This study examines the relationship between student perceptions and their intention to use generative artificial intelligence (GenAI) in higher education. With a sample of 405 students participating in the study, their knowledge, perceived value, and perceived cost of using the technology were measured by an Expectancy-Value Theory (EVT) instrument. The scales were first validated and the correlations between the different components were subsequently estimated. The results indicate a strong positive correlation between perceived value and intention to use generative AI, and a weak negative correlation between perceived cost and intention to use. As we continue to explore the implications of GenAI in education and other domains, it is crucial to carefully consider the potential long-term consequences and the ethical dilemmas that may arise from widespread adoption.