It is common practice to value a crypto asset simply by the market cap and the amount of tokens in circulation:
Market Cap = Token Price * Token Supply
…but it is a very simple consideration to make, sort of like saying that if 6 gold nuggets are totaling $600,000, then each nugget is worth $100,000.
Who decides that?
Let’s look together at a model of how crypto assets can be valued: we will start from stamps down to NFTs.
The Equation of exchange depicts the amount of items in circulation based on how they are used:
M * V = P * Q
Money, Velocity, Price Level and Quantity
London Bridge is Falling Down
We are in charge of a post office and decide to issue 20 new stamps to commemorate the Queen of England
- M is the number of stamps
- V represents how many times we will use the same type of stamp
- P is the average number of stamps used every expedition
- Q is the number of expeditions in a given time
Let’s have an average of 5 people showing up each week to make a single shipment.
To avoid having the post office flooded by too-cheap shipments, or deserted if too expensive, we set a price (T) of $5 for each stamp.
- P = 1, because only a single stamp per shipment is used
- M = 20, because 20 are the different stamps
- Q = 52 (weeks) * 5 people, which is 260 shipments per year
Multiplying Q and T we get an annual profit: of $1,300
We have all the data except V, which we can easily calculate like this:
Stamp Coins
After a few years, considering we have a regular customer base by now, we decide that we might even sell all the stamps in advance at a discounted price, assuming they are bought in bulk before the beginning of the year: we can invest the amount and still make it pay off, and our customers will benefit as well.
So we create 1000 Stamp Coins: the same 5 people still want to ship one package per week and are willing to make an annual subscription in advance paying 4 euros per shipment.
So assuming each person buys the same amount of Stamp Coins:
• P = 200 because that is the Stamp Coins used in each shipment
• T = 4/P = $0.02
• M = 1000, as the total number of Stamp Coins
• Q =52 (weeks) * 5 people, the usual 260 shipments per year
With 260 shipments (Q) and 200 tokens used for each shipment (P), we will earn Q*P*T = $1040 one year in advance.
Again, we only have to calculate V, which is how many times a single Postal Token is used during the year.
With 20 people every four weeks?
• 260 shipments per year and 50 tokens per person, for a T value of 4/50 = $0.08
• P = 50 because that is the Stamp Coins used in each shipment
• M = 1000, like the number of Stamp Coins
• Q = 13 (short months) * 20 people, or always 260 shipments per year
With 260 shipments (Q) and 50 tokens used for each shipment (P), we will earn Q*P*T which is the same $1040 as in the previous case
Again, we only have to calculate V:
It is evident that Velocity is a function of time: small and more frequent groups of people speed it up, while large and less frequent groups slow it down.
Velocity therefore can be quantified by the average use of a token over a given period, or by the average interval between uses.
There are 8760 hours in a year, while tokens used for 260*3 = 780 hours, amounting to 7980 hours of “rest” for our mailers, or 91.1 % of the year.
However, this value does not take into account the possibility that there may be multiple mailings at the same time, so it is good to introduce the concept of Idle time:
μ is given by the 8760 total hours / the 3 hours needed for delivery, equivalent to 2920
Applying the concept to velocity it follows that:
which, compared to 260, takes into account possible competing shipments.
If we instead considered a delivery time of one day, the velocity obtained would be much lower and equal to:
Until now we have completely overlooked the possibility that someone might hold back some Stamp Coin.
If he did, the circulating tokens would decrease
M = N * (1 — holding %)
Where M is the amount of tokens used and N is the total number of tokens.
If in our example 20% of the tokens were held, we would see M go from 1000 to 800
By distributing the remaining tokens equally, each person would receive 40 tokens (10 less) yet still be willing to spend $4 to get them, with the price per token increased to $0.1, “coincidentally” the same holding percentage.
The Baumol-Tobin formula for calculating the cheapest amount of tokens to buy :
where K is the dollar / Stamp Coins exchange fee, Y is how much we would spend that year (suppose eight shipments of $4) and “i” is the annual interest rate, which we might consider to be 2%
that is $20
We can consider the holding percentage as the average H of the amount we hold in a certain amount of time divided by the sum of itself and the average y we spend on each activity:
H can be determined as the average between having 20 Stamp Coins and 0, so we can divide the Baumol-Tobin equation by two and insert it into the equation:
At last, we can recalculate the value of M
By picking up the Exchange Equation
M * V = P * Q
Where M are the total tokens, V is the Velocity, P are tokens per activity and Q the total activities.
We can multiply the left-hand side by A (dollar value) and equate it to a variable C representing the total costs of the activity.
A*M*V = C
Evaluating a Bitcoin
Since Bitcoin is considered crypto gold, let’s see what would happen if it supplanted it:
• there are 190000 tons of gold in the world
• each kg is worth $55000
• for a total value of $10.45 trillion
• we divide this sum by the 21 million Bitcoins
• we will approximately get a value of $500,000 for a single Bitcoin
At this point, we can put everything together:
where:
• A is the value of the individual token
• C is the total management cost
• i is the interest rate
• k is the cost of transferring assets
• N is the total number of tokens
• Q is the annual amount of transactions
• Y is each user’s average annual transaction expenditure
• μ is the total time divided by the average time of a transaction
Let’s consider Ethereum
- N: 100 million, but the percentage of staking is increasing: only 80% of tokens are in circulation
- i: let’s say 2%
- k: we can assume $1 for a transaction from FIAT to cryptocurrency
- μ: the move to POS pushed Ethereum’s transaction time to 12 seconds
- in a year there are 365*24*60*60 seconds, so:
If Ethereum processed all VISA payments:
Q: 200 trillion transactions per year
C: 11.6 trillion payments made through VISA in one year
Y: C / 2.5 trillion VISA = $4640
If Ethereum processed all of the world’s email:
• Q: 121 trillion emails per year
• C: with a cost of about $0.1 per 1000 emails, we have 121 trillion *0.1/1000 =$12.1 trillion
- Y: 12.1 / 4.26 trillion users = $2.84
If Ethereum processed all whatsapp messages:
• Q: 54,7 trillion of messages per year
• C: 10$ Is the cost of the monthly subscription to a sim card *12 months * 2 billion users = 240 billion dollars
- Y: 960 billion / 2 billion users = $480
If Ethereum processed all the text messages in the world:
• Q: 54.7 trillion whatsapp messages per year + 121 trillion emails per year + 5 trillion telegram messages + 3 trillion messenger messages + 2 trillion text messages for a total of 186 trillion
• C: 960 trillion for whatsapp + 12 for email: total of 972 trillion
- Y: 972 trillion / 5 trillion users = $194.4
NFTs
Luckily, NFTs, in contrast to their fungible counterpart, can be evalued through 4 components: Liquidity, Utility, History and Future Value.
• Liquidity: high liquidity results in higher value of NFTs. Tokens created on the chain have a higher value than off-chain assets
• Utility: the utility value depends on how the NFT can be used. Two main categories with high utility value are tickets and game assets.
• History: NFTs with peculiar historical value are often issued by famous artists or companies with a strong brand.
- Future value: comes from both valuation changes and future cash flow. Valuation is determined by scarcity of supply and speculation.
Conclusions
After an encouraging comparison with gold, the specific application of the model becomes evident in all its pessimism with the example related to VISA payments.
Things get better with email and messaging, but the estimated value obtained is still low, and large Velocity tends to lower it even further, as they encourage the reuse of the same token over shorter periods.
While “C” management costs are practically irrelevant, 95% staking would dramatically decrease Ethereums in circulation, bringing our equations to results similar to today, except for VISA, that one is irredeemable :-D
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