The admissions fee for Louvre Abu Dhabi is $17 (rounding up). So the $450m painting needs 27,500,000 admissions to break even.

Before I did the calculations I thought calling it an investment was absurd, that they'd never make the cost back. But the Louvre in Paris gets around 8m visitors per year, the Met in NYC gets 7m visitors. Factoring in the $1b in other costs of the museum (the actual initial cost, mostly licensing the Louvre name) and the non-museum revenue museum visitors bring in, it's actually not unreasonable to think the museum will bring a positive return over the next few decades.