Investing Roadmap Part 2: How much do you need to retire?

In my previous post, I spoke about having goals for investing. My goals fall into the second category, Investing to achieve some target and/or goal, and that goal is to not have to work.

Now, most people don’t want to work. Given the choice, I would rather sit on my balcony all day sipping an espresso reading books, researching companies, or in the living room watching a good film. However, work is a reality of life: we have to pay the bills somehow (how will I buy the espresso?). So, to be able to get to the point where I don’t have to work to make money, I need to have some inflow of cash which handles all of my regular expenses. This is a fairly mechanical exercise:

  1. Identify your monthly expenses, and multiply by 12 to annualize
  2. Add in any annual expenses (e.g. property tax on your residence, if you own a home)
  3. Add inflation up to the point that you wish to retire
  4. Factor in personal taxes

After the four steps above, you’ll have your required annual pre-tax income for when you wish to stop working.  Here is an example:

Monthly Expenses
Rent $1,500.00
Groceries $300.00
Entertainment $400.00
Insurance $100.00
Utilities $200.00
Transportation $200.00
Pet care $75.00
Mobile phone $85.00
Internet $50.00
Netflix / TV $10.00
Computer / Technology $100.00
Maintenance Fees $350.00
Emergency Funds $200.00
Total Monthly $3,570.00
Annualized $42,840.00
Annual Expenses
Vacation $5,000.00
Property Taxes $3,000.00
Total Annual Expenses $8,000.00
Total Expenses $50,840.00
Implied Tax Rate 40%
Total Annual (Gross) $84,733.33

From the example above, if I were to stop working today, I would need ~$84.7M ($M=000) in annual income to maintain my current lifestyle.

However, there is a small wrinkle in that this is in today’s dollars, and we need to factor in inflation (step #3 above).  For example, if we assume 2% inflation (i.e. on average costs will go up 2% next year), our pre-tax income shoots up to ~$86.4M.  And to further complicate things, inflation is an unknown: we don’t know what inflation will be.  Say for example I wish to stop working in 10 years, in 2025.  What inflation rate do I use for 2016, 2017, 2018, etc.?

My own workplace uses a 2.25% inflation assumption for each year.  I would prefer to account for some variability, and one way to account for this variability is to run a simulation, using a range of acceptable inflation values.  Specifically, a Monte Carlo simulation, wherein I have run 100,000 trials using an inflation assumption of 2.25% +/- 1.00% per year for the next 27 years.  One iteration of the simulation gives results such as the following:

Year Pre-tax income
(Jan 1)
Inflation Assumption Pre-tax income (Dec 31)
2015 $85,000 3.21% $87,729
2016 $87,729 3.13% $90,474
2017 $90,474 2.68% $92,899
2018 $92,899 1.29% $94,098
2019 $94,098 1.89% $95,876
2020 $95,876 2.56% $98,330
2021 $98,330 2.13% $100,425
2022 $100,425 2.67% $103,106
2023 $103,106 3.15% $106,354
2024 $106,354 1.39% $107,832
2025 $107,832 1.87% $109,849
2026 $109,849 1.93% $111,969
2027 $111,969 2.64% $114,925
2028 $114,925 1.67% $116,844
2029 $116,844 2.60% $119,882
2030 $119,882 3.24% $123,766
2031 $123,766 2.79% $127,219
2032 $127,219 2.88% $130,883
2033 $130,883 1.88% $133,344
2034 $133,344 1.91% $135,891
2035 $135,891 1.79% $138,323
2036 $138,323 2.36% $141,588
2037 $141,588 2.85% $145,623
2038 $145,623 2.85% $149,773
2039 $149,773 2.67% $153,772
2040 $153,772 2.89% $158,216
2041 $158,216 2.17% $161,649

As you can see, by the time we hit 2041, to live at my current lifestyle, I would require $158.2M in annual income.  The inflation also bounces around a lot, as each year the inflation is estimates to be somewhere between 1.25% and 3.25%.

Now, if we run this simulation 100,000 times, we get the following for the required income in 2041 (only first 10 entries shown):

Sequence # 2041 pre-tax income
1 $158,216.33
2 $160,945.75
3 $142,668.57
4 $160,712.46
5 $160,133.85
6 $160,235.08
7 $146,449.32
8 $150,616.91
9 $161,482.05
10 $152,456.35

But, what do we do with those numbers?  The answers is to perform some statistical analysis on each year, and come up with what we feel is a reliable number.  If we focus on 2041 as our example, here is the histogram:

Histogram of Required Income in 2041

For the above, we have a median required income of $154,922.16, and a mean income of $154,991.19.  However, the median and mean are the mid-point and average required incomes respectively.  Whilst the median is $154,992.16, there is a chance that it will be above that.  What I am interested in is the required income with a certain level of confidence.  If we do some more analysis on the histogram, we can break up all of the salary ranges into buckets, and from there interpolate the expected required income in 2041 with 95% confidence:

Bucket # Low High Count Cumulative Probability
1 $134,510.51 $135,685.09 1 0.0010%
2 $135,685.09 $136,859.67 0 0.0010%
3 $136,859.67 $138,034.25 1 0.0020%
4 $138,034.25 $139,208.83 6 0.0080%
5 $139,208.83 $140,383.41 12 0.0200%
6 $140,383.41 $141,557.99 55 0.0750%
7 $141,557.99 $142,732.57 156 0.2310%
8 $142,732.57 $143,907.15 338 0.5690%
9 $143,907.15 $145,081.73 682 1.2510%
10 $145,081.73 $146,256.31 1296 2.5470%
11 $146,256.31 $147,430.89 2098 4.6450%
12 $147,430.89 $148,605.47 3325 7.9700%
13 $148,605.47 $149,780.05 4653 12.6230%
14 $149,780.05 $150,954.63 6419 19.0420%
15 $150,954.63 $152,129.21 8000 27.0420%
16 $152,129.21 $153,303.79 9048 36.0900%
17 $153,303.79 $154,478.37 10070 46.1600%
18 $154,478.37 $155,652.94 10061 56.2210%
19 $155,652.94 $156,827.52 9678 65.8990%
20 $156,827.52 $158,002.10 8773 74.6720%
21 $158,002.10 $159,176.68 7376 82.0480%
22 $159,176.68 $160,351.26 5833 87.8810%
23 $160,351.26 $161,525.84 4249 92.1300%
24 $161,525.84 $162,700.42 3006 95.1360%
25 $162,700.42 $163,875.00 2057 97.1930%
26 $163,875.00 $165,049.58 1224 98.4170%
27 $165,049.58 $166,224.16 721 99.1380%
28 $166,224.16 $167,398.74 453 99.5910%
29 $167,398.74 $168,573.32 214 99.8050%
30 $168,573.32 $169,747.90 126 99.9310%
31 $169,747.90 $170,922.48 43 99.9740%
32 $170,922.48 $172,097.06 14 99.9880%
33 $172,097.06 $173,271.64 7 99.9950%
34 $173,271.64 $174,446.22 5 100.0000%
100000 100.0000%

Based on the above, our required income, at 95% confidence, is $162,647.28.  In other words, I can say with a degree of confidence that my required income in 2041 will always be at, or less than, $162,647.28; put another way: there is only a 5% chance that I will need more than $162,647.28 in annual income to live comfortably in 2041.

However, that is only for the year 2041.  It would be nice to see a bunch of years, say, from 2026 to 2041.  I won’t display all of the histograms and such, but here is the summary table:

Year Income Required at 95% confidence Mean Income Required Median Income Required
2026 $114,667.71 $111,013.30 $110,991.02
2027 $117,397.60 $113,512.43 $113,484.70
2028 $120,183.67 $116,061.47 $116,037.66
2029 $123,019.43 $118,672.26 $118,654.49
2030 $125,975.59 $121,345.28 $121,319.06
2031 $128,935.52 $124,077.19 $124,044.14
2032 $131,995.18 $126,871.97 $126,845.13
2033 $135,073.08 $129,724.75 $126,845.13
2034 $138,286.34 $132,644.87 $129,688.96
2035 $141,521.77 $135,624.14 $129,688.96
2036 $144,833.57 $138,672.78 $138,639.86
2037 $148,260.68 $141,794.27 $141,765.55
2038 $151,705.86 $144,983.10 $144,948.96
2039 $155,291.29 $148,242.42 $148,193.00
2040 $158,933.22 $151,579.05 $151,517.82
2041 $162,647.28 $154,991.19 $154,922.16

At the outset of this post, I said that my goal was to not to have to work.  From the above, I now know how much income I need in any given year, to maintain my current lifestyle, while factoring in inflation.  So, if my investments happen to generate at least $114,667.71 in income in 2026, I know that I can then quit my job and not have to worry about anything.

In one of my upcoming posts, I’ll talk about forecasting my expected income, which is the flipside of this discussion.



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