The DKK is 14 cents to the US dollar Greenland if not supported by Danish is in the dumpster in short order.
The annual state grant (the so-called block grant) and the expenses the Danish state has in Greenland (Greenlanders and Faroese don’t pay towards the budget of the state, so that’s all paid for by Danish taxpayers) is generally estimated by researchers to roughly equal the profits Danish businesses and publicly owned harbours gain from exports to Greenland, the profits Danish fishing companies make in Greenland (not that much) and the profits from processing Greenlandic fish and seafood in Denmark. So if you think of “Denmark” as a country it doesn't cost it anything, if you think of the Danish state it’s less than 1 billion USD annually, but hard to say precisely, and the taxes from the profits mentioned above should be deducted.
In 2015 Greenland cost slightly below 4.3 billion DKK based on the state grant of 3.7 billion DKK plus the functions the Greenlandic government could choose to administer, but so far hasn't taken over (that includes the judicial system and correctional facilities). You can then add the costs of Danish military presence in Greenland, the foreign service representing Greenland abroad and the Arctic Council etc. The defense costs for Greenland amount to approximately 700 mio. DKK a year (and rising), but it’s hard to separate them completely from other defense costs (e.g. the Arctic Command in Nuuk is also responsible for the Faroe Islands).
A bit above 5 billion DKK a year is probably the best estimate, maybe close to 5.5 billion as prices have gone up since 2015 (Greenlandic inflation is above the Danish). As mentioned above the taxes of the profits from Greenland related economic activities in Denmark should then by deducted, but I have no reliable numbers for that. If you want to deduct income taxes from employees working in Greenland related companies the calculation becomes even more complex.
In general the societal cost, which is close to zero, is considered more important by Danish politicians than the cost of the state. The benefits of easier access to political leaders from great powers and networking opportunities related to the Arctic cooperation then make the benefits exceed the costs. But it’s hard to put a price on that.
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Dazed and confused.............the fog is closing in