# 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 is discounted at the cost of equity to value 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.

### FCFE from Net Income

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:

Free Cash Flow to Equity

= NI + NCE − NCI ± WC − FC + NB

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

### FCFE from Cash Flows from Operations

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

### FCFE from FCFF

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

FCFE = FCFF − Interest × (1 - Tax Rate) + NB

## Equity Valuation using FCFE

When the FCFE is discounted at a company’s cost of equity, it gives us the intrinsic value of the company's equity. Either a single stage or a multi-stage model can be used.

### Single Stage FCFE Valuation

The single stage model considers the free cash flow to equity stream to be a perpetuity which grows at a growth rate g.

V_{0} = | FCFE_{0} × (1 + g) |

k_{e} − g |

### Multi-Stage FCFE Valuation

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_{E} = | FCFE_{1} | + | FCFE_{2} | +....+ | FCFE_{n} | + | TV_{n} |

(1 + k_{e})^{1} | (1 + k_{e})^{2} | (1 + k_{e})^{n} | (1 + k_{e})^{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, k_{e} is the cost of equity and TV is the terminal value.

## Example: Multi-Stage Free Cash Flow Equity Valuation

Nutritioner, Inc. produces nutrition formula for infants. The company's cash flows from operations for the most recent financial year is $20 million, interest expense is $2 million and tax rate is 20%. The company is expected to grow at 15% in the first three years and at 5% annual rate there-after. There is no change in borrowing during the period.

If the company's weighted average cost of capital is 8%, prevailing risk-free interest rate is 3%, the market risk premium is 5% and the company's beta coefficient is 1.5, work out the company's value using its free cash flow to equity.

### Solution

Since the company has high growth g_{h} in the first three years and constant growth g_{c} there-after, we need to use the multi-stage FCFE model.

#### Finding Free Cash Flow to Equity

Let us first find the current free cash flow to equity:

FCFE_{0}

= CFO − Interest × (1 - 20%) + NB

= $20 million − $2 million × (1 - 20%) + 0

= $18.4 million

At 15% growth rate, the FCFE_{1}, FCFE_{2} and FCFE_{3} work out to $21.16 million, $24.33 million and $27.98 million respectively, as shown below.

FCFE_{1}

= FCFE_{0} × (1 + g_{h})

= $18.4 million × (1 + 15%)

= $21.16 million

FCFE_{2}

= FCFE_{1} × (1 + g_{h})

= FCFE_{0} × (1 + g_{h})^{2}

= $18.4 million × (1 + 15%)^{2}

= $24.33 million

FCFE_{3}

= FCFE_{2} × (1 + g_{h})

= FCFE_{0} × (1 + g_{h})^{3}

= $18.4 million × (1 + 15%)^{3}

= $27.98 million

#### Finding Required Return on Equity

Next, we need to find the terminal value of the company's equity at the end of Year 3. But before we could do that we need to estimate the company's required return on equity (i.e. cost of equity) which we can work out using the capital asset pricing model (CAPM):

Cost of Equity (k_{e})

= Risk-Free Rate + Beta × Market Risk Premium

= 3% + 1.5 × 5%

= 10.5%

#### Finding Terminal Value

The company's terminal value at end of Year 3 is $554.32 million

TV = | FCFE_{3} × (1 + g_{c}) | = | $27.98 × (1 + 5%) | = $554.32 million |

k_{e} − g_{c} | 10.3% − 5% |

#### Finding Equity Value

We have all the intermediate figures needed to find the equity value at time 0:

V_{E} = | $21.16M | + | $24.33M | + | $27.98M + $554.32M | =$473.18M |

(1 + k_{e})^{1} | (1 + k_{e})^{2} | (1 + k_{e})^{3} |

The following table lists all the cash flows and how their present value is determined:

Year | 0 | 1 | 2 | 3 |
---|---|---|---|---|

FCFE | 18.40 | 21.16 | 24.33 | 27.98 |

TV | 554.40 | |||

CF | 21.16 | 24.33 | 582.39 | |

Discount Factor | 0.9066 | 0.8220 | 0.7452 | |

PV | 473.18 | 19.18 | 20.00 | 433.99 |

We have discounted FCFE at the cost of equity instead of the weighted-average cost of capital (WACC). It is because WACC includes cost of debt too while FCFE already subtracts charge for debt capital. Discounting FCFE using WACC would double-count the cost of debt.

by Obaidullah Jan, ACA, CFA and last modified on

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