# FCFF and FCFE Valuation Approaches

## Present Value of FCFF

The free cash flow to the firm (FCFF) valuation approach estimates the firm’s value as the present value of future FCFF discounted at the weighted average cost of capital:

$$\text{Firm Value}= ∑_{\text{t}=1}^∞\frac{\text{FCFF}_\text{t}}{(1+\text{WACC})^\text{t}}$$

Using the weighted average cost of capital (WACC) to discounted FCFF gives the total value of the firm. The value of equity is estimated by deducting the market value of debt from the value of the firm.

$$\text{Equity Value}=\text{Firm Value}-\text{Market Value of Debt}$$

The value per share can be arrived at by dividing the total value of equity by the number of outstanding shares.

WACC is the weighted average of the after-tax required rates of return of debt and equity. The weights are proportions of the firm’s total market value to debt and equity. However, analysts may also use target weights. WACC depends on the riskiness of the cash flows. The higher the WACC figure, the riskier the cash flows.

WACC is calculated as:

$$\text{WACC}= \frac{\text{MV}(\text{Debt})}{\text{MV}(\text{Debt})+\text{MV}(\text{Equity})} \text{r}_\text{d} (1-\text{t})+\frac{\text{MV}(\text{Equity})}{\text{MV}(\text{Debt})+\text{MV}(\text{Equity})}\text{r}$$

Where:

$$\text{r}=$$ Cost of equity.

$$\text{r}_{\text{d}}=$$ Before tax cost of debt.

$$\text{t}=$$ Marginal corporate income tax rate.

## Present Value of FCFE

The value of equity can be arrived at by discounting the free cash flow to equity (FCFE) at the required rate of return of equity, $$r$$.

$$\text{Equity value}=\sum_{\text{t}=1}^{∞}\frac{\text{FCFF}_\text{t}}{(1+\text{r})^\text{t}}$$

Exam tip #1: Dividing the value of equity by the number of outstanding shares gives the value per share.

Exam tip #2: When using FCFF, divide by $$(1+\text{WACC})$$. When using FCFE, divide by $$(1+\text{r})$$.

## Question

Given the firm’s value, which of the following is the most appropriate way of computing the value of equity?

1. Adding the value of assets to the value of the firm.
2. Deducting the value of assets from the value of the firm.
3. Deducting the market value of debt from the value of the firm.

#### Solution

Given the firm’s value, the value of equity can be computed by subtracting the market value of debt.

$$\text{Equity Value}=\text{Firm Value}-\text{Market Value of Debt}$$

A is incorrect. Adding the value of the assets to the firm’s value is not a method of computing the value of equity.

B is incorrect. Deducting the value of assets from the firm’s value would not give one the value of equity.

Reading 24: Free Cash Flow Valuation

LOS 24 (a) Compare the free cash flow to the firm (FCFF) and free cash flow to equity (FCFE) approaches to valuation.

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