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How does 83b election work when paying fair market value at time of grant?
Yes, you would pay no taxes at the time of purchase. In fact, this is not uncommon. Many early employees of startup companies are offered stock options that can be "early-exercised" (exercised before they vest). In such a case, an employee who exercises immediately upon grant (and assuming the exercise price of the option is the FMV at the time of grant) purchases the stock at FMV, and there no no tax paid when filing 83(b) election.