I’m a big fan of crypto “currency.” I am convinced that Bitcoin or a similar system will afford a new class of open infrastructure apps. These apps will be profoundly disruptive, driving down costs for consumers and devastating incumbents’ revenue streams. They will do for payments—and possibly other categories—what open source has done to enterprise software over the last 15 years.

A few days ago, Fred Ehrsam’s excellent piece on Bitcoin in Recode. Fred observes that Bitcoin will eat the payments industry (one can hope) and suggests one method for valuing bitcoin:

In the present, the value of bitcoin as a currency can be viewed as the sum of the cost savings of using the bitcoin network for payments rather than alternative payment networks.

I don’t think this is right. This is the upper bound on the value of bitcoin, but not the lower bound. If Coinbase owned bitcoin and could control the value, they’d price it to lower costs by 50%, kill Visa et al, make $250M a year, and buy yachts. But they don’t.

A better way to arrive at a valuation is by looking at how it would be used to facilitate payments at scale, and asking what the value would need to be. Bitcoin is volatile fuel for financial transactions. Because of this, institutions who were only interested in using it for payments (and not stored value) would have as little as possible on hand at all times.

Eventually it’s likely users of bitcoin would buy and sell it in realtime on efficient exchanges to meet transaction demand. This suggests that the long-term price will be a function of realtime demand.

If this is the case, **the price of bitcoin will ultimately settle at the value of fiat currency (C) that needs to move somewhere per minute, multiplied by the average number of minutes needed to clear a transaction (M), over the average number of bitcoins available for trading (A)**. That’s: C*M/A.

Let’s break that down and get a little more precise and try to plug some numbers into this formula. First, on currency, let’s assume that Bitcoin becomes as big as Mastercard. Mastercard represent about two trillion dollars transferred annually, or around $4M per minute.

An interesting property of the Bitcoin protocol is that it takes around 10 minutes to verify a transaction on average. Assuming transactions are evenly distributed, the average transaction takes about five minutes to clear.

The final variable above (A) is the number of Bitcoins in circulation. The theoretical maximum this can be is 21 million bitcoins, but this isn’t the number that matters. We care about the number “in play.” Since bitcoin are lost forever when someone loses their key, hard drives crash, or are temporarily out of play as speculators and Liberatarians hold them, etc. it’s likely that the practical number will be much lower. Let’s use 10M to make the math simple.

So, in the example above, if you replaced the Mastercard payment system with bitcoin, each bitcoin would have a value of $4M * 5 / 10M, or $2. If you add in Visa, Diner’s Club, Discover, and American Express the number jumps to around $6.

I couldn’t easily find numbers on interbank (et al) transfers, so we’ll let the HackerNews figure out how that factors in. Assuming it’s 10x the payments number, this still puts the long-term value of bitcoin at $60, an order of magnitude less than it’s trading at today.

Of course there could be other applications for bitcoin outside of payments that further increase demand. However, payments is the killer app and it’s hard to see how bitcoin maintains a utility value anywhere near current prices.