Stock Prices, Valuation, Stock Market Volatility and Hindsight Bias

What I am reading today are the after the fact opinions about why stock market volatility occurred in recent days. The term used to describe this phenomenon is hindsight bias. Please see (presented below this essay) an article published Barry Ritholtz on the Bloomberg blog on October 11, 2018 that is one of the best articles I have read about recent stock market volatility and the need to explain it as if we saw it coming. As Ritholtz says in his article:

"Thus, often wrong, seldom in doubt, we opine with great certainty about things of which we know next to nothing. It almost goes without saying, but the less knowledge we are burdened with, the greater degree of confidence in our forecasts."

The headline worries of the day and explanations I have heard for recent stock market volatility are:

1) Actions of the Fed - increasing interest rates;
2) the ongoing trade war with China;
3) inflation and higher input costs for consumers and businesses;
4) the carry trade;
5) central banks removing liquidity;
6) political risks in the U.S. and around the world; and
7) an elevated U.S. stock market, among other concerns

I apologize if I have missed something.

I make investment decisions based on math in an effort to judge investment opportunities in terms of estimates of future returns and risk in specific stocks and bonds. There are many models available used to value stocks. An imperfect but simple model used to judge individual stock and market values and prices is designed to estimate justified (intrinsic) PE ratios. The model formula is as follows:

P/E ratio = earnings retention x earnings growth rate / required return or cost of capital - earnings growth rate

note: earnings retention equals total earnings less dividends/total earnings

Individual stock or market returns over a holding period are a function of entry price (P/E x earnings based on historic or future earnings), earnings during a holding period and exit price (PE x future historic or future earnings) plus dividends collected along the way.
On a daily basis, the stock market makes a judgment call on future earnings and capital costs that are directly influenced by interest rates, earnings growth rate prospects and earnings retention. Plugging these individual variables into the above formula suggests that:

1) lower earnings growth rates imply lower PE ratios / higher earnings growth rates imply higher P/E ratios;
2) higher capital costs imply lower PE ratios / lower capital costs imply increased PE ratios, and;
3) higher dividend payout ratios imply lower PE ratios / lower dividend payout ratios imply higher PE ratios.

Based on a PE multiple valuation approach, future stock prices are based on future earnings growth and the PE multiple applied to future earnings at the end on an investment horizon in the market or given stock. Using this approach and in general, stock returns are based on earnings growth and change in PE multiples between the entry and exit point in an investment. Worry list items outlined above effect earnings estimates and therefore stock prices. Current market worries may or may not be future worries even though they may affect current perceived intrinsic PE multiples as described below.

In addition to earnings, worry list expectations outlined above can be classified into the formula described above as cost of capital or growth rate factors that affect intrinsic PE ratios and therefore stock prices. For example, if the stock market view of the day or week is that forward earnings will decline or capital costs will increase at the margin, due to one or more of the reasons listed above, a stock price decline may be explained by the earnings growth rate decline and higher discount rate assumption on the PE ratio as modeled in the above formula. The opposite is also true, meaning that if the market view changes to a more robust forward earnings growth estimate or lower cost of capital assumption, stock prices would benefit from the change in model assumptions on the PE ratio. Finally, if forward assumptions change in connection to an increased earnings growth rate and higher capital costs then the PE ratio would be influenced by the assumption with the largest mathematical influence in the model, which means PE's could increase even if cost of capital (i.e. interest rate) assumptions increased, for example. Because of this reason, rate increases do not necessarily mean PE ratios and stock prices fall. Although there is a limit here, this phenomenon has occurred in recent years in stocks that I follow and own as valuation multiples have been sustained and increased to some degree, in a rising rate environment so far. The key to the above is figuring out what expectations are priced into the stock at any given time.

The stock market is a forward looking mechanism that is discounting information about the future on an ongoing daily basis. The volatility of recent days may or may not tell us anything about the future. I agree with Barry Ritholtz's view (described in the article below) that the volatility may be best explained as a random walk which means the volatility this week potentially has little meaning long-term (measured in years) which is the period of time I am investing in.

Because I follow a longer term investment horizon strategy, negative short-term overall market volatility tends to be my friend as it allows me to in general buy a stream of earnings at a lower valuation which tends to lead to higher returns over time with all other factors being equal. Stock period holding returns come from earnings growth and entry/exit multiples along with dividends, where applicable. As I am willing to hold onto positions for years over my investment horizon Ritholtz's view appeals to me. While I do not believe so, maybe this is a form of confirmation bias. Time will tell.

I am not making a market call as I do not invest this way. I do not know if we will see a significant stock market decline in October or in the near future. Experience and history tell me that we may one day face significant negative volatility and or a recession. I simply do not know if and when. In the meantime, I will hold onto my stock bets that are based on the long-term fundamentals of specific companies who are growing earnings/cash flows and are generating positive ROIC's as opposed to being worried about the market or economy as a whole. It is worth noting that if further meaningful negative volatility occurs, stocks may become more attractive bargains over the long-run. Or maybe not. We will have to cross this bridge when we come to it. In the meantime we will wait and see and avoid doing the impossible which is accurately predicting the direction of the market over the near term.

If my investment horizon was short or I did not have the ability to deal with volatility, recent market activity might be scary, dangerous and rightfully so. In this case, it may or may not be wise to be in the stock market depending upon one's circumstances and risk tolerance. On the other hand, downward market volatility tends to be a positive for long-term value investors with a horizon because it allows them to make long term multi-year bets at lower valuations with positive asymmetric return characteristics with the caveat that they may need to own stocks into a future market decline due to a recession or other volatility inducing event should one or more occur during their investment horizon.

As usual I recommend that investors do their homework and follow sensible strategies based on their individual circumstances.
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The Stock-Market Meltdown That Everyone Saw Coming
At least they saw it coming with the benefit of hindsight. The reality is, the explanations can’t account for what is probably a random event.

By Barry Ritholtz
October 11, 2018, 6:50 AM PDT

Easy to spot in advance.

Barry Ritholtz is a Bloomberg Opinion columnist. He founded Ritholtz Wealth Management and was chief executive and director of equity research at FusionIQ, a quantitative research firm. He is the author of “Bailout Nation.”

Now seems like the right time to offer an after-the-fact explanation in great detail and with complete and utter certainty of what just occurred in the markets, and why.

Hindsight bias permitting, the factors that led to this sudden and unexpected decrease in share prices are just so obvious. Simple, compelling language describing cause and effect is both comforting and reassuring. The alternative to this soothing narrative is an unimaginable world of random disconcerting events. This stands in stark contrast to how we prefer to see the world around us: orderly, predictable, subject to expert management and prediction.

Sorry, to say, but that isn’t how it works.

We would have shared this explanation before the market dropped, had we been so inclined, but that would have spoiled the fun. Our powers of rationalization are somewhat less persuasive a priori than our overly optimistic belief in our own abilities. Besides, it is much easier to convince you of the reasons for what just happened than persuade of what is about to happen.

Thus, often wrong, seldom in doubt, we opine with great certainty about things of which we know next to nothing. It almost goes without saying, but the less knowledge we are burdened with, the greater the degree of confidence in our forecasts.

Why did the market suddenly drop 3 percent on Wednesday? It is as obvious as the nose on your face that the Fed’s tightening of monetary policy by raising interest rates to curb financial risk-taking is to blame. But we’ve known about this for a while, haven’t we?

As an alternative, maybe you’d like to blame elevated stock valuations, which surely is a valid point in the U.S., except that lagging emerging markets fell just as hard, and they are cheap, very cheap — certainly much less richly valued than U.S. and European markets.

No, you’re all wrong: It’s the trade war started by President Donald Trump. Not only is the U.S. dollar too strong, but tariffs are crushing an already weakened China, which hurts all of its emerging-market suppliers. But we’ve known about this too for a while, haven’t we?
Wrong again, say the partisan fire-breathers: It’s the Demon-Rats, and the possibility they will take control of the House of Representatives in the midterms, putting at risk all of the Trump pro-growth policies that are solely responsible for the healthy U.S. economy. Again, has anything changed in terms of the electoral outlook?

This market panic — or is it a crash, or a bear market? — was the worst day we have experienced since February of this year. It has now brought markets all the way back to levels not seen since – wait for it – July of this year. Was the market so bad then? This decline follows a market that has tripled since 2009, had zero volatility in 2017, and has continually confounded all experts who in one way or another couldn’t explain why the market was as good as it was.

Just for the sake of a little more perspective: This was the 20th time since the bear market ended in 2009 that the Standard & Poor’s 500 Index had a one-day loss of 3 percent. The Nasdaq-100 Index had its eighth 4 percent down day (although it was the biggest one-day fall since August 2011). Meanwhile, Wednesday’s decline has left the Standard & Poor’s 500 Index all of 5.2 percent below its September high.

True, some stocks were hit much harder than others. Facebook Inc. and Netflix Inc. are now officially in a bear market (if you believe a 20 percent decline is a bear market, but you already know I think that is nonsense).

But enough with facts. Go right ahead and feel free to try on any of your favorite after-the-fact-explanations about why markets fell. It really isn’t that hard. Just take your favorite pre-existing belief system and seek out facts that are consistent with that. Who am I to stand between you and your confirmation bias?

But the reality is simply this: The random walk thesis of how markets move is the best explanation we have. The alternative is looking at these events retrospectively, and from that vantage point they all seem so blindingly obvious. But if they were so obvious, why didn’t we see them coming?

The Financial Crises Ten Years Later

Much has been written in recent days about the financial crises ten years ago. The major themes of the articles are: (1) what caused it? (2) can it happen again? and; (3) when will the next market crash come? From the crises low during March 2009 through September 4, 2018 the S&P 500 has increased approximately 186% ex dividends, which is equivalent to an approximate annual return of roughly 10.86% ex dividends. For much of the same period, 10 year U.S. Treasury Notes have largely traded in 2% the 3% yield range, which implies an equity risk premium of 8% to 9%. See the charts below for SPY ETF prices as a benchmark for the S&P 500 and ten year treasury yields between January 2009 and September 2018.

Investors prescient enough to be out of the stock market before the crash who then jumped into the S&P 500 index as a passive investor in March 2009, at the crises lows would have earned the market return of 10.86% ex dividends per year. Investors who parked investment dollars in a fund that was invested in the S&P 500 and managed by a professional money manager at the March 2009 lows had about a  90% chance of being beat by the market, so their S&P 500 holding period return (net of fees) was likely less than 10.86% ex dividends.

The odds of putting money to work at the march 2009 low and holding on for a decade for professional fund managers or individual investors is extremely low. Looking backward, we know that the market beat 90%+ of small, medium and large cap money managers during most of the ten year period since the crash.[1] We also know that investors putting money into the stock market at the crises lows faced an unprecedented level of uncertainty looking ahead into the future. Investors who stayed out of the stock market in the U.S. after early 2009, missed a long bull market and part or all of a of a 186% gain, which was a much higher return earned by those who played it safe by buying  2% to 3% yield to maturity ten year treasury bonds or staying in cash equivalents.

Today, ten years after the crash there are a steady stream of opinions about the next crash or not, put out by investors on main street and Wall Street. The reality is that the "next crash or not," is very difficult to, if not impossible to reliably predict in terms of timing, effect and magnitude. Simply put, this kind of certainty does not exist in the markets, in my opinion.

Some of the most sophisticated and successful professional investors (pros) I know spend little if any time predicting the future of the economy or markets in an effort to time the market. They also stay invested and tend not to be focused on timing their entry or exit from markets. Pros are constrained by factors such as investing mandates, flow of funds in and out of their funds at suboptimal times and benchmark tracking, that can hurt their performance. The professional investing community is a talented hardworking group of people with the skills and resources that have an advantage over individual investors but tend to cancel each other out, making it very difficult for them to beat the market in any given year or series of years.

Markets are dominated by pros that have advantages over less sophisticated individual investors in terms of training, research and knowledge of how to use information flow among other factors. Despite this, pros cannot reliability time the economy, the market or other factors that may affect the financial markets. Individuals who try to compete head on with the pros have little chance of beating the market. On the other hand individuals do have some legitimate advantages over the pros that include, self defined and theoretically unconstrained investment horizons, personal discretion to be in the market or not, asset allocation discretion and investment strategy flexibility, among other factors.  

Similar to the pros, individual investors have no advantage or edge in terms of practicing market timing. Anecdotally speaking, I have yet to meet an individual investor who has been successful and beat the public markets over time through market timing based on economic or market forecasts. In other words trying to jump in and out of the market around recession and economic forecasts is difficult to bordering on impossible and therefore is not a viable investment strategy.

Ten years after the crash the best investors that I follow and mimic, spend little time trying to predict the next one as their and my investment strategy is not based on market or economic forecasts. I have had little success in the past trying the time the market or attempting to figure out its direction day-to-day and month-to-month, etc. based where I think the economy might go. The lesson from previous market crashes and dislocations is that forecasters do not accurately forecast them as to timing and severity. The case can be made that top down predictions of future recessions and market collapses will be no better than past predictions.

As a bottom up individual investor I do not focus on market and economic or market collapse forecasts as my primary lens is a focus on buying small pieces of equity of public companies that can be held onto for many years, if not longer. I have also been a buyer of debt, commodities and real estate, among other asset classes. I have not used leverage in my accounts. I typically invest in companies that are reasonably financed, have a competitive advantage and the potential to earn high ROIC’s well above their weighted average cost of capital. I have invested in small, medium and large cap stocks in Asia, Europe and the United States and also in ETF’s from time to time. My portfolio has been weighted toward large cap U.S. companies that do business in the U.S. and abroad.  I identify investment targets through my own primary research and the research of others.  Most of my current equity positions were purchased when the company I invested in was out of favor on Wall Street due to worries, concerns and company difficulties at the time of purchase. In recent years I have also invested alongside select activist investors that I follow. My portfolio typically consists of no more than 10 to 15 positions and typically includes heavy concentration in 3 to 5 positions.  I attempt to reduce the correlation between the positions through security selection and by running several investment strategies at once, e.g. growth, value and special situations investing in equity; debt and commodity investing; and event driven bets such as the Greek debt crises and the Japanese tsunami disaster, among others.

I have not managed the portfolio against benchmarks, but for illustration purposes below I compare my results against the S&P 500 index due to the large proportion of large cap U.S. stocks in my portfolio. In recent years my returns have approximated the S&P 500 while holding significant liquid cash equivalents (i.e. 20% to 30% of the portfolio). The portfolio has outperformed the S&P 500 in the current year and the last 12 months due to the performance of stocks that I purchased several years ago as well as a reduced cash weighting. I have made no effort to time the market and held several stocks for years with my biggest bet held more than a decade (i.e. before the previous market crash).

Total return	YTD
At 8/31/18	2018	1 yr	3yr	5yr	8yr
Portfolio - A	15.78%	30.45%	16.89%	13.95%	14.48%
Portfolio - B	21.00%	39.00%	16.30%	14.00%	19.60%
Combined total	17.14%	32.67%	16.74%	13.96%	15.81%
weighted average return
S&P 500 return	9.94%	19.66%	16.11%	14.52%	10.60%
Excess return - A	5.84%	10.79%	0.78%	-0.57%	3.88%
Excess return - B	11.06%	19.34%	0.19%	-0.52%	9.00%
Return above S&P 500 index	7.20%	13.01%	0.63%	-0.56%	5.21%
- combined

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[1] Per "Risk-Adjusted SPIVA Score: Evaluation of Active Managers' Performance Through a Risk Lens" research published by S&P Dow Jones Indices, for year-end 2017.

Business Growth and Liquidity

An owner of an IT consulting firm spoke to me the other day about his business. His chief concern was finding and growing revenue so he can grow his business. He indicated that in some years he has generated more fee revenue than others, which caused him to take-out or contribute funds to his business. Business has been good of late, so he was struggling trying to figure out which projects to take on (e.g. large projects with deferred fee collections and average realization rates or small projects that would cash flow sooner at lower estimated realization rates). His decision will impact how large his business will grow into the future. His problem of determining how fast he can grow his business is similar to other business owners and CEO’s I have advised and worked for. I listened to his dilemma and responded to him by indicating that I understand his problem. I congratulated him on his success and also commented that it is possible he ends up in a liquidity crises or worse by growing revenue too fast given his liquidity profile and financial model. With a look of disbelief, he asked me how. My answer is as follows.

While most public and private businesses I have worked in, modeled and followed, desire and are typically focused on growth, a smaller number actually perform financial planning in a manner that, explicitly focuses on the limits of sustainable growth (also known as known as the sustainable growth rate (SGR). The definition of the term is as follows.

SGR is the maximum amount sales can increase without depleting financial resources which means that there is a limit to revenue growth based on a given company financial model. For an owner/operator consultant/CEO trying to grow a practice to growing Fortune 500 businesses, it generally takes resources (i.e. more assets that must be paid for) to increase sales.

The concept was developed by Professor Robert Higgins of the University of Washington. Put another way, what he describes in general, is the maximum rate of sales expansion an enterprise can undertake without issuing debt or equity in a given unaltered capital structure. Since all company balance sheets must be comprised of total assets that equal the sum of total liabilities and equity, equity growth allows for growth in liabilities which determines the rate in which assets can expand, which in turn determines the growth rate in sales, as sales bear a relationship to the asset base in a given enterprise. As Robert Higgins indicated, a company’s SGR is equivalent to its growth rate in equity defined as PRAT. [i]  PRAT represents relationships between profit margins, assets turnover, leverage and earnings retention as follows:

P = profit margin

A = asset turnover ratio, (P x A = return on assets (ROA))

T = assets to equity ratio (i.e. leverage ratio)

R = retention rate (i.e. the portion of net income retained in the business)

The first three terms (i.e. P, A and T) are sourced from the DuPont ROE calculation method which is:

(Net income/sales) x (Sales/total assets) = ROA x (Assets/equity) = ROE

ROE is then multiplied with the earnings retention rate to arrive at the sustainable growth rate as follows:

ROE x (earnings retention rate) = sustainable growth rate in revenue (SGR)

Higgins points out that SGR is the only revenue growth rate that is consistent with stable values in the four ratios and that at least one ratio must change if a company grows at any other rate than the SGR. Which means that operating performance (measured by ROA) or its financial policy (i.e. leverage or earnings retention) must change? Companies with growth rates higher than SGR result in cash deficits. In response, companies can increase profit margins or asset turnover thereby altering ROA or change financial policies (i.e. leverage, equity issuance and earnings retention). Higgins indicates that for long-term sustainable growth issues some combination of debt increase, equity issuance, increased profits, divesting marginal activities or merger with a cash cow would need to take place. Listed below is a summary of the SGR:

Figure 1 - Summary of SGR (Gray boxes are ROA related components, Green boxes are financial policy components)

Source: ‘How Much Growth Can Borrows Sustain?”, George W Kester, 2002

In Figure 2 below we present the hypothetical financial statements of a professional services firm that bills time at rates that absorb payroll and other operating costs plus is sufficient to service debt and/or make investments in assets.

Figure 2 – Hypothetical Balance Sheet and P&L of Professional Services Firm

Source: “How Fast Can Your Company Afford to Grow,” Neil C. Churchill & John W. Mullins, Harvard Business School Publishing, 2001 and Gregg Carlson calculations/assumptions

Plugging numbers from the financial statements into the SGR model yields the following results:

Net Income/sales = profit margin of 5%

Sales/Assets = asset turnover ratio of $2,000/$682 = 2.93

Assets/Equity = leverage ratio of $682/$432 = 1.57[ii]

Equals ROE and SGR due to 0%/100% debt to equity = 23.00%

The model indicates that the revenue SGR is 23%, which means that growth rates above this number require better operational performance (profit margin and/or asset turnover = ROA) or changes to the capital structure (e.g. debt/equity issuance and/or increased earnings retention) in order to avoid cash deficits,  liquidity & working capital issues and/or a conversation with your banker. An entrepreneur, owner or CEO would need look at their realistic options in terms of operational performance, financing/capital structure options, asset sales/divestitures or mergers. On the other hand, entrepreneurs, CEO’s and owners who run enterprises at growth rates that are less than their sustainable growth rates face issues of slow growth, cash buildup and underutilized resources.

As an advisor to entrepreneurs, CEOs and business owners I have also used other model-analytical tools to address the above issues such as building explicit forecasts of company financial statements (P&L/Cash Flow/Balance Sheet) and  cash receipt/disbursement models(daily/weekly/monthly/annual)  to calculate liquidity needs and cash flows.

In addition to SGR model described above and explicit forecasts, I have found the operating cash cycle model to be a useful companion to explicit forecasts as well as a logical framework as a management and communication tool. 

It is well known that businesses require cash and growing businesses typically require more cash to fund working capital, operating expenses and investments in facilities and equipment. A key concern of growing businesses is to achieve a balance between generating and consuming cash. I have found that focusing on the operating cash cycle to be a useful approach to managing liquidity and determining the self financing revenue growth rate. The discussion here is based on an analytical framework described by Neil C. Churchill and John W. Mullins in a framework they developed for calculating the self financeable revenue growth rate of a business.[iii]

Churchill and Mullins state that a growing business can find itself out of business by outgrowing its cash resources. They address the issue by developing a calculation known as the self financeable growth rate (SFG). They develop a framework to determine what growth rate its current operations can sustain and define three model factors as follows:

1)      Operating cash cycle – the amount of time company money is tied up in inventory and other current assets before a company is paid for the goods and services it produces;[iv]

2)      Amount of cash needed to finance each dollar of sales, including working capital and operating expenses; and

3)      The amount of cash generated by each dollar of sales.

Like the Higgins SGR model described here, the Churchill and Mullins SFG framework goes beyond the calculation of sustainable revenue growth rates as a tool that provides insight into how operational efficiency, profit margins, product lines and customer segments can fuel revenue growth or not.

The operating cash cycle is a calculation of how many days cash is tied up in working capital before money is returned to the company in the form of customer payments for goods or services sold. The shorter the cycle the faster a company can redeploy its cash and growth from internal resources. In other words, the fewer days in receivables and inventory, the higher the turnover and the larger the number of days in payables, the better the SFR.

In addition to working capital, the SGR framework addresses how much cash is tied up in operating expenses by calculating how much is invested in operating expenses per dollar of sales and how long  the cash is tied up in the operating cash cycle.

The SGR framework also considers how much cash per dollar of sales flows to the bottom line and is available to fund the next operating cycle after being consumed by cost of sales and operating expenses.

Based on the above, an operating cash cycle (OCC) growth rate and the number of OCC’s can be calculated to arrive at an annual self financeable sales growth rate (SFG). In Figure 2 – Hypothetical Balance Sheet and P&L of a Professional Services Firm, I show the calculations described here as follows:

1)      Cash tied up per revenue/sales dollar in COS and operations adjusted for time (.40 +.08 =  .48);

2)      Cash generated per revenue/sales dollar (.05);

3)      Self financeable growth rate (SFG) calculation (cash generated by sales divided by cash tied up in operations) (.05 divided by .48 = 10.39% (SFG);

4)      Calculation of number of OCC’s per year (365 divided by OCC 166 = 2.198;

5)      Annual SFG is SFG (10.39%) x OCC’s per year (2.2 rounded) = 22.83%

The SFG is the sustainable rate at which sales/revenue can grow. If the business grows revenue at less than this rate, with all other variables held constant, the business will produce more cash that it will need to fund its growth. On the other hand, if its revenue growth rate is higher than its SFR, it will be strapped for cash.

Levers that the entrepreneur, business owner or CEO have for speeding up cash flow in a way to allow for increased SFR growth rates  while avoiding the use of external financing fall within the three areas and include; speeding cash flow through higher receivable and inventory turnover, reducing operating expenses and/or increasing prices and margins. In this model example I have not made adjustments for taxes, depreciation, asset replacement, major investments in R&D and marketing as well as differing cash and operating characteristics for different product lines within a business. In real life the entrepreneur, business owner or CEO will need to do so.[v] The model is capable of handling these inputs.

For an entrepreneur, business owner or CEO who must make liquidity influencing decisions such as what customer or projects to take on, where to price products/services vis-a-vis turnover/margins, what investments to make or dissolve, how large to let assets grow and what target returns to aim for, the models described here are helpful. In small businesses, I have seen the concepts described here managed by intuition in lieu of a formal process. Size, growth and complexity typically require more robust analytical and decision making processes. Bigger businesses I have been involved with have traditionally dealt with financial modeling of growth through an explicit forecasting process of profitability, cash flow and assets/liabilities/equity. In many of these cases, I used all or parts of these models to validate explicit forecasts. In other cases, I have used modeling concepts discussed here in lieu of explicit forecasts. The concepts modeled here have been used to advise and provide insight to entrepreneurs, business owners and CEO’s in support of business decision making processes.

I have used a professional services firm as an example to illustrate the concepts in the two models presented here. In the future, I will provide additional examples of how these and other related models might be used to analyze the growth rates and liquidity characteristics of businesses with varying financial models such as “asset heavy” hotels and casinos or companies with significant R&D investment in intellectual capital, among others.

For additional resources see the footnotes below.[vi]

                                                        

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[i] Analysis for Financial Management, Sixth Edition, Robert Higgins, 2001

[ii] The model requires that beginning period equity be used for the calculation.  End of period equity of $532 and net income of $100 = $432 of beginning period equity as the model assumes no other changes in equity between the beginning and end of year.

[iii] The discussion of the operating cash cycle framework was sourced from, “How Fast Can Your Company Afford to Grow? Neil C. Churchill and John Mullins, Harvard Business School Publishing, 2001. The financial statement data and assumptions example used here are based on the article and then modified by Gregg Carlson as a hypothetical example of a professional services firm.

[iv] The components of the operating cash cycle include days of holding inventory, receivables and other current assets as well as days in accounts payable and other current liabilities to determine the length of time cash is tied up.

[v] For additional information here, see page 8 – 9 of the article, “How Fast Can Your Company Afford to Grow?, Neil C. Churchill and John Mullins, Harvard Business School Publishing, 2001.

[vi] For additional information on cash flows and liquidity issues see:

“Growth, Vitality, And Cash Flows: High-Frequency Evidence from 1 Million Small Businesses,” JP Morgan Chase Institute, September 2016;

“How Much Growth Can Borrowers Sustain?, George Kester, 2002 and was originally published in June 1991 in The Journal of Commercial Bank Lending;

“How Fast Should Your Company Grow?”, William E. Furman, Jr., Harvard Business Review, January 1984