LOS ANGELES — After flirting with the prospect of bringing Viacom Inc. and CBS Corp. together as one company, Shari Redstone on Monday abruptly pulled the plug on the proposed consolidation.

“Over the past few months, after careful assessment and meetings with the leadership of both companies, we have concluded that this is not the right time to merge the companies,” Shari Redstone and her father, Sumner Redstone, said in a letter to both firms’ boards of directors.

The Redstones control nearly 80 percent of the voting shares of both companies through their Massachusetts-based investment vehicle National Amusements Inc.

National Amusements President Shari Redstone, who is also vice chair of Viacom and CBS, this year has asserted her authority over the family’s holdings amid her 93-year-old father’s deteriorating health.

Initially, the Redstones viewed a merger as the best way to boost the value of Viacom, whose stock has fallen dramatically in the last two years, and make the family’s media empire whole again. The proposed consolidation was expected to be a crowning achievement for the aging media mogul — bringing together his sprawling media assets into one large company that could better navigate the challenges facing traditional media companies as consumer viewing habits change.

Shari Redstone was widely expected to tap CBS Chief Executive Leslie Moonves to run the combined company. However, the marriage broke down over proposed valuations for Viacom and Moonves’ request for autonomy running the combined company, according to three people familiar with the situation who were not authorized to discuss the matter.

Moonves had been seeking assurances to run the merged company as he saw fit because CBS is substantially stronger. Moonves wanted the power to make changes in Viacom personnel, and he wanted a board with whom he felt comfortable.

Moonves, at one point, favored a provision that any change in his status as chief executive would require a super-majority vote of the combined company’s board, according to one of the knowledgeable people. That would have diluted the Redstone family’s clout to make changes like it did earlier this year when it shook up the Viacom board.

Some Viacom board members were uncomfortable with such a measure, particularly after the Redstone family’s high-profile and expensive battle to unseat Viacom’s previous CEO, Philippe Dauman. However, another person said merger plans were halted before the two committees attempted to hammer out an agreement with Moonves to give him the latitude that he said he would need.

In the end, though, trying to put a value on Viacom’s shares proved too complicated. CBS board members did not want to punish their shareholders by paying too high a price for Viacom given the ratings declines at key networks and missteps at Paramount Pictures.

The Hollywood movie studio lost nearly $450 million in the last fiscal year, and its film pipeline has been meager.

Just before Thanksgiving, Viacom’s board committee made a case to CBS’ special committee members that Viacom’s shares were worth considerably more than current trading levels — and more than what CBS was willing to pay.

CBS wasn’t prepared to go above $38 to $40 a share for Viacom, which has lost nearly 50 percent of its value in the last two years.

News that the Redstones were abandoning the merger talks sent Viacom’s shares tumbling more than 7 percent to about $35 a share. CBS shares were down about 2 percent to $61 a share — still higher than a few months ago.

There were other factors, too.

Since the proposal was first made by the Redstone family in late September, Viacom directors named Bob Bakish as interim chief executive, and five new board members — installed in early September — have become engaged in the affairs of the media company. He is expected to be named the permanent CEO.

Shari Redstone, who has become more active in Viacom’s management, appeared encouraged by Bakish’s plans for Viacom and his energy in his first month on the job.

“Following the management changes that the Viacom board put in place, we have been very impressed with the forward-looking thinking and strategic plan being pursued under Bob Bakish’s leadership,” Shari Redstone said in the letter to the boards of Viacom and CBS.

Monday’s move was not particularly surprising, said Marci Ryvicker, media analyst with Wells Fargo Securities.

“We had been saying that the longer this took, the more likely a deal was NOT going to happen,” Ryvicker said in a research note.

“We think the underlying issue came down to value — we don’t know that either company was able to get to a valuation that made sense for their respective shareholders,” she said.

Guggenheim Securities analyst Michael Morris wrote in a report that Viacom’s success “will continue to hinge on the popular acceptance of the company’s television and film programming.”

“To that end, while we are incrementally optimistic on new programming leadership at (television networks) it is early in the process, and we remain cautious on the unchanged leadership at Paramount,” Morris wrote.

National Amusements framed the decision as increased confidence in Viacom’s new leadership and a belief that the two companies could thrive on their own.

“We know Viacom has tremendous assets that are currently undervalued, and we are confident that with this new strong management team, the value of these assets can be unleashed,” the Redstones’ letter said.

“At the same time, CBS continues to perform exceptionally well under Les Moonves, and we have every reason to believe that momentum will continue on a stand-alone basis.”