Bitcoin (BTC), the cryptocurrency, is supported by a network of independent miners and is always mining blocks. Each block is a challenging computational problem, and the difficulty is adjusted based on the computational power of the entire network so that one block is mined every 10 minutes. The computer that mines the block (solves the problem) collects the transaction fees associated from any transactions processed in that block and, currently, 25 new BTC. So, given we can estimate the reward for mining a block (in BTC) and the amount of electricity the network spend mining the block, can we quantify the value of BTC in dollars (USD)?
Fundamentally, the value of BTC should be greater than or equal to the energy cost needed to keep the network running. If miners receive less value from the BTC they earn than from the electricity they put into mining they will leave the network, and the average amount of BTC each remaining miner receives will increase. If the value of BTC is excessively high compared to the electricity input miners will enter the network and the average amount of BTC each miner receives will decrease. The decision to enter or leave the market is unique for each miner, but we assume the long run average value of BTC in dollars is greater than or equal to the cost of mining. So mathematically,
(transaction fees + new BTC) = cost of electricity * energy input
The left hand side of the equation is the number of BTC per block. We have already covered new BTC. This amount of new BTC decreases by half every 4 years, and the last new BTC is expected to be awarded in 2140. So why mine blocks when no more coins are being awarded? When the block is mined, transactions are processed. These are other people, not necessarily the miner, exchanging BTC. If someone wants a transaction processed they attach a fee. These fees are awarded to computer that mines the block. In the long run individuals will only continue to mine if the reward, transaction fees, offsets the cost of mining, electricity costs. We will ignore capital and overhead costs (e.g. taxes, cost of buildings, miners, and labor) to simplify the analysis, but including these will increase the lower bound of dollars per BTC.
The right hand side of the equation is the dollars spent mining each block and relies on electricity being priced in traditional fiat currencies. A reasonable estimate for the average price of electricity across the network is $0.05/kWh. This is slightly less than the world average because large scale BTC mining is done in cooler climates to ease cooling costs or areas with cheap electricity. Energy input, like cost of electricity, is an average across the network. The energy consumption per Gigahash is continuing to improve, but current ASIC miners are estimated to consume 5 Watts/(Gigahash/second), also here. The size of the network, measured as hashrate, is readily available. Below are the variables used with estimated values: