Narrative and Numbers: The Value of Stories in Business (Columbia Business School Publishing)

by Aswath Damodaran

The crisis of 2008 was a cautionary note to those who would let common sense be overwhelmed by complex mathematical models.

you have to recognize both the limits and the dangers of data-driven analysis, in which biases are hidden behind layers of numbers, imprecision is masked by precise-looking estimates, and decision makers let models make choices for them on what to do and when to do it.

Not all stories that are possible are plausible, and among all plausible stories, only a few are probable.

Early in the life cycle, when a business is young, unformed, and has little history, its value is driven primarily by narrative, with wide differences across investors and over time. As a company ages and develops a history, the numbers start to play a bigger role in value, and the differences across investors and over time start to narrow. Using the story/number framework, I look at how the process changes over the life cycle of a firm, from start-up to liquidation.

Paul Zak, a neuroeconomist at Claremont Graduate University, identified a neurochemical called oxytocin, a molecule in the hypothalamus of the human brain.1 He argues that oxytocin, whose synthesis and release is associated with trust and caring, is created and released when a person listens to a powerful story (or narrative) and that this release can lead to changes in the listener’s postnarrative behavior. In addition, during stressful moments in stories, the brain releases cortisol, allowing the listener to focus. Other research also finds that happy endings trigger the limbic portion of the brain, its reward center, to release dopamine, a trigger for hope and optimism.

When a storyteller has wandered into fantasyland, the easiest way to bring him or her back to Earth is with data that suggests the journey is either impossible or improbable. Similarly, when a story is so powerful that it overwhelms listeners, all it may take are a few pragmatic questions about what it will take to deliver the promised outcomes to bring listeners back to their senses.

In his book on storytelling, Christopher Booker contends that there are only seven basic plots for stories that have been mined for hundreds of years, and he lists them as follows:5 In the first one, overcoming the monster, you have the underdog, usually smaller and perceived to be weaker, beating out

an evil adversary. A rebirth is a story of renewal, in which a person is reborn to live a better life. In a quest, the protagonist goes on a mission to find an item or thing that will save him or her and perhaps the world. It is what makes myths like Lord of the Rings and Star Wars so appealing to audiences. A rags-to-riches story is about transformation, with someone or something who is poor and weak rising to become wealthy and powerful. In a voyage and return, the characters embark either intentionally or accidentally on a journey of discovery that ends with them returning, usually wiser, happier, or richer, to their point of origin. In comedy the intent is to make you laugh with the players or at them as they stumble through life’s challenges, and in a tragedy you get the flip side: the objective here is to make you cry. Booker makes the compelling case that everything from high literature to pulp novels, opera to soap opera, and Shakespearean drama to James Bond movies draw from these seven themes.

With young start-ups in particular, and even with some established businesses, the story of the business can be tightly tied to the story of the founder, and it is the founder’s story that draws investors to the business. In particular, founder-based

stories can be one of five types: 1. The Horatio Alger story: This is a classic, especially in the United States, and it is a variant of the rags-to-riches story. Investors are attracted to this story by the tenacity of the founder in making something of himself or herself in the face of immense odds. 2. The charisma story: In this narrative the founder’s story is built around an epiphany, a moment when he or she gets a vision of business opportunity and then proceeds to fulfill that vision. Elon Musk has founded or cofounded many businesses, including SpaceX, Tesla, and SolarCity, but with each of these businesses, investors are as much drawn to him, as a charismatic founder, as they are to the companies themselves. 3. The connections story: In some businesses, it is who you know that gives you the advantage, and founders who have the right connections, either because of family background or due to their past roles as politicians or regulators, are given special deference. 4. The celebrity story: Investors are sometimes drawn to the celebrity status of a founder, in the belief this status will allow them to attract business and generate value. Jack Nicklaus, Magic Johnson, and Oprah Winfrey have all used their celebrity status to build successful businesses, with many investors being drawn to the celebrities’ names as much as to the businesses themselves. 5. The experience story: It is the track record of some founders that dra...

Business Stories Business stories can range across the spectrum, and the one you use will depend on where the business is in the corporate life cycle and what the competition it is facing looks like. Again, at the risk of both overgeneralizing and not spanning the spectrum of possible stories, a few classic business stories are presented in table 3.1.

Table 3.1 Types of Business Stories Business story Type of business Investment pitch The bully Company with a large market share, a superior brand name, access to lots of capital, and a reputation for ruthlessness They will steamroll competition to deliver ever-increasing revenues and profits. The underdog Company that is a distant second (or lower) in market share in a business, with claims to a better or cheaper product than the dominant company They will work harder than the dominant player at pleasing customers, perhaps with a kinder, gentler corporate image. The eureka moment Company that claims to have found an unmet need in the market, usually in a serendipitous way, and then has come up with a way of meeting that need They will succeed as a business by filling the unmet need. The better mousetrap Company that contends it has a better way of delivering an existing product or service that will be more desirable and better suited to the need They will eat into the market share of the existing players in the market.

The disruptor Company that changes the way a business is run, altering fundamental ways in which the product or service is delivered The status quo is ineffective and inefficient, and disruption will change the business (while making money). The low-cost player Company that has found a way to reduce the cost of doing business and is willing to cut prices on the expectation that it can sell a lot more Increased sales will more than make up for lower margins. The missionary Comp...

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Stories create connections and get remembered, but numbers convince people.

The Illusion of Objectivity The fact that the way you frame numbers can change the way people respond to them provides a segue into the second delusion about numbers—numbers are objective and number crunchers have no agendas. Really? As you will see in detail in the next chapter, the process of collecting, analyzing, and presenting data provides multiple opportunities for bias to enter the process. To make things worse, in the hands of a skilled number cruncher, this bias can be hidden far better with numbers than with stories.

a sophisticated measurement tool, is that you may not only let the numbers overwhelm your common sense but that you will not prepare yourself properly for the dangers ahead. That, unfortunately, was what happened at banks around the world during the banking crisis in 2008. In the two decades prior to the crisis, these banks had developed a risk measure called “value at risk” (VAR), which allowed them to see in numerical terms their worst-case scenarios in terms of losses from their businesses. In the intervening period, risk-management experts and academics refined VAR to make it more powerful and more complex, with the stated intent of making it more effective. As bank managers became increasingly reliant on VAR, they also let down their guards and concluded that if the computed VAR was within their defined safe limits, their risk taking was also under control. In 2008 that delusion fell apart, as the weaknesses in VAR’s core assumptions were exposed and banks that

SELECTION BIAS As we are all taught in our introductory statistics classes, it is perfectly reasonable to sample from a larger population and draw conclusions about that population, but only if that sample is random. That may sound like a simple task, but it can be very difficult to accomplish in the context of business

In some cases, the sampling bias you introduce can be explicit when you pick and choose the observations in your sample to deliver the result you want. Thus, a researcher who starts off with the objective of showing that companies generally take good investments may decide to use only companies in the S&P 500 in his sample. Since these are the largest market capitalization companies in the United States and they reached that status because of their success in the past, it should not be surprising that they have a history

SURVIVOR BIAS The other challenge in sampling is survivor bias, that is, the bias introduced by ignoring the portions of your universe that have been removed from your data for one reason or another. As a simple example of survivor bias, consider research done by Stephen Brown, my colleague at New York University, on hedge fund returns. While many studies looking at hedge fund returns over time had concluded that they earned “excess” returns (over and above expectations), Professor Brown argued that the mistake many analysts were making was that they were starting with the hedge funds in existence today and working backward to see what returns those funds earned over time. By doing so, the analysts were missing the harsh reality of the hedge fund business, which is that the worst-performing hedge funds go out of business and not counting the returns from those funds pushes up the computed return for the sample.

There are other summary statistics designed to capture the spread of numbers in your sample, with the skewness measuring the symmetry in your sample numbers and the kurtosis the frequency of numbers that are very different from your mean.

We put too much trust in the average: With all of the data and analytical tools at our disposal, you would not expect this, but a substantial proportion of business and investment decisions are still based on the average. I see investors and analysts contending that a stock is cheap because it trades at a PE that is lower than the sector average or that a company has too much debt because its debt ratio is higher than the average for the market. The average is not only a poor central measure on which to focus in distributions that are not symmetric, but it strikes me as a waste to not use the rest of the data. While an analyst in the 1960s could have countered with the argument that using all of the data was time-consuming and unwieldy, what conceivable excuse can be offered in today’s data environment?

Normality is not the norm: One of the shameful legacies of statistics classes is that the only distribution most of us remember is the normal distribution. It is an extremely elegant and convenient distribution, since it can not only be fully characterized by just two summary statistics, the mean and the standard deviation, but it lends itself to probability statements such as “that has only a 1 percent chance of happening since it is 3 standard deviations away from the mean.” Unfortunately, most real-world phenomena are not normally distributed, and that is especially true for data we look at in business and finance. In spite of that, analysts and researchers continue to use the normal distribution as their basis for making predictions and building models and are constantly surprised by outcomes that fall outside their ranges.1 3. The outlier problem: The problem with outliers is that they make your findings weaker. Not surprisingly, the way researchers respond to outliers is by ridding themselves of the source of the trouble. Removing outliers, though, is a dangerous game; it opens the door to bias, since outliers that don’t fit your priors are quick to be removed, but outliers that do fit your priors are maintained. In fact, if you view your job in business and investing as dealing with crises, you can argue that it is the outliers you should be paying the most attention to, not the data that neatly fits your hypothesis.

The bottom line is that there is no room in investing for passive listeners and whether you are a founder, a manager, or an investor, you ultimately have to play the storyteller role.

It has to be simple: A simple story that makes sense will leave a more lasting impression than a complex story in which it is tough to make connections. 2. It has to be credible: Business stories need to be credible for investors to act on them. If you are a skillful enough storyteller you may be able to get away with leaving unexplained loose ends, but those loose ends will eventually imperil your story and perhaps your business. 3. It has to inspire: Ultimately, you don’t tell a business story to win creativity awards but to inspire your audience (employees, customers, and potential investors) to buy into the story. 4. It should lead to action: Once your audience buys into your story, you want them

employees by choosing to come to work for your company, customers by buying your products and services, and investors by putting their money in your business.

you are describing a company that follows established business models, that is, the status quo, in how it operates, your story is a simple one. You will still have to find a business dimension, such as having a lower cost structure or being able to charge a price premium, where you can differentiate yourself from the competition. In contrast, a company that plans to challenge established business practices is following a disruption model. Again, which one you pick will depend on the company you are valuing and the business you are targeting.

Chinese conditions but played a key role in the evolution and growth of the Chinese e-commerce market, as China has become the second-largest online market in the world. One key difference between the Chinese e-tailing market and U.S. online retail is that the former has historically been much more dependent on online marketplaces (as opposed to retailer-based online sites), largely because of Alibaba’s influence. 2. Differentiate and dominate: The story of how Alibaba beat eBay and Amazon is grist for strategic storytellers, but at its core, there are three reasons why Alibaba won (and eBay lost). The first is economic. By charging no transactions fees initially and depending entirely on modest advertising charges, Alibaba made itself a bargain to retailers, relative to competitors. The second is that Alibaba molded its offerings to Chinese culture and consumer behavior. The Economist’s characterization of Taobao as an online bazaar is apt, since the site is set up for online haggling between buyers and sellers. Third, the site is also attuned to the fact that the Chinese retail market is splintered, with thousands of small and midsized retailers who lack visibility, credibility, and payment-processing skills online, and Taobao offers all of those. The visibility comes from the traffic on the site; the credibility from Alibaba’s system of independent verification, paid for by sellers; and payment processing from Alipay. In 2013 about 75 percent of all online ...

and investors in their own products and investment abilities, the greater the overpricing. While both groups are predisposed to overconfidence, that overconfidence tends to increase with success in the market. Not surprisingly, therefore, the longer a market boom lasts in a business space, the larger the overpricing will tend to get in that space. In fact, you can make a reasonable argument that overpricing will increase in markets where you have more experienced VCs and serial entrepreneurs, since experience often adds to overconfidence. 2. The size of the market: As the target market gets bigger, it is far more likely that it will attract more entrants, and if you add in the overconfidence they bring to the game, the collective overpricing will increase. 3. Uncertainty: The more uncertainty there is about business models and the capacity to convert them into end revenues, the more overconfidence will skew the numbers, leading to greater overpricing in the market. 4. Winner-take-all markets: The overpricing will be much greater in markets in which there are global networking benefits (i.e., growth feeds on itself) and winners can walk away with dominant market shares. Since the payoff to success is greater in these markets, misestimating the probability of success will have a much bigger effect on value.

the storyteller’s views on revenue growth, profit margins, reinvestment, or risk, but that the storyteller’s views on these are internally inconsistent, that is, they are at war with one another. The simplest device that I have for finding these inconsistencies is what I call the iron triangle of value (shown in figure 7.8). Figure 7.8 The iron triangle of value. The three corners of the triangle—growth, risk, and reinvestment—are the drivers of the value of a business, as you will see in the next chapter. For each variable, the effects on value are predictable. As growth increases, value will go up, but as risk or reinvestment increases, value will go down. Not surprisingly,

income and cash flows. If your business is built on low capital intensity, that is, it can scale up easily, it is the reinvestment that will show that advantage, remaining low for big increases in revenues. If a business is low risk, the discount rate that you use to bring the cash flows back to today will be lower (and the value higher). Figure 8.3 summarizes the effects. Figure 8.3 Connecting stories to valuation inputs. Simplistic though this framework may be, it is remarkably flexible in terms of being able to factor in story lines for companies across the life cycle and in different businesses.

As an urban car service company, the market that it is pursuing is the taxicab and car service market in cities. Aggregating the taxicab and car service revenues of cities, I obtain a value of $100 billion for the urban car service market. 2. The local networking benefits will allow Uber to emerge as the dominant player in a subset of cities, while facing competitors (both domestic and foreign) in others. The market share that I assign in steady state for the company is 10 percent. While this is far higher than the highest market share of any of the existing players in this splintered business, it is capped at 10 percent rather than 30 or 40 percent because my story does not presume global networking benefits. 3. Uber’s first-mover status, its strong capital position, and its technological edge will allow the company to maintain the revenue-sharing agreement that it has with drivers (80 percent to the driver, 20 percent to Uber) and sustain strong operating margins (40 percent in steady state). 4. Continuing on its prevailing path of not owning cars or investing in infrastructure, the company will be able to generate $5 in revenues for every dollar in capital invested. To provide some perspective, the median value for this statistic across all U.S. companies is about 1.5 ($1.50 in sales for every dollar invested in capital) and a sales-to-capital ratio of 5.0 would be around the 90th percentile of all companies. Figure 8.4 summarizes thes...

If you look back at the valuations I am setting up just in this chapter, each of the companies I have valued has qualitative strengths that are at the core of their success. Uber is managed by a risk-taking team that aggressively seeks out opportunities and is backed by skilled technology, but that is why I feel comfortable making the assumption that they will conquer the ride-sharing market over the next decade.

Find comparable or similar assets in the market: While the conventional practice for doing relative valuation, at least in the context of stocks, is to look at other companies in the same sector as the company you are pricing, it is ultimately a subjective judgment and will depend

largely on how investors in the market classify a company. Thus, if Tesla is being treated by investors as a tech company and not an automobile company, the pricing may very well have to do the same. 2. Look for the pricing metric that investors use in pricing these companies: When pricing companies, it is not your place or mine to determine what investors should be using to price companies, but what they actually are using. Thus, if the metric investors focus on when pricing social media companies is the number of users these companies have, you should focus on that metric in pricing your company. 3. Price your company: Now that you have the metric or metrics that investors are using to price companies, you can price your company based on that metric and the pricing ratios across the comparable companies. Using the social media example again, if social media companies are being priced based on users, and the average price that the market was paying was $100/user in 2013, you would have priced Twitter, which had 240 million users in October 2013, at approximately $24 billion.

One aspect of DCF valuation that both trips up and troubles those using it is the role of the terminal value. If you are valuing a business, it is almost inevitable that the terminal value will be a substantial contributor to the value that you estimate for the value today, accounting for 60 percent, 70 percent, or even more than 100 percent of the current value. Rather than view that as a weakness of the model, as some are apt to do, consider it a reflection of how you make money as an equity investor in a business.

I would tighten that constraint by suggesting that the risk-free rate be used as the proxy for nominal growth in the economy, thus bringing the currency choice into the growth estimate; if you are working with a higher-inflation currency, both your risk-free rate and expected growth rate in perpetuity will be much higher.

Thus, if you generate a return of 12 percent on the capital invested in new projects, you will need to reinvest 25 percent of your after-tax operating income in perpetuity to be able to grow at 3 percent a year. In fact, if the return on capital you generate is equal to your cost of capital, the terminal value will not change as growth changes, since growth becomes a neutral variable.

wrong. To get from the operating asset value to the value of equity in a business and from that equity to value of equity per share in a publicly traded company requires judgments on the following:

There are many venture capitalists who are dead set against the use of DCF approaches in valuing companies, and their disdain for the approach may reflect their exposure to a rigid version of the model.

Marginal return on capital = Change in operating income/Reinvestment This marginal return on invested capital is a rough measure of how good you think your company’s investments will be in the future. If it is too high or too low, and that judgment can be made by comparing it with the company’s cost of capital, its historical return on capital, or industry averages, it is a red flag that you should revisit your growth and reinvestment assumptions.

The process of deconstructing valuations is simple if you use the structure that was developed to convert stories to numbers. Thus, when you see projected revenues for a company in a valuation spreadsheet

Figure 9.2 Deconstructing a valuation. Conclusion