Estimating Break Even Mining Costs to Predict Where Corrections Will Bottom
For many Bitcoin investors a key benchmark of how low the Bitcoin market price can go is the cost of production during the mining process. This cost depends on both extrinsic factors such as geography, as well as intrinsic factors relating to choice of mining hardware and as such it is difficult, if not impossible, to find a single figure to cover all mining operations worldwide. However, by making a few assumptions and taking a purely statistical approach, we can arrive at figure which may serve as a general rule of thumb for the lowest order.
The Process
As of writing global hashing rate is approximately 35 million Terahashes/s (TH/s). For this process I assume an idealistic mining unit with properties identical to an Antminer S9, which is currently the leading commercial/retail mining unit in terms of popularity. The manufacturer’s website offers the following relevant information:
Price: USD 780
Power: 1.3 kW
Hashing rate: 13,500 GH/s
Efficiency: 93 % at 25 °C
This being the case we can estimate that it would take 2.8 million of these idealistic S9-like mining units to provide the entirety of global hashing power using the formula
# units = global hashing power ÷ unit hashing power ÷unit efficiency
China has some of the world’s cheapest electricity rates as well as average temperatures consistent with temperate regions. This is important as cooling is one of the largest overheads in mining. In addition, the country’s generally low operating costs also give it a competitive advantage. In fact, current estimates place 70 % of global hashing power in China, the majority of which is located in the Sichuan region. Here electricity prices are as low as 0.4 yuan per kWh (USD 0.06).
If we simply assume that the entirety of global hashing power is subject to the same framework conditions as companies based in Sichuan, then the annual electricity cost of operating one mining unit non-stop is approximately:
1.3 kW * 24 hr * 365 d * 0.06 USD/kWh = USD 680
The unit specifications provided by the manufacturer are specified for a nominal ambient temperature of 25 °C with the upper limit of operating range being 40 °C. As such a large portion of a miner’s overheads are given over to system cooling. This is very difficult to estimate as it depends not just on the cooling hardware but also how it has been installed as well as the spatial properties of the factory relating to ventilation. However it is possible to estimate a basic baseline figure using simple physics. If a single unit is 93 % efficient, then at 1.3 kW it must dissipate 0.09 J of thermal energy per second. This heat energy needs to be removed by any cooling system. Assuming that cooling is 100 % efficient (forget thermodynamics for an instant) then it will expend the same amount of energy during cooling. Performing a similar calculation to the one above, the baseline annual electricity cost of cooling 1 unit is therefore approximately USD 50.
Additionally acquisition costs include 1 power supply unit (PSU) per mining unit which typically cost USD 100 retail. Cooling acquisition costs are assumed to be 5 % of unit costs, therefore USD 40.
In order to estimate income, we can employ a purely statistical approach. If there is a total of 2.8 million ideal mining units, each operated under the same conditions, then the probability that any one random unit solves the next block is
1 / 2.8 million = 3.6e-7
Now 1 block is solved every 10 minutes (600 seconds) on average. Therefore it is straightforward to show that the number of blocks discovered on a given day is approximately 144. Likewise we can show that the number of blocks a random unit solves in one day is
144 blocks * 3.6e-7 = 5.2e-5
To estimate the number of days it takes a random unit to discover 1 block we simply invert this number!
Number of days to solve 1 block = 19300 days or about 52 years…
With the current block reward of 12.5 Bitcoins per block, we can estimate an annual income of 0.24 BTC per unit.
A basic break even (BE) cost for one unit is therefore given by setting the difference between income and electricity and acquisition costs to zero such that
0.24 BTC * BE -USD 680 -USD 780 -USD 50 -USD 40 -USD 100= 0
Re-arranging
BE = USD 6900
This means that a new mining unit would just break even if the price of Bitcoin remained at USD 6900 for one whole year.
A More Realistic Example?
The above figure ignores operating costs such as personnel and building costs, which may add an additional 1000 USD per person per month to spread over all mining units (ignoring building costs altogether). Typical professional mining operations are in the megawatt range or roughly 800 S9-like mining units per MW. For a new 1 MW start-up with a skeleton crew of two technicians, we can work out a block solving probability of 1:3625. Based on this, the miner will earn 0.5 BTC everyday! However due to the huge initial outlay, the one-year BE cost is USD 7350 and this is with a 1.5 % discount which some academic sources quote as a typical bulk buyer discount.
BE Price as Bottom Indicator for Bitcoin
So can we use the break even price as an indicator for where the bottom of a correction should be? Well, Bitcoin has a relatively limited history after all, but some basic back testing shows a definite “maybe”.
Discussion
In the current market climate this represents a massive entry barrier, given the uncertain nature of this asset class. In addition, even though established operations may have already paid off their initial acquisition costs, the heat sensitive nature of the ASIC components means that repairs and replacements are commonplace. It follows that replacement mining units will also be subject to this BE price.
Many miners, including in China, will not have the benefit of such cheap energy and therefore the average BE price will be somewhat higher. In fact, it is not clear what percentage of Chinese miners are subject to these low energy tariffs, however I assume the difference to be negligible. Likewise as the Chinese proportion of global hashing power is now 70 %, I also treat other production conditions, e.g. in Europe or North America, as negligible.
But what does this mean for investors looking to enter the cryptocurrency markets? As the goal of suppressed market price is to drive out less cost-efficient miners, miners operating close to the baseline figure will be the ones that win out in a prolonged bear market. In such cases we can expect the price to bottom near the BE level.
If we look at the chart above we can see that there may be some truth to this, yet personally I would like more confirmation. Should this current correction stay within its current range, I’d give it more weight. In addition, there are variables that are really no more than back of the envelope. These include cooling and PSU costs. I also have no way of knowing just how representative the GPU mining rig I chose for the 2011 estimate really is.
Here is a link to the spreadsheet I used for calculating the model: https://drive.google.com/file/d/14GtNVidbfatLH4eEmyzrY-XWCTBHWegf/view?usp=sharing
References
Bitmain.com, Antminer S9 specs https://shop.bitmain.com/antminer_s9_asic_bitcoin_miner.htm?flag=specifications
Bitcoin.com, A Visit to a Bitcoin Mining Farm in Sichuan https://news.bitcoin.com/a-visit-to-a-bitcoin-mining-farm-in-sichuan-china-reveals-troubles-beyond-regulation/
Bitcoinwisdom.com, Hash Rate vs. Difficulty https://bitcoinwisdom.com/bitcoin/difficulty
Forbes.com, China Wage Levels Equal To Or Surpass Parts Of Europe https://www.forbes.com/sites/kenrapoza/2017/08/16/china-wage-levels-equal-to-or-surpass-parts-of-europe/#5c752c1e3e7f
J. Harvey-Buschel & C. Kisagun, Bitcoin Mining Decentralization via Cost Analysis, https://arxiv.org/pdf/1603.05240.pdf