How do you know for sure whether or not to use a closing? One good test is to ask yourself whether this email is more akin to an instant message/text or a business letter. If you're giving your teammate a quick update on an ongoing project, a formal closing might not be necessary; if you're throwing your hat in the ring for a promotion, it definitely is required. When all else fails, and you're still not sure, err on the side of caution and include it. You'll never go wrong by being too polite and respectful.
Business writing should be clear and concise. Take care, however, that your document does not turn out as an endless series of short, choppy sentences. Keep in mind also that “concise” does not have to mean “blunt”—you still need to think about your tone and the audience for whom you are writing. Consider the following examples: After carefully reviewing this proposal, we have decided to prioritize other projects this quarter.