We study two-sided matching where one side (colleges) can make monetary transfers (offer stipends) to the other (students). Colleges have fixed budgets and strict preferences over sets of students. One different feature of our model is that colleges value money only to the extent that it allows them to enroll better or additional students. A student can attend at most one college and receive a stipend from it. Each student has preferences over college-stipend bundles. Conditions that are essential for most of the results in the literature fail in the presence of budget constraints. We define pairwise stability and show that a pairwise stable allocation always exists. We construct an algorithm that always selects a pairwise stable allocation. The rule defined through this algorithm is incentive compatible for students: no student should benefit from misrepresenting his preferences. Finally, we show that no incentive compatible rule selects Pareto-undominated pairwise stable allocation.