I believe your equation here has a misplaced variable. Instead of number of stars born annually," it's supposed to be number of stars in the galaxy. That would radically change the final estimate. See Carl Sagan's demonstration: <a href=""https://www.youtube.com/watch?v=2s1qTUqOv88"">https://www.youtube.com/watch?v=2s1qTUqOv88</a>. His conservative estimate still comes to millions of civilizations in our own galaxy."