NEW YORK (TheStreet) -- Time  (TIME)  turned down a bid from billionaire investor Edgar Bronfman Jr., the New York Post reported earlier today. 

"There's a lot of speculation about anybody who's in print that the change is pretty dramatic. We're doing some work for another magazine company that's a private piece of work," Methuselah Advisors managing partner John Chachas said on BloombergTV's "Bloomberg Markets: Americas" on Monday afternoon. 

The boards of media companies have to "look dutifully at well-financed proposals that create shareholder value," he added. These companies will have to decide whether to turn down cash bids at significant premiums.

"I think there are times when that's perfectly warranted," he noted. 

The merger possibilities for the sector represent "hundreds of millions of dollars" in synergy, Chachas claimed. "I think the investors in these companies are going to demand that the boards be really, really scrupulous in their analysis."

However, studies have shown that all the digital media growth is concentrated in Alphabet's  (GOOGL) Google and Facebook  (FB) .

If the studies are true, then we may have hit a "new plateau," he said. Digital media may not be the "nirvana" people said it would be in the future. 

Going forward, investors will have to look at what things young people want - such as Snapchat's new video-recording glasses called Spectacles, Chachas said. 

(Alphabet and Facebook are held in Jim Cramer's charitable trust Action Alerts PLUS. See all of his holding with a free trial here.)

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