With Bitcoin (BTC 0.33%) turning in its best January performance since 2013, it's no surprise that analysts are ratcheting up their price targets for this suddenly hot crypto. Bitcoin was up nearly 40% in January, and that has led to a completely revised outlook for just how high this crypto could fly in coming years.

Cathie Wood of Ark Invest -- known for her previously controversial $1 million price target for Bitcoin -- has just ratcheted up her Bitcoin price prediction. She now thinks Bitcoin could skyrocket to $1.48 million by 2030. But just how feasible is that prediction?

The long-term growth story for Bitcoin

According to Wood, the case for Bitcoin at these stratospheric levels is really a story of enormous growth on a global scale. Over time, the story goes, Bitcoin will account for a larger and larger share of global assets held by institutions. It will continue to scale globally as more nations accept it as legal tender, and as more people use Bitcoin to carry out online transactions.

This story gets more interesting when Ark Invest lays out the specific numbers behind its assumptions. Ark Invest suggests there will be eight primary market segments (e.g., "emerging market currency" and "remittance asset") where Bitcoin will see growth. Based on estimates about the penetration rate for Bitcoin in each of those markets, it is possible to develop a bearish, a base case, and a bullish scenario for Bitcoin's price.

How fast can Bitcoin grow?

So, for example, Ark Invest suggests that Bitcoin could account for up to 10% of the M2 money supply of emerging market countries. Thus far, there are only two nations that have adopted Bitcoin as legal tender -- El Salvador and the Central African Republic -- so this seems a bit optimistic. According to some economists, nations that struggle with hyperinflation or devalued currencies could decide to embrace Bitcoin.

Ark Invest also suggests that Bitcoin could capture 25% of the "remittance asset" market, and 50% of the "digital gold" market. So, imagine one in four migrants around the world sending money back to family and loved ones in the form of Bitcoin, and one in two central banks around the world deciding to build their Bitcoin reserves instead of their physical gold reserves. In addition, Ark Invest suggests that Bitcoin will soon account for 6.5% of institutional investor portfolio holdings.

All of these numbers are aggressive, but not entirely unthinkable. It really depends on how you view global growth, and how much faith you have in fiat currency.

From my perspective, the "base case" estimates provided by Ark Invest make a lot more sense than the "bullish case" numbers. For example, in a base case scenario, Bitcoin will only account for 3% of the M2 money supply of emerging market countries. And Bitcoin will only account for 2.5% of institutional investor portfolios. The problem here is that even Ark Invest acknowledges that these "base case" assumptions only support a future price of $682,800 for Bitcoin, well below the pie-in-the-sky figure of $1.48 million.

Do the numbers make sense?

Moreover, it's helpful to stress-test these assumptions about Bitcoin against current asset values in global markets. Given that Bitcoin has a fixed coin supply of 21 million, a target price of $1.48 million implies a total market capitalization of $31 trillion.

Just how big of a number is that? Well, the total value of the world's physical gold supply is estimated to be worth about $12 trillion, so Bitcoin would be worth more than 2.5x all the gold in the world today. Moreover, the total value of the S&P 500 is approximately $32 trillion. So, Bitcoin would be worth almost the same as the 500 largest publicly traded companies in America today.

For that reason, I don't think $1.48 million is a reasonable price target for Bitcoin. Even a $1 million price target seems to be a bit of wishful thinking on the part of the Bitcoin bulls. That would imply a market cap of $21 trillion, which is nearly 10x the current market cap of Apple. Would you rather own all the Bitcoin in the world, or all the equity in 10 different Apple corporations?

While I'm long-term bullish on Bitcoin, I also think it's important to have a sense of scale here. If Warren Buffett thinks the value of all the Bitcoin in the world isn't even $25, and Cathie Wood thinks the value of all the Bitcoin in the world is $31 trillion, a rational person would say that the real value of Bitcoin is somewhere in the middle. I'm bullish that Bitcoin will eventually regain its $1 trillion market cap -- I just think it will take longer than some people think.