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Book value is basically the net asset value of the company. BVPS divides this value by the OS.

One compares Book to market cap to determine over under valued. Or BVPS to stock price. A financial valuation vs. a fundamental evaluation seen in the P/E ratio.

Berkshire Hathaway Inc. Created a series A & B to open up ownership to those which couldn't afford the old common share price. (Actually I'm not sure if they are tradable series preferred shares or just two classes of common. I think common) Because Warren Buffet didn't want to forward split the historical prestige of the original stock. But wanted to give retail a chance to get in and also overcome a problem with gifting tax wise. I think when Warren Buffet created the 2 classes he determined the "B"s to be 1/30 of the "A"s. And they had 1/200 voting rights. A few years ago the "B"s had a 50 to 1 split which made the price difference 1500 to 1.

They should track well. Only varying due to the level of investment community involved in the different price levels. "B"s trade more and "A"s are more long haul.

As for why 1 is undervalued and another over valued, I'm not sure where you found that info. I thought fundamentals were only given for "A"s. And the "A"s have a BVPS of 120525 with a stock price of 168200.