1. Chapter 2 Discounted Dividend 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. Comments on basic DCF model • Flat term structure of discount rates versus differing discount rates for different time horizons • Value of an asset at any point in time is always the PV of subsequent cash flows discounted back to that point in time.

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

6. Dividend discount model • The DDM defines cash flows as dividends. • Why? An investor who buys and holds a share of stock receives cash flows only in the form of dividends • Problems: • Companies that do not pay dividends. • No clear relationship between dividends and profitability

7. DDM (continued) • The DDM is most suitable when: • the company is dividend-paying • the board of directors has a dividend policy that has an understandable relationship to profitability • the investor has a non-control perspective.

8. 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)

9. Free cash flow • FCFF is a pre-debt cash flow concept • FCFE is a post-debt cash flow concept • FCFE can be viewed as measuring what a company can afford to pay out in dividends • FCF valuation is appropriate for investors who want to take a control perspective

10. 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).

11. FCF (continued) • FCF valuation is most suitable when: • the company is not dividend-paying. • the company is dividend paying but dividends significantly differ from FCFE. • The company’s FCF’s align with company’s profitability within a reasonable time horizon. • the investor has a control perspective. • FCF valuation is very popular with analysts.

12. Which is best, DDM, FCF, or RI? • One model may be more suitable for a particular application. • Analyst may have more expertise with one model. • Availability of information. • In practice, skill in application, including the quality of forecasts, is decisive for the usefulness of an analyst’s work.

13. 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

14. Discount rate determination • Weighted average cost of capital (WACC): the weighted average of the cost of equity, after-tax cost of debt, and cost of preferred stock

15. 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)

16. 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

17. 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).

18. Equity risk premium • Historical estimates: Average difference between equity market returns and government debt returns. • Choice between arithmetic mean return or geometric mean return (see Table 2-2 p. 50) • Survivorship bias • ERP varies over time • ERP differs in different markets (see Table 2-3 p. 51)

19. 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 bondyield

20. Dividend discount models (DDMs) • Single-period DDM: • Rate of return for single-period DDM

21. More DDMs • Two-period DDM: • Multiple-period DDM:

22. Indefinite HP DDM • For an indefinite holding period, the PV of future dividends is:

23. Forecasting future dividends • 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. Expected rate of return • The expected rate of return in the Gordon growth model is: • Implied growth rates can also be derived in the model.

30. PV of growth opportunities • If a firm has growing earnings and dividends, it can be worth more than a non-growing firm: • Value of growth = Value of growing firm – Value of assets in place (no growth) • OR

31. 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):

32. Strengths of Gordon growth model • Good for valuing stable-growth, dividend-paying companies • Good for valuing indexes • Simplicity and clarity, also helps understanding of relationships between V, r, g, and D • Can be used as a component in more complex models

33. Weaknesses of Gordon growth model • Calculated values are very sensitive to assumed values of g and r • Is not applicable to non-dividend-paying stocks • Is not applicable to unstable-growth, dividend paying stocks

34. Two-stage DDM • The two-stage DDM is based on the multiple-period model: • Assume the first n dividends grow at gS and dividends then grow at gL. The first n dividends are:

35. Two-stage DDM (cont) • Using Dn+1, the value of the stock at t=n is • The value at t = 0 is

36. Two-stage DDM example • Assume the following values • D0 is $1.00 • gS is 30% • Supernormal growth continues for 6 years • gL is 6% • The required rate of return is 12%

37. Two-stage DDM example

38. “Shortcut” two-stage DDM (not in the book) • If gS is constant during stage 1, this works: • For gS=30%, gL=6%, D0=1.00 and r=12%

39. 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.

40. 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 = 1.9981 = 4.9952

41. Using a P/E for terminal value

42. Valuing a non-dividend paying stock • This can be viewed as a special case of the two-stage DDM where the dividend in stage one is zero: • Forecasting the length of stage one and the dividend pattern in stage two are the challenges.

43. The H model • The basic two-stage model assumes a constant, extraordinary rate for the super-normal growth period that is followed by a constant, normal growth rate thereafter.

44. 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.

45. Three-stage DDM with three distinct stages • Assume the following for IBM: • Required rate of return is 12% • Current dividend is $0.55 • Growth rate and duration for phase one are 7.5% for two years • Growth rate and duration for phase two are 13.5% for the next four years • Growth rate in phase four is 11.25% forever

46. Three-stage DDM with three distinct stages

47. 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.

48. Spreadsheet modeling • Because of their widespread use, several analysts can work together or exchange information through the sharing of their spreadsheet models.

49. Finding r with trial & error • Johnson & Johnson’s current dividend of $.70 to grow by 14.5 percent for six years and then grow by 8 percent into perpetuity. J&J’s current price is $53.28. What is the expected return on an investment in J&J’s stock?

50. Finding r with trial & error • For a good initial guess, we can use the expected rate of return formula from the Gordon model as a first approximation: r = ($0.70  1.145)/$53.28 + 8% = 9.50%. Since we know that the growth rate in the first six years is more than 8 percent, the estimated rate of return must be above 9.5 percent. • Let’s use 9.5 percent and 10.0 percent to calculate the implied price.