When to Allow Makeup Exams
One good way to approach this kind of thing is to state a policy in your syllabus. For instance, you could have:


  Make-up exams will be given only in case of an emergency or unavoidable problems such as an illness requiring hospitalization. You must communicate with me as early as possible about the problem.


Under this policy, you would just tell the student no in this situation. Or you could craft a policy that does allow a make-up exam in this situation.

The advantage of having it spelled out in your syllabus is that it's communicated clearly, it's clear why you're making the decision you're making, and administrators will support you in your decision.

Personally, I just say no in the kind of situation you're describing. The student is making a commitment by taking the course, and the nature of the commitment was made clear from the start in the syllabus. It's quite a bit of extra work for me to write a different exam for one student and make arrangements for it to be proctored. When you're a college student, it's simply not reasonable to expect to have a week off from school with no consequences. Lots of other students would like to have a week off with no consequences.