run. This can easily be verified through FederalReserve.gov website. The above inflation target is in line with the price stability objective of the Fed.

In the given problem, let us first remove the impact of inflation on 60,000 and see how much it is worth in terms of purchasing power.

As we see, Mr. Garcia should be informed that an amount of $60,000 received at the end of 35 years shall only be worth $44581 at the end of 20 years. In other words, he shall be able to buy only 74% of the goods with the same amount of money. However, all this holds true if our inflation expectation turns out to be correct. Hence, he should be made aware that the cost of living shall continue to rise or in other words, his standard of living shall keep falling. To avoid the same, he should design his retirement plan in such a way that the annuity amount increases every year at least by the amount of inflation.

b. $60,000 annuity due is equivalent to: Present value of $60,000/year for 15 years + 60,000

Hence, accumulated sum at the end of 20 years = (60,000/0.04)* [1-(1.04)^-15] + 60,000 = 727,103.2

c. Total future value of the annuity = $727103.2

Let amount deposited be $x

Hence, 727103.2 = x/0.08 * (1.08²⁰ – 1)

Or, x = 15888.81

d. If rate of interest is 10%, then we have

727103.2 = x / 0.1 * (1.1²⁰ – 1)

Or, x = 12694.95