I was able to fgiure out the first part, but am having difficulting incorporatin
ID: 2384435 • Letter: I
Question
I was able to fgiure out the first part, but am having difficulting incorporating the random variable from part 2 as described in the highlighted text. I believe I am on the right track with the excel graphic at the very bottom, but again I am unsure. If you could provide the formulas for the cells that need to be changed it would be appreciated. Screen captures of the excel doc would also help to go a long way.
Tri-State Corporation
What will your portfolio be worth in 10 years? In 20 years? When you stop working? The
Human Resources Department at Tri-State Corporation was asked to develop a financial planning model that would help employees address these questions. Tom Gifford was asked to lead this effort and decided to begin by developing a financial plan for himself. Tom has a degree in business and, at the age of 25, is making $34,000 per year. After two years of contributions to his company’s retirement program and the receipt of a small inheritance,
Tom has accumulated a portfolio valued at $14,500. Tom plans to work 30 more years and hopes to accumulate a portfolio valued at $1,000,000. Can he do it?
Tom began with a few assumptions about his future salary, his new investment contributions, and his portfolio growth rate. He assumed 5% annual salary growth rate as reasonable and wanted to make new investment contributions at 4% of his salary. After some research on historical stock market performance, Tom decided that a 10% annual portfolio growth rate was reasonable. Using these assumptions, Tom developed the Excel worksheet shown in Figure 16.18. Tom’s specific situation and his assumptions are in the top portion of the worksheet (cells D3:D8). The worksheet provides a financial plan for the next five years. In computing the portfolio earnings for a given year, Tom assumed that his new investment contribution would occur evenly throughout the year, and thus half of the new investment could be included in the computation of the portfolio earnings for the year. Using Figure 16.18, we see that at age 29, Tom is projected to have a portfolio valued at $32,898.
Tom’s plan was to use this worksheet as a template to develop financial plans for the company’s employees. The assumptions in cells D3:D8 would be different for each employee, and rows would be added to the worksheet to reflect the number of years appropriate for each employee. After adding another 25 rows to the worksheet, Tom found that he could expect to have a portfolio of $627,937 after 30 years. Tom then took his results to show his boss, Kate Riegle.
Although Kate was pleased with Tom’s progress, she voiced several criticisms. One of the criticisms was the assumption of a constant annual salary growth rate. She noted that most employees experience some variation in the annual salary growth rate from year to year. In addition, she pointed out that the constant annual portfolio growth rate was unrealistic and that the actual growth rate would vary considerably from year to year. She further suggested that a simulation model for the portfolio projection might allow Tom to account for the random variability in the salary growth rate and the portfolio growth rate.
After some research, Tom and Kate decided to assume that the annual salary growth rate would vary from 0% to 10% and that a uniform probability distribution would provide a realistic approximation. Tri-State’s accounting firm suggested that the annual portfolio growth rate could be approximated by a normal probability distribution with a mean of 10% and a standard deviation of 5%. With this information, Tom set off to develop a simulation model that could be used by the company’s employees for financial planning.
1. Without considering the random variability in growth rates, extend the worksheet in
Figure 16.18 to 30 years. Confirm that by using the constant annual salary growth rate and the constant annual portfolio growth rate, Tom can expect to have a 30-year portfolio of $627,937. What would Tom’s annual investment rate have to increase to in order for his portfolio to reach a 30-year, $1,000,000 goal? Solved this part.
2. Incorporate the random variability of the annual salary growth rate and the annual portfolio growth rate into a simulation model. Assume that Tom is willing to use the annual investment rate that predicted a 30-year, $1,000,000 portfolio in part 1. Show how to simulate Tom’s 30-year financial plan. Use results from the simulation model to comment on the uncertainty associated with Tom reaching the 30-year, $1,000,000 goal. Discuss the advantages of repeating the simulation numerous times.
4. Assume that Tom is willing to consider working 35 years instead of 30 years. What is your assessment of this strategy if Tom’s goal is to have a portfolio worth $1,000,000?
1 Financial Analysis Portfolio Projection 25 $34,000 $14,500 5% 49' 10% 3 Age 4 Current Salary 5 Current Portfolio Annual Salary Growth Rate 7 Annual Investment Ratc Annual Portfolio Growth Rate Beginning Portfolio Ending 10 1 Ycar Age Portfolio 12 13 Salary Investment Eamings Portfolio 25 26 27 28 14.500 17,378 20,615 24,251 28,329 34.000 35,700 37,485 39,359 41,327 1,360 1,428 1,499 1,574 1,653 1,518 1,809 2,136 2,504 2,916 17.378 20,615 24,23 28,329 32,898 15 17Explanation / Answer
Portfolio Portfolio Portfolio New Portfolio Portfolio Portfolio Ending Ending Ending Year Age At Start At Start At Start Salary Investment Earnings Earnings Earnings Portfolio Portfolio Portfolio (valued at 10% (valued at 5% (valued at 15% (valued at 10% (valued at 5% (valued at 15% (valued at 10% (valued at 5% (valued at 15% Portfolio growth rate) Portfolio growth rate) Portfolio growth rate) Portfolio growth rate) Portfolio growth rate) Portfolio growth rate) Portfolio growth rate) Portfolio growth rate) Portfolio growth rate) 1 25 14,500 14,500 14,500 34,000 2,720 1,586 793 2,325 18,806 18,013 19,545 2 26 18,806 18,013 19,545 35,700 2,856 2,023 1,012 3,125 23,685 21,881 25,525 3 27 23,685 21,881 25,525 37,485 2,999 2,518 1,259 4,071 29,203 26,139 32,595 4 28 29,203 26,139 32,595 39,359 3,149 3,078 1,539 5,188 35,429 30,826 40,932 5 29 35,429 30,826 40,932 41,327 3,306 3,708 1,854 6,504 42,444 35,987 50,742 10 34 80,264 62,378 110,054 52,745 4,220 8,237 4,119 17,354 92,721 70,717 131,628 15 39 158,883 113,346 259,901 67,318 5,385 16,158 8,079 40,733 180,426 126,810 306,020 20 44 293,682 195,624 577,494 85,916 6,873 29,712 14,856 90,037 330,267 217,353 674,404 23 47 415,916 267,575 916,667 99,459 7,957 41,989 20,995 142,525 465,862 296,526 1,067,148 24 48 465,862 296,526 104,432 8,355 47,004 23,502 3,572 521,220 328,383 25 49 521,220 328,383 109,653 8,772 52,561 26,280 3,995 582,553 363,435 29 53 808,914 491,134 133,284 10,663 81,425 40,712 6,188 901,001 542,509 30 54 901,001 542,509 139,949 11,196 90,660 45,330 6,890 1,002,857 599,035 31 55 599,035 146,946 11,756 294 611,085 40 64 731,901 227,962 18,237 456 750,594 50 74 967,017 371,325 29,706 743 997,466 51 75 997,466 389,892 31,191 780 1,029,437
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