You do not need a license to broadcast. However, per the laws in your country, you may be responsible for paying royalties and licensing fees for each song played.
In the United States, for instance, ASCAP, BMI, SoundExchange & SESAC require payment for all of their artists. One way to reduce cost is to subscribe to a service that provides payments to these organizations at a discounted rate. In the United States, StreamLicensing.com offers such umbrella packages. Your country of residence may have different and/or additional legal requirements.
Updated: Mar. 17, 2014
