Data collection
Concerning data collection, a significant amount of publicly available data is an advantage of the bitcoin system. In particular, we use data retrieved from blockchain.info, a website that provides daily aggregates of bitcoin creation, transaction volume, transaction fees and network hash rate.
Value flows
For the analysis of sustainability, we first look at the expenses and revenues of miners and the resulting value flows from these. We start by inferring which mining hardware is in use during which specific period. This is necessary as the hardware investment represents a large cash outflow for the miners. Second, each hardware type comes with a different electricity power requirement, influencing the miner’s running expenses. Third, the computing performance of specific hardware directly determines the expected number of bitcoins mined by that hardware.
Formally, we solve an equation that models the total bitcoin hash rate on each day as a function of the hardware in operation. From the hardware in operation we can deduce the hardware spending and the electricity costs. Other expenses (pool expenses, bank costs and exchange fees) follow from the total production of bitcoins.
Starting from the observed total bitcoin hash rate, THt on day t, it must be the case that
$$ T{H}_t={\sum}_{i=1}^M HashRat{e}_i\times {N}_{it} $$
(1)
where HashRatei is the hash rate capability of the hardware of type i, and Nit is the number of machines of type i in operation on day t. We have a total of M machines, that are available for purchase over different periods of time (details are below), so we have Nit = 0 on many days.
We start on t = 0 with a single type of machine, the earliest machine available and set the number of them equal to THt/HashRate1. As long as no better type is available, the machines stay in operation to produce the total hash rate that we observe in the data. At a first increase in the hash rate, the number of machines increases to reach the total hash rate. At a decrease in the hash rate, we assume that new machines are throttled back or old machines are turned off.Footnote 5
Once a new machine becomes available, we assume that buyers choose between hardware types by picking the machine with the lowest estimated payback time. This way of calculating the attractiveness of an investment is common practice (Berk and DeMarzo 2014) and the simplicity of the technique fits the dynamism and fast-changing nature of the bitcoin miners. For each machine on the market, the payback time is computed using the 30-day moving average of the bitcoin price:
$$ PayBackTim{e}_{it}= HashRat{e}_i\times \left({P}_{\left\{t,t-30\right\}}-M{C}_i\right)/ FC\_i $$
(2)
where MC is the daily marginal cost of running machine i, i.e., the electricity costs, P{t, t − 30} is the average bitcoin price of the past 30 d (including mining fees) and FCi is the fixed cost of the machine, i.e., the purchase price. The index-number of the ‘best’ machine at each time t is \( {i}_t^{\ast } \).
Existing machines stay in operation as long as the marginal profit is positive, i.e., as long as HashRatei × Pt > MC. If that is not the case, we assume that they are switched off on that day. They can come online again if they become profitable again, for example, when the bitcoin price increases.
The combination of machines in operation on any given day is then simply equal to the number in operation on the previous day, minus machines that have become unprofitable, plus new machines of the type that have the lowest payback time. Let \( T{H}_t^{lost} \) denote the hash rate ‘lost’ by machines that are switched off because of the profitability condition. Then, we have that
$$ {N}_{it}=\left\{\begin{array}{cc}0& \mathrm{if}\ HashRat{e}_i\times {P}_t< MC\\ {}\left(T{H}_t-T{H}_{t-1}+T{H}_t^{lost}\right)/ HashRat{e}_i& \mathrm{if}\ i={i}_t^{\ast}\\ {}{N}_{i,t-1}& \mathrm{otherwise},\end{array}\right. $$
(3)
where THt − THt − 1 represents the increase in the total hash rate from day t − 1 to day t that is picked up by new machines coming into operation.
Although the hash rate is increasingly almost continuously in our sample period, there are a few instances where the hash rate declines. We allocate those decreases to the most recent machines that we assume are throttled back proportionally.Footnote 6 Since declines in the hash rate are rare and small (see Fig. 4 below), we use the most straightforward way of accounting for hash rate declines.
We now turn to the data that is fed into Eqs. (1) to (3) to determine purchases of new hardware. Figure 4 shows the hash rate and difficulty of the bitcoin network increasing by a factor of more than 347,000 from 2012 to 2016. There are two reasons why this happens. First, faster hardware is added to replace slower running hardware for which electricity expenses outnumber mining and transaction revenues. Second, new hardware is added to increase production, as bitcoin mining becomes increasingly popular. In both cases, we attribute the increase in computing power in the bitcoin network to new hardware.
Value flow: hardware investments
Regarding the purchasing of mining hardware, we assume that miners behave rationally and therefore buy the hardware with the lowest payback time. The payback time is calculated by taking the upfront investment in mining hardware divided by the average revenue per day (as a result of coins mined plus transaction fees minus energy costs of the preceding 30 days) resulting from that hardware. For each date the most energy-efficient hardware (energy cost per GH/s) compared to the most cost-efficient hardware (amount of computing power per $). Figure 5 shows the comparison between cost-($) and energy-efficient (en.) hardware in 2012. During the year the payback time of the cost-efficient hardware is shorter than that of energy-efficient hardware. The payback time in 2012 could differ from around 82 to 1051 days.
Figure 6 shows the estimated payback time for the full period and the revenue per GH/s from 2012 to 2016. The estimated payback time can be as short as 3 days, but is often between approximately 100 to 300 days. During the first 6 months of 2016, the payback time is so high, it would take decennia to earn back the hardware. The payback time in 2012 could range from around 82 to 1051 days.
At the beginning of our analysis period, we assume that the AMD 5830 is installed, which was the best available hardware at that time.
Regarding electricity costs, we use a fixed price of $0.12 per kWh, obtained from ovoenergy.comFootnote 7 as the average price across developed countries in our sample period.
Regarding the operation of mining hardware, we assume that mining hardware remains in operation until the daily electricity expenses related to that hardware is equal or higher than the expected revenues for that day, namely the value of the mined bitcoins and the transaction fees. In other words: after initial investment, the only incentive for miners to turn their hardware off is that the marginal expenses for mining (electricity) outweigh the marginal revenues.
The energy cost for a particular type of hardware is known. The expected number of bitcoins mined per day, as well as the transaction fees for a specific kind of hardware can be derived from the performance indicator (in GH/s) of that hardware. Therefore, in order to calculate the payback period, we must know the expected revenue. To estimate this, we convert the expected number of mined bitcoins to dollars, using the average value of the bitcoin 30 days prior to the investment. This assumes that miners possess no superior timing ability, which seems sensible.
Given the assumptions on purchasing and operations we can estimate the hardware in use over time. As the market of mining hardware is not transparent, the archived pagesFootnote 8 of a public wiki pageFootnote 9 are used to select the most cost-effective hardware over the period 2012 to 2016. This data was cross-referenced with discussions on the public forum bitcointalk.org to find the earliest moment new hardware was available to miners. The results are in Table 1.
Table 1 Hardware expenses 2012–2016 Since the performance of the bitcoin network is known, we can calculate the upfront hardware investment, if we assume all hardware was the AMD 5830 at that time. Then, for each subsequent day we can infer the hardware purchases using the increase in hash rate and available hardware on that day. With the assumption of positive marginal revenues, we also can calculate when new hardware is added or retired.
Table 1 shows the fast increase of the network’s performance rate due to the increasing availability of dedicated hardware for bitcoin mining. Note that, because the hardware is tailored to bitcoin mining, we consider the residual value of hardware zero as it cannot be used economically for other tasks.
Value flow: electricity expenses
Now that we know which specific kind of hardware is into operation during which specific period, we can also calculate the electricity consumption of that hardware, and related to that, the electricity expenses. We assume that mining is always running during the period of operation. Table 2 gives the daily expenses for electricity per GH/s for a particular type of hardware, as well as the total electricity expenses for the period the specific hardware was in production.
Table 2 – Energy Expenses 2012–2016 Figure 7 shows the rapidly increasing energy usage of the bitcoin network from 2014 to 2016. The energy consumption at the peak in 2014, around 5 mln kWh per day, means the bitcoin network is running at around 208 MW. This seems sensible, given the hash rate ultimo 2016 of 2 bln. GH/s and the efficiency of the Antminer S9 which uses 0.1 J per GH/s. This translates to a power use of 200 MW. It does question the earlier estimate of O'Dwyer and Malone (2014), who find a number that is close to the electricity use (3GW) of Ireland in 2014. Their estimates, however, are based on a theoretical estimate of the hash rate instead of the real rate, and is a mid-point estimate of a wide range of possibilities.
Figure 8 gives a graphical representation of our estimates of when certain hardware was in use. The height of the box for a specific kind of hardware indicates the energy expense per GH/s for that hardware. The hardware is phased out as soon as the revenue per GH/s crosses the electricity expense for that hardware (the top-right corner of each rectangle). The sudden drops of profitability during periods like the fourth quarter of 2013 and the second quarter of 2016, suggest the predicted gradual linear and exponential profit declines of online mining calculators are an unreliable tool for net cash flow prediction.
Value flow: other expenses
In order to mine bitcoins, miners will also have expenses to (1) pools, where about two thirds of the minersFootnote 10 pay a fee of approximately 1%Footnote 11 to a pool owner, (2) 0.5% exchange feesFootnote 12 in order to sell bitcoins for regular currencies and (3) 0.5% bank fees are assumed based on the exchange fees. Assuming that all mined bitcoins and earned transaction fees are immediately exchanged for dollars, exchange and bank expenses directly relate to the amount of bitcoins transferred and mined each day. The expenses are summarized in Table 3, by hardware type.
Table 3 Other expenses 2012–2016 Value transfers
We now know all components of the miner’s expenses and revenues. Table 4 summarizes the expenses and revenues, and calculates per hardware the estimated generated net cash flow. As can be seen from the table, the first part of our analysis period shows a positive net cash flow for miners. The numbers of the flows in Table 4 correspond to the numbered value transfers in Fig. 3. However, the last two periods have a loss. At the end of the measurement period, only the Antminer S9 was still running on a profitable basis, so the losses might be compensated in the later periods. Table 4 also shows that in some time periods the investments in hardware have been very profitable, such as with the Avalon 1 in 2013. The total profits for miners who have used the Avalon 1 in the right time period have been almost $ 50 mln.
Table 4 Miner Profits per machine 2012–2016 Table 5 maps the miner’s cash flows to the e3value model as introduced in Fig. 3. Most of the income stems from the generated bitcoins, while most of the costs are due to the hardware investments. The hardware expenses are by far the biggest expense to bitcoin miners. This upfront investment in hardware, combined with a high daily energy cost leads to considerable losses in the later years.
Table 5 Value flows of miners in bitcoin network (in mln USD) Marginal costs
Figure 9 shows the 30-day moving average of total revenues and expenses. As can be seen, the expenses related to bitcoin mining approach the revenues, which is also predicted by economic theory: under full competition, marginal revenue approaches marginal costs. This holds for normal goods as well as for virtual goods and currencies as bitcoin.
Figure 10 shows the marginal expenses (not counting the upfront hardware purchases) compared to marginal revenues. During 2015 and 2016 these lines approach each other, leading to very little profits. This makes it very difficult to have a return on investment on the acquired hardware. The sudden drop in revenue and expenses in mid 2016 is likely a result of the blockchain halving, where the bitcoin reward was halved from 25 to 12.5 per block, and the introduction of a new generation of mining hardware.
Results
Figure 11 shows the cumulative net cash flow that resulted from Fig. 7. Positive flows are followed by periods where money is invested in new hardware, leading to temporarily negative net cash flows. The value of the remaining hardware at the end of the measurement period is $425,040,520.84. By mid-2014, the high revenues of 2012 and 2013 are countered by high expenses, leading to a negative net cash flow from that moment on. It can be seen that this results in a positive net cash flow, but due to necessary new investments, the total net cash flow drops with each innovation. Energy prices determine the profitability of mining hardware, so it could be argued that these prices heavily influence the resulting profits. It is therefore meaningful to do a sensitivity analysis with respect the energy prices. For this purpose, we have also estimated the cumulative profit in scenarios where the energy price is reduced by 50% to $0.06/kWh or reduced by 75% to $0.03/kWh. Figure 9 shows the scenario with an energy price of $0.06/kWh still leads to a negative cumulative cash flow. Only the scenario in which energy is available for $0.03/kWh the bitcoin network is capable of generating a modest positive net cash flow over its complete lifetime.
Reaching the break-even point
A question we can ask is what the exchange rate of the bitcoin should have been in order to reach the break-even point for the modes. This price, as well as the percentage increase/decrease in the exchange rate is given below.
The estimates in Table 6 should be interpreted with care. It is likely to expect that a change in the exchange rate would influence other parameters too, e.g. the number of transactions and the number of miners. Since our analysis is based on factual data of the bitcoin network, we cannot compensate for these effects. To do so, a proper simulation model of the bitcoin network should be developed to include the market dynamics.
Table 6 Required break-even price bitcoin for miners from 2012 to 2016 with hardware purchased since 2012