Free Cash Flow to the Firm (FCFF) and Free Cash Flow to Equity (FCFE)

The value of common equity can be thought of as the present value of:

That's right! Free cash flows are those which remain after satisfying capital replacement, and free cash flows to equity are free cash flows after all debt has been serviced as well. When discounted to the present value, these should equate to the value of common equity.

Not quite. Free cash flows to the firm are used to pay both bondholders and stockholders. The value of debt must be subtracted from discounted FCFF to arrive at the value of equity.

No. Operating cash flows are too general for use in equity valuation, since some of these cash flows are needed to replace worn-out capital.

free cash flows to equity.

free cash flows to the firm.

after-tax operating cash flows.