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.