Tl;dr
Depending on which lost coin assumptions are considered, the value of one Bitcoin varies greatly. In the most extreme case, upwards of 40% of circulating Bitcoins could be lost forever. Considering lost coins, Bitcoins today are trading at a material discount of 5 to 40%.
Lost Coins: The Consequence of a Novel Feature
Self custody of Bitcoins requires radical agency. The decentralized nature of the bitcoin network only allows for transactions to be sent, never to be reversed, even if a mistake is made.
When choosing to self custody, Bitcoin hodlers are responsible for keeping their private keys safe. I like to think of this responsibility similar to keeping physical gold inside your house or burying it in your backyard. You have chosen to physically safekeep your gold, instead of relying on a third party that could potentially withold that gold. It’s your job to protect your gold from people that might attempt to take it from you. It is your job to keep track of your gold.
Over the years, this censorship resistant feature that prohibits BTC retrieval, honest or manipulative, has resulted in many Bitcoins being lost forever. Some Bitcoins are confirmed to be lost and can never be retrieved again, many more are probably lost, but there is no way to know for sure. Lost coins should effect the price of each individual Bitcoin.
Price ≠ Value
When thinking about price of bitcoins, what is a fair value? What exactly does one mean when asking the value of bitcoin?
Are they referring to the bitcoin network? or specifically one unit of account on said network, which the community calls a Bitcoin?
For this thought experiment, assume the number of Bitcoin available to transact will act as a proxy for shares of the bitcoin network. I feel comfortable with this model because the bitcoin network has one function: ensure the security of all Bitcoins on the bitcoin network.
Understanding Individual Share (Bitcoin) Price:
The price of one company share by itself does not indicate the value or price appreciation potential of a company or asset. Sorry, XRP won’t pump more than BTC due to XRP trading at $.61 and BTC trading at $18k. The price is simply a way to measure what percentage of the company or asset each investor owns.
To assess the value and growth potential of a company or asset, one must look to the market capitalization. If Apple is valued at $1T, that means the market cap is $1T. The share price is simply a reflection of company value divided by shares outstanding. This means share price is determined when the value of the company (market cap) is spread out over each of the outstanding shares. In our example, we don’t have a company or shares, we are using the bitcoin network instead of a company and Bitcoins instead of outstanding shares.
Why Would Lost Bitcoin Effect Price?
We now know that individual share price is simply the result of how many units or shares we wish to divide our company/asset, into. The bitcoin network has been divided into 21,000,000 units, Satoshi and the community call these units Bitcoins. Bitcoin price will increase as market cap increases: Bitcoins price = bitcoin network market cap/# outstanding Bitcoins. A 10% increase in market cap will result in a 10% increase in Bitcoin price, when shares outstanding are held constant:
$1.00 per shares = $1,000,000 Market Cap/1,000,000 shares
$1.10 per share = $1,100,000 Market Cap / 1,000,000 shares
The market believes that this company is 10% more valuable, this can be observed through the $100,000 increase in market cap. Because there are still 1,000,000 shares outstanding, the resulting price response was a 10% increase in share price. The share price increased by $.10.
Watch what happens the company decides to reduce the number of outstanding shares shares during the same period:
$1.00 per shares = $1,000,000 Market Cap/1,000,000 shares
$2.20 per share = $1,100,000 Market Cap / 500,000 shares
With only a 10% increase in market cap, the reduction of 500,000 available shares made the price of each share increase by 120%. Adjusting the number of shares outstanding has direct effect on the price of each individual share or in our case, each individual Bitcoin.
Ok, So How Many Bitcoins Are Lost?
Now we know that the number of Bitcoins in circulation is very important, but how many are actually in circulation? We know how many should be in circulation according to the bitcoin network’s issuance schedule, but how many of those Bitcoins are lost forever? It is difficult to know exactly. Here are some predictions:
Nakamoto Case: 4.7% of circulating BTC supply is lost forever.
- If Satoshi hasn’t sold a single BTC from their $16B stash, it is unlikely they ever will. — Satoshi Has 800,000 BTC that are likely gone forever
Probable Case: 20% of circulating BTC supply is lost forever.
- Satoshi Coins
- Burnt Bitcoins — 2,700 BTC burned
- Death with private key — $30B lost due to death of private key holders
- Lost or broken computers/hard drives — 7,500 BTC thrown away
- Forgotten private keys (passwords) — Elon Musk Makes Mistakes Too!
- Sending BTC to an incorrect destination (wallet address) — 800 BTC sent to random address, could be gone forever
- Natural disasters — China Floods Destroy Mining Operation
Edge Case: 40% of circulating BTC supply is lost forever.
- Satoshi Coins
- Known Losses
- Assumption of 20% of supply lost and unreported. Something similar to what happened to our friends here on Big Bang Theory.
Price Response From Lost Coins
As of December 9, 2020
BTC 20-day moving average: $18,169
BTC in circulation without considering lost coins: 18,566,000 BTC
BTC Market Capitalization: $18,169*18,566,000 = $337,325,654,000
Market participants currently accept a market cap of $337B. This is proven because the amount of BTC in circulation is known, market participants have been trading this circulating BTC at an average price of $18,169. But we know that a material amount of this circulating supply is lost forever.
What happens when we begin to account for lost coins in the model? To consider the price implication on individual Bitcoins, we must divide the accepted market capitalization by our new quantity of available Bitcoins.
Nakamoto Case
BTC Market Capitalization: $337,325,654,000
Available Bitcoin: 18,566,000 * (1-0.047) = 17,693,398 BTC
Appropriate BTC Price: 337,325,654,000/17,693,398 = $19,065.06
Probable Case
BTC Market Capitalization: $337,325,654,000
Available Bitcoin: 18,566,000 * (1–0.20) = 14,852,800 BTC
Appropriate BTC Price: 337,325,654,000/14,852,800 = $22,711.25
Edge Case
BTC Market Capitalization: $337,325,654,000
Available Bitcoin: 18,566,000 * (1–0.40) = 11,139,600 BTC
Appropriate BTC Price: 337,325,654,000/11,139,60 = $30,281.67
Conclusion
Bitcoin is likely trading at a discount. There are very likely less Bitcoins available than what the market currently understands. It is difficult to know exactly how many Bitcoins are permanently inaccessible or unavailable, but even in the highly probably “Nakamoto case”, nearly 5% of all Bitcoins are permanently unavailable. This suggests Bitcoins are trading at a discount of at least 4.92%.
p.s. If BTC reaches the market cap of gold ($9T), and the market accepts 40% of Bitcoins in circulation aren’t actually available to anyone, Bitcoins should trade for roughly $810,000/unit.
