# Free Cash Flow to Equity

Free cash flow to equity (FCFE) is the cash flow available for distribution to a company’s equity-holders. It equals free cash flow to firm minus after-tax interest expense plus net increase in debt. FCFE when discounted at the cost of equity returns the value of a company’s equity.

Free cash flow to equity is one of the two definitions of free cash flow; the other being the free cash flow to firm (FCFF). In general, the term free cash flow refers to the free cash flow to firm. FCFE differs from FCFF in that the free cash flow to firm is the cash flow that is available for distribution to both the debt-holders and equity-holders while the free cash flow to equity is the cash flow that’s available only for distribution to equity-holders. After-tax interest expense is subtracted from FCFF and net borrowing is added because they represent the cash paid to and cash raised from debt-holders.

## Formula

Free cash flow to equity (FCFE) can be determined by adjusting net income, cash flows from operations or free cash flow to firm. However, the exact adjustments depend on the starting figure.

If we start with net income, we must add non-cash expenses, subtract non-cash gains, add any decrease in assets or increase in liabilities, subtract any increase in assets or decrease in liabilities, add after-tax interest income and subtract net capital expenditures. This is represented by the following formula:

$$ FCFE=NI+NCE-NCI±WC-FC+NB $$

Where NI is net income, NCE is non-cash expenses, NCG is the non-cash income, WC represent the net adjustment on account of working capital changes, FC is the net capital expenditure and NB is net borrowing.

If we start from the cash flow from operations (CFO), we must subtract net capital expenditure and add net borrowing. We also need to subtract after-tax interest expense if the same is not subtracted while calculating cash flow from operations.

$$ FCFE=CFO-FC+NB $$

We can also work out FCFE by adjusting FCFF: we need to subtract after-tax interest expense and add net borrowing.

$$ FCFE=FCFF-I×(1-t)+NB $$

## Valuation using FCFE

FCFE can be used to value a company’s equity by discounting it using the company’s cost of equity. Either a single stage or a multi-stage model can be used. The single stage model considers the free cash flow to equity stream to be a perpetuity which grows at a growth rate g. The multi-stage model forecasts the cash flows for each year in the foreseeable future period, works out a terminal value at the end of the initial high-growth period and discount both the initial stage cash flows and terminal value using the cost of equity.

$$ V_0=\frac{{\rm FCFE}_0\times\left(1+g\right)}{r-g} $$

$$ V_E\ \left(Multi\ Stage\right)=\frac{{\rm FCFE}_1}{\left(1+r\right)^1}+\frac{{\rm FCFE}_2}{\left(1+r\right)^2}+\ldots\\+\frac{{\rm FCFE}_n}{\left(1+r\right)^n}+\frac{TV}{\left(1+r\right)^n} $$

Where FCFE_{0}, FCFE_{1}, FCFE_{2} and FCFE_{n} represent for the free cash flow to equity last year, first year, second year and nth year, g is the growth rate, r is the cost of equity and TV is the terminal value.