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## Chapter 2 Discounted Dividend Valuation

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**Challenges**• Defining and forecasting CF’s • Estimating appropriate discount rate**Basic DCF model**• An asset’s value is the present value of its (expected) future cash flows**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.**Three alternative definitions of cash flow**• Dividend discount model • Free cash flow model • Residual income model**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**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.**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)**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**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).**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.**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.**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**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**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)**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**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).**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)**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**Dividend discount models (DDMs)**• Single-period DDM: • Rate of return for single-period DDM**More DDMs**• Two-period DDM: • Multiple-period DDM:**Indefinite HP DDM**• For an indefinite holding period, the PV of future dividends is:**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)**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**Gordon Growth Model**• Assumes a stylized pattern of growth, specifically constant growth: Dt = Dt-1(1+g) Or Dt = D0(1 + g)t**Gordon Growth Model**• PV of dividend stream is: • Which can be simplified to:**Gordon growth model**• Valuations are very sensitive to inputs. Assuming D1 = 0.83, the value of a stock is:**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.**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.**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**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):**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**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**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:**Two-stage DDM (cont)**• Using Dn+1, the value of the stock at t=n is • The value at t = 0 is**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%**“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%**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.**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**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.**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.**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.**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**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.**Spreadsheet modeling**• Because of their widespread use, several analysts can work together or exchange information through the sharing of their spreadsheet models.**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?**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.