In a randomized controlled trial, a decision needs to be made about the total number of subjects for adequate statistical power. One way to increase the power of a trial is by including a predictive covariate in the model. In this article, the effects of various covariate adjustment strategies on increasing the power is studied for discrete-time survival endpoints; the circumstances are examined under which the covariate adjustment results in a sufficient increase in power. Using a predictive covariate may increase the costs for each subject, so it is useful to quantify when using a covariate is a cost-efficient strategy. The results reveal that using a covariate is highly recommended if the costs for measuring the covariate are relatively small and the correlation with the outcome sufficiently high. (Contains 6 tables and 2 figures.)