Send a message to an entire group of recipients
One of the major flaw in this approach is that you wont have the option to remove a member from the group. If you want to you will have to send a new shared secret to each of the other members which is not very scalable if the group is large or the number of people leaving the group is large. 

There are a lot of ways to accomplish broadcast key distribution,
One of the methods is Logical Key Hierarchy (LKH). The basic idea of this scheme is arrange members at leaves of a key tree, each member receives keys on its path. In this scheme both entry and exit of members has low computation and communication overhead.