Generative Artificial Intelligence (GAI) models such as ChatGPT have experienced a surge in popularity, attracting 100 million active users in 2 months and generating an estimated 10 million daily queries. Despite this remarkable adoption, there remains a limited understanding to which extent this innovative technology influences higher education. This research paper investigates the impact of GAI on university students and Higher Education Institutions (HEIs). The study adopts a mixed-methods approach, combining a comprehensive survey with scenario analysis to explore potential benefits, drawbacks, and transformative changes the new technology brings. Using an online survey with 130 participants we assessed students' perspectives and attitudes concerning present ChatGPT usage in academics. Results show that students use the current technology for tasks like assignment writing and exam preparation and believe it to be a effective help in achieving academic goals. The scenario analysis afterwards projected potential future scenarios, providing valuable insights into the possibilities and challenges associated with incorporating GAI into higher education. The main motivation is to gain a tangible and precise understanding of the potential consequences for HEIs and to provide guidance responding to the evolving learning environment. The findings indicate that irresponsible and excessive use of the technology could result in significant challenges. Hence, HEIs must develop stringent policies, reevaluate learning objectives, upskill their lecturers, adjust the curriculum and reconsider examination approaches.