You are a senior Certified Financial Planner for Charles Schwab. You recently hired a college graduate, as a junior analyst, who is working with a client on retirement planning. You have asked the junior analyst to provide you with his approach and analysis before he reviews it with his client. The junior analyst's approach for his 24-year-old client assumes the following:

• Annual 401K contribution: 15% of base salary
• Employer matching contribution: 5% up to the first 10% of employee contribution
• Constant salary increase of 4% annually (current salary is $125,000.00)
• Chosen investment vehicles will grow 6% and 6.5%, annually

The client informs the analyst she plans to work until age 60, giving her 36 years to invest. Over the 36-year investment period, the analyst surmises his client will amass an investment total over $4M.

You ask the analyst to re-do his assessment using a Monte Carlo simulation with modest ranges to simulate change in salary and annual returns on chosen investments. Figure 6 below shows the results of a single simulation.

1. Why is a simulation more suitable than constant/linear assumptions for estimating the client's portfolio at retirement?

2. Figure 7 below shows subsequent simulation runs. How many times did the analyst run the simulation?

3. What is the probability the client will have at least $5.5M at retirement? based on figure 7

Figure 6 Retirement Planning Simulation Yearly 401K Contribution 16.0% Employer Match of Salary 6.0% Salary increase 4.0% Vanguard Balanced Index Fund Expected annual return 6.0% 9 Boston Trust Asset Management Fund 10 Expected annual return 5% 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Salary Annual 401K Employer Vanguard Boston Trust Roth IRA Age Increase Salary Contribution Match Return 401K Balance Return Balance Final Balance 24 $80,000 $12,000 $4,000 $16,000 $5,500 $21,500 25 2.47% $81,979 $12,297 $4,099 -2.02% $32,072 -1.51% $10,917 $12.999 26 4.81% $85,919 $12,888 $4296 9.86% $52,419 -1.30% $16,275 $68,694 27 4.02% $09,371 $13,406 $4,469 3.90% $72,339 -3.33% $21,233 $93,572 28 4.61% $93,492 $14,024 $4,675 13.20% $100,585 -8.42% $24.944 $125,529 29 4.14% $97,360 $14,604 $4,868 9.22% $129,333 -2.09% $29,924 $159, 256 30 4.54% $101,783 $15,267 $5,089 1.84% $152,072 -1.20% $35,054 $187,136 31 4.44% $106,297 $15,945 $5,315 13.03% $193,142 5.70% $42.562 $235,704 32 3.87% $110,411 $16,562 $5,521 9.53% $233,623 2.07% $48,942 $282,565 33 2.93% $113,642 $17,046 $5,682 5.83 $269,974 -1.03% $53,940 $323,914 34 2.97% $117,016 $17,552 $5,851 4.17% $304,635 5.67% $62,496 $367,131 35 2.49% $119,925 $17,989 $5,996 17.77% $382.754 12.68% $75,919 $458,673 36 3.89% $124,585 $18,000 $6.229 9.00% $441,427 25.20% $100.550 $541,976 37 2.45% $127,642 $18,000 $6,382 3.51% $450,329 7.17% $113,259 $563,588 38 4.28% $133,109 $18,000 $6,655 9.89% $519,522 12.07% $132,427 $651,948 39 3.92% $138,324 $18,000 $6,916 -1.23% $538,071 -2.51% $134,608 $672,678 40 3.36% $142,979 $18,000 $7,149 14.05% $638,823 15.33% $160,740 $799,563 41 2.63% $146, 742 $18,000 $7,337 10.35 $730,274 9.24% $181,086 $911,360 42 4.17% $152,861 $18,000 $7,643 -0.46% $752,548 -0.05% $186,503 $939,051 43 3.18% $157,721 $18,000 $7,888 3.00% $801,619 1.88% $195,502 $997, 121 44 4.62% $165,006 $18,000 $8,250 3.76% $858,050 4.46% $209,720 $1,067,770 45 2.58% $169,260 $18,000 $8,463 1.74% $899,409 13.59% $243,715 $1,143,124 46 3.58% $175,318 $18,000 $8,766 4.33% $965,124 -6.14% $234,257 $1,199,381 47 4.96% $184,019 $18,000 $9,201 -0.16% $990,759 -3.79% $230,873 $1,221,633 48 2.07% $187,824 $18,000 $9,391 10.59% $1,123,040 16.15% $273,670 $1,396,710 49 4.72% $196,686 $18,000 $9,834 -5.04 $1,094,281 7.08% $298,539 $1,392,820 50 3.12% $202,824 $18,000 $10,141 11.04% $1,243,184 9.81% $333,312 $1,576,495 51 2.84% $208,582 $18,000 $10,429 17.68% $1,491,413 5.68% $357,734 $1,849,147 52 3.72% $216,344 $18,000 $10,817 0.74% $1,531,291 12.66% $408,531 $1,939,822 53 4.96% $227,069 $18,000 $11,353 6.88% $1,665,956 3.19% $427,067 $2,093,023 54 2.59% $232,939 $18,000 $11,647 4.22% $1,765,916 10.25% $476,336 $2,242,252 2 96% $239,836 $18,000 $11,992 1.20% $1,817,071 16.21% $560,032 $2,377,103 56 3.10% $247,264 $18,000 $12,363 12.78% $2,079,717 9.17% $817,894 $2,697,611 4.60% $258,645 $18,000 $12,932 8.19% $2,280,909 -4.32% $597,730 $2,878,639 58 4.25% $289,629 $18,000 $13,481 -0.15% $2,308,986 6.51% $843,168 $2,952, 154 2.97% $277,634 $18,000 $13.882 6.01% $2,479,714 15.12% $746,888 $3,226,602 3.15% $285 385 $18,000 $14,319 6.40% $2,670,638 -7.20% $699,602 $3,370,240 88% 9 &&23 Figure 7 FIGURE 12.18 Statistical Analysis of Retirement Model Simulation Results AB AC AD AE AF AG AH AL AJ AK AL AM AN Histogram 300 250 200 150 235 2 Summary Statistics 3 Average $3,587,194.56 4 Standard Deviation $757,860 20 5 Minimum $1,851,529.41 6 Maximum $6,338,890 20 7 & Frequency Distribution 9 Upper Cell Limit Cumulative Frequency Frequency $1,500,000 0 0 $2,000,000 3 3 $2,500,000 52 $3,000,000 183 $3,500,000 494 259 $4,000,000 730 236 $4,500,000 873 143 $5,000,000 955 82 $5,500,000 30 $6,000,000 998 13 $6,500,000 1000 2 $7,000,000 1000 0 $7,500,000 1000 0 $8,000,000 1000 0 $8,500,000 0 $9,000,000 1000 0 U. 300 985 . $1.500.000 0.00 $2.000,00 $2.500.000 S400.000 SS.CO S. SSD $7.500.000 SS. SLO,000 S.500.000 00000 1000 SL. Figure 6 Retirement Planning Simulation Yearly 401K Contribution 16.0% Employer Match of Salary 6.0% Salary increase 4.0% Vanguard Balanced Index Fund Expected annual return 6.0% 9 Boston Trust Asset Management Fund 10 Expected annual return 5% 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Salary Annual 401K Employer Vanguard Boston Trust Roth IRA Age Increase Salary Contribution Match Return 401K Balance Return Balance Final Balance 24 $80,000 $12,000 $4,000 $16,000 $5,500 $21,500 25 2.47% $81,979 $12,297 $4,099 -2.02% $32,072 -1.51% $10,917 $12.999 26 4.81% $85,919 $12,888 $4296 9.86% $52,419 -1.30% $16,275 $68,694 27 4.02% $09,371 $13,406 $4,469 3.90% $72,339 -3.33% $21,233 $93,572 28 4.61% $93,492 $14,024 $4,675 13.20% $100,585 -8.42% $24.944 $125,529 29 4.14% $97,360 $14,604 $4,868 9.22% $129,333 -2.09% $29,924 $159, 256 30 4.54% $101,783 $15,267 $5,089 1.84% $152,072 -1.20% $35,054 $187,136 31 4.44% $106,297 $15,945 $5,315 13.03% $193,142 5.70% $42.562 $235,704 32 3.87% $110,411 $16,562 $5,521 9.53% $233,623 2.07% $48,942 $282,565 33 2.93% $113,642 $17,046 $5,682 5.83 $269,974 -1.03% $53,940 $323,914 34 2.97% $117,016 $17,552 $5,851 4.17% $304,635 5.67% $62,496 $367,131 35 2.49% $119,925 $17,989 $5,996 17.77% $382.754 12.68% $75,919 $458,673 36 3.89% $124,585 $18,000 $6.229 9.00% $441,427 25.20% $100.550 $541,976 37 2.45% $127,642 $18,000 $6,382 3.51% $450,329 7.17% $113,259 $563,588 38 4.28% $133,109 $18,000 $6,655 9.89% $519,522 12.07% $132,427 $651,948 39 3.92% $138,324 $18,000 $6,916 -1.23% $538,071 -2.51% $134,608 $672,678 40 3.36% $142,979 $18,000 $7,149 14.05% $638,823 15.33% $160,740 $799,563 41 2.63% $146, 742 $18,000 $7,337 10.35 $730,274 9.24% $181,086 $911,360 42 4.17% $152,861 $18,000 $7,643 -0.46% $752,548 -0.05% $186,503 $939,051 43 3.18% $157,721 $18,000 $7,888 3.00% $801,619 1.88% $195,502 $997, 121 44 4.62% $165,006 $18,000 $8,250 3.76% $858,050 4.46% $209,720 $1,067,770 45 2.58% $169,260 $18,000 $8,463 1.74% $899,409 13.59% $243,715 $1,143,124 46 3.58% $175,318 $18,000 $8,766 4.33% $965,124 -6.14% $234,257 $1,199,381 47 4.96% $184,019 $18,000 $9,201 -0.16% $990,759 -3.79% $230,873 $1,221,633 48 2.07% $187,824 $18,000 $9,391 10.59% $1,123,040 16.15% $273,670 $1,396,710 49 4.72% $196,686 $18,000 $9,834 -5.04 $1,094,281 7.08% $298,539 $1,392,820 50 3.12% $202,824 $18,000 $10,141 11.04% $1,243,184 9.81% $333,312 $1,576,495 51 2.84% $208,582 $18,000 $10,429 17.68% $1,491,413 5.68% $357,734 $1,849,147 52 3.72% $216,344 $18,000 $10,817 0.74% $1,531,291 12.66% $408,531 $1,939,822 53 4.96% $227,069 $18,000 $11,353 6.88% $1,665,956 3.19% $427,067 $2,093,023 54 2.59% $232,939 $18,000 $11,647 4.22% $1,765,916 10.25% $476,336 $2,242,252 2 96% $239,836 $18,000 $11,992 1.20% $1,817,071 16.21% $560,032 $2,377,103 56 3.10% $247,264 $18,000 $12,363 12.78% $2,079,717 9.17% $817,894 $2,697,611 4.60% $258,645 $18,000 $12,932 8.19% $2,280,909 -4.32% $597,730 $2,878,639 58 4.25% $289,629 $18,000 $13,481 -0.15% $2,308,986 6.51% $843,168 $2,952, 154 2.97% $277,634 $18,000 $13.882 6.01% $2,479,714 15.12% $746,888 $3,226,602 3.15% $285 385 $18,000 $14,319 6.40% $2,670,638 -7.20% $699,602 $3,370,240 88% 9 &&23 Figure 7 FIGURE 12.18 Statistical Analysis of Retirement Model Simulation Results AB AC AD AE AF AG AH AL AJ AK AL AM AN Histogram 300 250 200 150 235 2 Summary Statistics 3 Average $3,587,194.56 4 Standard Deviation $757,860 20 5 Minimum $1,851,529.41 6 Maximum $6,338,890 20 7 & Frequency Distribution 9 Upper Cell Limit Cumulative Frequency Frequency $1,500,000 0 0 $2,000,000 3 3 $2,500,000 52 $3,000,000 183 $3,500,000 494 259 $4,000,000 730 236 $4,500,000 873 143 $5,000,000 955 82 $5,500,000 30 $6,000,000 998 13 $6,500,000 1000 2 $7,000,000 1000 0 $7,500,000 1000 0 $8,000,000 1000 0 $8,500,000 0 $9,000,000 1000 0 U. 300 985 . $1.500.000 0.00 $2.000,00 $2.500.000 S400.000 SS.CO S. SSD $7.500.000 SS. SLO,000 S.500.000 00000 1000 SL