Many real-time systems needing an on-line schedulability test require exact schedulability analysis. In this paper we evaluate standard initial values for the iterative procedure to calculate worst-case response times of periodic tasks under fixed priority preemptive scheduling and arbitrary phasing. For discrete scheduling, we show that the number of iterations needed to determine the worst-case response time of a task using standard initial values increases logarithmically for an increasing worst-case computation time of that task. We present a new initial value, and prove that the number of iterations for that value is bounded. The costs of using the standard and new initial values are compared by means of an experiment. We briefly discuss the applicability of the initial value in other contexts, such as best-case response time analysis and jitter analysis.