Discounted Cash Flow (DCF)

Background

The value of a firm is the sum of the value of its equity and value of its debt. This is also the sum of the Enterprise Value and cash and cash equivalents.

$$\begin{array}{rl}\text{Firm Value}& =\text{Equity Value}+\text{Debt Value}\\ & =\text{Enterprise Value}+\text{Cash and Cash Equivalents}\\ \text{Enterprise Value}& =\text{Equity Value}+\text{Net Debt}\end{array}$$

Where:

• Net Debt = Total Debt - Cash and Cash Equivalents

DCF Steps

1. Identify Free Cash Flows to the Firm (FCFF)
2. Recognize time value of money

Using this, we can calculate the Enterprise Value.

$$EV=\frac{FCF{F}_1}{(1+WACC{)}^1}+\frac{FCF{F}_2}{(1+WACC{)}^2}+...+\frac{FCF{F}_n}{(1+WACC{)}^n}$$

Free Cash Flows to the Firm (FCFF)

Free Cashflow to the Firm represents cash flows to which all stakeholders (providers of capital) make claim. That is:

$$\begin{array}{rl}FCFF& =EBIT(1-t)\\ & +\text{Depreciation and Amortization}\\ & -\text{Capital Expenditures}\\ & -\Delta \text{Net Working Capital}\end{array}$$

So FCFF is the Net Operating Profit After Tax, then we add back depreciation which is non-cash, subtract any investments into long-term assets, and subtract investments in short-term assets.

Example

Valuation of MatureCorp

• Find $EV$, $V_{Equity}$, and price per share
  • Firm has $200,000 in debt @ an interest rate of 10% per year
  • There are 100k shares outstanding
  • Tax rate is 40%
  • Firm is at a very mature stage. Thus:
    • It expects to generate $220,000 EBIT in perpetuity (all earnings are paid as dividends → no reinvestment)
    • Future capital expenditures offset depreciation
    • No future additional working capital investments are required
  • WACC is 13.2%

Solution

1. Calculate FCFF

$$FCFF=EBIT\times (1-t)=\$220,000\times (1-0.4)=\$132,000$$

2. FCFF is constant in perpetuity

$$EV=\frac{\$132,000}{13.2\%}\Rightarrow EV=\$1,000,000$$

3. Fair value of equity

$$V_{Equity}=EV-V_{NetDebt}$$ $$V_{Equity}=\$1,000,000-\$200,000\Rightarrow V_{Equity}=\$800,000$$

4. Price per share

P=\frac{\$800,000}{100,000}=$8.0

Two-Stage

Similar to Dividend Discount Model, we can also split the DCF into two stages:

Present value of Stage 1

$$\text{PV of FCFF}=\frac{FCF{F}_1}{(1+WACC{)}^1}+\frac{FCF{F}_2}{(1+WACC{)}^2}+\cdots +\frac{FCF{F}_n}{(1+WACC{)}^n}$$

Present value of Stage 2

$$\text{PV of }T{V}_n=\frac{FCF{F}_n(1+g)}{WACC-g}\times \frac{1}{(1+WACC{)}^n}$$

Using this two-stage approach

$$EV=\text{PV 1st Stage}+\text{PV 2nd Stage}$$

Example