Bitcoin’s Cost of Production — A Model for Bitcoin Valuation
Bitcoin, since its inception, has remained an enigma to most. Is it a speculative bubble destined to burst to zero or the currency of the future? Perhaps an argument could be made in favor of recognizing it as a commodity? How does one justify its price, and more importantly its price action? Technical analysts across platforms, TradingView, Twitter or Telegram alike, are divided on the direction of the price per bitcoin. At the time of writing this article, Bitcoin is trading at an average of $9,094 per coin on the major exchanges. Calls are being made for a dip to mid $5ks, while bulls seem to opine that come May, we are going to witness a price of more than $13k per bitcoin.
Existing Valuation Models and their Limitations
The Stock to Flow Model
Among those models based on fundamental properties of Bitcoin, the Stock to Flow model by planB, based on the concept of scarcity of future issuance, has caught traction among Bitcoin enthusiasts. Further studies in this domain, especially the proof of cointegration of flow with price by Nick, have legitimized the model further. Given that the future values of its independent variables are set in stone (or rather, in code), the future range of the model’s price can be accurately projected.
While I am personally impressed by this model and refer to it for very large timeframe trading, it is not the best tool for a swing trader looking at time horizons of a quarter or less. During an extreme bull market phase, the actual price of a bitcoin can be seen trading at over 4 times that predicted by the model, while blindly following the prediction could see ones account underwater by as much as half the predicted price during the nadir of a bear cycle. Its range of residuals is too wide.
This model also fails to value other Proof of Work (PoW) cryptocurrencies, viz. Litecoin, Bitcoin Cash, ZCash, Monero among others. However, it is not to say that these cryptos are priced at zero, if anything they’ve held their market share over the last 24 months, hence there needs to be a better explanation to their valuations.
Finally, the model assumes that the process of mining bitcoins will continue until the mining of the final block in 2142, in which case the value of a bitcoin then will be infinite. However, the flow of bitcoins will drop to zero in the event of mining cease prior to 2142. If that happens tomorrow, or five years later, will the price of the value of a bitcoin shoot up to infinity in a short span? No. If anything, its price is expected to drop significantly as a reaction to such a black swan event.
Bitcoin Energy-Value Equivalence
This model by Charles Edwards attempts to value a bitcoin-based on the cost of energy to it. It is a much more practical approach to valuing Bitcoin than its stock to flow — a premature end to Bitcoin’s mining is likely to tank its price instead of launching it to infinity, and can also be used to value other PoW cryptos and their bitcoin-pairs, e.g., by valuing Bitcoin Cash (BCH) in US Dollars, the value of BCH-BTC pair in satoshis can be obtained.
However, as with the Stock to Flow model, the Energy-Value Equivalence model is too smooth to be sensitive to price movements. In extreme bear market scenarios, the price of a bitcoin traded at 60% below the model price in 2011 and 2015, while it bottomed at only 45% below the same in late 2018. The inability of this model to be a uniform bottom indicator leaves scope for further modeling on the basis of the cost of production.
DataDater’s Bitcoin Cost of Production (CoP) Model
One of the drawbacks of the energy-value equivalence model lies in its ignorance of including capital expenditure (CapEx) as part of the process to arrive at the cost of mining Bitcoin. CapEx for bitcoin mining would imply the cost of purchasing a mining rig, setting up farm infrastructure, regulatory/legal expenses, etc. Also, the operating expenditure (OpEx) would include labor expense and pooling fees in addition to power expense, which the model ignores.
Therefore, the CoP model attempts to compute both the CapEx and OpEx involved in mining bitcoins. The process is explained below:
Calculating CapEx
The model is developed from data post-May 2011, as Field-programmable Gate Array (FPGA) miners were introduced about then. Also, the model assumes that the mining pool tends to use the most efficient rig (for obvious competitive reasons), hence the Antminer rigs are referred to for most parts in this valuation process.
Data pertaining to cost and ratings of the currently in-use Antminer rigs have been obtained from the Antminer website while those of their legacy counterparts from e-commerce sites such as Amazon or Alibaba.
An average rig has a lifespan of about 2–3 years, hence the purchase cost is adjusted for depreciation using the declining-balance depreciation method. Further, in most cases, newer rigs are introduced before a previous model runs its lifespan, as a result, the effective cost of the previous rig depends on the number of bitcoins it hs mined till the time of its replacement. This is called the units-of-production depreciation method. For instance, the S3 was in use for approximately 153 days (July 2014 to December 2014) and mined an average of 0.97 bitcoins in that period. Hence, its effective purchase price was $299/0.97 = $308.24. It is to be noted that the model assumes that the entire mining network has been taking the same time to switch from one rig to the next released rig for all rig releases.
Calculating Opex
To calculate the cost of electricity for mining bitcoins, data of the network hashrate and daily coin issuance, are fetched from Coinmetrics. From this, the number of hashes required to mine 1 bitcoin is calculated as Hashrate/Daily Issuance. This value is then divided by the mining righashrate to obtain the time required to mine 1 bitcoin in an hour. This time value is multiplied by the power rating of the rig to obtain the number of units in kWh required to mine 1 bitcoin. Finally, this unit count is multiplied by the cost of consuming electricity in US Dollars to obtain the cost of electricity to mine 1 bitcoin.
To illustrate the above-mentioned method, the daily network Hashrate on 13 October 2014 was 266,217.37*60*60*24 Tera hashes and 3,875 bitcoins were mined on that day.
Thus, (266,217.37*60*60*24)/3875 = 5,935,788.59 hashes were required to mine 1 bitcoin.
The S3, with a hashrate of 0.43 Th/s would have taken (5,935,788.59/0.43)/(60*60) = 3.84 hours to mine than bitcoin.
Given, the power rating of the prevalent S3 to be 339.57 W and an average global cost of electricity being $0.06, this could have incurred a cost of 3.84*339.57*$0.06 = $78.12.
Therefore, the total cost of mining 1 bitcoin on 13 October 2014 was CapEx + OpEx = $308.24 + $78.12 = $386.36. This is close to the actual price of $391.99 on that day.
Do note that miners most likely purchase the rigs at a discount and probably pay less tariffs for electricity, but this discount is offset by additional costs of infrastructure, labor, pool fees, and other overheads. For the sake of simplicity, these costs have been ignored and the mining-rig price and tariffs have been taken as they have been.
The following chart illustrates the CoP model price against the actual price per bitcoin.
Takeaways from the Model
The model illustrates how the price of a bitcoin gravitates towards its cost of production. This is in accordance with that mentioned by its creator Satoshi Nakamoto in its whitepaper.
The introduction of a more efficient mining rig, leads to a drop in production cost, while the cost doubles in the event of a block reward halving. The shift from GPUs to FPGAs in mid-2011 and to Application-Specific Integrated Circuits (ASIC)s in 2013 greatly influenced the mining costs.
At present, the cost of mining 1 bitcoin is about $7,577.51. Assuming the network hash power remaining the same and with the introduction of the S19 Pro, this cost is expected to be at $13,964.11 at the time of the next block reward halving in early May 2020.
Future Projections of CoP and Price Predictions
The cost of mining depends mainly on the cost and efficiency of the mining rig — it contributes about 70% of the total cost of production. Only 30% of the mining cost is attributed to the operational cost which largely consists of electricity costs of running the mining hardware.
By predicting the effective cost (Hashrate*Efficiency*Cost) of the future ASIC miners and the network hashrate through regression of previous data, the cost of mining a bitcoin can be estimated. It is to be noted that during this period, the cost of electricity is assumed to remain constant while no paradigm improvements occur in the efficiency of mining rigs, unlike in late 2013 when FPGAs gave way to ASICs, leading to a rocketing of efficiency and jettisoning of cost.
The following charts show the exponential growth of the cost of ASIC miners and the network hashrate, indicating that the price of bitcoin is expected to rise in the future.
Extending the CoP Model for other PoW Cryptocurrencies
To test the validity of this cost-based model, it was applied to other PoW cryptocurrencies. If the model is to be reliable for analysing Bitcoin’s price, it should be the same for other PoW alts too.
Below is the result of the analysis of Bitcoin Cash (BCH) by this model.
As with Bitcoin, the model serves as a reliable indicator of Bitcoin Cash’s floor price.
Further, this model is useful in valuing an alternative cryptocurrency (altcoin) in terms of units of Bitcoin or satoshis. The ratio of CoP of BCH to BTC’s in US Dollar usually contains that of their price.
Key Takeaways
The CoP model is useful in valuing PoW alts. It is also useful in valuing these alts against Bitcoin. If the price of the alt is much higher than its CoP, it is expected to be in a local bubble and hence drop in a not too distant future. We saw this with BCH in late 2017.
Comparing the CoP Model with Indices of Other Assets
There is confusion regarding the relationship between the price of Bitcoin with the indices of stock markets, commodities, currencies, and energy. Some analysts claim that Bitcoin is more akin to scarce metals such as gold and that in the event of a meltdown of the securities market or the collapse of a major fiat currency, the price of Bitcoin should rise. Their detractors doubt the validity of this risk-off narrative and feel that Bitcoin’s price would drop should there be a global recession, while the third kind reason that Bitcoin is a completely uncorrelated asset to major instruments of investment, and that its rise will not be affected by the wider market happenings.
The CoP model of valuation leads us to the future scope of analysing Bitcoin’s production cost with the major market indices.
Summary
- The CoP model is reliable for obtaining an intrinsic floor price of Bitcoin. This is the price that a bitcoin tends to move towards and serves as an over/undervaluation metric.
- The model expects the price of a bitcoin to rise, given the rising trend of the effective cost of ASIC miners and network hashrate.
- It is also useful for valuing PoW altcoins.
- It can be used to analyse the effect of other markets on that of Bitcoin. This analysis will be conducted in the near future.
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