How to Value Bitcoin

1. Unlike other instruments, there is no proven or accepted model for valuing bitcoin

The problem with pricing bitcoin in dollars is not that the market isn’t efficient. The problem is that there is no arithmetic model we can apply to say how many dollars a bitcoin is worth. Here, I try to offer a simple formula based on some reasonable assumptions that individuals can speculate about.

Valuation models are necessary to have any objective discussion about what some financial instrument is worth. With stocks, bonds, options and other derivatives it is straightforward to develop a formula based on the quantity and likelihood of dollars that those instruments are expected to return in the future.

A stock will pay dividends in dollars

A bond will pay coupons in dollars and then its face value in dollars.

An option will allow you to buy (or sell) a stock below (or above) the market price, in dollars, on or before its strike date.

But a bitcoin will never spit out any amount of dollars.

So how do we get to any precise way to value bitcoin?

Gold also doesn’t ever spit out a dollar. But an argument made by gold investors is that its value is what people will pay in dollars to make jewelry out of it or to use it in industrial applications. (Although they have no way of precisely valuing this. All we can know is that that is a lower value in dollars than the current spot price of gold, because the market isn’t paying those prices for that gold held as bullion.)

But bitcoins can’t be used to make jewelry, in industry, or for any application other than money. So we cannot look to gold — at least not in the ‘gold has non-monetary value too’ perspective.

2. Basing bitcoin value on its share of future use as money

But wait … A dollar will actually also never spit out a dollar. Its only value is its application as money. While we know that a dollar’s use as money declines because of inflation, we don’t know precisely the rate of inflation however because that is up to the issuers who themselves don’t know what the rate of inflation will be. (It’s worth mentioning that CPI and inflation are not actually one in the same.) We can nevertheless value a dollar based on its present and future purchasing power (and it is precisely because its purchasing power is declining that we now find it rational to spend instead of save).

So then the real valuation bet on bitcoin is foremost that it will be better at being money than dollars (and other monies) (at least for some people in some situations). It is thus in a market share battle against dollars and other ‘monies.’

To value bitcoin we need to know what the value of all ‘monies’ are and what bitcoin’s share of those monies is. Or rather, we need to know what the value of all ‘monies’ will be and what bitcoin’s share of those monies will be then too.

But when is this ‘then’? Well, it turns out it’s always further in the future because this definition is recursive. At any point in time, bitcoin’s value in dollars is always dependent on what its share of all monies will be further into the future.

However, we can get to a pretty decent valuation if we get to a belief of what its stable share will arrive at, and when that might be. Say, for example, you believe that bitcoin will get to one half of 1% of all ‘monies’ by 2025 and stay there forever. Say you also accept the $36.8 trillion number at worldatlas.com and don’t expect it to change at all over the next 5 years. And let’s say you’re 100% certain of that outcome and that your current opportunity cost for spending money (your discount rate) is 5%. So today you’d value bitcoin at (1% * $36.8 trillion)/(1.05)⁵ . This happens to be $144 billion, which is about what bitcoin is worth at the time I’m writing this.

The formula is simply:

where:

PVB = Present Value of Bitcoin: today’s value of all the bitcoins in circulation

SSoAM = Stable Share of All Monies: bitcoin’s share of the value of all monies in the future

SVoAM = Stable Value of All Monies: The stable value at that time in the future

DR = Discount Rate: the annual opportunity cost of money and the level of uncertainty of this outcome (the higher, the less certainty)

YUS = Years Until Stability: The number of years until this stability period is reached.

This formula is useful if you do foresee stability arising and think you can come to a reasonable expectation around when that stability will arrive and what it will be.

3. Applying this formula to your expectations

If you want to try to apply this formula to your own perspective, ask yourself these questions (and then plug the answers in).

1. What do you think is reasonable for bitcoin’s total share of all the money in the world to be? 1%, 5%, 10%, 25%, 55%, 100%?

2. How long do you think it will take until that share is achieved? 5 years, 10 years, 25 years, 100 years?

3. What will the total value of all the money in the world be then? (Or you could just use the supply number today and then you can inflate the answer you get later by what you expect the money supply to grow to). $36 trillion, $50 trillion, $100 trillion, $1 quadrillion?

4. What’s a reasonable discount rate to use given the risk of this outcome? 3%, 5%, 10%, 25%, 30%?

You can copy the formula below and just replace the letters with values into Google spreadsheets, Microsoft Excel or your browser’s address bar to get your answer. Note that SSoAM and DR are percentages so you should use “.01” for 1%. Also note SVoAM is a big number — in the tens of trillions to quadrillions even, so as a shortcut you may want to enter it in billions or millions and just multiply the result in your head by thousands or millions.

What to copy into your spreadsheet or browser:

= (SSoAM * SVoAM) / ((1+DR)^YUS)

4. Some sample conclusions:

Here’s a few interesting values this formula spits out:

Looking out ten years, if you think bitcoin can get to 5% of a worldwide supply of $50 trillion at that time, and are prepared to discount that at a rate of 10% back to now, you get a present value of bitcoin of close to, but just under $1 trillion ($964 billion).

Even further out, if you think bitcoin is headed to a 10% share of that worldwide monetary value, but that it will take it 25 years to do so, and in that time the worldwide total value of money is $1 quadrillion, then you’re looking at a present value of bitcoin of just under $1 trillion if you apply a 25% discount rate. But if you only apply a 20% discount rate to that then you get $2.6 trillion as the present value of bitcoin.

Now, because of the power of compounding, when you start to look out 100 years into the future, the discount rate becomes very sensitive. But if you assume, and rightly so, that there is a 100% likelihood of bitcoin becoming 100% of the world’s money supply in 100 years, which at that time will be worth $100 quintillion, then a 14.4% discount rate gets to you $143 billion which is exactly what bitcoin is worth at the time I’m writing this.