Justified Token Value — Part 1

PRToken Justified Price Over Time

As a Chartered Financial Analyst who has spent a year immersing himself in crypto as part of founding Frontier where we are all in on blockchain, I’ve been encouraged by the recent efforts by the crypto community to develop more formal frameworks for valuing tokens (see the “Acknowledgement’s” section at the end of this post for some important contributions and contributors).

I share the goal of many of the contributors to the nascent field of token valuation which is to see more rigor applied to justifying the value of token sales prior to ICOs. Undoubtedly, as more institutional money moves into crypto, to be perceived as a “quality ICO”, justifying token value quantitatively and not just qualitatively will become the norm.

This blog post series is split into three parts (for the sake of readability; and to spare me from writing for a week while Boris Mann, Anthony Nicalo, and the rest of the Frontier team build our startup). The post series propose two models for valuing tokens and establishing a justified token value or market price: one model for valuing tokens which provide distributions (rent, fees, profit share, dividends, etc.) to token holders and a second model for tokens where returns to token holders are due to appreciation in the price of the tokens.

This post covers tokens whose value are underpinned by distributions; the Part 2 post will cover tokens whose value are underpinned by expected price appreciation, and; the Part 3 post will extend both models from the basic models used in Part 1 and 2 to more realistic models which better match the token economies behind the ICOs that we see today.

A simple Google Sheets model accompanies each post. Here is the model in MS Excel, should you prefer.

Note: the Excel model has useful Data Tables — my favourite feature of Excel — the results of which are “value saved” in the Google Sheets version.

The models presented in Part 1 and 2 are deliberately simple while my accompanying posts are guides sprinkled with a few key insights. My intent is that anyone with some experience building financial models can follow along.


The year 2017 has seen a raft of ICOs; by the end of July, $1.38 billion had been raised via ICOs in 2017 or 83% of total funding raised since the first ICO in 2013. Since the start of 2017, the two foremost platform tokens, bitcoin and Ether — have appreciated 280% and 3900% respectively.

The market is so frothy and moving so fast that investors are practically throwing money at tokens that meet a bare minimum smell test. In the midst of the frenzy, rational voices are speaking out and keen minds are working out in the open to develop the tools that will help individual investors and institutional investors make considered decisions about which ICOs to participate in or not.

The Token Summit hosted by William Mougayar on May 25, 2017, was a positive step, bringing together many of the people interested in self-regulating ICOs to discuss valuation. A spurt of Medium posts either side of the Token Summit have elucidated on token valuation; but for the layman or practitioner, it is still very challenging to find a simple financial model for valuing the different types of tokens in existence.

My post and accompanying financial models are an attempt to address this need. I look forward to feedback from the community — I have no doubt, that as we put our heads together, we will be able to develop cogent models for token valuation and I hope my modest contribution is useful in this collective endeavour.

Generalized Models for Valuing Token Projects

Sid Kala, in his blog post “Framework for Valuing Crypto Tokens” argued that:

“for a crypto token holder, the value of the token comes from three primary sources, just like a regular stock: dividends, buybacks, and price appreciation.”

I agree; however, I would generalize these to two sources: distributions (whether dividends, a share of profits, rent, fees, etc.) and token price appreciation (noting that buybacks reduce token supply and thereby increase the price of the remaining tokens in distribution).

If the above holds true then we require two generalized models to value any token issued by a startup (or established company): 1) a model which can value a stream of distributions over time, and, 2) a model which can project and value an increase in the price of a token.

A model for 1) is relatively straight forward. Discounted Cash Flow models are well established in the world of finance and are most appropriate, in my opinion. For 2), I suggest borrowing from classical economic theory, specifically the Equation of Exchange and the Quantity Theory of Money, which is the subject of Part 2 of my post series (to be released approximately a month after this).

Model Notes

If you haven’t done so already, please take a look at the Google Sheets model (or MS Excel model) that accompanies this blog post. Take a look at the leftmost worksheet labeled “Token w. Distributions” first.

General model notes:

  • Model assumptions that drive calculations use blue font
  • The model runs quarterly, for 36 quarters (9 years)
  • Cash flows beyond quarter 36 are accounted for by a Terminal Value, and
  • A token called “PRToken” is used for illustration

The model is deliberately designed to be as simple as possible to focus on core concepts:

  • User growth driving transaction growth over time
  • Flow through of fees to token holders (the token holder cash flow)
  • Using a Terminal Value to account for fees beyond the time period explicitly modeled, and
  • Valuing the fees to token holders based on a Discount Rate

PRToken characteristics and platform ecosystem

  • PRToken supply: fixed at 1,000,000,000 tokens
  • Maximum number of users: 100,000,000
  • Growth of the ecosystem: S-curve distribution; modeled using a logistic function (more on this below)
  • PRToken platform fees: 1% of transaction value; the token holders collectively receive 100% of platform fees.

Modeling User Growth Over Time

In my opinion, S-curves are appropriate for modeling most types of user adoption and growth. An alternative is an H-model with a base number of users growing at a rate that linearly decreases over time till it reaches a stable growth rate. But the shape of the cumulative number of users of PRToken modeled with an H-model would look more like the top half of a “C” vs. an “S” — an “S” more correctly models the slow build up of users as the initial users of the technology (innovators) are followed by early adopters; and accelerating user growth as the early majority discover the tech; and slowing growth as the late majority and laggards finally adopt the tech many years later.

To define an S-curves mathematically, a logistic function is used. A logistic function is described as:

Y = L / (1 + e^-k(X-Xo))


  • “L” is the total number of users on the PRToken platform
  • “k” is a constant that dictates the steepness of the S-curve around the inflection point “Xo”
  • “Xo” is the inflection point of the S-curve, which is typically half of the maximum “X”
  • “X” represents units along an axis in a coordinate system (e.g. units of time)

The two key variables that drive the model are “L” — the total number of users, which describes the size of the ecosystem — and “k” which controls the steepness of the curve around the inflection point (Xo). A “k” value of greater than 1 lead to a very steep curve around “Xo” which is unrealistic. On the other hand, “k”s below 0.3 may lead to abnormally high starting user numbers.

In the case of PRToken, the ecosystem when fully matured will comprise 100,000,000 users; this is analogous to Serviceable Obtainable Market (or Target Market) in startup parlance. I have assumed that PRToken takes 9 full years (split into quarters) to fully penetrate its SOM — by way of comparison, Twitter has taken a similar length of time to grow to 300 million users. Additionally, recognizing that scale is becoming easier with modern tech stacks and the influx of VC and ICO dollars, 9 years seems like a reasonable length of time for a platform to scale to the point of capturing the vast majority of the opportunity.

A suggestion: play with the “L”, “k”, and “Xo” variables in the model. Review how the shape of the S-curve changes while varying one variable at a time.

Discounted Cash Flow Analysis of Tokens

The following describes the PRToken platform economics:

  • Recap: Users transact on the PRToken platform; the platform charges a percentage of transaction volume (1%) as fees; token holders are entitled to a share of the fees (100%), pro-rata based on the proportion of tokens they own relative to total token supply
  • To keep things simple, 100% of users are assumed to transact; average transaction value is $100; the platform charges 1% fees; 100% of fees flow through to users; hence for every $100 of transactions on the platform, the holders of tokens earn $1 in distributions
  • Based on the math, the maximum distributions to token holders per quarter is $100,000,000, when the SOM is fully penetrated (i.e. PRToken user base grows to 100M approximately in Quarter 36)
  • There are no costs assumed; or another way to think about it is the $100 in transactions per user is net of costs (e.g. gas)

The number of users grow as defined by the S-curve (logistic function) equation. Transactions grow proportionately to users as do platform fees and distributions to token holders.

Distributions to all token holders start at $23,343 for Q1 2018. The distributions grow modestly at first. There is a steep growth in distributions several quarters leading up to the inflection point in the S-curve which occurs in Quarter 18 of the model (Q2 2022). At the inflection point, distributions are $50,000,000 for the quarter. The growth rate of distributions subsequently tails off. By Quarter 23 (Q3 2023), over 90% of the platform’s total distributions per quarter is achieved. By Quarter 24 (Q4 2023) 95% is achieved. By Quarter 28 (Q4 2024) 99% is achieved.

As the S-curve driving the growth of users, transactions, fees, and distributions asymptotically reaches their ceiling, the growth rate in distributions beyond Quarter 36 is negligible. As such, the Terminal Value of distributions to token holders into the distant future can be modeled as a perpetuity using the formula:

Terminal Value = Quarter 36 distribution / Discount Rate

These cash flows to token holders including the Terminal Value are discounted back to the present using a Discount Rate. A quarterly Discount Rate of 15% (equivalent to an annual Discount Rate of 75%) is used (see section “Discount Rate” for an explanation).

The Present Value (“PV”) of the distributions (including Terminal Value) is calculated as $65,151,545. Based on a total token supply of 1,000,000,000 PRTokens, each token has a justified value of $0.065152 (which is the PV divided by the token supply) at the point of the project start (i.e. the ICO).

What does this mean?

In a nutshell, if PRToken has an ICO, then the justified market cap, from a fundamental analysis perspective, should be the Present Value of the future distributions, which in this example is $65.2M; and based on the supply of 1B tokens, the justified price per token is $0.065152.

Learnings from the Token w. Distributions Model

For any token platform, which relies on distributions to underpin the value of the token and with a similar S-curve of ecosystem growth to that modeled, we can model how much cash flow to the token holders is required to justify the market cap for ICOs of select sizes:

Cash Flow to Token Holders Required to Justify Token Market Cap & Price

We can see from the above table that the platform would have to generate cash flow per quarter of $153.5M at platform maturity to justify a market cap of $100M and cash flow per quarter of $1.53B to justify a market cap of $1B.

Crypto Tokens that Pay Out Distributions

Most protocol tokens do not pay out distributions. Examples of crypto tokens that pay fees are:

  • Augur; $292M market cap
  • Peerplays; $18.9M market cap
  • Ethbits; $38K market cap

Source: https://coinmarketcap.com/

To justify the current market cap of Augur, at maturity (assumption: 9 years from now) REP holders (the name of Augur’s token) would require to be earning $450M per quarter or $ 1.8B per year. By way of comparison, energy stocks such as Kinder Morgan or Conoco Phillips pay a similar amount in dividends. Is Augur going to scale to as large a company/ecosystem as Conoco Phillips? I would wager not — on Augur’s own prediction platform :)

But then, distributions are not the only reason REP holders hold REP: some REP holders derive utility from using the Augur platform and reporting on the outcome of events; others also hold REP for price appreciation (the subject of Part 2 of my blog post series).

Note: I have deliberately omitted TaaS and other tokenized funds from the above list. The value of these tokens is driven by the Net Asset Value of their underlying holdings.

What Discount Rate to Use

With any DCF model, the discussion invariably leads to what Discount Rate should be used to discount the cash flows back to the present. A Discount Rate is used to evaluate an investment’s required rate of return by an investor. The Discount Rate should always be risk adjusted, that is, it should include a premium to compensate investors for risk based on the magnitude of the risk incurred by the investor.

In the world of finance, typically one of two methods are used to calculate a Discount Rate: the Capital Asset Pricing Model (CAPM) or the Weighted Average Cost of Capital (WACC).

CAPM is a model to assess how the market prices risk. WACC is used to make investment decisions based on the opportunity cost of deploying the capital of the firm, that is the weighted average required rate of return by the firm’s debt and equity providers (adjusted for the tax advantage of debt over equity). Intuitively, a firm should invest in projects that yield higher rates of return than the return required by its capital providers.

In the world of Venture Capital — which is a useful sector to look to for inspiration on how to value tokens issued via ICOs, since all ICOs that I am aware of at the moment (which themselves are not funds) are for startups — a probability adjusted Discount Rate is used. In other words, a base Discount Rate used to value free cash flow from a startup (given that it is successful) is adjusted for the probability of its success.

LPs typically expect an IRR of 15% — 20%, which is the IRR of a 3x — 4x return on investment in 7 — 10 years (from the time of capital call). With a minimal use of leverage (unlike Private Equity which is highly leveraged), the WACC of the VC firm is effectively the required rate of return of the LPs. I have assumed 15% as reasonable for a base Discount Rate in my model.

A simple method to adjust the Discount Rate is to divide it by the probability of success. So if the WACC of a VC is 15%, and they invest in a company which has a 20% probability of success, the probability adjusted Discount Rate used would be (15% / 20% =) 75%.

Note: this adjustment is a “good enough” solution. A more rigorous adjustment of Discount Rate for probability of success is provided by Sanjay Bhagat in his paper “Why Do Venture Capitalists Use Such High Discount Rates?”

The following table presents a sensitivity analysis of a justified market cap and token value for PRToken based on the Discount Rate used:

Sensitivity Analysis on Market Cap & Price to Discount Rate

We see that a decision to use a 60% annual Discount Rate (12.5% quarterly) instead of a 75% annual Discount Rate (15.0% quarterly) leads to an increase in the justified market cap from $65.2M to $111.3M, an increase of 71%!

Other Factors that Affect Discount Rate

There are many reasons why people may argue that the Discount Rate should be lower or higher, amongst which are:

  • The immaturity of blockchain and Web 3.0 decentralized stacks technology is a case for using a higher Discount Rate. Since the underlying technology on which token ecosystems are built are in their infancy, there is no hard evidence as yet that they are going to be transformative as we think they are; where is the example of a blockchain or Web 3.0 stack performing at the scale and security to service enterprise clients, institutions, and governments? To my (albeit limited) knowledge, there are some good Proof of Concepts, prototypes, and MVPs but we are still a year or more away from deployed enterprise solutions.
  • Tokens are more liquid than Early Stage equity. Illiquidity Discount Rate adjustments are around 2% to 4%. Hence it can be argued that the additional liquidity of a token, warrants a 2% to 4% adjustment of the Discount Rate (downwards). If so, this would be applied to the WACC base discount rate before the probability for success is applied, e.g. (15%–2%=13%)/20% = 65% Discount Rate per annum (13.3% per quarter). The justified market cap for PRToken with a 65% annual Discount Rate is $92.2M which is 41.5% higher than without the liquidity premium.

Note: I have not explicitly adjusted the Discount Rate in the model for either of the above; in a sense, I treat them as netting each other out.

Discount Rate Bands by Stage & Due Diligence

VCs know that it is very difficult to pick winners consistently. Hence rather than use different probabilities of success for individual startups, they use different probabilities of success for the stage of a startup.

The following table presents Discount Rate by stage and the associated probability of success:

Discount Rate Adjusted for Probability of Success by Stage

Note: the base Discount Rate for the investor, in this case, is assumed to be 15%.

What Discount Rate to use is perhaps the most significant decision regarding the model input variables. Whatever your perspective is on the base Discount Rate, it is essential while constructing a portfolio of tokens to use the same Discount Rates by stage across all the tokens you are evaluating. My suggested best practice approach is to establish Discount Rate bands by stage. Where a company falls within the band is determined by quantitative and qualitative factors uncovered during due diligence.

Discount Rate Bands by Stage

Due diligence on the company having the token sale would include investigation and assessment of the following (non-exhaustive) questions:

  • How experienced is the team?
  • Do they have an MVP?
  • How big is the developer community (evidenced by Github pull requests)?
  • What is the legal structure behind the ICO vehicle and development team?
  • Is the ICO compliant with the regulations of the domicile the ICO vehicle is incorporated in?
  • Is it compliant with regulations in the domiciles where the majority of investors reside?
  • What governance structures are in place?
  • What decisions have been made about token supply and distribution?
  • …and other factors

Here are two resources from William Mougayar on the type of due diligence that should be conducted:

At some point, it would be useful to link a due diligence scoring sheet to where in the Discount Rate band a startup about to ICO falls. A Seed Stage startup which scores highly across the due diligence factors may receive a 70% Discount Rate when its token is valued. As noted before, this may yield a double digit percentage increase in its justified market cap and token price.

Any takers for this project? If so, please send me a copy or better yet open source it!

Change in Token Value Over Time

As we have seen in the preceding section, one VC method for valuing startups uses different Discount Rates based on the stage of the company. If a VC invested in a company at the Seed Stage and had to make a decision about what price/valuation to invest in a follow-on round at the Growth Stage, it is important to note that the user model, the revenue model, the distributions forecasts and potential exit or Terminal Value do not change significantly (if the VC did a reasonable job in its initial pro forma projections). What changes at this second valuation, later in time, is the Discount Rate. Why? Because progress has been made by the company: early traction is turning into rapid growth as the company’s marketing and sales efforts ramp up. The company’s product/technology has matured beyond early teething problems, and there is more confidence in its ability to scale.

In other words, the follow-on investment is at a lower risk level because there is more evidence of the company’s progress — this is reflected in a higher probability of success and hence a lower discount rate. The compensation for taking on less risk (relatively speaking) is that investors in the new round pay a higher price per share (the valuation of the Growth Stage company is higher) than investors in the first round.

For companies trending in the right direction (i.e. where the user model and revenue model hasn’t fallen off a cliff), as the probability of success increases based on progress, Discount Rates for new investment fall over time. Generalized, over time, investment decisions get de-risked based on new information.

Note: in this blog post we are only concerned about successful companies. If over time there is evidence of lack of progress then the Discount Rate for new investment may stay the same or increase. The pro-forma projections would likely also change.

I propose that — for rational investors — it is this increase in the probability of success over time leading to lower Discount Rates which justifies a token price increase over time.

In the model, please take a look at the worksheet labeled “Token w. Dist — Value Increase.” I have assumed discount rates decreasing (every four quarters) from 15% per quarter (75% per annum) to 5% per quarter (20% per annum) over the 36 quarter (9 year) period modeled. Everything else in the worksheet is the same as the “Token w. Distributions” worksheet.

This decrease in Discount Rates drives a valuation increase in the market cap from $65M to $2.1B over the 36 quarters and in the price per token from $0.065 to $2.064 — a 31.75x return to the innovators who bought the token during the ICO; not bad!

Note: the Terminal Value is (re-)calculated within each PV calculation (Row 8) because the Terminal Value is defined as:

Terminal Value = the final quarter $ distribution / the (new) Discount Rate.

In reality, each step along the way, the model might be fine-tuned to capture new information. Perhaps the estimate of the market size (100M users) was off by a factor of 3. Maybe many users simply hold on to tokens and do not transact. All of these can be accounted for as new information confirms assumptions or requires them to be adjusted. Nevertheless, the expectation from Day 1 pre-investment is to forecast the economics of the platform as best we see it, to apply a discount rate for the applicable stage reflective of the probability of success for companies at that stage and fine-tuned for company specific qualitative factors, and not overpay for our investment.

Justified Token Value vs. Speculative Value

If investors paid $0.25 for tokens — instead of the justified token price of $0.065 — in the hypothetical PRToken ICO, then the investors have collectively decided that the discount rate should be 10.71% per quarter (50% p.a.) which equates to a probability of success of 30% instead of 20%. This is potentially mispricing risk; in other words, speculating.

Chris Burniske, a prolific and respected cryptoeconomist, has developed a metric and nomenclature for decomposing the current market price of a token into its Current Utility Value (“CUV”) and its Discounted Expected Utility Value (“DEUV”).

I like the idea behind this — it is useful to decompose the current token price into a justified price and a speculative premium (or discount). Chris’ CUV and DEUV metrics are a neat tool; though I would argue to use a risk (probability) adjusted rate of return that starts much higher (75%) instead of the 30% expected rate of return. This would make the Discounted Expected Utility Value smaller to begin with.

Chris proposes a J-curve where CUV and DEUV vary over time. As an early mini-peak in the price of a token takes place, the DEUV comprises the bulk of the token price while the CUV comprises only a small share. Connecting Chris’ idea to mine: hype surrounding the token launch has caused investors to misprice risk; they implicitly assess a higher probability of success than they should given the stage of the startup and hence discount the future expected utility at too low a discount rate, leading to a rise in the Discounted Expected Utility Value. When the promise of the new tech fails to materialize the investors enter the Trough of Disillusionment where the opposite happens; investors become too pessimistic on the chances of the startup succeeding, and the Discount Rate that they use to discount future expected utility value skyrockets; compressing the price of the token close to its Current Utility Value; and so on.


Discounted Cash Flow models are a financial industry standard for evaluating projects or companies that distribute cash to their funders/investors. Though there are few tokens that provide distributions to token holders due to the risk of running afoul of securities regulations, understanding how to value these tokens is a good place to start as the theory around DCF valuation is well developed. My recommendations are to use S-curves to model user, revenue, and distribution growth and to take a page from VC books and use a Discount Rate based on stage.

Tokens that rely on price appreciation to underpin their value will be looked at in my next post. The third post will address the limitations of the basic models that accompany Part 1 and 2 (e.g. fixed token supply).


Notable contributions to the burgeoning field of cryptoeconomics and token valuation over the course of the year have been made by:

There are many others; Frontier will keep adding to our reading list.