Introductory algebra-based physics courses can present unique motivational challenges for pre-health students, who often perceive physics as irrelevant or intimidating. According to Expectancy-Value Theory, students' performance and persistence are shaped not only by their expectations for success, but also by the perceived value and cost of engagement. This study quantitatively examines the role of perceived cost--such as effort, emotional toll, and opportunity cost--among students enrolled in an active learning, algebra-based physics course designed for life science majors. Our findings reveal that higher perceived costs are negatively correlated with physics identity and intentions to continue in the course sequence, particularly among students who have a low physics identity. Regression analysis of perceived cost before the course results in only emotional cost having a negative effect on students' physics identity. This negative correlation persisted in post course experience, and the added cost of outside effort was statistically significant in negatively affecting physics identity. These findings suggest the persisting emotional anxiety towards physics impedes students from believing they can do well in physics even before they enter the course.