Machine learning can be used to classify patients in a hospital. Here, the classifier has to minimize the cost of misclassifying the patient and minimize the costs of the tests. Unfortunately, obtaining features may be costly, e.g., taking blood tests or doing an x-ray scan. Furthermore, it is possible that acquiring those test results may take a few days. To train such a classifier, several machine learning algorithms exist. Decision trees appear as favourites since, unlike other classifiers, decision trees do not need all feature values to classify an instance. Current approaches, however, only use heuristics to find a local optimum. Although heuristics are relatively fast, they are not optimal and therefore may not capture well the underlying characteristics of the given dataset. We propose an optimal approach to train cost-sensitive decision trees while also considering these delayed tests. Here we show, smaller trees with higher accuracy and a lower cost can be constructed, compared to a heuristic approach. We use dynamic programming to allow us to skip many calculations, which speeds up the programming time to seconds.