Researchers and practitioners alike increasingly often perceive flaky tests as a major challenge in software engineering. They spend a lot of effort trying to detect, repair, and mitigate the negative effects of flaky tests. However, it is yet unclear where and to what extent the costs of flaky tests manifest in industrial CI development processes. In this study, we compile cost factors introduced by flaky tests in CI development from research and practice and derive a cost model that allows gaining insight into the costs incurred. We then instantiate this model in a case study of a large, commercial software project with ~30 developers and ~1M SLoC. We analyze five years of development history, including CI test logs, commits from the VCS, issue tickets, and tracked work time to quantify the cost factors implied by flaky tests. We find that the time spent dealing with flaky tests in the studied project represents at least 2.5% of the productive developer time. This effort is divided into investigating potentially flaky test failures, which accounts for 1.1% of the total time spent, repairing flaky tests adds another 1.3%, and developing tools to monitor flaky tests adds 0.1%. Contrary to most other studies, we find the cost for rerunning tests to be negligible and inexpensive. Automatically rerunning a test costs 0.02~cents, while not rerunning and thus letting the pipeline fail results in a manual investigation costing $5.67 in our context. The insights gained from our case study have led to the decision to shift effort from investigation and repair to automatically rerunning tests. Our cost model can help practitioners analyze the cost of flaky tests in their context and make informed decisions. Furthermore, our case study provides a first step to better understand the costs of flaky tests, which can lead researchers to industry-relevant problems.