I cannot find any current data, but back in 2011-2012 when Japan was considering fully privatizing its metro systems, reports were that they were profitable.
Tokyo Metro, which carries more than 6 million passengers each day over a 195 kilometre network of tracks, posted a 36.8 billion yen net profit for the financial year ended March 2011 on sales of 372 billion yen.
And this does not seem uncommon for Tokyo's system::
According to a Tokyo Metro public relations representative, 6.33 million people on average used Tokyo Metro’s nine subway routes, which together have 179 stations, on a daily basis in fiscal 2009, when it logged a profit of ¥63.5 billion.
Tokyo’s other major subway company, Toei Chikatetsu, which hosts four lines and is operated by the Tokyo Metropolitan Bureau of Transportation, averaged 2.34 million passengers per day in 2008, and made a profit of ¥12.2 billion in 2009. Toei Chikatetsu has 106 stations.
But despite the figures, both companies had long-term debts, ¥735 billion for Tokyo Metro and more than ¥1.1 trillion for Toei Chikatetsu, in fiscal 2009 — a result of the enormous sum necessary to construct and maintain their lines.
The Osaka Municipal Subway made a Y167.7 billion profit in the 12 months to March 31, and carried debt of Y597.6 billion.
Both have pretty old infrastructure, comparable in age with Moscow's. Do note however the issue of long-term debt, for all the Japanese examples. This is unlike HK's but the latter has had a unique corporate structure...
Since the HK metro is an accepted answer, it bears reminid how it differs from almost any other metro (except one being built in Shenzen).
According to a 2015 CNN article, "How Hong Kong's subway turns a $2 billion annual profit" which frankly sounds quite astounding... but
How does Hong Kong's train and bus network manage to clear its mind-boggling margins?
First off, this is one impressive subway system. Even with more than 5 million daily commuters, MTR trains boast a 99.9% on-time arrival rate. Fares are notoriously cheap ($.50 to $3), but cover roughly 175% of the system's operating costs.
But the company's real profits are derived from a lesser-known side of the business: property development. Some 50 major properties across Hong Kong are owned, developed or managed by MTR, including two of the city's tallest skyscrapers.
"Sometimes critics say it's a property development firm doing a side business of rail," said Tim Hau, a professor at University of Hong Kong's School of Economics and Finance.
And more about the corporate model, now being emulated in Shenzen as well:
The most successful metro system in the world, in terms
of profitability, is probably Hong Kong’s Mass Transit
Railway corporation (MTR). By itself, that is not surprising.
The system moves about 5 million people a day,
roughly the same as the London Underground, but it
has around half the track length to maintain: 210km
compared with London’s 400km. What is surprising is
the sheer scale of the difference. Although the level of
MTR’s fares is around a third that of the London or New
York systems, it made a profit of $2bn (£1.5bn) in 2015,
news website CNN Money reported on March 30, 2015.
By contrast, Transport for London covers only £4.8bn of
its £10.2bn budget from revenue, according to figures on
its website, and New York spends $2.5bn (£1.9bn) just to
service its debt, according to CNN Money. [...]
The reason for this extraordinary financial performance
was explained last June by Lincoln Leong,
the chief executive of MTR, in an article he wrote for
McKinsey, a business consultancy (Leong 2016). This
attributed the corporation’s success in large part to a
development finance model called “rail plus property”,
or R+P. The idea behind R+P is the easier-said-than-done
principle of capturing the rise in property values
caused by a new metro line. Building underground
railway systems is a notoriously expensive business but,
even so, construction costs can be considerably less than
the gross value uplift. In the case of London’s Crossrail
system, for example, the development cost was £14.8bn
but the total increase in property prices around its stations
has been put at £35bn (CBRE, 2016). MTR has
become adept at capturing this uplift.
The system, as explained by Mr Leong, works as follows.
For new rail lines, the government of Hong Kong
provides MTR with “development rights” in the vicinity
of its stations. If it chooses to exercise these rights, MTR
pays the government the land’s market value without
the railway and makes its profit from the higher value
of the land with the railway. To maximise this revenue,
MTR tenders for a private developer to partner with,
builds an asset and takes a portion of the resulting sale
or rental income. This then provides the money to keep
the system operating with its celebrated efficiency as
well as proving the capital for further extensions, sparing
MTR from having to compete with every other
public agency for state funding. For example, revenues
from R+P developments along MTR’s Tseung Kwan O
line, opened in 2002 to serve a new town in the New
Territories, financed the entire £300m cost of the work.
And a somewhat crticial US/NY perspective, which roughly shows under what conditions metros can be profitable:
Detailed comparative analyses of New York City subways and four Southeast Asian transit
systems revealed that Hong Kong’s subways are profitable because of high asset productivity
resulting from a strategic “prudent commercial” design for high utilization and traffic density, a
land-grant financing framework, more commercial freedoms, lower overhead costs and asset
replacement needs. Conversely, Singapore and Taipei’s subways are operated by concessioned
carriers (akin to New York’s historic IRT and BMT) and not actually profitable when
government-provided initial capital construction funds are accounted for at typical government
bonding interest rates. Infrastructure ownership was separated to attract investors and allow
government-controlled carriers to function as quasi-private entities. Network design choices
with consequences in density and utilization explain the higher productivity in Asia. New
York’s system was not designed for maximum capital and operating cost-efficiency or
productivity but to provide high coverage and service levels at lower traffic densities in a
socially conscious and inclusive approach, whereas Taiwan and Singapore governments made
design decisions and chose governance structures that enabled higher productivity.
comparisons in performance, profitability, and productivity should be avoided unless care is
taken to analyze impacts of governance, social contexts, design criteria, and reasons for their
differences. Nonetheless, comparisons and benchmarking can yield valuable insights for
operations improvement under prevailing local constraints.
Basically amortizing the initial investment is really difficult for most metro projects. Do we consider for example that the Moscow metro was built in part with forced labor? Or that its construction meant causing starvation in other parts of the coutry?
The construction of the Metro was a major priority for Stalin, who saw it as a way to demonstrate the superiority of socialism over the capitalist world, which at the time was deep in the Great Depression.
The thousands of workers who dug the first subway needed to be fed, along with the tens of thousands who built massive steel plants and tractor factories during the same time. And the Soviets needed hard currency to buy foreign-built machinery for their new industries.
That meant taking the Soviet Union's grain harvest from the farming regions and leaving the people on the farms to starve.
If you consider grandafathered-in infrastrucutre not entirely built on market-economy terms, it's somewhat easier to claim profitablity.