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I assume that the taxable income here is a result of the exercise, reported to you on a W-2?

Assuming these were NonQualified stock options then the "spread" between what you paid to exercise the options and the "fair market value" of the stock acquired is considered "compensation"  and, like compensation paid in cash, gets taxed. 

I'm not sure what you mean by "does cost of purchase offset?"  Your cost of purchase comprises a portion of you basis in the stock.  That "spread" comprises the rest of your basis in the stock.  In other words, your basis per share is the same as the per share "fair market value" used by the employer to calculate the compensation. 

        (GROSS number of shares exercised) x (per share "fair market value") =  compensation reported on W-2

Apparently you DID figure you were getting something of value here, otherwise you wouldn't have exercised.

Tom Young