Here's the pitch on autonomous vehicles: They could completely reshape the economics of ride-hailing, and Uber Technologies Inc. (UBER) and Lyft Inc. (LYFT) are sitting in prime position to benefit.

Bank of America Securities analyst Justin Post argues that AVs have become "a central focus for investors" in mobility stocks, and for good reason. Americans drive roughly 3 trillion miles every year, according to Federal Highway Administration data. Uber and Lyft currently capture a mere 1% of that massive market.

But here's where it gets interesting. If driverless vehicles can slash the cost per mile and adoption goes mainstream, Post thinks AV ride-hailing could grab 20% of annual U.S. vehicle miles traveled over the next 15 years. At an estimated $1.50 to $2.00 per mile, that translates to a market opportunity worth $900 billion to $1.2 trillion in the United States alone.

The Ratings: Post maintains a Buy rating on Uber with a $119 price target, while rating Lyft Underperform with a $19 target.

The Growth Math: If Uber successfully integrates autonomous vehicles into its platform, the analyst projects U.S. mobility bookings could grow at a compound annual rate of 13% to 20%, depending on whether the company captures 30% to 70% market share.

There's a legitimate concern that cheaper AVs might squeeze margins, but Post believes Uber can maintain its U.S. mobility margins around the 10% level even in an autonomous future.

Price Action: Uber shares declined 3.88% to $88.98, while Lyft dropped 2.67% to $21.89 at the time of publication on Tuesday.