The success of a security attack crucially depends on the resources available to an attacker: time, budget, skill level, and risk appetite. Insight in these dependencies and the most vulnerable system parts is key to providing effective counter measures. This paper considers attack trees, one of the most prominent security formalisms for threat analysis. We provide an effective way to compute the resources needed for a successful attack, as well as the associated attack paths. These paths provide the optimal ways, from the perspective of the attacker, to attack the system, and provide a ranking of the most vulnerable system parts. By exploiting the priced timed automaton model checker Uppaal CORA, we realize important advantages over earlier attack tree analysis methods: we can handle more complex gates, temporal dependencies between attack steps, shared subtrees, and realistic, multi-parametric cost structures. Furthermore, due to its compositionality, our approach is flexible and easy to extend. We illustrate our approach with several standard case studies from the literature, showing that our method agrees with existing analyses of these cases, and can incorporate additional data, leading to more informative results.