Stephen Colbert’s announcement on Thursday night that “The Late Show” was being canceled by CBS stunned the entertainment industry, the public and even his staff.

But the writing had been on the wall for some time.

“The Late Show,” a fixture of the network for over three decades, was racking up losses of tens of millions of dollars a year, and the gap was growing fast, according to two people familiar with the show’s finances. Like other late-night shows before it, “The Late Show” was canceled when the network could not figure how to make the finances work in an entertainment world increasingly dominated by streaming.

So as CBS executives mapped out the schedule and budget for next year, George Cheeks, CBS’s president, decided in recent weeks that the network couldn’t take those losses any more, the two people said. Mr. Colbert learned of the decision on Wednesday night. Shari Redstone, the controlling shareholder of Paramount, CBS’s parent company, learned about it on Thursday, according to two other people.

The cancellation underscores just how rapidly the late-night genre has fallen. Not even “The Late Show,” the highest rated of those network talk shows, was safe, as many in the entertainment industry assumed it was.

Nevertheless, questions lingered on Friday about whether political calculations — not strictly financial ones — had played a role in the decision as well.

Paramount is closing a multibillion-dollar merger with the movie studio Skydance, a deal that still requires approval from the Trump administration. Early this month, Paramount agreed to pay President Trump $16 million to settle a lawsuit over an interview on CBS’s “60 Minutes.” Mr. Colbert, a longtime critic of Mr. Trump, called that settlement “a big fat bribe” on his show this week.

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