Kyrila and Sandra, I need to correct both of you. Sandra, it's not quite as simple as you describe for producing a major musical. For most of these shows materials must be rented, not purchased, and all fees paid up front before anything is shipped. The royalties are based on your number of performances, ticket price, and seating capacity. For our group, producing a major musical runs between $1500 and $2000 just for the rights, royalties, and materials. (This for 6 performances in a 210 seat theatre.)
Many shows are restricted from productions in certain areas or not available to amateurs, or have other restrictions limiting productions. For recent musicals like TITANIC, these restrictions apply if the show is currently running on Broadway, and in some cases if a professional company is touring the show.
TITANIC until recently has been a restricted show. However, Kyrila, it HAS been released during the past year for amateur productions. This announcement was made in the TAMS-WITMARK catalog for this season. If you visit the TAMS-WITMARK website you will find a "testimonial" from a high school other than the one you name.
We considered the show for this season, but it has a large cast including many young tenor roles, (Bride, Farrel, Barrett) so we decided the show is a bit out of our reach right now. I'll keep hoping, though!