1. Discounted Cash Flow Valuation

2. Challenges Defining and forecasting CF’s
Estimating appropriate discount rate

3. Basic DCF model
An asset’s value is the present value of its (expected) future cash flows

4. Three alternative definitions of cash flow
Dividend discount model
Free cash flow model
Residual income model

5. Free cash flow
Free cash flow to the firm (FCFF) is cash flow from operations minus capital expenditures
Free cash flow to equity (FCFE) is cash flow from operations minus capital expenditures minus net payments to debtholders (interest and principal)

6. FCF valuation
PV of FCFF is the total value of the company. Value of equity is PV of FCFF minus the market value of outstanding debt.
PV of FCFE is the value of equity.
Discount rate for FCFF is the WACC. Discount rate for FCFE is the cost of equity (required rate of return for equity).

7. Intro to Free Cash Flows
Dividends are the cash flows actually paid to stockholders
Free cash flows are the cash flows available for distribution.

8. Defining Free Cash Flow
Free cash flow to equity (FCFE) is the cash flow available to the firm’s common equity holders after all operating expenses, interest and principal payments have been paid, and necessary investments in working and fixed capital have been made.
FCFE is the cash flow from operations minus capital expenditures minus payments to (and plus receipts from) debtholders.

9. Valuing FCFE
The value of equity can also be found by discounting FCFE at the required rate of return on equity (r):
Since FCFE is the cash flow remaining for equity holders after all other claims have been satisfied, discounting FCFE by r (the required rate of return on equity) gives the value of the firm’s equity.
Dividing the total value of equity by the number of outstanding shares gives the value per share.

10. Discount rate determination
Jargon
Discount rate: any rate used in finding the present value of a future cash flow
Risk premium: compensation for risk, measured relative to the risk-free rate
Required rate of return: minimum return required by investor to invest in an asset
Cost of equity: required rate of return on common stock

11. Two major approaches for cost of equity
Equilibrium models:
Capital asset pricing model (CAPM)
Arbitrage pricing theory (APT)
Bond yield plus risk premium method (BYPRP)

12. CAPM
Expected return is the risk-free rate plus a risk premium related to the asset’s beta:
E(Ri) = RF + i[E(RM) – RF]
The beta is i = Cov(Ri,RM)/Var(RM)
[E(RM) – RF] is the market risk premium or the equity risk premium

13. CAPM What do we use for the risk-free rate of return?
Choice is often a short-term rate such as the 30-day T-bill rate or a long-term government bond rate.
We usually match the duration of the bond rate with the investment period, so we use the long-term government bond rate.
Risk-free rate must be coordinated with how the equity risk premium is calculated (i.e., both based on same bond maturity).

14. Equity risk premium
Historical estimates: Average difference between equity market returns and government debt returns.
Choice between arithmetic mean return or geometric mean return
Survivorship bias
ERP varies over time
ERP differs in different markets

15. Equity risk premium
Expectational method is forward looking instead of historical
One common estimate of this type:
GGM equity risk premium estimate
= dividend yield on index based on year-ahead dividends
+ consensus long-term earnings growth rate
- current long-term government bond yield

16. Sources of error in using models
Three sources of error in using CAPM or APT models:
Model uncertainty – Is the model correct?
Input uncertainty – Are the equity risk premium or factor risk premiums and risk-free rate correct?
Uncertainty about current values of stock beta or factor sensitivities

17. BYPRP method
The bond yield plus risk premium method finds the cost of equity as:
BYPRP cost of equity
= YTM on the company’s long-term debt
+ Risk premium
The typical risk premium added is 3-4 percent.

18. Single-stage, constant-growth FCFE valuation model
FCFE in any period will be equal to FCFE in the preceding period times (1 + g):
FCFEt = FCFEt–1 (1 + g).
The value of equity if FCFE is growing at a constant rate is
The discount rate is r, the required return on equity. The growth rate of FCFF and the growth rate of FCFE are frequently not equivalent.

19. Computing FCFF from Net Income
This equation can be written more compactly as
FCFF = NI + Depreciation + Int(1 – Tax rate) – Inv(FC) – Inv(WC) Or
FCFF = EBIT(1-tax rate) + depreciation – Cap. Expend. – change in working capital – change in other assets

20. Forecasting free cash flows
Computing FCFF and FCFE based upon historical accounting data is straightforward. Often times, this data is then used directly in a single-stage DCF valuation model.
On other occasions, the analyst desires to forecast future FCFF or FCFE directly. In this case, the analyst must forecast the individual components of free cash flow. This section extends our previous presentation on computing FCFF and FCFE to the more complex task of forecasting FCFF and FCFE. We present FCFF and FCFE valuation models in the next section.

21. Forecasting free cash flows
Given that we have a variety of ways in which to derive free cash flow on a historical basis, it should come as no surprise that there are several methods of forecasting free cash flow.
One approach is to compute historical free cash flow and apply some constant growth rate. This approach would be appropriate if free cash flow for the firm tended to grow at a constant rate and if historical relationships between free cash flow and fundamental factors were expected to be maintained.

22. Forecasting FCFE
If the firm finances a fixed percentage of its capital spending and investments in working capital with debt, the calculation of FCFE is simplified. Let DR be the debt ratio, debt as a percentage of assets. In this case, FCFE can be written as
FCFE = NI – (1 – DR)(Capital Spending – Depreciation)
– (1 – DR)Inv(WC)
When building FCFE valuation models, the logic, that debt financing is used to finance a constant fraction of investments, is very useful. This equation is pretty common.

23. Forecasting future dividends or FCFE
Using stylized growth patterns
Constant growth forever (the Gordon growth model)
Two-distinct stages of growth (the two-stage growth model and the H model)
Three distinct stages of growth (the three-stage growth model)

24. Forecasting future dividends
Forecast dividends for a visible time horizon, and then handle the value of the remaining future dividends either by
Assigning a stylized growth pattern to dividends after the terminal point
Estimate a stock price at the terminal point using some method such as a multiple of forecasted book value or earnings per share

25. Gordon Growth Model
Assumes a stylized pattern of growth, specifically constant growth:
Dt = Dt-1(1+g) Or
Dt = D0(1 + g)t

26. Gordon Growth Model PV of dividend stream is:
Which can be simplified to:

27. Gordon growth model
Valuations are very sensitive to inputs. Assuming D1 = 0.83, the value of a stock is:

28. Other Gordon Growth issues
Generally, it is illogical to have a perpetual dividend growth rate that exceeds the growth rate of GDP
Perpetuity value (g = 0):
Negative growth rates are also acceptable in the model.

29. Gordon Model & P/E ratios
If E is next year’s earnings (leading P/E):
If E is this year’s earnings (trailing P/E):

30. Using a P/E for terminal value
The terminal value at the beginning of the second stage was found above with a Gordon growth model, assuming a long-term sustainable growth rate.
The terminal value can also be found using another method to estimate the terminal value at t = n. You can also use a P/E ratio, applied to estimated earnings at t = n.

31. Using a P/E for terminal value
For DuPont, assume
D0 = 1.40
gS = 9.3% for four years
Payout ratio = 40%
r = 11.5%
Trailing P/E for t = 4 is 11.0
Forecasted EPS for year 4 is
E4 = 1.40(1.093)4 / 0.40 = =

32. Using a P/E for terminal value

33. Three-stage DDM There are two popular version of the three-stage DDM
The first version is like the two-stage model, only the firm is assumed to have a constant dividend growth rate in each of the three stages.
A second version of the three-stage DDM combines the two-stage DDM and the H model. In the first stage, dividends grow at a high, constant (supernormal) rate for the whole period. In the second stage, dividends decline linearly as they do in the H model. Finally, in stage three, dividends grow at a sustainable, constant rate.

34. Spreadsheet modeling
Spreadsheets allow the analyst to build very complicated models that would be very cumbersome to describe using algebra.
Built-in functions such as those to find rates of return use algorithms to get a numerical answer when a mathematical solution would be impossible or extremely complicated.

35. Strengths of multistage DDMs
Can accommodate a variety of patterns of future dividend streams.
Even though they may not replicate the future dividends exactly, they can be a useful approximation.
The expected rates of return can be imputed by finding the discount rate that equates the present value of the dividend stream to the current stock price.

36. Strengths of multistage DDMs
Because of the variety of DDMs available, the analyst is both enabled and compelled to evaluate carefully the assumptions about the stock under examination.
Spreadsheets are widely available, allowing the analyst to construct and solve an almost limitless number of models.

37. Weaknesses of multistage DDMs
Garbage in, garbage out. If the inputs are not economically meaningful, the outputs from the model will be of questionable value.
Analysts sometimes employ models that they do not understand fully.
Valuations are very sensitive to the inputs to the models.

38. Forecasting growth rates
There are three basic methods for forecasting growth rates:
Using analyst forecasts
Using historical rates (use historical dividend growth rate or use a statistical forecasting model based on historical data)
Using company and industry fundamentals

39. Finding g The simplest model of the dividend growth rate is:
g = b x ROE
where g = Dividend growth rate
b = Earnings retention rate (1 – payout ratio)
ROE = Return on equity.