One, a business can support a product line that produces a net loss as long as there are enough profits to balance those losses against elsewhere. An example I remember was when I worked for a hotel that had a "poolside bar"; this was not a swim-up bar in the pool but a standing bar adjacent to it. That bar never sold enough beer, wine, sodas or juices to pay for it's expenses...but it was a hotel in Scottsdale, Arizona - at the time a very tourist oriented city - and having drinks served poolside was an expectation, so the bar would be open every day until they closed and demolished the hotel.
Two, while many are assuming that CBS wanted to make a profit on the Late Late Show the loss of money seems like a bad thing...unless the goal of certain people was something other than to "make money". Many of us think that mainstream media skews the writing on shows to shore up perspectives and ideologies of one "side" or the other (FOX News is right-wing, most of the rest are left-wing, etc.); add to this that this show was a legacy show, having it's beginnings in 1995 with Tom Snyder (formerly of "The Tomorrow Show") and there are likely other reasons besides a simple profit motive for this show to be kept on the air while costing more than it made for the company.