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 $120,000 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 Energys 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.

1. A key aspect of this Component III is the $120,000 Provide Andrew Potts for 16 years. According to the website inflationdata.com, the annual inflation rate over the past century has been 3.24 percent.. What is the present value of the $120,000,

a. An annual inflation rate of 3.24 percent? (2 points)

b. A monthly inflation rate of 0.27 percent (Note: 3.22% 12 = 0.27 percent)? (2 points)

c. The annual inflation rate rising to 4.86 (Note: 3.24% x 1.5 = 4.86%) (2 points)

2. Identify the size of the sum Garcia Energy must accumulate by the end of year 20 to provide the 16-year, $120,000 annuity due. (4 points)

3. Identify the size of Garcia Energys 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 Energys 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 month (3 points)

5. If the payments made to Mr. Potts (or his descendants) is a perpetuity of $120,000 annually beginning one year after Andrews 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-year annuity needed (3 points)