The difficulty of estimating the cost of a Ubuntu release without any information from Canonical is shown by the differences in the calculations of how much a release would cost if made from scratch.
In 2007, Wayne Richardson calculated that, if a Ubuntu release was made from scratch, then the cost would be just over 7 billion dollars. (By contrast, the same method applied to Debian by James E. Bromberger in 2012 came up with a figure of $19.1 billion, but Debian carries more packages and supports more architectures than Ubuntu.) However, commenters on his figures came up with estimates of $250 and $350 million. All these estimates would require an additional 10-12 percent to bring them up to date, but such great variations can hardly be reconciled.
At any rate, all these figures would need adjustments for the fact that Ubuntu is not made from scratch. Ubuntu receives most of its software from Debian, which in return receives them from upstream projects such as the Linux kernel or LibreOffice. What remains is general coordination, such as packaging and checking dependencies and installation scripts, at least some of which is done by volunteer members of the Ubuntu community.
Fortunately, other approaches are more promising. The About page of the Canonical website notes that the company has "over 500 staff." Since the figures are approximate, we might as well round them down to make them as conservative as possible, so let's assume 500 employees, each with an average salary of $70,000. These figures would put Canonical's labor costs at $35 million per year. Half that for Ubuntu's twice yearly release, and each release might be said to cost about $17.5 million.
However, not all of Canonical's staff are directly engaged in producing Ubuntu's releases. Some are involved in sales, marketing, administration and business development. But how many?
In 2010, Ubuntu Community Leader Jono Bacon mentioned that Ubuntu employed about 70 developers. Add an arbitrary fifty percent to that figure to take in non-coding contributions to a release, such as documentation, localization and artwork, and the salary bill is about $7.3 million a year. Half that, and each release carries a price tag of $3.65 million for development.
This figure is high enough by itself. Yet in addition to the usual responsibilities of assembling a distribution, for at least three years, a special Design Team has been working on general branding and the Unity interface. This design team was said in 2009 to consist of 14 people, "who comprise a mix of different disciplines: visual/graphics designers, interaction designers and technical people."
Many members of the design team are consultants, so they probably earn more than average staffers at Canonical. However, even using the same salary average as everyone else, the 14 members of the design team (assuming their numbers have remained constant) must cost at least $525,000 per release -- a 14 percent addition to the total. This cost might be justified as necessary to give Ubuntu a distinct identity and interface, but is a considerable addition to the cost of a release.
On top of salaries, Canonical also has infrastructure costs. The company has also been consistently generous over the years about paying for employees and community volunteers to attend conferences and assisting projects that fit its plans. However, information about those expenses is completely unavailable.
The best that can be done is to add another arbitrary estimate to the salary figures. The result? An estimate of $3.8-4.2 million for each Ubuntu release.
Or to put the cost in terms of one of Ubuntu's desktop services, to make a release pay for itself, Canonical would have to sell over 200,000 music CDs to break, even if it received the full profit on each one. But of course, Canonical only has an affiliate deal to stock its store, so the number of necessary sales would be actually be several times higher.
Assuming that these figures have any validity (and they may not), then not only can no single desktop service pay for Ubuntu's development cost, but not all of the desktop services combined.
The figures are nowhere near close enough for Canonical to have any reasonable chance of making Ubuntu profitable by itself. The most it can do is to defray the costs to whatever extent is possible -- which, most likely, isn't much. If as much as 15-20 percent of the development costs were defrayed, then Ubuntu would be doing extraordinarily well.