The increasingly-fragile nature of Rupert Murdoch’s hold on News Corp. has refocused attention on its dual-class share structure. As John Gapper noted last week, such structures aren’t particularly good for minority shareholders like you or me. And if you plug today’s share price into the Breakingviews Murdoch discount calculator, you’ll see that the company is trading at roughly 30 percent below its fair value.

Or, to put it another way, if Murdoch and his voting control were to disappear tomorrow, the shares could jump a good amount.

Murdoch has a seemingly inviolable 39.7 percent position in the Class B voting shares of News Corp. No one else comes close: The only other shareholder with more than 2 percent of the Class B stock is Prince Alwaleed, with his 7 percent stake. The Class B shares are exactly the same as Class A shares, with the single difference that Class B shares have voting rights at the annual meeting and Class A shares don’t. Both classes of share trade on the Nasdaq; here’s a chart of how they’ve behaved over the past few years.

The blue line is the B shares, the red line is the A shares and the yellow line is the difference between the two. It’s currently about 45 cents per share, down from a high of $2.60 per share in April last year.

Why do the voting shares trade at a premium, if Murdoch always gets what he wants in any case? One reason is that if Murdoch’s successor wants to adopt a single share class, the holders of B shares will want to be paid a premium for allowing that to happen. Another reason is that Murdoch himself is only interested in voting shares: If and when he looks to increase his own shareholding in News Corp, it’s the B shares he’s going to buy, and he’ll happily pay a premium to do so.

But still, the fact is that Murdoch has only about a 12 percent interest in News Corp, and less than a 40 percent voting interest. What would happen if an aggressive corporate raider of some description came out with a knockout bid for the company at say $23 per share? Such a bid would come straight out of the Murdoch playbook — it’s how he bought Dow Jones. And even if Prince Alwaleed stuck loyally to Rupert’s side, the rest of the voting shares could end up approving the deal.

What’s more, under News Corp.’s certificate of incorporation, the holders of A shares do actually have a vote in the event that there’s a vote on a takeover bid which would change control of the company. (See section 4(a)(i)(C).)

News Corp. would not last long in its present format were any takeover bid to prove successful: It would surely be chopped up and sold off in pieces. But that just makes it that much more attractive to corporate-raider types — there’s a pretty predictable going rate for the cable, TV, and movie-studio assets, and even the newspapers would likely spark an interesting bidding war. I can certainly see Roger Ailes easily lining up funding to buy Fox News and turn it into an independent company.

None of this is exactly likely — for one thing, there are precious few bidders out there with the wherewithal to raise $60 billion or so in takeover funds for a media company. In its decision today to put News Corp. on ratings watch negative, S&P didn’t say anything about the risk of a leveraged buyout. And frankly you’d need to be more than a little crazy to enter into a hostile takeover bid against Rupert Murdoch.

But there’s one final twist here: Rupert Murdoch is adamant that he doesn’t actually control 39.7 percent of the Class B shares. Indeed, his personal holding is decidedly modest, at just 1.3 percent of the Class B shares. The other 38.4 percent belongs to the Murdoch Family Trust. Here’s what the proxy statement has to say about all this:

Cruden Financial Services LLC, a Delaware limited liability company (“Cruden Financial Services”), the corporate trustee of the Murdoch Family Trust, has the power to vote and to dispose or direct the vote and disposition of the reported Class B Common Stock. In addition, Cruden Financial Services has the power to exercise the limited vote and to dispose or direct the limited vote and disposition of the reported Class A Common Stock. As a result of Mr. K.R. Murdoch’s ability to appoint certain members of the board of directors of Cruden Financial Services, Mr. K.R. Murdoch may be deemed to be a beneficial owner of the shares beneficially owned by the Murdoch Family Trust. Mr. K.R. Murdoch, however, disclaims any beneficial ownership of such shares.

If Murdoch’s children — the beneficiaries of the Family Trust — come to the conclusion that either they won’t or that they don’t want to inherit News Corp as a monolithic entity, then it’s conceivable that even Murdoch’s own stake in the company might not automatically vote against a compellingly high bid. Certainly a breakup and cash-out would make the fraught question of who inherits what a lot easier: At the moment there’s quite a lot of tension surrounding the question of what exactly will end up going to Murdoch’s two youngest daughters.

All of this is highly speculative, of course. Murdoch’s parliamentary testimony Tuesday could have been a disaster, giving independent directors or his family cover to drop their support and making News Corp seem vulnerable to takeover. Fortunately for Murdoch, that didn’t happen.