DCF Approaches • Dividends = cash paid to shareholders • Free cash flow = cash available to pay shareholders • Residual income = economic profit
Discounting Dividends • Advantages: • Stable and predictable • Theoretically justified • Disadvantages: • Some firms don’t pay dividends • May not be related to earnings • Key point: Valuation metric (e.g., dividends or FCF) must be measurable and related to earnings power
DDM: How To • Process: Discount the future dividends at the required rate of return: Step 1: Estimate future dividends Step 2: Discount at required return Step 3: Value = PV (dividends)
Terminal Value • Usual process: • Estimate near-term dividends • Then calculate terminal value • Terminal value represents the PV of all dividends beyond the initial period • Data needs: 1) dividends paid during estimation period, 2) terminal value, and 3) required return
DDM: When to Use • DDM appropriate if: • Company has history of dividend payments • Dividends related to earnings • Take minority shareholder perspective • What if DDM is not appropriate? • FCF • Residual income An Alternative
Calculate Required Return • Calculate required return: Required in all DCF valuation! • Three primary methods 1) Capital asset pricing model (CAPM) 2) Arbitrage pricing theory (APT) 3) Bond yield plus risk premium approach
Calculate Required Return: CAPM • Details in SS#18: • Formula: Market risk premium Risk-free rate Beta (systematic risk)
Estimating CAPM Components • Risk-free rate: 20-year T-bond yield • Beta: Slope coefficient from regression of excess returns on excess market returns • Market risk premium: 1) Historical geometric mean 2) GGM equity risk premium
Calculate Required Return: APT • Formula: • APT is a multi-factor model Factor risk premiums Risk-free rate Factor sensitivities
Calculate Required Return: APT • Problem: Factors NOT specified by theory • BIRR version is closest to “accepted” factors: 1) Investor confidence risk 2) Time horizon risk 3) Inflation risk 4) Business-cycle risk 5) Market-timing risk • EXAM DAY: You will be given factors! Do not memorize
Calculate Required Return: APT Example • Assume: • Risk-free rate of 3% • Threefactors and sensitivities Solution Ri = 3% + 1.1(2%) + 1.2(4%) + 0.8(3%) = 12.4%
Calculate Required Return:Build-Up Method • More ad hoc • Used when beta estimates “unreliable” • Method: • Ri = co. bond yield + equity risk premium • Inputs will be given: • Risk premium (≈ 3 to 4%) and bond yield • Your job: add two numbers together!
Calculate Required Return:Limitations of Methods • All approaches have limitations: • Model uncertainty: Use CAPM or APT? How many APT factors? CAPM proxy? • Input uncertainty: Must estimate risk premiums and risk-free rate • Factor sensitivities: Are the betas correct?
Return and Price Convergence • Valuation can be used for “stock picking”: • Calculate intrinsic value • Buy undervalued securities • Earn superior return as market adjusts • Expected HPR > required return = BUY! • Market price must converge to intrinsic value • If not: Superior returns will not be realized
Dividend Discount Models • The Rule: Value is present value of all future dividends discounted at required return. • That is: • Problem: Requires estimation of infinite CFs The basic model
Dividend Discount Models Problem: Need a price in future! • One period: • Two period: • n-period: • Key point: Advanced models are based on simplifying assumptions for future price
Dividend Discount Models • Simplifying assumptions for future growth: 1) Constant growth (Gordon model) 2) Two-stage growth 3) H-model 4) Other assumptions (e.g., N-stage, spreadsheet)
DDM: Constant Growth (Gordon) Assumptions: 1) Dividend (D1) expected in 1 year • Dividends grow at constant rate (g) forever 3) Growth rate less than required return (r > g) Situations in which model is useful: 1) Mature (late in life cycle) firms 2) Broad-based equity index 3) Terminal value in more complex models • International valuation • Can be used to calculate P/E ratio (later)
DDM: Constant Growth (Gordon) Dividend expected in 1 year Dividend “just paid” Required return on equity Long-term dividend growth rate
DDM: Constant Growth (Gordon)Example • Assume: • Firm paid a dividend yesterday of $10 • Dividends will grow at 5%forever • r = 10% • What is a share worth?
DDM: Constant Growth (Gordon) • Correct Answer • Wrong Answer
DDM: Implied Growth Rate Example • Assume: • Firm just paid $1.20 dividend per share • Required return is 13% • Market price is $15.75 • Implied dividend growth rate is:
Perpetual Cash Flows • Point: Perpetual cash flows can be valued • Preferred stock • “No growth” assets • Formula: P0 = CF1 / r • Example: • CF1 = $12 • r = 10% • Value = $12/0.10 = $120
DDM: PV of Growth Opportunities • PVGO estimates portion of price attributable to future growth • Method: Segment firm value into two sources: 1) Perpetual earnings at current level 2) PV of growth opportunities (PVGO)
DDM: PVGO Example • Calculate PVGO: • Earnings of $12per share next year • Required return is 10% • Stock is trading for $140 • Solution: PVGO = $140 ─ ($12/0.10) = $140 ─ $120 = $20 • Note: “Buy” signal is combination of high growth potential and SMALL PVGO “No growth” value
DDM: Constant Growth (Gordon) Strengths: • Use for mature, stable, dividend paying firms • Supplements other methods Weaknesses: • Very sensitive to estimates of g • Difficult to use with non-dividend-paying stocks • Minority perspective only
DDM: Multi-Stage Models • Problem:Constant g assumption often unrealistic • Solution:Multi-stage models(2-stage, H, etc) • Two-stageassumes a “drop-off” in growth Important!!
DDM: Multi-Stage Models • H-model: Assumes a gradual decrease in g as firm matures
DDM: Multi-Stage Models • Three-stage model • Three distinct phases • High followed by lower followed by perpetual growth • High-growth phase + H-model pattern • High followed by linearly declining followed by perpetual growth
Phases of Growth • Initial growth phase - Use three-stage model • Rapid earnings growth/no dividends • ROE > r • Transitional phase – Use two-stage/H model • Earnings and dividend growth slow • ROE approaching r • Maturity phase – Use GGM • Growth at economy-wide rate • ROE = r
Terminal Value • Terminal value: PV of all CFs beyond the estimation horizon • All multi-stage models estimate CFs for some fixed period • However, equities have infinite lives • Point: Must calculate a terminal value with: • Gordon growth model • Price multiple Two methods
Application: The Two-Stage Model • Two stages of growth: • Initial high-growth phase • Perpetual stable-growth phase • Two approaches • Formula • Timeline • Suggestion: Use the timeline — it provides the flexibility to solve many types of problems
Application: The Two-Stage Model • Methodology: Individual estimation of the first set of dividends followed by the calculation of a terminal value • Note: Very important concept From Gordon growth model or price multiple
Application: The Two-Stage Model • Timeline example: • Dividends of $2.50 and$4.00 at the end of each of the next two years • Stage 2 constant growth = 4% • Required return = 12% • Calculate the value today
The Two-Stage Model: Another Example g = 4% Year 0 1 2 3 4 5 6 7 8 • Assume: • Current dividend is $10 • Stage 1: Grow at 15% for the first 5 years • Stage 2: Grow at 4% forever • Required return is 10%. • Calculate P0
D1 = _____________ D2 = _____________ D3 = _____________ D4 = _____________ D5 = _____________ P5 = _____________
P0 = ? 0 1 2 3 4 5 6
Solution: Using the hard-to-memorize formula: = $274 … with a low probability of success!!
Application: The H-Model • Problem: Two-stage model assumes high growth rate will suddenly drop • The H-model: More realistic assumption • Firm will start with high growth rate • Growth declines linearly over “2H” years • Note: Only an approximation; more accurate the shorter the declining growth period
Application: The H-Model Short-term “high” growth rate Most recent dividend Half # of years for decline Long-term “low” growth rate Required return
DDMs and Implied Return • Point: DDM can be used to find implied r • “Drive model in reverse” • Example - Solving GGM for r: • With lots of algebra, also applies to: • Two-stage • H-model
The Multi-Period Models • Strengths • Great versatility • Solve “forward and reverse” • Weaknesses • Require high-quality inputs (GIGO) • Model must be fully understood • Value estimates sensitive to g and r
SGR: The Sustainable Growth Rate • SGR: The only rate at which a firm can grow without changing key financial ratios and without issuing new equity • Important concept: SGR is frequently the method for calculating the firm’s growth rate
SGR: The Sustainable Growth Rate • DuPont equation: • Note: Always use beginning of year balance sheet numbers on exam (unless told otherwise)
SGR: Sustainable Growth Rate • If you combine DuPont and SGR, you get: • There you have it—the PRAT model!
FCF Defined • FCFF(FreeCashFlowtotheFirm) • Cash available to firm’s investors (bondholders and common shareholders) • FCFE(FreeCashFlowtoEquity) • Cash available to firm’s common shareholders after paying bondholders; • Not equal to dividends actually paid
FCFF vs. FCFE Know! • Firm value = FCFF discounted at WACC • Equity value = FCFE discounted at required return on equity • Use FCFE when capital structure not volatile • Use FCFF when high debt levels, negative FCFE • Equity value = firm value – MV of debt