Can Elon Musk buy Twitter?

When Elon Musk lobbed in a $43 billion offer for Twitter, absent was any indication of how he might pay for it.

Would-be buyers—especially surprise ones who want to pressure a target’s board to capitulate—typically show up with the money in hand, or at least a guarantee from a bank that the funding will be there. Like so much else with Mr. Musk, however, the Tesla chief went a different route: His filing Thursday says only that the deal hinges on “completion of anticipated financing.”

Mr. Musk is very rich. His Tesla stake is worth some $176 billion. He has options to acquire millions more shares of the car maker. He also is founder of SpaceX, one of the world’s most valuable private companies. He could sell his stakes in those companies, but that would trigger big tax bills and reduce his control. Mr. Musk doesn’t take a salary from Tesla, and he has said in the past that he is cash poor.

That leaves borrowing, using his stakes as collateral. But even that would strain his finances.

Tesla allows executives to borrow against their stakes—but only up 25% of the value of the shares they pledge. Mr. Musk owned 172.6 million shares of Tesla as of Dec. 31, filings show, with options to acquire 60 million more.

If he could pledge all the shares he owned as of the end of 2021, he would be able in theory to borrow about $43 billion—just about the value he has put on Twitter. (Because he owns 9% already, he would need to come up with about $39 billion to buy the rest.) But as of last August, according to securities filings, he had already pledged 88 million of those shares for personal loans. That could reduce his credit limit.

Moreover, it isn’t clear whether a bank would even make a loan that big secured by a single stock, especially one as unpredictable as Tesla. In the past two months, the electric-vehicle maker has traded as high as $1,145 and as low as $764. Stocks that swing around wildly make for risky collateral because their value could drop quickly, leaving the bank with losses.

Mr. Musk said he has hired Morgan Stanley as his financial adviser, a bank known for top-shelf merger advice but not big loans.