Free Cash Flows to Firm (FCFF)
The Free Cash Flows to Firm measure the cash generated by the company and that is available for the stakeholders (debt and equity holders), it is therefore the cash left after all costs of doing business have been paid. The FCFF are the same no matter what the financing mix of the company is, they are calculated on an unlevered basis.
There are different formulas to calculate the FCFF, the two formulas below are the most commonly used:
As you may have notice, the actual income tax paid by the Company is not used in the calculation, the reason for this is that the actual income tax paid includes the tax deductibility of interests, and since the FCFF must not be impacted by the financing, it is necessary to neutralize them by recalculating the income tax based on the taxable income excluding interests.
Free Cash Flows to Equity (FCFE) and Cash to Shareholders
The Free Cash Flows to Equity calculate the maximum theoretical cash that would be available for distribution to shareholders, it is the cash left after all costs of doing business and all debt holders have been paid.
The Cash to Shareholders is the actual cash that is paid to shareholders, it takes into account all the constraints that may prevent the company from paying the full value of the FCFE to its shareholders (minimum cash balance to retain, lack of retained earnings, etc.).
Debt Cash Flows
Debt Cash Flows measure the cash flows to creditors from their point of view.
The Project Cash Flow Check
A company generate cash flows for three types of stakeholders:

Its shareholders, through the payment of dividends or repayment of shareholder loans

Its creditors, through the payment of interests and the repayment of the principal of the debt

The government, through the payment of the corporate income tax
At any point in time you must have the three following formulas returning the same value:
This check is very useful to make sure that no cash appears or disappears somewhere in the model and it should always be included in any financial model.