DCF Myth 3.2: If you don't look, its not there!

In this, the last of my three posts on uncertainty, I complete the cycle I started with a look at the responses (healthy and unhealthy) to uncertainty and followed up with an examination of the Margin of Safety, by taking a more extended look at one approach that I have found helpful in dealing with uncertainty, which is to run simulations. Before you read this post, I should warn you that I am not an expert on simulations and that the knowledge I bring to this process is minimalist and my interests are pragmatic. So, if you are an expert in statistics or a master simulator, you may find my ramblings to be amateurish and I apologize in advance. 

Setting the Stage

The tools that we use in finance were developed in simpler times, when data was often difficult (or expensive) to access and sophisticated statistical tools required machine power that was beyond the reach of most in the finance community. It should come as no surprise then that in discounted cash flow valuation, we have historically used point estimates ( single numbers that reflect best judgments at the time of the valuation) for variables that have probability distributions attached to them. To illustrate, in my valuation of Apple in February 2016, I used a revenue growth rate of 2.2% and a target operating margin of 25%, to arrive at my estimate of value per share of $129.80.

It goes without saying (but I will say it anyway) that I will be wrong on both these numbers, at least in hindsight, but there is a more creative way of looking at this estimation concern. Rather than enter a single number for each variable, what if I were able to enter a probability distribution? Thus, my estimate for revenue growth would still have an expected value of 2.2% (since that was my best estimate) but would also include a probability distribution that reflected my uncertainty about that value. That distribution would capture not only the magnitude of my uncertainty (in a variance or a standard deviation) but also which direction I expect to be wrong more often (whether the growth is more likely to be lower than my expected value or higher).  Similarly, the expected value for the operating margin can stay at 25% but I can build in a range that reflects my uncertainty about this number.

Once you input the variables as distributions, you have laid the foundations for a probabilistic valuation or more specifically, for a simulation, where in each run, you pick one outcome out of each distribution (which can be higher or lower than your expected values) and estimate a value for the company based on the drawn outcomes. Once you have run enough simulations, your output will be a distribution of values across simulations. If the distributions of your variables are built around expected values that match up to the numbers that you used in your point estimate valuation, the expected value across the simulations will be close to your point estimate value. That may seem to make the simulation process pointless, but there are side benefits that you get from simulations that enrich your decision process. In addition to the expected value, you will get a measure of how much variability there is in this value (and thus the risk you face), the likelihood that you could be wrong in your judgment of whether the stock is under and over valued and the potential payoffs to be right and wrong. 

Statistical Distributions: A Short Preview

It is a sad truth that most of us who go through statistics classes quickly consign them to the “I am never going to use this stuff” heap and move on, but there is no discipline that is more important in today’s world of big data and decision making under uncertainty. If you are one of those fortunate souls who not only remembers your statistics class fondly but also the probability distributions that you encountered during the class, you can skip this section. If, like me, the only memory you have of your statistics class is of a bell curve and a normal distribution, you need to expand your statistical reach beyond a normal distribution, because much of what happens in the real world (which is what you use probability distributions to capture) is not normally distributed. At the risk of over simplifying the choices, here are some basic classifications of uncertainties/ risks::

1. Discrete versus Continuous Distributions: Assume that you are valuing an oil company in Venezuela and that you are concerned that the firm may be nationalized, a risk that either occurs or does not, i.e., a discrete risk. In contrast, the oil company's earnings will move with oil prices but take on a continuum of values, making it a continuous risk. With currency risk, the risk of devaluation in a fixed exchange rate currency is discrete risk but the risk in a floating rate currency is continuous.
2. Symmetric versus Asymmetric Distributions (Symmetric, Positive skewed, Negative skewed): While we don't tend to think of upside risk, risk can deliver outcomes that are better than expected or worse than expected. If the magnitude and likelihood of positive outcomes and negative outcomes is similar, you have a symmetric distribution. Thus, if the expected operating margin for Apple is 25% and can vary with equal probability from 20% to 30%, it is symmetrically distributed. In contrast, if the expected revenue growth for Apple is 2%, the worse possible outcome is that it could drop to -5%, but there remains a chance (albeit a small one) that revenue growth could jump back to 25% (if Apple introduces a disruptive new product in a big market), you have an a positively skewed distribution. In contrast, if the expected tax rate for a company is 35%, with the maximum value equal to the statutory tax rate of 40% (in the US) but with values as low as 0%, 5% or 10% possible (though not likely), you are looking at a negatively skewed distribution.
3. Extreme outcome likelihood (Thin versus Fat Tails): There is one final contrast that can be drawn between different risks. With some variables, the values will be clustered around the expected value and extreme outcomes, while possible, don't occur very often; these are thin tail distributions. In contrast, there are other variables, where the expected value is just the center of the distribution and actual outcome that are different from the expected value occur frequently, resulting in fat tail distributions.

I know that this is a very cursory breakdown, but if you are interested, I do have a short paper on the basics of statistical distributions (link below), written specifically with simulations in mind. 

Simulation Tools

I was taught simulation in my statistics class, the old fashioned way. My professor came in with three glass jars filled with little pieces of paper, with numbers written on them, representing the different possible outcomes on each variable in the problem (and I don't even remember what the problem was). He then proceeded to draw one piece of paper (one outcome) out of each jar and worked out the solution, with those numbers and wrote it on the board. I remember him meticulously returning those pieces of paper back into the jar (sampling with replacement) and at the end of the class, he proceeded to compute the distribution of his solutions.

While the glass jar simulation is still feasible for simulating simple processes with one or two variables that take on only a few outcomes, it is not a comprehensive way of simulating more complex processes or continues distributions. In fact, the biggest impediment to using simulation until recently would have been the cost of running one, requiring the use of a mainframe computer. Those days are now behind us, with the evolution of technology both in the form of hardware (more powerful personal computers) and software. Much as it is subject to abuse, Microsoft Excel has become the lingua franca of valuation, allowing us to work with numbers with ease. There are some who are conversant enough with Excel's bells and whistles to build simulation capabilities into their spreadsheets, but I am afraid that I am not one of those. Coming to my aid, though, are offerings that are add-ons to Excel that allow for the conversion of any Excel spreadsheet almost magically into a simulation.

I normally don't make plugs for products and services, even if I like them, on my posts, because I am sure that you get inundated with commercial offerings that show up insidiously in Facebook and blog posts. I am going to make an exception and praise Crystal Ball, the Excel add-on that I use for simulations. It is an Oracle product and you can get a trial version by going here. (Just to be clear, I pay for my version of Crystal Ball and have no official connections to Oracle.) I like it simply because it is unobtrusive, adding a menu item to my Excel toolbar, and has an extremely easy learning curve.

My only critique of it, as a Mac user, is that it is offered only as a PC version and I have to run my Mac in MS Windows, a process that I find painful. I have also heard good things about @Risk, another excel add-on, but have not used it.

Simulation in Valuation

There are two aspects of the valuation process that make it particularly well suited to Monte Carlo simulations. The first is that uncertainty is the name of the game in valuation, as I noted in my first post in the series. The second is that valuation inputs are often estimated from data, and that data can be plentiful at least on some variables, making it easier to estimate the probability distributions that lie at the heart of simulations. The sequence is described in the picture below:

Step 1: Start with a base case valuation
The first place to start a simulation is with a base case valuation. In a base case valuation, you do a valuation with your best estimates for the inputs into value from revenue growth to margins to risk measures. Much as you will be tempted to use conservative estimates, you should avoid the temptation and make your judgments on expected values. In the case of Apple, the numbers that I use in my base case valuation are very close to those that I used just a couple of months ago, when I valued the company after its previous earnings report and are captured in the picture below:

Download spreadsheet

In my base case, at least, it looks like Apple is significantly under valued, priced at $93/share, with my value coming in at $126.47, just a little bit lower my valuation a few months ago. I did lower my revenue growth rate to 1.50%, reflecting the bad news about revenues in the most recent 10Q.

Step 2: Identify your driver variables

While there are multiple inputs into valuation models that determine value, it remains true that a few of these inputs drive value and that the rest go along for the ride. But how do you find these value drivers? There are two indicators that you can use. The first requires trial and error, where you change each input variable to see which ones have the greatest effect on value. It is one reason that I like parsimonious models, where you use fewer inputs and aggregate numbers as much as you can. The second is more intuitive, where you focus on the variable that investors in the company seem to be most in disagreement about. My Apple valuation is built around four inputs: revenue growth (growth), operating margin (profitability), the sales to capital ratio (investment efficiency) and cost of capital (risk). The graph below captures how much value changes as a function of these inputs:

As you can see the sales to capital ratio has little effect on value per share, largely because the base case growth rate that I use for Apple is so low. Revenue growth and operating margin both affect value significantly and cost of capital to a much lesser degree. Note that the value per share is higher than the current price though every single what-if analysis, but that reflects the fact that only variable at a time in being changed in this analysis. It is entirely possible that if both revenue growth and operating margins drop at the same time, the value per share will be lower than $93 (the stock price at the time of this analysis) and one of the advantages of a Monte Carlo simulation is that you can build in interconnections between variables. Looking at the variables through the lens that investors have been using to drive the stock price down, it seems like the front runner for value driver has to be revenue growth, as Apple reported its first year on year negative revenue growth in the last quarter and concerns grow about whether the iPhone franchise is peaking. Following next on the value driver list is the operating margin, as the competition in the smart phone business heats up.

Step 3: The Data Assessment

Once you have the value drivers identified, the next step is collecting data on these variables, as a precursor for developing probability distributions. In developing the distributions, you can draw on the following:

1. Past data: If the value driver is a macroeconomic variable, say interest rates or oil prices, you can draw on historical data going back in time. My favored site for all things macroeconomic is FRED, the Federal Reserve data site in St. Louis, a site that combines great data with an easy interface and is free. I have included data on interest rate, inflation, GDP growth and the weighted dollar for those of you interested in US data in the attached link. For data on other countries, currencies and markets, you can try the World Bank data base, not as friendly as FRED, but rich in its own way.
2. Company history: For companies that have been in existence for a long time, you can mine the historical data to get a measure of how key company-specific variables (revenues, operating margin, tax rate) vary over time. 
3. Sector data: You can also look at cross sectional differences in key variables across companies in a sector. Thus, to estimate the operating margin for Amazon, you could look at the distribution of margins across retail companies.: If the value driver is a macroeconomic variable, say interest rates or oil prices, you can draw on historical data going back in time. My favored site for all things macroeconomic is FRED, the Federal Reserve data site in St. Louis, a site that combines great data with an easy interface and is free. I have included data on interest rate, inflation, GDP growth and the weighted dollar for those of you interested in US data in the attached link. For data on other countries, currencies and markets, you can try the World Bank data base, not as friendly as FRED, but rich in its own way.

In the case of Apple, I isolated my data assessment to three variables: revenue growth, operating margin and the cost of capital.  To get some perspective on the range and variability in revenue growth rates and operating margins, I started by looking at the values for these numbers annually from 1990 to 2015:

This extended time period does distract from the profound changes wrought at Apple over the last decade by the iPhone. To takes a closer look at its effects, I looked at growth and margins at Apple for every quarter from 2005 to the first quarter of 2016 :

Superimposed on this graph of gyrating revenue growth, I have traced the introduction of the different iPhone models that have been largely responsible for Apple's explosive growth over the last decade. There are a few interesting patterns in this graph. The first is that revenue growth is clearly driven by the iPhone cycle, peaking soon after each new model is introduced and fading in the quarters after. The second is that the effect of a new iPhone on revenue growth has declined with each new model, not surprising given the scaling up of revenues as a result of prior models. The third is that the operating margins have been steady through the iPhone cycles, with only a midl dip in the last cycle. There is good news and bad news in this graph for Apple optimists. The good news is that the iPhone 7 will deliver an accelerator to the growth but the bad news is that it will be milder that the prior versions; if the trend lines hold up, you are likely to see only a 10-15% revenue growth in the quarters right after its introduction. 

To get some perspective on what the revenue growth would look like for Apple, if it's iPhone franchise fades, I looked at the compounded annual revenue growth for US technology firms older than 25 years that were still listed and publicly traded in 2016:

Of the 343 firms in the sample, 26.2% saw their revenues decline over the last 10 years. There is a sampling bias inherent in this analysis, since the technology firms with the worst revenue growth declines over the period may not have survived until 2016. At the same time, there were a healthy subset of aging technology firms that were able to generate revenue growth in the double digits over a ten-year period. 

Step 4: Distributional Assumptions
There is no magic formula for converting the data that you have collected into probability distributions, and as with much else in valuation, you have to make your best judgments on three dimensions.

1. Distribution Type: In the section above, I broadly categorized the uncertainties you face into discrete vs continuous, symmetric vs skewed and fat tail vs thin tail. At the risk of being tarred and feathered for bending statistical rules, I have summarized the distribution choices based on upon these categorizations. The picture is not comprehensive but it can provide a road map though the choices:
   
2. Distribution Parameters: Once you have picked a distribution, you will have to input the parameters of the distribution. Thus, if you had the good luck to have a variable be normally distributed, you will only be asked for an expected value and a standard deviation. As you go to more complicated distributions, one way to assess your parameter choices to look at the full distribution, based upon your parameter choices, and pass it through the common sense test.

In the case of Apple, I will use the historical data from the company, the cross sectional distribution of revenue growth across older technology companies as well as a healthy dose of subjective reasoning to pick a lognormal distribution, with parameters picked to yield values ranging from -4% on the downside to +10% on the upside. On the target operating margin, I will build my distribution around the 25% that I assumed in my base case and assume more symmetry in the outcomes; I will use a triangular distribution to prevent even the outside chance of infinite margins in either direction.

Note the correlation between the two, which I will talk about in the next section.

Step 5: Build in constraints and correlations
There are two additional benefits that come with simulations. The first is that you can build in constraints that will affect the company's operations, and its value, that are either internally or externally imposed. For an example of an external constraint, consider a company with a large debt load. That does not apply to Apple but it would to Valeant. If the company's value drops below the debt due, you could set the equity value to zero, on the assumption that the company will be in default. As another example, assume that you are valuing a bank and that you model regulatory capital requirements as part of your valuation. If the regulatory capital drops below the minimum required, you can require the company to issue more shares (thus reducing the value of your equity).  The second advantage of a simulation is that you can build in correlations across variables, making it more real life. Thus, if  you believe that bad outcomes on margins (lower margins than expected) are more likely to go with bad outcomes on revenue growth (revenue growth lower than anticipated), you can build in a positive correlation between the variables. With Apple, I see few binding constraints that will affect the valuation. The company has little chance of default and is not covered by regulatory constraints on capital. I do see revenues and operating margins moving together and I build in this expectation by assuming a correlation of 0.50 (lower than the historical correlation of 0.61 between revenues and operating margin from 1989 to 2015 at Apple).

Step 6: Run the simulations

Using my base case valuation of Apple (which yielded the value per share of $126.47) as my starting point and inputting the distributional assumptions for revenue growth and operating margin, as well as the correlation between the two, I used Crystal Ball to run the simulations (leaving the number at the default of 100,000) and generated the following distribution for value:

The percentiles of value and other key statistics are listed on the side. Could Apple be worth less than $93/share. Yes, but the probability is less than 10%, at least based on my assumptions. Having bought and sold Apple three times in the last six years (selling my shares last summer), this is undoubtedly getting old, but I am an Apple shareholder again. I am not a diehard believer in the margin of safety, but if I were, I could use this value distribution to create a more flexible version of it, increasing it for companies with volatile value distributions and reducing it for firms with more stable ones.

The most serious concern that I have, as an investor, is that I am valuing cash , which at $232 billion is almost a third of my estimated value for Apple, as a neutral asset (with an expected tax liability of $28 billion). Some of you, who have visions of Apple disrupting new businesses with the iCar or the iPlane may feel that this is too pessimistic and that there should be a premium attached for these future disruptions. My concern is the opposite, i.e., that Apple will try to do too much with its cash, not too little. In my post on aging technology companies, I argued that, like aging movie stars in search of youth, some older tech companies throw money at bad growth possibilities. With the amount of money that Apple has to throw around, that could be deadly to its stockholders and I have to hope and pray that the company remains restrained, as it has been for much of the last decade.

Conclusion

Uncertainty is a fact of life in valuation and nothing is gained by denying its existence. Simulations offer you an opportunity to look uncertainty in the face, make your best judgments and examine the outcomes. Ironically, being more open about how wrong you can be in your value judgments  will make you feel more comfortable about dealing with uncertainty, not less. If staring into the abyss is what scares you, take a peek and you may be surprised at how much less scared you feel.

YouTube video


Attachments

1. Paper on probability distributions
2. Apple valuation - May 2016
3. Link to Oracle Crystal Ball trial offer

Uncertainty Posts

1. DCF Myth 3: You cannot do a valuation, when there is too much uncertainty
2. The Margin of Safety: Excuse for Inaction or Tool for Action?
3. Facing up to Uncertainty: Probabilities and Simulations

DCF Myth Posts
Introductory Post: DCF Valuations: Academic Exercise, Sales Pitch or Investor Tool

1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
2. A DCF is an exercise in modeling & number crunching. 
3. You cannot do a DCF when there is too much uncertainty.
4. The most critical input in a DCF is the discount rate and if you don’t believe in modern portfolio theory (or beta), you cannot use a DCF.
5. If most of your value in a DCF comes from the terminal value, there is something wrong with your DCF.
6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
7. A DCF cannot value brand name or other intangibles. 
8. A DCF yields a conservative estimate of value. 
9. If your DCF value changes significantly over time, there is something wrong with your valuation.
10. A DCF is an academic exercise.

DCF Myth 2: A DCF is an exercise in modeling and number crunching!

Most people don't trust DCF valuations, and with good reason. Analysts find ways to hide their bias in their inputs and use complexity to intimidate those who not as well versed in the valuation game. This may surprise you, but I understand and share that mistrust, especially since I know how easy it is to manipulate numbers to yield almost any value that you want, and to delude yourself, in the process. It is for this reason that I have argued that the test of a valuation is not in the inputs or in the modeling, but in the story underlying the numbers and how well that story holds up to scrutiny. 

Left brain, meet right brain!

This fall, as I have twice a year, for almost 30 years, I will be teaching a valuation class at the Stern School of Business at New York University. When the 300 registered students walk into my classroom, I know that they will come in with preconceptions about what the class will cover. Many will bring in their laptops, with the latest version of Microsoft Excel installed, eagerly anticipating session after session on modeling, hoping to become Excel Ninjas, by the time the class is done. They expect it to be a class about numbers, more numbers and still more numbers, with Greek alphabets (alphas and betas) thrown in. 

I begin the class by asking students to tell me whether each of them is more comfortable with numbers or with stories, and not surprisingly, the class draws disproportionately large numbers of the former, but there are more than a handful of the latter. (There are a number of tests online, like this one, that you can take to make this judgment for yourself, but most of us have a sense without tests.). I then explain my vision of valuation, as a bridge between the two groups, a way of connecting narratives to numbers. 

While this picture is only an abstraction in that first class, the rest of the class is really my attempt to flesh out the picture and make the bridge real. I don’t always succeed, but my vision of a successful class is that my number-crunchers walk out of to with a little more imagination and that my storytellers acquire a bit more discipline along the way.

Connecting Stories to Numbers: The Process

The process by which you connect stories to numbers is neither obvious nor intuitive but it can be learned. In an earlier post on the topic, I laid out five steps in this process, not intended to be either exhaustive or sequential.

To illustrate, consider Amazon, a high profile company where the world is dividend into those that believe that it is a extraordinary company with a plan to conquer the world and those that use it as an example of how you can fool a lot of people for a really long time. In a post in October 2014, I valued Amazon and arrived at a value of $175 per share. 

Rather than get stuck into the details, it is worth laying bare the narrative that I have for Amazon that is determining its value. In my story, Amazon will continue on its path of delivering high revenue growth (with revenues growing to $249 billion by year 10), generally by selling products or offering services at or below cost for the near future (note that margins stay close to zero for the next 5 years), but will eventually start to use its market power to deliver profits, but this market power will be checked by the entry of new players into the retail business, leaving the target margin at a number (7.36%) that reflects the overall retail business in 2014. 

To see where the optimists in the spectrum come up with higher value, consider an alternative narrative, where Amazon’s market power is unchecked allowing it to expand into more extensively in the media market (with revenues of $329 billion in year 10) and earn an operating margin of 12.84% (the 75th percentile of retail/media firms). Those changes increase the value per share to $468/share.

To complete the process, consider the pessimistic narrative. In their story, they see Amazon as a company with a charismatic CEO (Jeff Bezos) who is less interested in creating a profitable business than he is in changing the retail world. In that story, Amazon will continue to grow revenues with little attention paid to margins, with the end game being world domination (at least of the retail business). In the valuation, that translates into higher revenue growth and paper-thin operating margins (2.85%, the 25th percentile of large US retail/media firms), even in steady state, the value per share drops to $32/share.

I followed up my post on narratives and numbers with one on how a change, shift or break in the narrative can translate into a significant change in value, and why the conventional view that intrinsic value, if done right, is timeless is nonsense. Using earnings reports as the vehicles that deliver news about narratives, I looked at my narratives for Apple, Twitter and Facebook in August 2014, and valued them. Since the last few weeks have brought new earnings reports from all three companies, I will be doing an updated version of that post in the next few days.

If you are a number cruncher, this process may seem too free form and subjective to you, and if you are a storyteller, the numbers will seem made up. To me, though, it is the essence of valuation and If you are interested in my extended discussion of this process of connecting narratives to numbers, you may want to take a look at this keynote talk that I gave at the CFA Institute Conference last year. I have to warn you that the length of the webcast (almost 3 hours) could lead you to seek the protection of the Geneva Conventions.

Tie to the life cycle: The Investor Angle

While narrative and numbers are tied together in every company’s valuation, the importance of each in driving value will shift over a company’s life cycle, as it evolves from a start up to a mature firm to one in decline. Very early in the life cycle, when numbers on the company are either scarce or uninformative, it is almost entirely narrative that drives value. In addition, that narrative can also have a much wider range of possibilities and end values, depending on the path that you map out for the company. In December 2014, I let readers pick their narrative for Uber and mapped out widely divergent values (ranging from less than $1 billion to in excess of $90 billion) for the company, based on the narrative path picked.

Uber: Narrative and Value (December 2014)

As companies mature, the numbers start to get weighted more, as it becomes more difficult for companies to not only break away from the past, but the pathways narrow. If you are valuing Coca Cola, for instance, it is more difficult to visualize explosive breakaways (either up or down in the narrative), though not impossible.  If you are an investor uninterested in valuing companies, there are still lessons that you can draw from the link between where a company is in its life cycle and the importance of narrative/numbers.

1. Value Differences: If you get big differences in the perceived value of a young company, they come from fundamentally different narratives about the company, not disagreements about the numbers. Thus, if your assessment of Etsy's value is very different from mine, it is not because we disagree about revenue growth next year but because we have fundamentally different narratives about the company.
2. Value focus: Early in the life cycle, large value changes have to come from large narrative shifts (resulting in large changes in value). Consequently, the focus when you scrutinize earnings reports and other news announcements should be on whether they change your narrative, not on whether the company met or beat some metric (earnings per share, revenues, number of users). To illustrate, much as I have taken issue with the market pricing of Tesla, I think it seems to me an over reaction, to knock off 15% of its price because it sold 50,000 cars instead of 55,000, since I see little change in the narrative for Tesla, as a consequence. In contrast, I do think that Tesla's announcement of a $5 billion investment in a battery factory is cause for a big narrative change (though I am still trying to figure out in which direction), as it may shift your view of the company for an auto manufacturer to an energy producer. (I know.. I know.. It is time for another look at Tesla as well, and I will..)
3. Value mistakes: If the essence of investing is finding misvalued companies, it seems to me that the odds of doing so are greater early in a company’s life cycle, where narratives can get mangled or when investors over react to incremental reports. As the investment world gets flatter (in terms of everyone having access to past numbers), the most successful investors of the next millennium will be those are skilled at creating and fine tuning narratives for young companies or those in transition. 

Tie to the Life Cycle: Implications for managers

The link between narratives and value has implications for those who run businesses and for what defines success for a top manager as companies move through the life cycle. 

1. Narrative control: If it is narrative that drives value early in the process, it should as come as no surprise that the most successful entrepreneurs are the ones who are best at establishing narratives that are compelling, plausible and potentially profitable. Thus, Tesla is lucky to have Elon Musk as a CEO, and Uber has been fortunate with Travis Kalanick at its helm. Both men have their faults (who does not?), but they are enormously gifted storytellers, who (for the most part) have the discipline to stick with their narratives, even in the face of distractions. 
2. Narrative consistency: One characteristic that sets apart top managers at those young growth companies that have succeeded is that they have (a) not changed their narratives substantively and (b) have acted consistently with their narratives. The stand out example for this is Jeff Bezos, who has stuck with his narrative of “revenues now, profits later” story for Amazon, sometimes to the chagrin of analysts, and everything that the company has done and continues to do advances that narrative. Mark Zuckerberg has been almost as impressive in his focus on turning Facebook’s immense user base into profits, albeit over a shorter period, but one reason for Twitter’s travails is that there seems to be no coherent narrative emerging about how the company ultimately plans to make money.
3. Bar Mitzvah Moments: In keeping with the theme of this post, which is that narratives have to be tied to numbers, it is worth emphasizing that even the most compelling and consistent narrative will ultimately fail, if the company cannot deliver the numbers to back it up. It is true that this “day of reckoning”, which I labeled a “bar mitzvah” moment, may come later for some companies than for others, but when it does come, you need a management team that recognizes that the market has shifted its focus from narrative to numbers, and behaves accordingly. 

I have tried to capture the change in balance between narrative and numbers, with the management qualities that are most needed at each stage in the picture below:

As a company makes it move from young start-up to growth company to mature business, the characteristics that make up a good CEO will change as well. One argument for a strong board of directors and shareholder power even at a well managed young company is that there may well come a time when the top management has to change with the times or be changed.

Work on your weak side

There is no one path to valuation nirvana, but I think that you need to find a balance between your storytelling and your number crunching skills, for your valuations to have heft. This balance may come easier to you than it did to me, since my natural instincts are to go with the numbers, and building my storytelling side has been slow going, at times. With each valuation that I do, I still have to force myself to be explicit about the narrative that I am building my valuation around, even when it seems obvious, and each time I do it, it gets a little easier. If you are a natural storyteller, you will probably find yourself resisting just as strongly to working with numbers, but I believe that you too will find a way to strengthen your weak side. I would like to think that a valuation that is the result of both sides of my brain working together is better than one that emerges out of only my left side, but even if it is not, it is a lot more fun getting there.

Blog Posts

1. Narrative and Numbers: Modeling, Story Telling and Investing (June 2014)
2. If you build it (revenues), they (profits) will come: Amazon's Field of Dreams (October 2014)
3. Reacting to Earnings Reports: Narrative Adjustments and Value Effects (August 2014)
4. Up, up and away: A Crowd Valuation of Uber (December 2014)
5. Twitter's Bar Mitzvah: Is social media coming of age? (November 17, 2014)
6. Reacting to Earnings Reports II: Apple, Twitter and Facebook revisited (August 2015) (Still to come)

Valuations

1. Amazon Valuation (October 2014)
2. Uber Valuation (December 2014)

Other

1. My keynote talk at the CFA Conference in November 2014

DCF Myth Posts

Introductory Post: DCF Valuations: Academic Exercise, Sales Pitch or Investor Tool

1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
2. A DCF is an exercise in modeling & number crunching. 
3. You cannot do a DCF when there is too much uncertainty.
4. It's all about D in the DCF (Myths 4.1, 4.2, 4.3, 4.4 & 4.5)
5. The Terminal Value: Elephant in the Room! (Myths 5.1, 5.2, 5.3, 5.4 & 5.5)
6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
7. A DCF cannot value brand name or other intangibles. 
8. A DCF yields a conservative estimate of value. 
9. If your DCF value changes significantly over time, there is something wrong with your valuation.
10. A DCF is an academic exercise.