# Free Cash Flow Valuation

In free cash flow valuation, intrinsic value of a company equals the present value of its free cash flow, the net cash flow left over for distribution to stockholders and debt-holders in each period.

There are two approaches to valuation using free cash flow. The first involves discounting projected free cash flow to firm (FCFF) at the weighted average cost of the capital (WACC) to find a company's total value (i.e. sum of its equity and debt). The second involves discounting the free cash flow to equity (FCFE) at the cost of equity to find the value of the company's shareholders equity.

## Formula

The most basic single-stage free cash flow valuation models are similar to the dividend discount model.

When we are interested in finding total value of a company, we need to discount the free cash flow to firm at the company's cost of capital:

 Firm Value = FCFF0 × (1 + g) = FCFF1 WACC − g WACC − g

Where FCFF1 is the free cash flow to firm expected next year, WACC is the weighted-average cost of capital and g is the growth rate of FCFF.

We can determine the company's equity value from its total firm value by subtracting the market value of debt:

Equity Value = Total Business Value − Market Value of Debt

If we have to work with free cash flow to equity (FCFE) which is expected to grow at rate g, we need to use the cost of equity (ke) in the denominator:

 Equity Value = FCFE1 ke − g

In real life more complex valuation models project cash flows by using more precise period on period growth rates.

## Examples

### Example 1: FCFF Valuation Model

Free cash flow to firm for Frontier Ceramics is currently \$300 million but is expected to grow by 4% each year forever. If the company's cost of capital is 10%, how much is it worth? If market value of debt is \$3,000 million and FC has 200 million shares outstanding, find per share value of FC.

Solution

 Firm Value = \$300 M × (1 + 4%) = \$5,200 M WACC − g

The model applied here essentially calculates the present value of a growing perpetuity. The relevant FCFF is calculated by projecting current year FCFF at the growth rate for one year.

If market value of debt is \$3,000 million, value of equity is \$2,200 million

Ve = Vf − Vd = \$5,200 M − \$3,000 M = \$2,200 M

Per share intrinsic value for FC is \$11 [= \$2,200 M ÷ \$200 M].

### Example 2: FCFE Valuation Model

PQ has 1 million shares outstanding. Its projected FCFE for next year is \$30 million, its required return on equity is 13% and perpetual growth rate of FCFE is 5.5%. Find the intrinsic value of the company's share.

Solution

In FCFE valuation model, we need to discount the free cash flow to equity at the cost of equity (ke):

 Total Equity Value = \$30 million = \$400 million 13% − 5.5%

To find the intrinsic value per share, divide total equity value by total number of shares of common stock outstanding:

 Intrinsic Value per Share = \$400 million = \$400 1 million