Can the options of the order (call) be exercised if the BPA ordering period has expired?
This response is written without knowledge of all term and conditions of the master BPA and the resulting order.
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The question background indicates that the BPA ordering period will ends prior to "completion of the order" (the "period of performance"?), but the actual question asks if options can be exercised (not necessarily performed) after the BPA ordering period ends. These are two different scenarios. However, if the order against the BPA that resulted in a three year base period and two option years was placed within the BPA's original ordering period, I do not see a problem. The period of performance for the base year and options can extend beyond the master BPA's expiration date. There’s no need to require the task order period of performance to coincide with master BPA period of performance.
If the issue is whether options can be exercised after the BPA ordering period has actually ended, then the answer is yes. As long as the base year was exercised before the master BPA ordering period ended, an option stemming from the exercise of the base year can also be exercise. However, you couldn't place an "order" outside of an "ordering period."
Please consider consulting your organization's legal counsel for additional advice on the matter.