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The break-even point is really hard to judge, because it will vary wildly depending on how much of the production and advertising get covered by things outside the box-office haul (many of which you already mention: product placements, advertising partnerships, tax breaks, merchandising, home video, streaming, TV broadcasting, etc), not to mention advertising itself isn't included in the budget. The amount that the studio takes from ticket receipts will also vary; they usually make more off opening weekend sales than subsequent weeks and the amount they get internationally will vary (not to mention China is notoriously difficult to deal with, so despite being a huge market the studios can have trouble making money there). So, if you look at it like this:
Budget: $250mil
Advertising: $200mil (typically 50-150% of budget)
Opening Weekend Take: $132mil (somewhere around 60% of sales)
Full Run Take: $72mil (somewhere around 40% of sales, estimated $345mil domestic total)
International Take: $130mil (around 25% of sales, estimated 40/60 split for $518mil international total)
That leaves $116mil to be covered by other avenues. That's not an insurmountable amount, but if it weren't for costs being covered by things outside just tickets the movie would probably be a money loser (which is actually going to be true for most films).
I've read numerous places that BvS had a 420 million production budget, is that true?