The Free Cash Flow to Equity Model

Equity Valuation in R

Cliff Ang

Senior Vice President, Compass Lexecon

What is "Free Cash Flow"?

"Free Cash Flows" are cash flows after you have paid out
- All your suppliers, employees, lenders, and government (taxes) and
- Setting aside money for capital investments and additional working capital needs and
- Net of new borrowings and debt repayments
No effect on firm's projected operations
No effect on firm's projected growth

After-Tax Income

[1] Revenues
[2] Less: Cost of Goods Sold
$ ================== $
[3] Gross Profit
[4] Less: Operating Expenses
$ ================== $
[5] Operating Income or EBIT
[6] Less: Interest Expense
$ ================== $
[7] Pre-Tax Income
[8] Less: Taxes
$ ================== $
[9] After-Tax Income

# Also called "Sales"

# Earnings Before Interest & Taxes
# Compensation to debt holders

# Payment to the government

# Also called "Net Income"

Adjustments to Arrive to FCFE

[9] After-Tax Income

[10] Add: Depreciation and Amortization

[11] Less: Capital Expenditures

[12] Less: Increases in Working Capital

$ ================== $
[13] Free Cash Flow to Equity

# Non-cash charge. Cash spent at time of purchase

# Cash spent on capital investments

# Cash spent on additional working capital needs

Terminal Value

Terminal Value (TV) is the value of the cash flows beyond the forecast period

Commonly estimated using the Perpetuity with Growth Model, which is

$$TV = \frac{FCFE_{T+1}}{k_e - g} = \frac{FCFE_T * (1 + g)}{k_e - g}$$

where

$FCFE_{T+1}$ = Free Cash Flow to Equity the year after the end of the forecast period
$k_e$ = Cost of Equity
$g$ = Perpetuity Growth Rate (PGR)

Terminal Value in R

Suppose you have a 5 year forecast period, such that $FCFE_5$ = $ \$100 $. Assume that $g$ = 3% and $k_e$ = 15%, then in R:

FCFE_5 <- 100

g <- 0.03

k_e <- 0.15

FCFE_5 * (1 + g) / (k_e - g)

858.3333

Let's practice!

Equity Valuation in R