Computing the margin of victory (MOV) in an Instant Runoff Voting (IRV) election is NP-hard. In an IRV election with winning candidate w, the MOV defines the smallest number of cast votes that, if modified, result in the election of a candidate other than w. The ability to compute such margins has significant value. Arguments over the correctness of an election outcome usually rely on the size of the electoral margin. Risk-limiting audits use the size of this margin to determine how much post-election auditing is required. We present an efficient branch-and-bound algorithm for computing exact margins that substantially improves on the current best-known approach. Although exponential in the worst case, our algorithm runs efficiently in practice, computing margins in instances that could not be solved by the current state-of-the-art in a reasonable time frame.