The Alternative Minimum Tax (AMT) is a separate tax system that exists alongside the regular income tax system. It was designed to ensure that high-income individuals pay a minimum amount of tax by limiting certain deductions and credits that can reduce taxable income. If your income exceeds the AMT exemption amount, you need to calculate your tax liability under both the regular tax system and the AMT system, and pay the higher amount.

Exercising incentive stock options (ISOs) can trigger the AMT because the spread between the exercise price and the fair market value of the stock at the time of exercise is included as income for AMT purposes. If you exercise ISOs and don't sell the stock in the same year, you would need to add the spread to your income when calculating AMT.

To calculate AMT, you need to determine your Alternative Minimum Taxable Income (AMTI), which includes your regular income plus certain adjustments and preference items. The AMTI is then reduced by the AMT exemption amount, which varies depending on your filing status. The exemption amount starts to phase out once your AMTI reaches a certain threshold. The remaining AMTI is then subject to the AMT tax rates, which are either 26% or 28%, depending on your income level.

If you owe AMT, you may be eligible for an AMT credit, which can be used to reduce your tax obligation in future years. It's important to consult with a tax professional to understand how exercising stock options may impact your tax liability and to explore strategies to minimize AMT, such as selling the stock in the same year or considering early exercising with an 83(b) election.