# How to value crypto by cost of production: Introducing P/P

Apr 10, 2018 · 10 min read

This article is a continuation of developing fundamental ways to value crypto, as outlined here and here. The four main ways we have to value crypto right now are from its use as a currency, stock, product, or network. This will address valuation from the product perspective.

Everything costs less to mine than to buy them on the market. We wouldn’t have miners otherwise. What are the implications? Let’s find out. We also introduce a ratio we use at Ledger to think about this.

# Introduction

To understand the value behind a digital asset, we need to figure out how we get them in the first place. We can get them in the following ways:

1. On an exchange (with fiat currency or another token)

2. From another person (say, in exchange for a coffee)

3. By producing them ourselves (mining)

Viewing the source of digital assets as #1 or #2 lends to valuing them as a currency or network. #3 is where the production model comes in.

Adam Hayes first introduced this model to try and figure out how valuable this mining process was. For those of you not familiar with mining, it’s essentially a huge computational and energy intensive effort to maintain the integrity of a token’s PoW (Proof-of-Work) consensus algorithm, which is needed to verify the blockchain. I’m not going to get into depth on the process behind mining, but if you want to get more this is a good article. At the very least, viewing the inputs of electricity and energy as tangible monetary value should represent a token’s worth.

If we were miners, we would mine a coin as long as the market value of it is greater than the cost for us to do it. Given a perfectly competitive & efficient market, in theory, the monetary value of said coin should drift to whatever the cost of mining is at that time. Let’s consider this to be the base value of a coin, which can then be given by the following formula:

# Background

Now that we have our fundamental relationship, let’s dive into the numerator and denominator of the term to better understand where they come from. We will scale the terms of the equation daily to make it easier to compute.

1) The numerator: Energy Cost

The total cost of the energy used, put in terms of daily output, can be expressed as follows:

The Hash Power, ρ, is going to be dependent on the coin we are mining. But we can estimate values for both \$/kWh and ϵ, Energy Efficiency. Let’s start by figuring out what a reasonable estimate for the price of electricity, the \$/kWh term, would be.

a) Cost of electricity (\$/kWh)

It’s not just the cost of electricity that plays into a miner’s decision to choose a location — internet speeds and a low temperature environment to reduce cooling costs are equally as important. Given the specifications for mining and the fact that it occurs in so many different countries with different electricity costs, how do we estimate this? Luckily, a great study conducted in 2017 by Judge Business School at the University of Cambridge, among many other things, mapped out mining facilities across the globe. Check it out.

With this, we can get a pretty good picture of the distribution of mining efforts. It’s a pretty safe bet that around 50% of mining occurs in China, especially in the Sichuan and Neimonggu (Western Inner Mongolia) provinces. Around 25% of the mining occurs in Eastern Europe, namely Georgia. The remaining 25% is mostly from the U.S. and Canada, with increasing efforts coming from European countries like Sweden, Iceland, and Estonia. There are mining efforts that went undetermined in Thailand, Hong Kong, Venezuela, and Poland that are significant as well. I’ve compiled a range of electricity prices from various sources for these countries in the table below.

Before going further, a couple notes: China has low electricity prices primarily due to the lobbying of hydroelectric plants in more rural areas. This might get changed soon due to the adverse environmental impacts. Georgia recently increased it’s price in 2017. Mining in the USA can only be done in cooler climates which takes out most of the cheap industrial electricity spots in the south. However, places like Montana, Idaho, and Oregon have 5–6c/kWh industrial electricity which is a real steal. Canada, Sweden, Iceland, and Estonia are all up-and-coming places to mine given the emphasis on renewable energy sources and the fact that there is little need to spend money on cooling. Thailand, Poland, and Hong Kong seem to be too costly right now. Finally, Venezuela looks like it is a dream come true: .2c/kWh?? That’s 5% of China’s cost. Not really though, unless you’re fine with being arrested. Stay far far far away.

Ok, so now we know where digital assets (well, technically only bitcoin, but let’s assume that its proportional) are mined and how much electricity costs. Lets boil these two pieces of information down into a range.

The total global energy cost to mine is somewhere between 5.5 to 8.8 cents/kWh. As we progress technologically, we expect this number will only go down.

b) Energy Efficiency (W/Hs)

This is the other metric we can determine in figuring out the total cost of energy spent in a day mining. The table below summarizes the gold standard which serious miners use. The only coins analyzed in this article are those that can be mined with ASIC right now; other GPU only coins (ethereum, monero, zcash, etc.) will eventually be able to be mined in this manner as well — or they will fork/switch to PoS. The upcoming E3 and X3 show this reality.

This is how it looks substituting everything in, with lower and upper bounds of cost per coin:

Awesome, now we are done with the numerator.

This part depends on many things, but because we are only looking at a couple popular ASIC-minable coins this simplifies our analysis. Other coins will have a different formula to use, so beware trying to extend this.

# Analysis

Ok. Sorry for all the background. Let’s combine everything together now to create a model to value the production cost of these coins now. Substituting these two parts in the the Fundamental Cost of Production equation at the beginning, we get the following final valuation metrics (note that ρ, the hash power, ends up cancelling out):

Using data from bitinfocharts, including transaction fees for block rewards, we can plug in values to solve for the price ranges. Doing this, we arrive at the following conclusion, which, given our assumptions (free mining equipment, no cooling or labor costs), is definitely a conservative estimate:

BTC Price Range: \$1765 to \$2824

LTC Price Range: \$27 to \$44

BCH Price Range: \$169 to \$270

At the time of writing, BTC is around \$7000, LTC around \$117, and BCH around \$650. So, does that mean that everything we have in the market is overvalued? If we go by an efficient markets hypothesis, yes. Everyone would opt to mine over buying a coin on an exchange or from somebody else.

## But what do these ranges really mean?

At face value, they are the cost (minus the initial cost of the equipment, since that should be negligible over time) to produce a singular coin. But we really shouldn’t be treating this as the value of the coin. Rather, it is an asset’s base worth. It is the value that the coin needs to be in order for miners to be incentivized (positive expected value) to continue to validate the network.

To show why, it would probably be helpful to draw an analogy. Apple trades at around \$170/share. However, if you were to take their book value (assets-liabilities) and divide that over all of it’s shareholders, each person would only receive \$28! Ok but Apple’s a funny company so lets look at Google. Google trades over \$1,000/share but it’s book value/share is \$220. We can go down the line of technology companies and see similar numbers.

What I’m getting at here is the difference between market value and book value in traditional finance; book value represents the current “net worth” of a company. It doesn’t factor in anything else. Market value is what investors see in a company. Let’s bridge this gap and apply it to crypto.

# Introducing Price/Production (P/P)

The cost it takes to produce a coin can be thought of, loosely, as it’s book value, or its “base value”. This is a number that can be associated with it’s value; yet it doesn’t represent the other drivers behind a token’s future speculative price.

At Ledger, we are big fans of crypto ratio analysis, or comparable valuations. With this in mind, let’s bring in a metric from traditional finance that we use to judge things with hard to determine fundamental values (such as earnings, or network value in crypto’s case). Price/Book (P/B) is helpful in trying to understand which companies are trading above/below their true net worth. Obviously this case is a little bit different, since we are quite literally producing a new, completely equivalent coin (share), but there is a relationship here that is important to point out and understand.

Creating a metric of Price/Production (P/P) allows us to see the premium at which a coin is trading on the market compared to the variable cost of producing it.

Let’s see what these current multiples are, approximately, for the coins that we analyzed. A lower multiple is better, since it indicates a closer value to reality.

Bitcoin P/P: 2.5x to 3.9x

Litecoin P/P: 2.7x to 4.3x

Bitcoin Cash P/P: 2.4x to 3.9x

All of these assets have similar ranges; indicating that there are currently no relative differences between their production costs. How does this metric vary historically then? Lets see. We will assume the low end of the cost of production just to be on the safe side. The dates were capped because these were the only reasonable time-frames where the earlier assumptions (such as the cost of electricity and mining efficiency) would hold.

From these graphs, we can see that when a coin is worth more than around 20x the low bound of its cost of production (i.e. P/P > 20), it has been an indicator of a bubble. We can also see that P/P has been trending down over the past year, which makes sense because prices are more accurately reflecting the cost to mine them (supporting an efficient market hypothesis). Sorry miners; if you couldn’t tell, the golden days might be over.

# Discussion

The potential to produce digital assets from computational power is one angle behind valuation that a lot of investors overlook. However, as we show in this article, it is a very important source to consider when evaluating a minable, PoW token.

P/P allows us to quantify the difference in market price and production cost (which we liken to book value). It has uses in determining the relative value of a token to comparables, but equally as interesting is determining historical trends to see trends relative to itself.

When trying to apply this more broadly, we need to keep in mind that mining is highly dynamic and metrics (cost of electricity, mining efficiency, block rewards, etc.) will change. Looking to see how P/P changes with that will give us important insights into how the production angle is being reflected in valuation.

As energy costs trend downward over time and difficulty of mining increases, we will be seeing very interesting shifts in the cost to mine. The long, long term reality is that these assets will eventually have a zero cost of production and the market value would go to 0 or very low to reflect that. This means that it would not be worth it for somebody to create a minable token. However, we believe this is a distant case that will be compensated for by increasing difficulty and lower block rewards, and is hardly of consideration when looking at other consensus mechanisms (PoS, DPoS, etc.)

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