Speculation that CBS Corp. might sell its outdoor advertising unit has been recycled so many times that UBS Securities LLC ran a research update this month under the headline "CBS Outdoor for Sale ... Again?" But why stop with outdoor? Why not sell CBS Radio, too, and take the rest of the company private?

This has been a dealmaker's dream since the dark days of 2009, when in March CBS stock slipped perilously close to $3 per share. Back then, of course, nobody had the cash or courage to entertain such a transaction. But the fact that the stock has recovered to trade above $30 per share shouldn't preclude CBS from reconfiguring itself in ways better suited to its overseers.

Few California-born executives are as "Hollywood" as CBS president and CEO Les Moonves, despite hailing from Long Island. Even 89-year-old Sumner Redstone, who's not only Moonves' boss but CBS's self-deluded "founder," has spent the better part of the past decade ensconced as an Angeleno.

Investment bankers are confident that, after orchestrating a take-private, CBS brass could still muster resources to pursue what has long been the apple of Moonves' eye (aside from Julie Chen, that is): acquire a movie studio, one along the lines of mini-major Lions Gate Entertainment Corp., the addition of which would transform half-decade-old CBS Films into a bona fide major.

CBS's investors might enjoy the ride, too. CBS Outdoor has long been perceived as divestiture material because, unlike other segments, it doesn't deal in content. Less recognized is outdoor's utter dependency on advertising -- a dependency the market severely punishes to offset the discretion afforded ad-budget managers on confronting economic uncertainty. (Remember that drop in CBS stock to almost $3 per share in March 2009? The fall began from $35.75 per share in July 2007 and retreated in lockstep with ad spending.)

In a report issued before the most recent speculation about CBS Outdoor even began, Todd Juenger of Bernstein Research identified the segment's sale as a good way for CBS to reduce its industry-high reliance on advertising. He then backed it out from his 2012 forecast, which lowered CBS's dependence on ads by 20% (to $7.5 billion from $9.4 billion) and reduced their contribution to CBS revenue to 58% from 64%. The lower beta, Juenger concluded, "could drive significant CBS share appreciation."

Going Hollywood would also require CBS to jettison Simon & Schuster. But that divestiture strikes Pivotal Research Group analyst Brian Wieser as relatively pain-free.

"We believe that publishing and outdoor businesses remain with CBS as financial assets rather than strategic ones," he wrote on initiating CBS coverage this month. "These two units are part of CBS for legacy reasons, but for as long as each contributes favorably to CBS overall and no buyer offers a compelling price, we expect them to remain inside of CBS."

Next up would be CBS Radio. "Moonves doesn't really like it that much," says a banker who expects CBS's 127 radio stations will eventually go, "but it delivers huge cash flows." A problem with CBS Radio, however, is the lack of transparency. Radio Ink magazine estimates the medium contributed $1.34 billion to total CBS revenue last year, whereas the company groups its radio revenue with that contributed by its 29 television stations in a segment called local broadcasting. This suggests radio accounts for 50% of the segment's revenue of $2.7 billion and 9% of total revenue of $14.2 billion.

As for buyers, sources acknowledge French outdoor advertiser JCDecaux SA's long-standing interest in CBS Outdoor's U.S. assets, although some think private equity might back a run by well-respected though smaller Van Wagner Communications LLC. Simon & Schuster may have "been available for years," as one banker puts it, but the emergence of e-books could renew demand in an old-line publisher with a backlist waiting to be digitized. As for radio, Cumulus Media Inc.'s take-out of Citadel Broadcasting Corp. last year demonstrated the return of consolidation in a big way.

Moreover, a sum-of-parts analysis indicates the three businesses impeding CBS from becoming a purer Hollywood player account for 27% of an enterprise value of $26 billion. Their sale would make a swell down payment, obviously, to set up the rest of a take-private play. Then, with the addition of Blackstone Group LP or Kohlberg Kravis Roberts & Co. LP, CBS's script would have all the elements for a Hollywood ending.

Richard Morgan covers media for The Deal magazine.