Sumner Redstone is accustomed to lavishly overpaying executives who work for him. But board members at CBS and Viacom may justify their compensation if they can figure out terms to unite the companies that will satisfy the mogul and his daughter, Shari — who control 80% of the votes — as well as independent shareholders.

Investors have widely disparate ideas about how much the companies are worth. That suggests any deal terms will displease some owners who might argue that the Redstones — with interests in both companies — served themselves at other investors’ expense.

The Redstones yesterday called for the boards at both companies to explore an all stock deal. It’s easy to see why.

They have a problem at Viacom. Its networks have been losing eyeballs and advertisers — and the company will have a leadership vacuum after November 15 when interim chief Tom Dooley leaves. CBS seems to provide a tidy solution. It’s a programming powerhouse with a chief, Les Moonves, who’s widely considered one of the best in the business.

Even if he can’t work magic, a deal could make Viacom’s networks including Nickelodeon, Comedy Central, MTV, BET, and Spike more important to distributors trying to decide what services to jettison when they craft new skinny bundles. They’ll be reluctant to take on Viacom if they know it could also jeopardize their access to CBS’ must-have programming.

“Taken together, CBS and Viacom deliver a massive 23% of all national viewers…but are paid only 14% of the affiliate fee pie,” MoffettNathanson Research’s Michael Nathanson says. By uniting they could “rebuild and rebrand channels as [Fox] has just done with Fox Sports 1 and FXX.”

The Redstones probably made their deal pitch feeling confident that Moonves would agree to run a combined company (for God knows how much money), despite his recent comment that CBS is “happy with the position we are playing now.”

Yet the Street is split. For example, Wells Fargo Securities’ Marci Ryvicker says that Viacom “needs to be fixed – not slapped onto another [company]. The best way to do this, in our view, is to hire a CEO who is SOLELY focused on [Viacom] and who has the incentive and wherewithal to make big strategic change and investment.”

Drexel Hamilton’s Tony Wible also has reservations. “Merging the two companies could be disruptive and create animosity,” he says. A forced merger could distract Moonves from focusing on “the hit programs that are needed to sustain [CBS’] growth.”

And BTIG’s Rich Greenfield says CBS should pay a premium price for Viacom shares. He expects “Viacom’s relative performance to rebound notably in 2017 (as performance normalizes), with CBS pressured by a far tougher advertising environment year-over-year.”

Based on today’s closing stock prices, Viacom has a market value of $15.9 billion while CBS is worth $24.6 billion.

Are there terms that both companies’ backers might consider reasonable? Per usual, the devil’s in the details.

There’s a general consensus on a deal’s basic synergies — the antiseptic term often used for layoffs and budget cuts.

Analysts expect about $200 million in savings just by moving from two boards and management teams to one.

They’re also in the same ballpark when it comes to other cost savings.

RBC Capital Markets’ Steven Cahall said in June that a combined company could see $300 million by reducing spending for programming.

Nathanson uses a $400 million “placeholder” figure: Anywhere from $222 million to $333 million could come from a 40% to 60% cut in the combined companies’ corporate costs. Other targeted reductions could fall between $100 million to $200 million.

Morgan Stanley’s Benjamin Swinburne’s estimate falls around $450 million — although he adds that “it is an open question as to whether those would be offset by new investments to improve programming performance.”

Those numbers suggest that, if CBS wants to buy Viacom, it might have to take on debt — probably leading it to stop buying back its stock. That would displease shareholders who have liked the $8 billion the company spent over the last three years to improve the value of its shares.

What to do? The numbers might work if execs find more savings or revenue opportunities than analysts imagine. Or they could sell some Viacom assets and use some of the proceeds to repurchase shares, Barclays’ Kannan Venkateshwar says.

He believes the company could see about $1 billion by selling its interests in Epix, Channel 5 and a joint venture in India — and figures that Paramount could net at least $5 billion, and possibly more considering how much bigger it is than DreamWorks Animation which sold for $3.8 billion.

Brean Capital’s Alan Gould has another idea: Viacom should buy out CBS in an all stock deal that offers its investors a 25% premium over the stock’s 60-day average.

“CBS clearly has the upper hand,” he says. Viacom “needs the programming expertise and negotiating leverage of CBS. CBS is fine with or without [Viacom].” Yes, Moonves and his board would have to accept the terms. But “if the controlling shareholder of both companies wants the deal and Viacom makes an attractive enough offer, then we assume a deal can get done.”