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nine_k a day ago

Big acts grossing colossal figures can continue that for a longer time. But the growth of the fee is exponential, while sales never grow exponentially for indefinite time. I can agree that the base of 2 may be too low; let's take 4 instead.

Let's assume that Dreamworks are so good that they get $500M a year for a particular IP. For 10 years they enjoy free coverage.

But even if on year 25 of coverage they would still have been making some money on the franchise, next year they go badly into the red.

The code:

  def fee(y): 
    return 0 if y <= 10 else 10 * 4 ** (y - 11)

  def total_fee(y): 
    return sum(fee(yy) for yy in range(1, y + 1))

  def total_revenue(years, yearly_revenue=500_000_000): 
    return yearly_revenue * years

  def balance(y):
    f = total_fee(y) / 1_000_000
    r = total_revenue(y) / 1_000_000
    return "%2d %8.1fM %8.1fM %6.1fM" % (y, f, r, r - f)

  for y in range(21, 27):
    print(balance(y))
Output:

  21     14.0M  10500.0M 10486.0M
  22     55.9M  11000.0M 10944.1M
  23    223.7M  11500.0M 11276.3M
  24    894.8M  12000.0M 11105.2M
  25   3579.1M  12500.0M 8920.9M
  26  14316.6M  13000.0M -1316.6M
As we see, the optimum total revenue is achieved after 23 years of protection, and then it goes down fast, turning negative on year 26.

And this is for a mega-popular franchise, that makes half a billion every year in a row for more than two decades. It's a very rare hit, comparable to Star Wars maybe, or the Mickey Mouse. Most IPs don't stay so staunchly popular for this long.

You can try playing with the parameters and check outcomes for different revenue shapes and fee bases.