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In the US, minting coins is quite definitely a profit-making proposition for the government, and in conjunction with a mass-marketing venture such as the one planned for the Artemis Project, minting coins could be a profitable venture for us, too.
A few factors:
The cost of the materials in even the largest coins (excluding precious metals) is negligible. The one-cent coin was changed from mostly copper to copper electroplated over zinc in 1982, when copper prices were rising. The cost of no other coin's metal is anything above 15% of face value.
The total cost of producing the coin (material and manufacturing) subtracted from the face value is the "seniorage." The US government makes quite a lot of money on this (ever since coins started only representing money, rather than being made out of precious metals and actually worth something).
When the mint sells coins to collectors, either proof sets, mint sets, or commemoratives, the mark-up over face value is enormous. In 1999, the Mint sold Proof Sets for $19.95 (for $1.91 face value, plus an attractive case) and Mint Sets for $13.95 ($3.82 face value). These sets include copies of all 5 reverse designs for the quarter (part of the 50 states quarters program). The previous rates were about about $15 for $.91 face value Proof Set, and $9 for the $1.91 face value Mint Set. Commemoratives go for outrageous sums, depending on content, number of designs, and perceived popularity.
Ever since the Mint started offering pre-issue discounts, they get a much better idea of how many they're going to sell, and can produce numbers that tend to match. Also, since these are all collectors' items, unsold inventory appreciates in value, and will sell eventually.
The program may have had an axe to grind, but selling collectors' coins has always been profitable for the US government. Why else would all those other countries be doing the same thing? (You must have surely seen the ads for commemorative coins from tiny Pacific island nations--coins commemorating the US space program and everything else.)
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