Question

Explain how to use the free cash flow valuation model to find the price per share of common equity.

Answer 1

Free cash Plow Valuation Model

It measures a company's financial flexibility, there is two approaches to valuation using free cash flow. The first includes discounting projected free cash flow to firm (FCFF) as the weighted average cost of the capital (WACC) to find the company's total value. The second, discounting the Free cash flow to equity (FCFE) at the cost of equity to find the value of the company's shareholders equity.

Formula

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.

When 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 (k_e) in the denominator:

Equity Value =	FCFE1
ke − g

Taking some example of each case:

case 1 :- FCFF valuation Model

FCFF is $ 600 million and expected growth is 6% each year, company cost of capital is 15%, how much is it worth? If market value of debt is $6,000 million and FC has 200 million shares outstanding, find per share value of FC.

sol:-

Firm Value =	FCFF0 × (1 + g)
WACC − g

Firm Value = $600 x (1 + 6%) / 15% - 6% = $7067 M

If market value of debt is $6,000 million, value of equity is million

value of equity = value of firm - value of debt

= 7067 - 6000 = $1067 M

per share intrinsic value for FC = $1067 M/ $200 M = $5.335.

case 2 :- FCFE valuation Model

Company has 10 million shares outstanding. Its projected FCFE for next year is $20 million, its required return on equity is 10% and perpetual growth rate of FCFE is 5%. Find the intrinsic value of the company's share.

Sol:-

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 (k_e).

Equity Value =	FCFE
ke − g

= $20 million / 10% - 5% = $400 million

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 / 10 Million = $40.