# 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:

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. # Why do you invest? A few people may stumble into financial security. But for most people, the only way to attain financial security is to save and invest over a long period of time. You just need to have your money work for you. That’s investing. Simply put, you want to invest in order to create wealth. It’s relatively painless, and the rewards are plentiful. By investing in the stock market, you’ll have a lot more money for things like retirement, education, recreation — or you could pass on your riches to the next generation so that you become your family’s Most Cherished Ancestor. Whether you’re starting from scratch or have a few thousand dollars saved, Investing Basics will help get you going on the road to financial (and Foolish!) well-being. Now that the markets are showing signs of life, the pundits and financial writers are pumping out investing articles of all kinds. Gold is prominently mentioned as are a wide variety of stocks, mutual funds, and exotic ETFs. More so than ever, when I read these articles I ask myself this question: Why should I invest in that? Or taken one step further, the question becomes: Why do I invest? I actually struggled for a long time on how to open up this post, but taking a page from Finding Forrester, sometimes it is easier to let someone else write the intro for you. It should come as no surprise that many folks have asked the age old question of, “why?”. In fact, everything that I say in this entry, has likely been written in greater detail, depth, and clarity, by someone else. However, it is a necessary step in my overall roadmap of investing. So, the question as it stands, why do you invest? And as an extension to that, how do you know that you did it well? The three quotes cited above contain a wealth of information on the how and why of investing. At the end of the day, If we ignore the mechanics of investing (e.g. compound interest, “buy low, sell high”, “long time horizons”, etc.), the reason that any of of invest is a deeply personal one. However, in my view the reasons for investing can be broken down into one of three categories: 1. We invest for personal gain 2. We invest to achieve some target and/or goal 3. We invest for someone else Fundamentally, these three reasons cover pretty much every scenario. Saving for retirement? That is #1 or #2. Helping a relative? That is #3. Saving for school? #2. The reason that I have broken everything down into three categories, is that the why of investing is useless without some type of barometer as to how well you are investing . If you are saving for school, you know if you are successful if you have enough for your tuition. If you are saving for retirement, then you have enough if you know that you can be financially secure after you stop working. If you are saving for personal gain (e.g., “I just want to be rich”), you are successful if the personal decisions you make in your investing are better than those that would be made if you paid someone else to handle your money (e.g. a financial advisor). There are really only two ways to monitor your performance: absolute, and relative. In absolute measurements, you have some fixed, quantifiable goal against which you are measuring yourself. If you are saving for your child’s education, and you know that the total cost will be$50,000 with tuition, books, and residence fees, then you have an absolute target against which to work.  Contrasting this are relative measurements.  These measurements are typically against some benchmark, and fundamentally reflect the opportunity cost of investing relative to some other means.  For example, if your benchmark is one of the couch potato portfolios, the performance of your investment decisions shows how much better (worse) you have done by managing your own money, instead of following the couch potato formula.

With the above in mind, the question should not be “Why do I invest?”.  Rather, it should be, “Am I meeting my investment goal?”  Defining your investment goal will lay the foundation on which you base all of your future decisions.

-10d

# Stock Indices

ETF investing has become one of the primary vehicles for many individual investors, since it offers a low-cost, low-maintenance approach to investing, with results that match the overall market. The reason for this is that most ETF strategies revolve around investing in market-index ETFs. A great reference for this type of investing can be found at the Canadian Couch Potato blog, or at the original couch potato site at MoneySense Magazine.

When I started off investing on my own, I purchased Canadian Market Index Stocks such as XIC and XIU. At a high level, I understood that an index based ETF basically held the holdings of the index it represented; for example, XIC holds all of the equities in the S&P/TSX Capped Composite Index. But what is an index anyways?

In its broadest sense, an index provides an overview of the performance of the underlying securities, either through a price-weighted or value-weighted average. What constitutes inclusion in that group of securities depends on what the index is trying to achieve. Standard & Poors is one of the primary index publishers, and they have several such as the S&P/TSX 60, S&P/TSX Capped Composite, S&P/TSX SmallCap, etc. Each of these indices is designed to be representative of one dimension of the overall market. The 60 acts as a subset of the S&P/TSX Composite, but caps the total number of equities at 60. The SmallCap attempts to provide an overall barometer on the performance of small cap stocks on the TSX, etc.

Excluding the focus of the index, the other primary factor to take into account is whether or not it is price-weighted or value weighted.

(For the discussions below, a worksheet is available to play with, which can be found here.)

## Price-Weighted Indices

The most popular price-weighted index is the Dow Jones Industrial Average (DJIA). There are a number of articles on the Internet which speak to the history of the DJIA, and my interest is in what it means to be price-weighted.

Essentially, a price weighted index is exactly what it sounds like: an index whose value is more influenced by firms which have a higher price. The value of a price-weighted index is the sum of the prices of firms in that index, divided by some divisor. The divisor is the trickier part of the equation.

$DJIA=\frac{\sum_{i=1}^{30} P_{i}}{divisor}$

Where Pi is the price of firm i. When the DJIA was initially started, the divisor was 30, because there were 30 firms in the average. However, over time the divisor has had to be adjusted due to stock (reverse-)splits. I.e., when a stock splits, the total number of shares goes up, but the price of the stock goes down. However, the before and after values of the DJIA should be the same. With a little algebra, we can calculate the divisor after a (reverse-)split as:

$divisor_{new}=\frac{(\sum_{i=1}^{30}P'_{i})\times divisor_{old}}{\sum_{i=1}^{30}P_{i}}$

In the above, Pi are the prices before the (reverse-)split, and P’i are the prices after the split.

Over time, the divisor for the DJIA has become incredibly small, and the divisor as of 2010/07/02 was 0.132129493 (from 0.132319125). The reason for this is that, using the formula for divisornew above, over the years successive splits have made the divisor smaller and smaller.

The other thing to consider with a price weighted index is the weighting of the price itself, and how it affects the overall value of the index. That is, an equal percentage change for a stock will mean more (or less) if the stock price was large (small) relative to the index to begin with. For example, both IBM and Bank of America are stocks in the DJIA. However, they are incredibly different in terms of pricing. At one point during the week of October 29, 2012, IBM was trading at $193.27 a share, and Bank of America was trading at$9.12 a share. But why does this matter? It matters because a 5% shift in either stock will have a different overall effect on the index as a whole. A 5% shift in IBM results in a 77.289 point shift in the DJIA, but an identical shift of 5% for Bank of America only shifts the DJIA 3.6471 points!

This means that one should pay particular attention to what it means when news reports say that the Dow has moved – the context of the movement has to be taken into account to ensure that the movement isn’t being skewed by a heavy hitter such as IBM.

## Value-Weighted Indices

On the other end of the spectrum are value-weighted indices.

Looking at the sample spreadsheet, when we enter values for the split multiple, the sum of the market caps does not change. This is because (reverse-)splits automatically account for changes in the number of shares outstanding, and share price. This simplifies computation of the index because there is no denominator which must be continuously adjusted.

The other thing to notice is that changes in share price in a value weighted index are scaled appropriately to the weight of the firm in the index, measured by market cap. This means that the bigger the firm by market cap, the more weight it has. This also demonstrates that movements of the share price will be properly reflected in the index, and that the percentage move of a given security in the index will be properly reflected in the change of the index itself. But why does this matter?

Consider two hypothetical stocks, each with a market cap of $1,000,000,000. Further, assume that stock #1 has a share price of$5.23, and stock #2 has share price of $198.53. This is summarized below: Stock Share Price Shares Outstanding Market Cap Stock 1$5.23 191,204,588.91 $1,000,000,000 Stock 2$198.53 5,037,022.11 $1,000,000,000 As discussed above for the DJIA, if both stocks change by 5%, this will not have an identical change on the stock. However, based on market cap alone, a movement of 5% in either stock will have the same effect on the inded. For this reason, a value-weighted index is often a better indicator of the performance of the cross-section of the market that the index is monitoring. # Basic vs. Diluted Weighted Average Number of Shares Whilst perusing the financial statements of firms while performing an analysis, often the EPS is listed in two forms: basic EPS (sometimes just "EPS"), and diluted EPS. Basic EPS is calculated as: $EPS=\frac{Net Income}{weighted average number of shares}$ Diluted EPS takes a little more work. With the diluted EPS, the weighted average number of shares is adjusted by the number of shares that would result from converting any dilutive securities to common shares. This adjustment is then adjusted again to adjust for any shares that could be purchased on the open market from the proceeds of the conversion, based on the average share price for the fiscal period. The total list of dilutive securities is vast, but as an example, here are some things to look for: • Convertible bonds • Convertible preferreds • Outstanding warrants • Employee options It should be noted that the treatment of dilution for different types of securities is not the same across the board. For example, proceeds of warrants and options are used to repurchase common stock, but there are no proceeds from convertible preferreds; however convertible preferreds would impact the preferred dividends that are paid, which would also affect the net income. An example would probably best illustrate the conversion. Say we were reviewing the financial statements for FirmCorp., and their 2011 annual statement had the following information: • Net Income:$123,555,000
• Weighted Average Number of Shares Outstanding (WANS): 591,223,552
• Series A Warrants: 5,533,000 outstanding, convertible to 5 common shares each at a price of $3.00/share ($15.00 total per warrant)
• Average share price for the period: $5.23 Our basic EPS calculation is simple: $EPS_{basic}=\frac{\123,555,000}{591,223,552}=\0.21$ To calculate the diluted EPS, we have to adjust the weighted average number of shares. From the above, we have 5,533,000 outstanding warrants, and each warrant can be converted to 5 shares at a cost of$3.00/share. If we were to convert all of the warrants, two things would result:

$NumShares=5,533,000\times5=27,665,000$
$CashInflow=5,533,000\times5\times\3.00=\82,995,000$

In the above, NumShares is the change in shares by converting all of the warrants, and CashInflow is the money received by converting the warrants. The proceeds from CashInflow would then be used to purchase any shares outstanding from the open market:

$ShareBuyback=\frac{\82,995,000}{\5.23}=15,869,025$

Our weighted average number of shares is then adjusted as follows:

$WANS_{diluted}=WANS+NumShares-ShareBuyback$
$WANS_{diluted}=591,223,552+27,665,000-15,869,025$
$WANS_{diluted}=603,019,527$

And our diluted EPS is then calculated as:

$EPS_{diluted}=\frac{\123,555,000}{603,019,527}=\0.20$

With the above explanation in mind, why does this matter? I’ve tossed the notion of basic vs. diluted EPS around in my evaluations, but as of late I have settled on basic EPS. Diluted EPS shows you the EPS if dilutive securities were converted to common shares. However, at the time of publishing the financial statements, the dilutive securities were not converted, and hence did not dilute the EPS. That said, I see little point in evaluating diluted EPS for a fiscal period that has already closed.

However, diluted EPS does give you a preview of the associated internal risks of the company’s financials. By reviewing financial statements, one can determine any potential future impacts if the shares were to be diluted. When analysts post EPS projections, they are often doing so based on the basic EPS; if you are performing a forward-looking evaluation on P/E, P/BV, P/E×P/BV, dividend payout ratio, etc., knowing what could happen if the weighted average number of shares were diluted may have a material impact on your analysis. So at the very least, diluted EPS can serve as a bellwether to potential negative impacts when analyzing a firms.

# My Initial Evaluation Methodology.

There isn’t one sure way of evaluating companies, and everybody’s method will depend on factors specific to their situation: time horizon, risk tolerance, experience, knowledge of the industry, etc. I thought it would be a useful exercise to document what I look for in a company when I am evaluating it to see if it would be a worthwhile addition to my portfolio. To that end, here are the key factors I look at.

• Earnings per Share

Commonly referred to as EPS, this is an indicator of how much of the net income is left to distribute to share holders for a given period. EPS is calculated as the total net earnings, divided by the total number of common shares outstanding. In addition to EPS, there is another variant called diluted EPS, which adjusts net income and total shares outstanding by factoring in events such as conversion of warrants, options, convertible shares, convertible bonds, etc. In short, the number of shares outstanding for diluted EPS is the theoretical number of shares outstanding if anything that couldbe converted to a common share, was converted, during the period.Typically I would want to see a rising EPS, with some caveats.

One must be sure to to understand why EPS is rising. For example, since EPS is net income divided by number of shares outstanding, reducing the number of shares outstanding is one way to boost the EPS. If a company reduces the total number of shares outstanding through a share buyback program which uses up free cash from the balance sheet, this is typically a good thing. However, if a company takes out a loan to repurchase shares, that may be a bad thing. EPS can also rise when net income rises, but there are different reasons net income may rise. For example, net income may rise because operating expenses have decreased, but operating expenses may have decreased because the company laid off half of its workforce; this may spell trouble for the comapny, and they are looking for ways to cut corners. But, cutting the workforce may not be a badthing, since the workforce may be cut due to increased operational efficiencies, so the firm simply doesn’t need the staff.In short, rising EPS is good, because it shows that year over year (YoY) the company is making more money. But, one must investigate the rise in EPS to ensure it isn’t rising at the expense of something else (pun intended).

• Dividend

As a dividend investor, the dividend is obviously the most important thing to look for; if the company were not paying a dividend, it wouldn’t even be on my radar.Typically a dividend should be rising over time, a topic which I will address in a future post.

• Dividend Payout Ratio (DPR)

The dividend payout ratio is the proportion of earnings (from EPS) that are paid out as dividends, and is reported as a percentage, calculated as Dividend/EPS. A typical company will have a dividend payout ratio that is less than 100%, but there are some types of companies where the dividend payout ratio is greater than 100%. Excluding those companies, the dividend payout ratio should be a number which is adequate for the industry, or the peers of the company being analyzed. A dividend payout ratio that is too high means that the company may be paying out too much of its dividend, leaving little cash for internal projects. A dividend payout ratio that is too low means that the company may be burning through too much cash internally, or may not be returning a fair portion of the earnings to the shareholders. I personally like to see a dividend payout ratio of less than or equal to 60%. Such a value provides enough of a cushion that a firm may still be able to pay out a dividend even when net income isn’t as strong as in previous periods. Firms such as those that weathered the recession of 2008 and still managed to increase their dividend would be good examples of firms that did not have a dividend payout ratio which was too aggressive, allowing them to continue to return value to shareholders even when sales were down.

• Share Price.

Of course, while dividend are great, one also would like the capital investment to increase over time, or at least stay in line with inflation. To that end, the share price of a firm should be rising over time. The actual growth rate of the share price is relative to the growth in the dividend itself. For example, a firm whose dividend rises YoY by only 1%, but whose share price increases by 4% per year, is better than a firm whose dividend yield rises 4% per year, but whose share price only rises 1% per year.

• Price to Earnings, Price to Book, and the P/E * P/BV Multiple.
• This last screen is one that I picked up from Benjamin Graham. Graham felt that the P/E of a stock (Price divided by EPS) should be less than 15, and that the price to book value (share price divided by the book value, where the book value is the equity (assets-liabilities) divided by the number of shares outstanding) ratio should be 1.5 or less, and combining these two numbers gives an upper limit of 22.5. Personally, I prefer an upper limit of 25, and this gives me some latitude with the P/E and P/BV. For example, even if the P/E is higher than 15, if the P/BV is extremely low, I would still consider the stock.

The point of this combined ratio is not to buy companies that are inherently overvalued. If a company sports a very high P/BV ratio, in theory, if the company were to be liquidated, the total assets remaining would not be sufficient to distribute to all of the shareholders. Likewise, if the P/E is very high, this means that the expectations of the companies future earnings as measured by the share price are extremely out of line with the share earnings themselves.

• Free Cash Flow from Operations.

One often overlooked indicator is the free cash flow from operations, which is essentially how much literal cash changed hands as a result of the firms day to day business(es). Dividends are ultimately paid out in cash, and if the dividends paid in a given period outweigh the actual cash that was earned in the period (actual cash excludes items such as accounts receivables, which are obligations for customers to pay cash in the future), this indicates that the dividends may be being funded from another source, e.g. leverage (which would show up as cash flow from financing activities) or selling assets (which would show up as cash flow from investing activities). When a firm starts paying dividends from non-operating cash streams, that is a big warning sign that the dividend is likely not sustainable.

And there you have it. The above points are my initial screens, but I also like to dive into some of the other details as well. However, the above provides a good starting point to identify which companies warrant further analysis.