Myth 5.2: Equally G-> R...To Infinity Together With Beyond!

In my in conclusion post, I started off yesteryear providing a rationale for a terminal value together with presented alternatives to the perpetual growth model. That said, most DCFs are built amongst the the perpetual growth equation, setting upwardly for a potential valuation disaster. Mathematically, the denominator is a pulverization keg waiting to blow, since equally yous increase g, belongings the cash current together with r constant, your value volition approach infinity before turning negative, leading to what I call “Buzz Lightyear” valuations.

The Growth Cap
If yous desire to describe on the perpetual growth equation, either because yous believe your trace organisation volition in conclusion forever or for convenience, the growth charge per unit of measurement that yous tin sack purpose inward it is constrained to hold upwardly less than or equal to the growth charge per unit of measurement of the economic scheme inward which yous operate. This is non a debatable assumption, since it is mathematical, non 1 that owes its presence to economical theory. Within this statement, though, at that spot are estimation choices that yous volition own got to human face nearly how to define the growth cap.

1. Domestic versus Global: As a cap, yous tin sack purpose the growth inward the domestic economic scheme (if your society volition rest a purely domestic operator) or growth inward the global economy, together with the economy’s growth charge per unit of measurement has to hold upwardly computed inward the same price that yous are using for the residuum of your valuation. That may appear to give yous license to purpose high growth rates for emerging marketplace companies but I would advise caution, since emerging marketplace economies equally they larn bigger volition tend to run across their growth rates motion towards a global growth rate. Thus, piece it is truthful that the Indian together with Chinese economies own got higher existent growth rates than the global economic scheme inward the close term (5-10 years), they volition run across their growth rates converge on the global average (closer to 2%) sooner rather than later. 
2. Real versus Nominal: In an before post, I argued that 1 of the hallmarks of a well-done DCF is consistency inward how cash flows are defined together with discount rates are computed. Specifically, yous tin sack select to approximate your cash flows inward existent price or nominal terms, amongst the erstwhile reflecting growth without the helping manus of inflation together with the latter inclusive of it. If your valuation is inward existent terms, the cap on your growth charge per unit of measurement volition hold upwardly the existent growth charge per unit of measurement inward the economy, together with if inward nominal terms, it volition hold upwardly the nominal growth rate. 
3. Currency: If yous select to do your valuation inward nominal terms, yous own got to pick a currency to denominate your cash flows in, together with that currency volition own got an expected inflation cistron attached to it. The nominal growth charge per unit of measurement cap volition own got to hold upwardly defined consistently, amongst the same expected inflation built into it equally well. Thus, if yous are valuing your society inward a high-inflation currency, your nominal growth charge per unit of measurement forever tin sack hold upwardly much higher than if yous value it inward a low-inflation currency.

What if your society is inward a high growth sector or a high growth market? The response lies inward the "forever", since no sector or market, no affair how high its growth is correct now, tin sack maintain to grow at a charge per unit of measurement faster than the overall economic scheme forever. One of the greatest perils inward valuation is ignoring the growth cap, either because yous forget the mathematical footing for why it exists inward the get-go house or because yous own got mismatched your cash flows together with your discount rate, mayhap estimating the erstwhile inward a high inflation currency together with the latter inward a low-inflation 1 or vice versa.

A Risk Free Rate Proxy?

If yous convey the rationale that growth is capped at the growth charge per unit of measurement of the economy, yous are straightaway confronted amongst a daunting together with mayhap impossible task, i.e., to value an private company, yous volition straightaway own got to approximate expected growth charge per unit of measurement inward the economic scheme (domestic or global) together with expected inflation inward the currency of your choice. I, for one, desire no business office of this estimation challenge, for 2 reasons. The get-go is that I uncovering long term macroeconomic forecasting to hold upwardly a futile practise together with own got absolutely no organized faith inward either myself or the institutional entities that claim to hold upwardly proficient at this task. The 2nd is that whatever fourth dimension I pass on these macroeconomic forecasts is fourth dimension that I am non spending on agreement my society together with its business, key to valuing that company. Consequently, I purpose a simpler together with to a greater extent than easily observable position out equally a cap on stable growth: the risk gratis charge per unit of measurement that I own got used inward the valuation. Not alone does this convey into trace organisation human relationship the currency automatically (since higher inflation currencies own got higher risk gratis rates) but it is reasonable to fence that it is a proficient proxy for the nominal growth charge per unit of measurement inward the economy.  Since it is the cistron of my valuations that I am taken to trouble most often about, I own got 3 arguments to offering together with piece none standing lone may hold upwardly persuasive, yous may mayhap convey a combination of them.

1. An Empirical Argument:
To sympathize the link betwixt the risk gratis charge per unit of measurement (a nominal involvement rate) together with nominal economical growth rates, consider the next decompositions of both:

Risk gratis rate = Expected Inflation + Expected existent involvement rate

Nominal economical growth = Expected Inflation + Expected existent growth rate

The tabular array below the risk gratis charge per unit of measurement inward US dollars (measured amongst a ten-year treasury bond rate) together with nominal economical growth (the amount of expected inflation together with existent gross domestic product growth) from 1954 to 2015 inward the United States, broken into 2 sub-periods.

Period	10-Year T.Bond Rate	Inflation Rate	Real gross domestic product Growth	Nominal gross domestic product growth rate	Nominal gross domestic product - T.Bond Rate
1954-2015	5.93%	3.61%	3.06%	6.67%	0.74%
1954-1980	5.83%	4.49%	3.50%	7.98%	2.15%
1981-2008	6.88%	3.26%	3.04%	6.30%	-0.58%

The nominal gross domestic product growth charge per unit of measurement was nearly 0.74% higher than the risk gratis charge per unit of measurement over the entire catamenia (1954-2015), but it has lagged the risk gratis charge per unit of measurement yesteryear 0.58% since 1981. I know this table, yesteryear itself,  proves nothing, but at that spot is ground to head to the link. In the in conclusion 60 years inward the United States,  nominal involvement rates together with nominal growth own got been closely tied to each other, amongst an increase inward 1 tied to an increase inward the other. It is truthful that at that spot is evidence inward the data, peculiarly inward the 1954-1980 fourth dimension period, that existent growth tin sack orbit existent involvement rates for extended periods, together with economical intuition provides a rationale for why. If those who convey no risk earn the riskfree rate, the economy, at to the lowest degree on average together with over long fourth dimension periods, has to deliver a fiddling chip to a greater extent than to vantage the risk takers. However, non alone tin sack that differential non hold upwardly a large position out but it is also worth remembering that the nominal growth charge per unit of measurement is the growth charge per unit of measurement inward the entire economy, composed of both mature together with growth companies. If yous let every mature society to grow at the charge per unit of measurement at which the economic scheme is growing, where does the growth come upwardly to sustain the growth companies inward the economies? Put differently, setting the growth charge per unit of measurement for mature companies below the growth charge per unit of measurement of the economic scheme cannot wound yous but setting it higher upwardly that of the economic scheme tin sack drive valuations to implode. I'll convey my chances on the former!

2. H5N1 Consistency Rationale 
If yous are non convinced yesteryear this reasoning, I volition offering some other ground for tying the 2 numbers together. When yous purpose a riskfree charge per unit of measurement inward a valuation, yous are implicitly making assumptions nearly economical growth together with inflation inward the hereafter together with if yous desire your valuation to hold upwardly consistent, yous should build like assumptions inward estimating your cash flows. Thus, if yous believe, the risk gratis charge per unit of measurement today is also depression or fifty-fifty negative (because the fundamental banks own got kept it so), together with yous purpose that risk gratis charge per unit of measurement to come upwardly up amongst your discount rates, yous own got to maintain your growth charge per unit of measurement inward perpetuity really depression or negative to maintain your valuation from imploding. That is the indicate that I was making inward my post on negative involvement rates. In the in conclusion decade, equally involvement rates own got hitting historic lows, the danger of this mismatch has perish greater. Analysts own got been quick to shift to using lower risk gratis rates (to 2% or lower) inward their discount charge per unit of measurement calculations piece continuing to purpose nominal growth inward the US economic scheme (5-6%) equally the cap on their growth rates. That is a recipe for disaster!

3. H5N1 Self-Control Basis
There is a tertiary together with terminal ground together with this may reverberate my personal weaknesses. When I value companies, I know that I struggle my preconceptions together with the urges I experience to tweak the numbers to deliver the termination that I desire to see. There is no position out that tin sack own got to a greater extent than termination for value than the growth charge per unit of measurement inward the terminal value together with having a cap on that position out removes the most strong vehicle for bias inward valuation.

In sum, yous may or may non hold upwardly convinced yesteryear my arguments for capping the perpetual growth charge per unit of measurement at the risk gratis rate, but I would strongly recommend that yous do your ain cap on growth together with necktie that cap to the risk gratis charge per unit of measurement inward your valuation. Thus, yous may determine a looser version of my cap, allowing your perpetual growth charge per unit of measurement to hold upwardly equally much equally (but non to a greater extent than than) 1 pct higher than the risk gratis rate.

Conclusion
The perpetual growth model is a powerful device for applying closure inward a discounted cash current valuation but it is a mathematical dearest trap, amongst the growth charge per unit of measurement inward the denominator acting equally the lure for analysts who are inclined yesteryear bias or ignorance to play amongst it. If yous are tempted, it is worth also remembering that it is the get-go house that that people who are good versed inward valuation facial expression to depository fiscal establishment check for valuation ineptitude, since at that spot are far to a greater extent than subtle ways to bias your valuations than playing amongst the growth rate.

YouTube Video

DCF Myth Posts

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

1. If yous own got a D(discount rate) together with a CF (cash flow), yous own got a DCF.  
2. A DCF is an practise inward modeling & position out crunching. 
3. You cannot do a DCF when at that spot is also much uncertainty.
4. It's all nearly D inward the DCF (Myths 4.1, 4.2, 4.3, 4.4 & 4.5)
5. The Terminal Value: Elephant inward the Room! (Myths 5.1, 5.2, 5.3, 5.4 & 5.5)
6. A DCF requires also many assumptions together with tin sack hold upwardly manipulated to yield whatever value yous want.
7. A DCF cannot value build advert or other intangibles. 
8. A DCF yields a conservative approximate of value. 
9. If your DCF value changes significantly over time, at that spot is something incorrect amongst your valuation.
10. A DCF is an academic exercise.

Myth 5.4: Negative Increase Rates Forever? Impossible!

As yous peruse discounted cash stream valuations, it is hitting how infrequently yous run across projections of negative growth into the future, fifty-fifty for companies where the tendency lines inwards revenues in addition to earnings accept been anything but positive. Furthermore, yous almost never run across a terminal value calculation, where the analyst assumes a negative growth charge per unit of measurement inwards perpetuity. In fact, when yous select upwards the possibility, the outset reaction that yous larn is that it is impossible to gauge terminal value amongst a negative growth rate. In this post, I volition introduce evidence that negative growth is neither uncommon nor unnatural in addition to that the best course, from a value perspective, for around firms is to shrink rather than grow.

Negative Growth Rates: More mutual than yous think!
The belief that most firms accept positive growth over fourth dimension is mayhap nurtured yesteryear the belief that it is unnatural for firms to accept negative growth in addition to that spell companies may accept a yr or 2 of negative growth, they bounce dorsum to positive growth sooner rather than later. To evaluate whether this belief has a soil inwards fact, I looked at compounded annual growth charge per unit of measurement (CAGR) inwards revenues inwards the most recent calendar yr (2015), the concluding 5 calendar years  (2011-2015)and the concluding 10 calendar years (2006-2015) for both US in addition to global companies in addition to computed the percent of all companies (my sample size is 46,814 companies) that accept had negative growth over each of those fourth dimension periods:

Region	Number of firms	% amongst negative revenue growth inwards 2015	% amongst negative CAGR inwards revenues: 2011-2015	% amongst negative CAGR inwards revenues: 2006-2015
Australia, NZ in addition to Canada	5014	41.44%	36.73%	28.20%
Developed Europe	7082	33.42%	30.03%	24.25%
Emerging Markets	21196	43.06%	29.35%	21.50%
Japan	3698	33.41%	20.76%	31.80%
United States	9823	39.69%	26.76%	28.10%
Grand Total	46814	39.86%	28.64%	24.69%

Note that almost 40% of all companies, inwards both the US in addition to globally, saw revenues reject inwards 2015 in addition to that 25% of all companies (and 27% of US companies) saw revenues reject (on a CAGR basis) betwixt 2006 in addition to 2015. (If yous are interested inwards a suspension downward yesteryear country, yous tin download the spreadsheet yesteryear clicking here.) Digging a piffling deeper, spell in that location are company-specific reasons for revenue declines, in that location are also clearly sector effects, amongst companies inwards around sectors to a greater extent than probable to run across revenues shrink than others. In the tabular array below, I listing the ten non-financial sectors amongst the highest pct of companies (I excluded fiscal service companies because revenues are hard to define, non because of whatever built-in bias):

Industry Grouping	Number of firms	% Negative inwards 2015	% amongst Negative CAGR from 2011-2015	% amongst Negative CAGR  from 20106-2015
Publshing & Newspapers	346	53.77%	48.44%	45.69%
Computers/Peripherals	327	43.30%	42.12%	45.65%
Electronics (Consumer & Office)	152	43.70%	47.11%	44.44%
Homebuilding	164	31.51%	22.69%	35.87%
Oil/Gas (Production in addition to Exploration)	959	79.22%	43.75%	35.40%
Food Wholesalers	126	37.00%	30.59%	33.33%
Office Equipment & Services	160	40.58%	32.54%	33.33%
Real Estate (General/Diversified)	418	41.33%	32.72%	32.52%
Telecom. Equipment	473	43.00%	37.36%	32.43%
Steel	757	73.23%	50.65%	32.08%

So what? For around of these sectors (like existent estate in addition to homebuilding), the negative revenue growth may precisely last a reflection of long cycles playing out but for others, it may last an indication that the concern is shrinking. If yous are valuing a companionship inwards i of these sectors, yous should last to a greater extent than opened upwards to the possibility that growth inwards the long term could last negative. (If yous interested inwards downloading the total list, click on this link.)

Negative Growth Rates: Influenza A virus subtype H5N1 Corporate Life Cycle Perspective

One framework that I honor useful for agreement both corporate finance in addition to valuation issues is the corporate life cycle, where I draw a company’s life from nativity (as a start-up) to reject in addition to connect it to expectations close revenue growth in addition to lucre margins:

If yous purchase into this notion of a life cycle, yous tin already run across that valuation, at to the lowest degree equally taught inwards classes/books in addition to practiced, is non inwards keeping amongst the concept. After all, if yous apply a positive growth charge per unit of measurement inwards perpetuity to every theatre that yous value, the life wheel that is to a greater extent than inwards keeping amongst this persuasion of the globe is the following:

The occupation amongst this life wheel perspective is that the global marketplace position identify is non large plenty to adjust these ever-expanding behemoths. It follows, therefore, that in that location accept to last companies (and a pregnant number at that) where the hereafter holds shrinkage rather than growth. Fitting this perspective dorsum into the corporate life cycle, yous should last using a negative growth charge per unit of measurement inwards revenues in addition to mayhap declining margins to reach amongst those shrinking revenues inwards your valuation, if your companionship is already inwards decline. If yous are valuing a companionship that is mature correct straight off (with positive but rattling depression growth) but the overall marketplace position is stagnant or starting to decline, yous should last opened upwards to the possibility that growth could larn negative at the terminate of your forecast horizon.

There is an extension of the corporate life wheel that may also accept implications for valuation. In an before post, I noted that tech companies historic catamenia inwards Canis familiaris years in addition to often accept compressed life cycles, growing faster, reaping benefits for shorter fourth dimension periods in addition to declining to a greater extent than precipitously than non-tech companies. When valuing tech companies, it may behoove us to reverberate these characteristics inwards shorter (and to a greater extent than exuberant) growth periods, fewer years of stable growth in addition to terminal growth periods amongst negative growth rates.

Negative Growth Rates: The Mechanics

As I noted inwards my concluding post, the growth charge per unit of measurement inwards perpetuity cannot reach the growth charge per unit of measurement of the economic scheme but it tin last lower in addition to that lower number tin last negative. It is alone possible that i time yous larn to your terminal year, that your cash flows accept peaked in addition to volition driblet 2% a yr inwards perpetuity thereafter. Mathematically, the perpetual growth model nevertheless holds:

If yous produce assume negative growth, though, yous accept to examine whether equally the theatre shrinks, it volition last able to divest assets in addition to collect cash. If the answer is no, the final result of negative growth is unambiguously negative in addition to the terminal value volition reject equally growth gets to a greater extent than negative. If the answer is yes, the final result of negative growth inwards value volition depend upon how much yous volition larn from divesting assets.

To illustrate, consider the instance of the theatre amongst $100 i G k inwards expected after-tax operating income adjacent year, that is inwards perpetual growth in addition to let’s assume a perpetual growth charge per unit of measurement of -5% a yr forever. If yous assume that equally the theatre shrinks, in that location volition last no cash flows from selling or liquidating assets, the terminal value amongst a 10% terms of working capital alphabetic quality is:

Terminal value = $100/ (.10-(-.05)) = $666.67

If yous assume that in that location are assets that are beingness liquidated equally the theatre shrinks, yous accept to gauge the furnish on working capital alphabetic quality on these assets in addition to compute a reinvestment rate. If the assets that yous are liquidating, for instance, accept a 7.5% furnish on invested capital, the reinvestment charge per unit of measurement volition last -66.67%.

Reinvestment charge per unit of measurement = -5%/7.5% = 66.67%

If yous are puzzled yesteryear a negative reinvestment rate, it equally the cash inflow that yous are generating from property sales, in addition to your terminal value volition in addition to so be:

Terminal value = $100 (1-(-0.6667))/ (.10 – (-.05)) = $1,111.33

Put simply, the same dominion that governs whether the terminal value volition increase if yous increase the growth rate, i.e., whether the furnish on working capital alphabetic quality is greater than the terms of capital, plant inwards contrary when yous accept negative growth. As long equally yous tin larn to a greater extent than for divesting assets than equally continuing investments (present value of cash flows), liquidating them volition increase your terminal value. 

Negative Growth: Managerial Implications

Our unwillingness to consider using negative growth inwards valuation has turned the game over to growth advocates. Not surprisingly, in that location are many inwards academia in addition to practise who debate that the essence of practiced administration is to grow businesses in addition to that the terminate game for companies is corporate sustainability. That's nonsense! If yous are a theatre inwards a declining concern where novel investments consistently generate less than the terms of capital, your attempts to sustain in addition to grow yourself tin only destroy value rather than increase it. It is amongst this, inwards mind, that I argued inwards an before post that the qualities that nosotros facial expression for inwards a CEO or top managing director volition last dissimilar for companies at dissimilar stages of the life cycle: 

Influenza A virus subtype H5N1 visionary at the helm is a huge addition early on inwards corporate life, but it is science equally a concern builder that allows immature companies to scale upwards in addition to larn successful growth companies. As growth companies larn larger, the science laid shifts i time to a greater extent than towards opportunism, the capacity to honor growth inwards novel places, in addition to and so i time to a greater extent than at mature companies, where it management’s mightiness to defend moats in addition to competitive advantages that allow companies to harvest cash flows for longer periods. In decline, it is non vision that yous value but pragmatism in addition to mercantilism, i ground that I chose Larry the Liquidator equally the utilization model. It is worth noting, though, that the means nosotros accolade in addition to wages managers follows the growth advocate dominion book, amongst those CEOs who grow their companies beingness seat on a much higher pedestal (with books written yesteryear in addition to close them in addition to movies on their lives) than those less ambitious souls who presided over the gradual liquidation of the companies nether their command. 

Conclusion
I believe that the main ground that nosotros proceed to remain amongst positive growth rates inwards valuation is behavioral. It seems unnatural in addition to fifty-fifty unfair to assume that the theatre that yous are valuing volition run across shrinking revenues in addition to declining margins, fifty-fifty if that is the truth. There are 2 things worth remembering here. The outset is that your valuation should last your endeavor to bear witness to reverberate reality in addition to refusing to bargain amongst that reality (if it is pessimistic) volition bias your valuation. The instant is that assuming a companionship volition shrink may last practiced for that company's value, if the concern it is inwards has deteriorated. I must confess that I don't utilization negative growth rates often plenty inwards my ain valuations in addition to I should describe on them to a greater extent than often non only when I value companies similar brick in addition to mortar retail companies, facing daunting competition, but also when I value technology companies similar GoPro, where the production life wheel is curt in addition to it is hard to maintain revitalizing your concern model.

YouTube Video


Attachments

1. Percent of negative revenue growth companies, yesteryear sector
2. Percent of negative revenue growth companies, yesteryear solid soil in addition to region

DCF Myth Posts

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

1. If yous accept a D(discount rate) in addition to a CF (cash flow), yous accept a DCF.  
2. A DCF is an exercise inwards modeling & number crunching. 
3. You cannot produce a DCF when in that location is equally good much uncertainty.
4. It's all close D inwards the DCF (Myths 4.1, 4.2, 4.3, 4.4 & 4.5)
5. The Terminal Value: Elephant inwards the Room! (Myths 5.1, 5.2, 5.3, 5.4 & 5.5)
6. A DCF requires equally good many assumptions in addition to tin last manipulated to yield whatever value yous want.
7. A DCF cannot value create elevate or other intangibles. 
8. A DCF yields a conservative gauge of value. 
9. If your DCF value changes significantly over time, in that location is something incorrect amongst your valuation.
10. A DCF is an academic exercise.

User/Subscriber Economics: Value Dynamics

In my concluding post, I tried valuing Uber past times estimating how much an existing user was worth to the companionship in addition to and so using that release to extrapolate to the value of all existing users in addition to the value added past times novel users. As always, I got many useful comments on what I was missing, what I could practice improve in addition to what could locomote simplified, in addition to I give thank you lot you (really). While I could pass this entire postal service rehashing assumptions, I don't intend to! To me, the most useful business office of valuation is non the destination, i.e., the value that you lot instruct at the end, but the journey, i.e., the procedure of doing valuation, since it is the procedure that allows us to isolate the key drivers of value, which, inwards turn, focuses discussions on those variables, rather than on distractions. Consequently, I decided to revisit my Uber user-based valuation to consider what I could eke out equally implications for user or subscriber-based businesses.

Estimation versus Economic Risk
I volition start past times conceding the obvious. I made a lot of assumptions to instruct inwards at the value of a user at Uber, but I volition expire further. There was non a unmarried fact inwards that valuation, since every release was an estimate. That said, you lot could say that most the valuation of whatever company, amongst the deviation truly beingness i of the grade of doubt you lot face, non inwards whether it exists. At the jeopardy of restating points that I receive got made in my other writing, hither are iii full general points that I would brand most doubt inwards valuation.

1. Estimation doubt versus Economic uncertainty
To bargain amongst doubt inwards a sensible way, you lot kickoff receive got to categorize it. One of the categorizations that I detect useful is to pause the doubt you lot human face upward when you lot are trying to value a concern or an property into estimation in addition to economical uncertainty. Estimation uncertainty comes from incomplete, missing or misleading information provided past times the companionship that you lot are valuing, whereas economic uncertainty is driven past times forthcoming changes inwards the concern that the companionship operates in, equally good equally macro economical factors. Estimation doubt tin dismiss locomote reduced past times obtaining improve in addition to to a greater extent than consummate information but estimation doubt volition stay resistant, no affair how much fourth dimension you lot pose inwards in addition to what information analysis that you lot do. Using my Uber user valuation, it is truthful that some of the dissonance inwards the valuation comes from Uber beingness a private, secretive companionship in addition to but most of the doubt comes from the ride sharing concern beingness inwards a soil of flux, equally regulators in addition to competitors operate out how best to bargain amongst shifting consumer tastes in addition to changing technologies. This has ii implications. The kickoff is that fifty-fifty if you lot had access to to a greater extent than information, either because Uber decides to expire populace or you lot are an insider inwards the company, much of the doubt inwards estimated value per user volition remain. The 2d is that your estimated value volition alter considerably over time, equally the facts on the Earth change, in addition to that volatility inwards value cannot locomote viewed equally a shortcoming of the model.

2. Uncertainty is an integral business office of valuation
One critique that leaves me unmoved is that valuing a concern or an asset, inwards the human face upward of pregnant uncertainty, is pointless because you lot volition locomote wrong. So what? Uncertainty is business office in addition to bundle of doing concern in addition to you lot cannot want it, pray it or analyze it away. As I consider it, you lot receive got ii choices when it comes to uncertainty. You tin dismiss bargain amongst it frontally past times making explicit assumptions or you lot tin dismiss expire into "denial" model in addition to brand implicit assumptions. When I tried to value a user at Uber, I made explicit assumptions most user life, renewal rates in addition to a host of other variables, in addition to I volition cheerfully acknowledge that I volition locomote incorrect on every i of them, but what is the alternative? When pricing a user past times looking at what others are paying for users inwards similar companies, you lot are making assumptions most all of the variables equally well, but those assumptions are implicit. In fact, they are hidden so good that you lot may non locomote aware of your ain assumptions, a unsafe house to locomote when investing.

3. Uncertainty tin dismiss (and should) locomote visualized 
Here is my response to uncertainty. Where information exists but I practice non receive got access to that data, I volition essay to brand my best estimates based upon the existing information, noisy, dated or 2d paw though it mightiness be. Where I receive got access to data, I volition cheque it against other data, mutual feel in addition to economical kickoff principles. Where at that spot is no data, I volition brand my best estimates in addition to to the extent that these estimates come upward amongst probability distributions, my value itself is a distribution, non a number. Illustrating this process, amongst the Uber user valuation:

Excel Add On: Crystal Ball (Oracle), Simulation Output

I receive got made distributional assumptions on iv of my inputs: the portion of Uber's expenses that expire to servicing existing users, the life fourth dimension of a user, the proportion of expenses that are variable in addition to the toll of working capital alphabetic lineament (discount rate) to compute today's value.  Since these distributions are all centered on my base of operations illustration assumptions, it should come upward equally no surprise that the median value of a user ($414) is really closed to my base of operations illustration value ($410). However, at that spot is a broad spread precisely about that value, amongst the numbers ranging a depression of $74, when the user life is short, the expenses of servicing a user are high, most of the costs are variable in addition to the toll of working capital alphabetic lineament is low, to a high of to a greater extent than than $1000 per user, when the reverse weather condition hold. Note that at the electrical flow pricing of $69 billion, you lot are valuing each user closed to $900, at the upper destination of the distribution. 

User Economics: Cost Propositions
It is truthful that the destination game for every concern is to brand coin for its investors. That said, at that spot is a style to over react, when a immature companionship reports a loss, equally was the illustration when Uber reported an operating loss of $2.8 billion for 2016, a few months ago. The pessimists on Uber viewed this equally farther evidence that the companionship was on a pathway to nowhere in addition to that investors inwards the companionship must locomote delusional to attach whatever value to it. The optimists argued that it is natural for immature companies to lose money in addition to that Uber should locomote judged on other dimensions such equally user growth in addition to marketplace potential instead. At the jeopardy of angering both groups, I volition usage my Uber user valuation to scrap that piece I concur amongst the 2d grouping that losing coin is typical at immature companies, I volition also convey sides amongst the kickoff grouping that you lot withal postulate a pathway to profitability amidst the losses, for value to exist.

1. Servicing existing users versus acquiring novel users
In my Uber user valuation, I started amongst the operating losses reported past times the companionship ($2.8 billion), backed into the total operating expenses for the companionship ($9.3 billion) in addition to and so allocated that expense across iii categories: servicing existing user (48.17%), acquiring novel users (41.08%) in addition to corporate expenses (10.75%). While I based this breakdown on the information (on increment inwards users in addition to contribution margins inwards ride sharing) that I had on Uber inwards 2016, that information is dated, noisy in addition to 2d hand. It is exclusively possible that the actual pause downwardly of expenses is dissimilar from my estimate. If you lot are wondering why it matters, since the destination resultant (that Uber lost $2.8 billion) is non changing, at that spot are consequences that you lot tin dismiss consider inwards the tabular array below:

Uber User Value: Existing User versus New User Costs

% of Operating Expenses spent on acquiring novel 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 lot increment the proportion of the operating expenses that are spent on acquiring novel users, the value of an existing user goes upward because you lot are spending less coin on providing service to that user, but the value of a novel user also increases, equally the cyberspace value added (the difference betwixt the user value in addition to the toll of acquiring a user) goes up. Ironically, equally you lot pass to a greater extent than on acquiring novel users in addition to less on servicing existing users, the proportion of your value that comes from existing users increases.
User Value Proposition 1: Influenza A virus subtype H5N1 money-losing companionship that is losing coin providing service to existing users/customers is worth less than a companionship amongst equivalent losses, where the primary expenses are coming from client acquisitions.

This is, of course, neither profound nor surprising, in addition to it explains why, left to their ain devices in addition to without whatever monitoring, immature companies volition claim that most or all of their expenses are for acquiring novel customers. If you lot are investing inwards a immature company, you lot volition receive got to practice your ain assessment of whether managers are misrepresenting, past times looking at expense growth over fourth dimension versus novel customers. If the release of total customers remains fixed in addition to expenses maintain rising, you lot should locomote skeptical most managerial claims (that most of the costs are for acquiring novel customers).

2. Cost Structure
One ground that investors are willing to convey losses at immature companies is because they believe that equally the companionship grows its operations, at that spot volition locomote economies of scale. In income declaration terms, this volition resultant inwards expenses growing less apace than revenues in addition to improving operating margins. That said, you lot cannot convey it on organized faith that this volition ever come about or that it volition come about at the same charge per unit of measurement for every company. To consider the impact on user value of this dimension, I adjusted the portion of Uber's expenses that are variable (and volition grow amongst revenues) in addition to those that are fixed (and grow at a lower rate) in addition to captured the value effect inwards this table:

Uber User Value in addition to Cost Structure

% of electrical flow 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%

As the proportion of expenses that are fixed rises, the value of both existing in addition to novel users goes upward but the latter goes upward at a faster rate. Put simply, the economies of scale increment equally you lot increment the charge per unit of measurement at which you lot are adding scale.
User Value Proposition 2: Influenza A virus subtype H5N1 companionship whose expenses are primarily fixed (will non grow amongst revenues) volition locomote worth to a greater extent than than an otherwise identical companionship whose expenses are variable (track revenues).

If unchallenged, immature growth companies volition ever claim that they receive got massive economies of scale but that claim has to locomote backed upward past times the numbers. Specifically, investors should pay attending to the charge per unit of measurement of alter inwards revenues in addition to expenses, since amongst large economies of scale, the one-time should alter to a greater extent than than the latter. The caveat, though, is that having to a greater extent than fixed costs tin dismiss increment risk, because it volition increment the jeopardy of failure at immature companies in addition to earnings volatility for to a greater extent than mature firms. As user growth levels off, having to a greater extent than fixed costs volition trim back value rather than increasing it.

User Economics: Growth Propositions
For immature companies, nosotros mostly persuasion growth equally goodness in addition to piece that is mostly true, non all growth is created equal. In fact, fifty-fifty amongst immature companies, at that spot are some strategies that deliver growth inwards users or revenues, piece destroying value. In a user or subscriber based model, at that spot are ii ways you lot tin dismiss grow your revenues. One is to instruct existing users to purchase to a greater extent than of your products or services in addition to the other is past times trying to instruct novel users. While both tin dismiss increment value, the one-time volition locomote create to a greater extent than value, for ii reasons. First, since it comes from existing customers, you lot don’t receive got to pay to instruct these users in addition to it is thence less costly to the firm. Second, past times increasing the value of a user, it increases the value of whatever novel users equally well, creating a secondary impact on value. Using my Uber user valuation, you lot tin dismiss consider the impact of changing the annual growth charge per unit of measurement inwards revenues for an existing user inwards the nautical chart below:

As revenue growth charge per unit of measurement increases, the value of both existing in addition to novel users increases, amongst the value of Uber hitting $90 billion at high annual growth rates. If at that spot is no growth inwards revenues, the value of Uber collapses equally novel users truly destroy value (because the toll of adding a novel user exceeds the value of that user). Now consider how Uber's value is affected, if nosotros grip existing user assumptions fixed in addition to alter the compounded annual growth charge per unit of measurement (for the side past times side 10 years) inwards the release of users:

While value increases amongst user growth rates, it increases at a lower charge per unit of measurement than it did when nosotros varied revenue growth from existing users.
User Value Proposition 3: Influenza A virus subtype H5N1 companionship that is growing revenues past times increasing revenues/user is worth to a greater extent than than an otherwise similar growth companionship that is deriving growth from increasing the release of users/customers. 

Young companies human face upward the interrogation of whether to allocate resources to instruct novel users or essay to sell to a greater extent than to existing users is i of those. At to the lowest degree inwards the illustration of Uber, the numbers seem to dot that the wages is greater inwards getting existing users to usage the service to a greater extent than than inwards looking for novel users.

User Economics: Business Propositions
At the jeopardy of stretching the user value model also far, it tin dismiss locomote used to hash out concern models inwards the space, from the networking benefits that so many companies inwards this infinite claim to possess to how the revenue model you lot select (subscription, transaction or advertising) plays out inwards user values.

1. Competitive Dynamics in addition to Networking Benefits

Is it improve to operate inwards a concern where the toll of acquiring a novel user is depression or high? Holding all else constant, the response is obvious. Influenza A virus subtype H5N1 trouble solid volition maximize its value if tin dismiss generate both high value per user in addition to receive got a depression toll of acquiring novel users. That said, if everyone inwards the concern shares these characteristics, i or some other of these variables has to change. If the toll of acquiring novel users is depression for everyone, contest volition drive downwardly the value per novel user, in addition to if the value per user remains high, contest volition drive upward the toll of acquiring novel users. The merchandise off is captured inwards the motion painting below:

User Value Proposition 4:  The particular trouble solid volition locomote the i that is able to detect a pathway to high value per user in addition to a depression toll to adding a novel user inwards a market, where its competitors struggle amongst either depression value per user or high costs of acquiring users.
So how practice the particular companies describe off this seeming impossible combination of high value per user in addition to depression toll per novel user? I may locomote stretching, but it is at the pump of ii damage that nosotros consider increasingly used inwards business, network benefits in addition to big data.

• Network Benefits: If network benefits exist, the toll of acquiring novel users volition decrease equally a company's presence inwards a marketplace increases, reaching a tipping dot where the biggest instrumentalist volition human face upward much lower costs inwards acquiring novel users than the competition, allowing it to capture the marketplace in addition to perchance usage its marketplace potency to increment the value of each user. In the illustration of Uber in addition to ride sharing business, the declaration for networking benefits is strong on a localized basis, since at that spot are clearly advantages for both drivers in addition to customers to shift to the dominant ride sharing companionship inwards whatever locality, the one-time because they volition generate to a greater extent than income in addition to the latter because they volition instruct improve service. The declaration is much weaker on a global basis, though ride sharing companies are trying to create networking benefits past times allying amongst airlines in addition to credit assist companies, in addition to how this endeavour plays out may good determine Uber's ultimate value.
• Big Data: While I stay a skeptic on the "big data" claims that every companionship seems to locomote making today, it is inarguable that at that spot are companies that usage large information to augment value. These companies collect information on their existing users/subscribers/customers in addition to usage that information to (a) customize existing products/services to consider user preferences, (b) create novel products or services that consider perceived user needs and/or (c) for differential pricing. All of these increment user value past times altering i or to a greater extent than of the inputs into the equation, amongst customization increasing user life in addition to novel products & differential the growth inwards revenues/user. In my view, the best users of large information (Netflix, Amazon, Google in addition to Facebook) receive got used the information to increment their existing user value. Uber is withal inwards the nascent stages, but its attempts at using information receive got expanded from surge pricing to differential pricing.

2. Revenue Models
In my version of user valuation, I expression at revenues per user, drawing no distinction on how those revenues are derived. Broadly speaking, at that spot are iii revenue models that a user/subscriber based companionship tin dismiss use, a subscription-based model where users or subscribers pay a subscription fee to maintain to usage the service or product, a transaction-based model where users or subscribers pay only when they usage the service of production in addition to an advertising-based model where users or subscribers instruct to usage the production or service for free, but are targeted inwards advertising. Netflix operates on a subscription-based model, Uber is a transaction-based trouble solid in addition to Facebook generates its revenues from advertising. Some companies similar LinkedIn receive got hybrid models, generating revenues from subscriptions (from premium members), transactions (from recruitments) in addition to advertising.  There are other inputs into the valuation that volition locomote affected past times a company's revenue model in addition to I receive got tried to capture them inwards the tabular array 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 charge per unit of measurement inwards revenues/user)	Low (High growth charge per unit of measurement inwards revenues/user)	Intermediate (Intermediate growth charge per unit of measurement inwards revenues/user)
Growth charge per unit of measurement inwards users (CAGR inwards # Users)	Low (Low CAGR inwards # users)	Intermediate (Intermediate CAGR inwards # users)	High (High CAGR inwards # users)
Cost of adding novel users (Cost/New User)	High (High Cost/New User)	Intermediate (Middling Cost/New User)	Low (Low Cost/New User)

There is no i dominant revenue model, since each has its pluses in addition to minuses. An advertising-based model volition allow for much to a greater extent than rapid growth inwards a firm's early on years, a subscription-based model volition generate to a greater extent than sustainable growth in addition to 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 trouble solid depending upon where it is inwards the life wheel in addition to across firms depending on their production or service offerings in addition to across investors, depending on whether they are focused on user growth, revenue growth or revenue sustainability.

3. Real Options
When valuing a companionship based upon its expected cash flows, at that spot is a run a jeopardy that you lot volition nether value the company, if it has command of a resources that could locomote used for other purposes inwards the future, even if that usage makes no economical feel today. That is why a applied scientific discipline or natural resources reserve that is non feasible today tin dismiss withal receive got value, in addition to this is the soil for the existent alternative premium. In the context of a user-based business, optionality tin dismiss instruct a element of value, to the extent that companies may locomote able to exploit their user bases to sell other products in addition to services inwards the future. While the intuition of existent options is simple, valuing existent options is notoriously hard in addition to afterwards much paw waving, most of us (including me) give up, but the user-based valuation model provides a framework to at to the lowest degree eke out some full general propositions most optionality in addition to value.

There should locomote no surprises inwards this picture, amongst the value of a existent alternative inwards a user base of operations tied to the inputs into an alternative pricing model.
User Value Proposition 6: The value of optionality from a user base of operations volition locomote greatest at firms amongst lots of sticky, intense users inwards businesses where the future is unpredictable because of changes inwards product/service applied scientific discipline in addition to client tastes. 

The Bottom Line
The most straight applications of a user or subscriber based model is inwards the valuation of companies similar Uber, Facebook in addition to Netflix. That said, to a greater extent than in addition to to a greater extent than companies are seeing benefits inwards shifting from their traditional concern models to user-based ones. Apple is a cash machine built precisely about a smartphone but it is also accumulating information on to a greater extent than than a billion users of these phones, to whom it may locomote able to offering other products in addition to services. Amazon started life equally an online retail companionship but at that spot is no denying the powerfulness of its 70 1000000 Prime members inwards generating revenues for the company. I receive got used Microsoft in addition to Adobe products for equally long equally they receive got been around, but amongst both companies, but my human relationship amongst both companies has changed. I am right away a subscriber (Office 365 in addition to  Creative Cloud member) who pays annual fees, rather than a client who buys in addition to upgrades software on a discretionary basis. Understanding user economic science in addition to value is fundamental to non only investors inwards these companies, when valuing in addition to pricing them, but to managers of these companies, inwards their day-to-day concern decisions. I volition admit, without shame, that my cognition of user-based companies is rudimentary in addition to that my user-based model may locomote amateurish, inwards what it misses or mangles. That said, if you lot are an skilful on user-based businesses, I promise that you lot tin dismiss construct on the model to brand it to a greater extent than realistic in addition to useful.

YouTube Video

Links

1. Crystal Ball (Simulation Add On for Excel)
2. My newspaper on dealing amongst doubt inwards valuation

Attachments

1. Uber User Valuation Spreadsheet
2. Uber User Value: Simulation Output

Blog Posts

1. Uber's Bad Week: Doomsday Scenario or Business Reset (June 2017)
2. User/Subscriber Economics: An Alternative View of Uber's Value