In my last post, I tried valuing Uber by estimating how much an existing user was worth to the company and then using that number to extrapolate to the value of all existing users and the value added by new users. As always, I got many useful comments on what I was missing, what I could do better and what could be simplified, and I thank you (really). While I could spend this entire post rehashing assumptions, I don't intend to! To me, the most useful part of valuation is not the destination, i.e., the value that you get at the end, but the journey, i.e., the process of doing valuation, since it is the process that allows us to isolate the key drivers of value, which, in turn, focuses discussions on those variables, rather than on distractions. Consequently, I decided to revisit my Uber user-based valuation to see what I could eke out as implications for user or subscriber-based businesses.
Estimation versus Economic Risk
I will start by conceding the obvious. I made a lot of assumptions to arrive at the value of a user at Uber, but I will go further. There was not a single fact in that valuation, since every number was an estimate. That said, you could say that about the valuation of any company, with the divergence really being one of the degree of uncertainty you face, not in whether it exists. At the risk of restating points that I have made in my other writing, here are three general points that I would make about uncertainty in valuation.
I will start by conceding the obvious. I made a lot of assumptions to arrive at the value of a user at Uber, but I will go further. There was not a single fact in that valuation, since every number was an estimate. That said, you could say that about the valuation of any company, with the divergence really being one of the degree of uncertainty you face, not in whether it exists. At the risk of restating points that I have made in my other writing, here are three general points that I would make about uncertainty in valuation.
1. Estimation uncertainty versus Economic uncertainty
To deal with uncertainty in a sensible way, you first have to categorize it. One of the categorizations that I find useful is to break the uncertainty you face when you are trying to value a business or an asset into estimation and economic uncertainty. Estimation uncertainty comes from incomplete, missing or misleading information provided by the company that you are valuing, whereas economic uncertainty is driven by forthcoming changes in the business that the company operates in, as well as macro economic factors. Estimation uncertainty can be reduced by obtaining better and more complete information but estimation uncertainty will remain resistant, no matter how much time you put in and what data analysis that you do. Using my Uber user valuation, it is true that some of the noise in the valuation comes from Uber being a private, secretive company and but most of the uncertainty comes from the ride sharing business being in a state of flux, as regulators and competitors work out how best to deal with shifting consumer tastes and changing technologies. This has two implications. The first is that even if you had access to more information, either because Uber decides to go public or you are an insider in the company, much of the uncertainty in estimated value per user will remain. The second is that your estimated value will change considerably over time, as the facts on the ground change, and that volatility in value cannot be viewed as a shortcoming of the model.
To deal with uncertainty in a sensible way, you first have to categorize it. One of the categorizations that I find useful is to break the uncertainty you face when you are trying to value a business or an asset into estimation and economic uncertainty. Estimation uncertainty comes from incomplete, missing or misleading information provided by the company that you are valuing, whereas economic uncertainty is driven by forthcoming changes in the business that the company operates in, as well as macro economic factors. Estimation uncertainty can be reduced by obtaining better and more complete information but estimation uncertainty will remain resistant, no matter how much time you put in and what data analysis that you do. Using my Uber user valuation, it is true that some of the noise in the valuation comes from Uber being a private, secretive company and but most of the uncertainty comes from the ride sharing business being in a state of flux, as regulators and competitors work out how best to deal with shifting consumer tastes and changing technologies. This has two implications. The first is that even if you had access to more information, either because Uber decides to go public or you are an insider in the company, much of the uncertainty in estimated value per user will remain. The second is that your estimated value will change considerably over time, as the facts on the ground change, and that volatility in value cannot be viewed as a shortcoming of the model.
2. Uncertainty is an integral part of valuation
One critique that leaves me unmoved is that valuing a business or an asset, in the face of significant uncertainty, is pointless because you will be wrong. So what? Uncertainty is part and parcel of doing business and you cannot wish it, pray it or analyze it away. As I see it, you have two choices when it comes to uncertainty. You can deal with it frontally by making explicit assumptions or you can go into "denial" model and make implicit assumptions. When I tried to value a user at Uber, I made explicit assumptions about user life, renewal rates and a host of other variables, and I will cheerfully admit that I will be wrong on every one of them, but what is the alternative? When pricing a user by looking at what others are paying for users in similar companies, you are making assumptions about all of the variables as well, but those assumptions are implicit. In fact, they are hidden so well that you may not be aware of your own assumptions, a dangerous place to be when investing.
One critique that leaves me unmoved is that valuing a business or an asset, in the face of significant uncertainty, is pointless because you will be wrong. So what? Uncertainty is part and parcel of doing business and you cannot wish it, pray it or analyze it away. As I see it, you have two choices when it comes to uncertainty. You can deal with it frontally by making explicit assumptions or you can go into "denial" model and make implicit assumptions. When I tried to value a user at Uber, I made explicit assumptions about user life, renewal rates and a host of other variables, and I will cheerfully admit that I will be wrong on every one of them, but what is the alternative? When pricing a user by looking at what others are paying for users in similar companies, you are making assumptions about all of the variables as well, but those assumptions are implicit. In fact, they are hidden so well that you may not be aware of your own assumptions, a dangerous place to be when investing.
3. Uncertainty can (and should) be visualized
Here is my response to uncertainty. Where data exists but I do not have access to that data, I will try to make my best estimates based upon the existing information, noisy, dated or second hand though it might be. Where I have access to data, I will check it against other data, common sense and economic first principles. Where there is no data, I will make my best estimates and to the extent that these estimates come with probability distributions, my value itself is a distribution, not a number. Illustrating this process, with the Uber user valuation:
Here is my response to uncertainty. Where data exists but I do not have access to that data, I will try to make my best estimates based upon the existing information, noisy, dated or second hand though it might be. Where I have access to data, I will check it against other data, common sense and economic first principles. Where there is no data, I will make my best estimates and to the extent that these estimates come with probability distributions, my value itself is a distribution, not a number. Illustrating this process, with the Uber user valuation:
 |
| Excel Add On: Crystal Ball (Oracle), Simulation Output |
I have made distributional assumptions on four of my inputs: the portion of Uber's expenses that go to servicing existing users, the life time of a user, the proportion of expenses that are variable and the cost of capital (discount rate) to compute today's value. Since these distributions are all centered on my base case assumptions, it should come as no surprise that the median value of a user ($414) is very close to my base case value ($410). However, there is a wide spread around that value, with the numbers ranging a low of $74, when the user life is short, the expenses of servicing a user are high, most of the costs are variable and the cost of capital is low, to a high of more than $1000 per user, when the opposite conditions hold. Note that at the current pricing of $69 billion, you are valuing each user close to $900, at the upper end of the distribution.
User Economics: Cost Propositions
It is true that the end game for every business is to make money for its investors. That said, there is a tendency to over react, when a young company reports a loss, as was the case when Uber reported an operating loss of $2.8 billion for 2016, a few months ago. The pessimists on Uber viewed this as further evidence that the company was on a pathway to nowhere and that investors in the company must be delusional to attach any value to it. The optimists argued that it is natural for young companies to lose money and that Uber should be judged on other dimensions such as user growth and market potential instead. At the risk of angering both groups, I will use my Uber user valuation to argue that while I agree with the second group that losing money is typical at young companies, I will also take sides with the first group that you still need a pathway to profitability amidst the losses, for value to exist.
It is true that the end game for every business is to make money for its investors. That said, there is a tendency to over react, when a young company reports a loss, as was the case when Uber reported an operating loss of $2.8 billion for 2016, a few months ago. The pessimists on Uber viewed this as further evidence that the company was on a pathway to nowhere and that investors in the company must be delusional to attach any value to it. The optimists argued that it is natural for young companies to lose money and that Uber should be judged on other dimensions such as user growth and market potential instead. At the risk of angering both groups, I will use my Uber user valuation to argue that while I agree with the second group that losing money is typical at young companies, I will also take sides with the first group that you still need a pathway to profitability amidst the losses, for value to exist.
1. Servicing existing users versus acquiring new users
In my Uber user valuation, I started with the operating losses reported by the company ($2.8 billion), backed into the total operating expenses for the company ($9.3 billion) and then allocated that expense across three categories: servicing existing user (48.17%), acquiring new users (41.08%) and corporate expenses (10.75%). While I based this breakdown on the information (on increase in users and contribution margins in ride sharing) that I had on Uber in 2016, that information is dated, noisy and second hand. It is entirely possible that the actual break down of expenses is different from my estimate. If you are wondering why it matters, since the end result (that Uber lost $2.8 billion) is not changing, there are consequences that you can see in the table below:
In my Uber user valuation, I started with the operating losses reported by the company ($2.8 billion), backed into the total operating expenses for the company ($9.3 billion) and then allocated that expense across three categories: servicing existing user (48.17%), acquiring new users (41.08%) and corporate expenses (10.75%). While I based this breakdown on the information (on increase in users and contribution margins in ride sharing) that I had on Uber in 2016, that information is dated, noisy and second hand. It is entirely possible that the actual break down of expenses is different from my estimate. If you are wondering why it matters, since the end result (that Uber lost $2.8 billion) is not changing, there are consequences that you can see in the table below:
Uber User Value: Existing User versus New User Costs
| % of Operating Expenses spent on acquiring new users | Value of Existing Users | Value of New Users | Uber User Value | % of Value from Existing users |
|---|---|---|---|---|
0%
|
$6,167
|
$18,147
|
$24,314
|
25.36%
|
20%
|
$10,619
|
$19,035
|
$29,654
|
35.81%
|
40%
|
$15,071
|
$19,923
|
$34,994
|
43.07%
|
60%
|
$19,523
|
$20,811
|
$40,334
|
48.40%
|
80%
|
$23,974
|
$21,699
|
$45,673
|
52.49%
|
100%
|
$28,426
|
$22,587
|
$51,013
|
55.72%
|
As you increase the proportion of the operating expenses that are spent on acquiring new users, the value of an existing user goes up because you are spending less money on providing service to that user, but the value of a new user also increases, as the net value added (the difference between the user value and the cost of acquiring a user) goes up. Ironically, as you spend more on acquiring new users and less on servicing existing users, the proportion of your value that comes from existing users increases.
User Value Proposition 1: A money-losing company that is losing money providing service to existing users/customers is worth less than a company with equivalent losses, where the primary expenses are coming from customer acquisitions.
User Value Proposition 1: A money-losing company that is losing money providing service to existing users/customers is worth less than a company with equivalent losses, where the primary expenses are coming from customer acquisitions.
This is, of course, neither profound nor surprising, and it explains why, left to their own devices and without any monitoring, young companies will claim that most or all of their expenses are for acquiring new customers. If you are investing in a young company, you will have to do your own assessment of whether managers are misrepresenting, by looking at expense growth over time versus new customers. If the number of total customers remains fixed and expenses keep rising, you should be skeptical about managerial claims (that most of the costs are for acquiring new customers).
2. Cost Structure
One reason that investors are willing to accept losses at young companies is because they believe that as the company grows its operations, there will be economies of scale. In income statement terms, this will result in expenses growing less quickly than revenues and improving operating margins. That said, you cannot take it on faith that this will always happen or that it will happen at the same rate for every company. To see the impact on user value of this dimension, I adjusted the portion of Uber's expenses that are variable (and will grow with revenues) and those that are fixed (and grow at a lower rate) and captured the value effect in this table:
As the proportion of expenses that are fixed rises, the value of both existing and new users goes up but the latter goes up at a faster rate. Put simply, the economies of scale increase as you increase the rate at which you are adding scale.
User Value Proposition 2: A company whose expenses are primarily fixed (will not grow with revenues) will be worth more than an otherwise identical company whose expenses are variable (track revenues).
One reason that investors are willing to accept losses at young companies is because they believe that as the company grows its operations, there will be economies of scale. In income statement terms, this will result in expenses growing less quickly than revenues and improving operating margins. That said, you cannot take it on faith that this will always happen or that it will happen at the same rate for every company. To see the impact on user value of this dimension, I adjusted the portion of Uber's expenses that are variable (and will grow with revenues) and those that are fixed (and grow at a lower rate) and captured the value effect in this table:
Uber User Value and Cost Structure
| % of current expenses that are fixed | Value of Existing Users | Value of New Users | Uber User Value | % of Value from Existing users |
|---|---|---|---|---|
0%
|
$14,733
|
$15,250
|
$29,983
|
49.14%
|
20%
|
$16,412
|
$20,191
|
$36,603
|
44.84%
|
40%
|
$17,834
|
$24,373
|
$42,207
|
42.25%
|
60%
|
$19,040
|
$27,924
|
$46,964
|
40.54%
|
80%
|
$20,068
|
$30,949
|
$51,017
|
39.34%
|
100%
|
$20,947
|
$33,536
|
$54,483
|
38.45%
|
User Value Proposition 2: A company whose expenses are primarily fixed (will not grow with revenues) will be worth more than an otherwise identical company whose expenses are variable (track revenues).
If unchallenged, young growth companies will always claim that they have massive economies of scale but that claim has to be backed up by the numbers. Specifically, investors should pay attention to the rate of change in revenues and expenses, since with large economies of scale, the former should change more than the latter. The caveat, though, is that having more fixed costs can increase risk, because it will increase the risk of failure at young companies and earnings volatility for more mature firms. As user growth levels off, having more fixed costs will reduce value rather than increasing it.
User Economics: Growth Propositions
For young companies, we generally view growth as good and while that is generally true, not all growth is created equal. In fact, even with young companies, there are some strategies that deliver growth in users or revenues, while destroying value. In a user or subscriber based model, there are two ways you can grow your revenues. One is to get existing users to buy more of your products or services and the other is by trying to acquire new users. While both can increase value, the former will be create more value, for two reasons. First, since it comes from existing customers, you don’t have to pay to acquire these users and it is thus less costly to the firm. Second, by increasing the value of a user, it increases the value of any new users as well, creating a secondary impact on value. Using my Uber user valuation, you can see the impact of changing the annual growth rate in revenues for an existing user in the chart below:
For young companies, we generally view growth as good and while that is generally true, not all growth is created equal. In fact, even with young companies, there are some strategies that deliver growth in users or revenues, while destroying value. In a user or subscriber based model, there are two ways you can grow your revenues. One is to get existing users to buy more of your products or services and the other is by trying to acquire new users. While both can increase value, the former will be create more value, for two reasons. First, since it comes from existing customers, you don’t have to pay to acquire these users and it is thus less costly to the firm. Second, by increasing the value of a user, it increases the value of any new users as well, creating a secondary impact on value. Using my Uber user valuation, you can see the impact of changing the annual growth rate in revenues for an existing user in the chart below:
While value increases with user growth rates, it increases at a lower rate than it did when we varied revenue growth from existing users.
User Value Proposition 3: A company that is growing revenues by increasing revenues/user is worth more than an otherwise similar growth company that is deriving growth from increasing the number of users/customers.
User Value Proposition 3: A company that is growing revenues by increasing revenues/user is worth more than an otherwise similar growth company that is deriving growth from increasing the number of users/customers.
Young companies face the question of whether to allocate resources to get new users or try to sell more to existing users is one of those. At least in the case of Uber, the numbers seem to indicate that the payoff is greater in getting existing users to use the service more than in looking for new users.
User Economics: Business Propositions
At the risk of stretching the user value model too far, it can be used to discuss business models in the space, from the networking benefits that so many companies in this space claim to possess to how the revenue model you choose (subscription, transaction or advertising) plays out in user values.
1. Competitive Dynamics and Networking Benefits
At the risk of stretching the user value model too far, it can be used to discuss business models in the space, from the networking benefits that so many companies in this space claim to possess to how the revenue model you choose (subscription, transaction or advertising) plays out in user values.
1. Competitive Dynamics and Networking Benefits
Is it better to operate in a business where the cost of acquiring a new user is low or high? Holding all else constant, the answer is obvious. A firm will maximize its value if can generate both high value per user and have a low cost of acquiring new users. That said, if everyone in the business shares these characteristics, one or another of these variables has to change. If the cost of acquiring new users is low for everyone, competition will drive down the value per new user, and if the value per user remains high, competition will drive up the cost of acquiring new users. The trade off is captured in the picture below:
User Value Proposition 4: The exceptional firm will be the one that is able to find a pathway to high value per user and a low cost to adding a new user in a market, where its competitors struggle with either low value per user or high costs of acquiring users.
So how do the exceptional companies pull off this seeming impossible combination of high value per user and low cost per new user? I may be stretching, but it is at the heart of two terms that we see increasingly used in business, network benefits and big data.
So how do the exceptional companies pull off this seeming impossible combination of high value per user and low cost per new user? I may be stretching, but it is at the heart of two terms that we see increasingly used in business, network benefits and big data.
- Network Benefits: If network benefits exist, the cost of acquiring new users will decrease as a company's presence in a market increases, reaching a tipping point where the biggest player will face much lower costs in acquiring new users than the competition, allowing it to capture the market and perhaps use its market dominance to increase the value of each user. In the case of Uber and ride sharing business, the argument for networking benefits is strong on a localized basis, since there are clearly advantages for both drivers and customers to shift to the dominant ride sharing company in any locality, the former because they will generate more income and the latter because they will get better service. The argument is much weaker on a global basis, though ride sharing companies are trying to create networking benefits by allying with airlines and credit care companies, and how this attempt plays out may well determine Uber's ultimate value.
- Big Data: While I remain a skeptic on the "big data" claims that every company seems to be making today, it is inarguable that there are companies that use big data to augment value. These companies collect data on their existing users/subscribers/customers and use that information to (a) customize existing products/services to meet user preferences, (b) create new products or services that meet perceived user needs and/or (c) for differential pricing. All of these increase user value by altering one or more of the inputs into the equation, with customization increasing user life and new products & differential the growth in revenues/user. In my view, the best users of big data (Netflix, Amazon, Google and Facebook) have used the data to increase their existing user value. Uber is still in the nascent stages, but its attempts at using data have expanded from surge pricing to differential pricing.
2. Revenue Models
In my version of user valuation, I look at revenues per user, drawing no distinction on how those revenues are derived. Broadly speaking, there are three revenue models that a user/subscriber based company can use, a subscription-based model where users or subscribers pay a subscription fee to continue to use the service or product, a transaction-based model where users or subscribers pay only when they use the service of product and an advertising-based model where users or subscribers get to use the product or service for free, but are targeted in advertising. Netflix operates on a subscription-based model, Uber is a transaction-based firm and Facebook generates its revenues from advertising. Some companies like LinkedIn have hybrid models, generating revenues from subscriptions (from premium members), transactions (from recruitments) and advertising. There are other inputs into the valuation that will be affected by a company's revenue model and I have tried to capture them in the table below:
There is no one dominant revenue model, since each has its pluses and minuses. An advertising-based model will allow for much more rapid growth in a firm's early years, a subscription-based model will generate more sustainable growth and a transaction-based model has the greatest potential for revenue growth from existing users.
User Value Proposition 5: The "optimal" revenue model may vary for a firm depending upon where it is in the life cycle and across firms depending on their product or service offerings and across investors, depending on whether they are focused on user growth, revenue growth or revenue sustainability.
3. Real Options
When valuing a company based upon its expected cash flows, there is a chance that you will under value the company, if it has control of a resource that could be used for other purposes in the future, even if that usage makes no economic sense today. That is why a technology or natural resource reserve that is not viable today can still have value, and this is the basis for the real option premium. In the context of a user-based business, optionality can become a component of value, to the extent that companies may be able to exploit their user bases to sell other products and services in the future. While the intuition of real options is simple, valuing real options is notoriously difficult and after much hand waving, most of us (including me) give up, but the user-based valuation model provides a framework to at least eke out some general propositions about optionality and value.
There should be no surprises in this picture, with the value of a real option in a user base tied to the inputs into an option pricing model.
User Value Proposition 6: The value of optionality from a user base will be greatest at firms with lots of sticky, intense users in businesses where the future is unpredictable because of changes in product/service technology and customer tastes.
In my version of user valuation, I look at revenues per user, drawing no distinction on how those revenues are derived. Broadly speaking, there are three revenue models that a user/subscriber based company can use, a subscription-based model where users or subscribers pay a subscription fee to continue to use the service or product, a transaction-based model where users or subscribers pay only when they use the service of product and an advertising-based model where users or subscribers get to use the product or service for free, but are targeted in advertising. Netflix operates on a subscription-based model, Uber is a transaction-based firm and Facebook generates its revenues from advertising. Some companies like LinkedIn have hybrid models, generating revenues from subscriptions (from premium members), transactions (from recruitments) and advertising. There are other inputs into the valuation that will be affected by a company's revenue model and I have tried to capture them in the table below:
| Subscription | Transaction | Advertising | |
|---|---|---|---|
| User Stickiness (User life & Renewal Probability) | High (High life & renewal probability) | Intermediate (Intermediate life & renewal probability) | Low (Low life & renewal probability) |
| Revenue per User Predictability (Discount rate) | High (Low Discount Rate) | Low Predictability (High Discount Rate) | Intermediate (Average Discount Rate) |
| Revenue per User Growth (Annual Growth Rate) | Low (Low growth rate in revenues/user) | Low (High growth rate in revenues/user) | Intermediate (Intermediate growth rate in revenues/user) |
| Growth rate in users (CAGR in # Users) | Low (Low CAGR in # users) | Intermediate (Intermediate CAGR in # users) | High (High CAGR in # users) |
| Cost of adding new users (Cost/New User) | High (High Cost/New User) | Intermediate (Middling Cost/New User) | Low (Low Cost/New User) |
User Value Proposition 5: The "optimal" revenue model may vary for a firm depending upon where it is in the life cycle and across firms depending on their product or service offerings and across investors, depending on whether they are focused on user growth, revenue growth or revenue sustainability.
3. Real Options
When valuing a company based upon its expected cash flows, there is a chance that you will under value the company, if it has control of a resource that could be used for other purposes in the future, even if that usage makes no economic sense today. That is why a technology or natural resource reserve that is not viable today can still have value, and this is the basis for the real option premium. In the context of a user-based business, optionality can become a component of value, to the extent that companies may be able to exploit their user bases to sell other products and services in the future. While the intuition of real options is simple, valuing real options is notoriously difficult and after much hand waving, most of us (including me) give up, but the user-based valuation model provides a framework to at least eke out some general propositions about optionality and value.
User Value Proposition 6: The value of optionality from a user base will be greatest at firms with lots of sticky, intense users in businesses where the future is unpredictable because of changes in product/service technology and customer tastes.
The Bottom Line
The most direct applications of a user or subscriber based model is in the valuation of companies like Uber, Facebook and Netflix. That said, more and more companies are seeing benefits in shifting from their traditional business models to user-based ones. Apple is a cash machine built around a smartphone but it is also accumulating information on more than a billion users of these phones, to whom it may be able to offer other products and services. Amazon started life as an online retail company but there is no denying the power of its seventy million Prime members in generating revenues for the company. I have used Microsoft and Adobe products for as long as they have been around, but with both companies, but my relationship with both companies has changed. I am now a subscriber (Office 365 and Creative Cloud member) who pays annual fees, rather than a customer who buys and upgrades software on a discretionary basis. Understanding user economics and value is central to not only investors in these companies, when valuing and pricing them, but to managers of these companies, in their day-to-day business decisions. I will admit, without shame, that my knowledge of user-based companies is rudimentary and that my user-based model may be amateurish, in what it misses or mangles. That said, if you are an expert on user-based businesses, I hope that you can build on the model to make it more realistic and useful.
YouTube Video
Links
Attachments
The most direct applications of a user or subscriber based model is in the valuation of companies like Uber, Facebook and Netflix. That said, more and more companies are seeing benefits in shifting from their traditional business models to user-based ones. Apple is a cash machine built around a smartphone but it is also accumulating information on more than a billion users of these phones, to whom it may be able to offer other products and services. Amazon started life as an online retail company but there is no denying the power of its seventy million Prime members in generating revenues for the company. I have used Microsoft and Adobe products for as long as they have been around, but with both companies, but my relationship with both companies has changed. I am now a subscriber (Office 365 and Creative Cloud member) who pays annual fees, rather than a customer who buys and upgrades software on a discretionary basis. Understanding user economics and value is central to not only investors in these companies, when valuing and pricing them, but to managers of these companies, in their day-to-day business decisions. I will admit, without shame, that my knowledge of user-based companies is rudimentary and that my user-based model may be amateurish, in what it misses or mangles. That said, if you are an expert on user-based businesses, I hope that you can build on the model to make it more realistic and useful.
YouTube Video
Links
Attachments
Hi Professor,
ReplyDeleteA very useful framework for evaluating a wide variety of companies and much appreciated you posted and shared this. By the way, this UCI alum appreciates having a fellow UC system person so deeply committed to leading the valuation profession and discussion.
Yale Bock, CFA
Y H & C Investments
Hi Professor,
ReplyDeleteVery much appreciate you posting this highly useful framework which is applicable across a wide variety of businesses. As an UCI alum, nice to see a fellow UC system person leading the valuation profession and discussion.
Yale Bock, CFA
Y H & C Investments
Hi Professor,
ReplyDeleteI got stuck trying to understand math of your table under "Competitive Dynamics and Networking Benefits" about high value vs. low value users, and was hoping you might explain!
How did you calculate the values in the table?
Thank you,
Dan