• Twitter should accept Elon Musk's $43 billion bid because its stock is overvalued, Michael Nathanson said.
  • "It's the best outcome for the shareholders who've been buried in the stock for a long time," he told CNBC Monday.
  • Twitter stock could plunge 37% to around $30 a share if Musk walks away, the media analyst added.

Twitter should accept Elon Musk's $43 billion bid to buy the social-media company because its stock is overvalued, according to top media analyst Michael Nathanson.

"Twitter board, Twitter investors — take the money and run," Nathanson, senior managing director at MoffetNathanson, said in a CNBC "Squawk Box" interview Monday.

The research firm believes Twitter is overvalued by $20 a share, he said.

"If you look at the options they have on valuation, you'd say the stock is overvalued," the analyst said.

"And if [Musk is] willing to actually pay $54.20 [per share] and finance it — to me, it's the best outcome for the shareholders who've been buried in the stock for a long time," he added.

Musk's offer of $54.20 a share represents a 54% premium on Twitter's closing price on January 28, the day before he began buying into the company. It's also 38% above its closing price on April 1, the day before the billionaire unveiled his 9.2% stake in the company, an SEC filing shows.

Twitter stock was last trading 0.6% lower in Tuesday's premarket session at $48.16 a share, and is up 12% so far this year.

"If they walk away... if he walks away, the stock's going back down to $30," Nathanson said.

"So I think you have to engage [Musk]. You have to hope that you find another bidder. If you could, you get the price up. But the reality is the stock's overvalued," he added.

"It's always traded on kind of the option of being a better company, but not the reality of their business model, which has always been kind of disappointing."

Twitter would still remain under pressure even without a potential deal going through, because Musk's open criticism of the micro-blogging company would continue, the analyst said.

After Twitter appointed Musk to its board earlier this month, the billionaire said he would push for significant changes. After initially accepting the board role, he went on to reject it.

Musk has slammed Twitter for failing to "adhere to free speech principles," and has pondered creating his own social media platform that prioritizes freedom of speech.

He's also been critical of its CEO Parag Agrawal, using a meme to compare him to Soviet dictator Joseph Stalin.

"That's not going to end," Nathanson said of Musk's criticism. "He's really upset with their moderation policies."

Now that Twitter has adopted a "poison pill" approach to avoid a hostile takeover, analysts say one option Musk has is to find a strategic partner for the bid and increase it to about $60 per share.

"$60 would be a gift," Nathanson said.

Other private equity investors such as Apollo Global Management and Thoma Bravo have reportedly expressed interest in participating in a bid for Twitter.

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