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Valuation Curriculum designed for use with the Iowa Electronic Markets by Roger Ignatius Thomas A. Rietz 1 Valuation: Lecture Outline Principles of Valuation Discounted Dividend Models Constant Dividend Model Constant Growth Model Discounted Cash flow Model Market Multiple Models P/E versus Past and Peers P/S versus Past and Peers P/CF versus Past and Peers Summary 2 Principles of Valuation Book Value Depreciated value of assets minus outstanding liabilities Liquidation Value Amount that would be raised if all assets were sold independently Market Value (P) Value according to market price of outstanding stock Intrinsic Value (V) NPV of future cash flows (discounted at investors’ required rate of return) 3 Intrinsic Valuation Procedure Asset Characteristics Investor Characteristics • Size of Future Cash flows • Assessment of Cash • Time of Future Cash flows flow Riskiness • Risk of Future Cash flows • Risk Preferences Investors’ Required Rate of Return (k) n CFt V t 1 1 k t Where Does the Discount Rate (k) Come From? CAPM: k = rf + bxRP Beta (b) is estimated using historical data and is available from many sources The risk free rate (rf) is the current Treasury rate Typically the 3-mo rate, but other are sometimes used The risk premium (RP) is a historical average relative to the rf used 5 Example: Estimating k for Wal-Mart (WMT) on 4/27/01 Inputs Three month Treasury rate: 3.75% Historical average RP (1926-1996): 8.74% Beta for Dell (from MoneyCentral): 0.9 Computing k: CAPM: k = 0.0375 + 0.9x0.0874 = 11.62% 6 Sensitivity to CAPM Inputs Required Return (k) from CAPM Change in Risk Free 26% Rate 24% 22% Change in Risk 20% Premium 18% 16% Change in Beta 14% (Scale Shows Change / 10) 12% 10% Initial values: 8% 6% Rf = 3.75% RP = 8.47% -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 Beta = 1.5 Change in Input 7 Discounted Dividend Models Stock pricing relationship: Dt P0 t 1 (1 k )t Dividends will be Forecast directly Assumed to be constant Assumed to grow at a constant rate or Some combination of the above 8 Constant Dividend (Zero Growth Model) Model Stock pricing relationship: Dt P0 t 1 (1 k )t If Dt is constant, then it is an ordinary perpetuity: Dt D1 P0 t 1 (1 k ) t k 9 Example: Wal-Mart (4/27/01) The current (annual) dividend is: $0.28 According to the constant dividend (zero growth) model: $0.28 P0WMT $2.41 0.1162 The price of Wal-Mart was actually $52.83 Can you explain the difference? 10 Sensitivity to Constant Dividend Model Inputs $9 Change in Dividend Stock Price from Constan $8 (Scale shows $7 Change / 10) Growth Model $6 Change in Discount Rate $5 $4 $3 $2 Initial values: $1 D0 = $0.50 $0 k = 12% -0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 Change in Input 11 Why do a firm’s dividends grow? Because earnings grow. Why? Because of reinvested funds Used to expand or to undertake new projects Used in positive NPV projects Leads to Earnings growth Investments growth and Dividend growth Constant Growth Model Stock pricing relationship: Dt P0 t 1 (1 k )t If Dt grows at a constant rate, g, then it is a growth perpetuity: D1 D1 D0 (1 g ) P0 t 1 (1 k ) k g k g t 13 How do You Estimate Growth (g)? Historical average Average analyst forecast Sustainable growth g = (1-Payout Ratio)xROE Required return versus dividend yield: D0 k D1 D0 (1 g ) P0 k g gg P0 P0 D 1 0 P0 NOTE: Must have g<k in the long run! 14 Estimating g for Wal-Mart (4/27/01) 5 year historical average: 19.72% Average 5-year analyst forecast: 14.4% Sustainable growth g = (1-0.17)x0.22 = 18.26% Required return versus dividend yield: 0.1162 $0.28 g $52.83 11.03% 1 $0.28 $52.83 What should it be? 1st 3 are too high b/c long run must have g<k Guess: 11%? 15 Example: Wal-Mart (4/27/01) Current (annual) dividend is: $0.28 If we use estimated growth of 11%: $0.28 1.11 P0 $50.13 0.1162 0.11 The price of Wal-Mart was actually $52.83 Notes: Must have g<k in long run As gk, the price increases without bound 16 Sensitivity to Constant Growth Model Inputs Change in Dividend $60 (Scale shows Stock Price from Constan Change / 10) $50 Change in Discount Growth Model $40 Rate $30 Growth Rate $20 $10 Initial values: D0 = $0.50 $0 k = 12% 0.00 0.01 0.02 0.03 0.04 0.05 -0.05 -0.04 -0.03 -0.02 -0.01 g = 6% Change in Input 17 Summary of Dividend Discount Models Represents the value of dividends received by shareholders Requires A discount rate (k) Dividends (D) Steady or zero growth (g, with g<k) Trouble valuing Companies with D=0 Fast growing companies with g>k 18 Discounted Cash Flow Model Shareholders receive or “own”: 1. Dividends 2. Re-invested earnings The effects of re-invested earnings are captured in dividend growth if a firm pays dividends and growth can be estimated An alternative valuation comes from valuing cash flows available to stockholders directly Useful for companies that pay no dividends 19 What Constitutes Cash flows? There is some debate over exactly what constitutes cash flows The GAAP cash flow statement: CF = NI + depreciation – preferred stock dividends This should represent CFs that are either 1. Paid out in common stock dividends or 2. Re-invested 20 What Discount Rate Should be used? It depends on the definition of CFs If CFs are defined as those available to all investors, WACC should be used If CFs are defined as those available to common stockholders, k from CAPM should be used We will use the latter 21 Example: Estimating k for K- Mart (K) on 4/27/01 Inputs Three month Treasury rate: 3.75% Historical average RP (1926-1996): 8.74% Beta for K-Mart (from MoneyCentral): 1 Computing k: CAPM: k = 0.0375 + 1x0.0874 = 12.49% 22 How do You Estimate Growth (g)? CFs will also grow Use methods similar to dividend growth, but Analysts forecasts are typically unavailable For many companies, dividend yield cannot be used b/c there is no dividend Often, earnings or sales growth are used Expenses and re-investment need to be relatively constant percentages of sales NOTE: Must have g<k in the long run! 23 Estimating g for K-Mart (4/27/01) From the historical income statement: Dec-00 Dec-99 Dec-98 Dec-97 Dec-96 Net Income $ (244.00) $ 403.00 $ 518.00 $ 249.00 $ (220.00) Dep & Amort $1,460.00 $2,070.00 $1,762.00 $1,555.00 $1,427.00 Pref Div $ - $ - $ - $ - $ - Cashflow $ 1,216.00 $ 2,473.00 $ 2,280.00 $ 1,804.00 $ 1,207.00 Growth -50.83% 8.46% 26.39% 49.46% Avg Growth: 8.37% 5 year sales growth: 2.35% Analysts’ 5 year earnings forecast: 10.3% Suppose, you believe K-Mart will not grow at all! 24 Example: K-Mart (4/27/01) According to the last statements: CF = $1,216 million Shares = 486.5 million CF/Share = $2.50 If we use estimated growth of 0.0%: $2.50 1.00 P0 $20.01 0.1249 0.00 The price of K-Mart was actually $9.82 What must the market be expecting for K- Mart’s growth in the future? 25 Sensitivity to Constant Growth Cash flow Model Inputs Change in Cashflow $60 (Scale shows Stock Price from Constan Change / 10) $50 Change in Discount Growth Model $40 Rate $30 Growth Rate $20 $10 Initial values: CF0 = $0.50 $0 k = 12% 0.00 0.01 0.02 0.03 0.04 0.05 -0.05 -0.04 -0.03 -0.02 -0.01 g = 6% Change in Input 26 Summary of Discounted Cash flow Models Represents the value of cash flows available to shareholders Requires A discount rate (k) A reasonable measure of cash flows o IMPORTANT: How much depreciation MUST be replaced ? Model assumes zero. Steady or zero growth (g, with g<k) Trouble valuing Companies with CF<0 Fast growing companies with g>k Companies with necessary replacement of depreciated assets 27 Market Multiples Valuations are derived by: 1. Forecasting earnings, sales or cash flows 2. Applying the company’s historical P/E, P/S or P/CF to forecast 3. Applying industry average P/E, P/S or P/CF to current inputs Why do P/E Ratios Make Sense? A company with a payout ratio of 1 will not grow and be valued at: D E P 1 1 P0 1 0 r r E1 r A company with a payout less than 1 will grow and be valued at: E P 1 PVGO P 1 PVGO r E r E 1 1 29 Logic of Market Multiple Models Sales, earnings and cash flow drive profits, growth and value P/S, P/E & P/CF ratios show the relationship between price and these value drivers Firms within an industry have similar sales, profit and cash flow patterns and similar required returns Therefore, a reasonable value for a firm is its sales, earnings or cash flows times the respective industry ratio 30 P/E Ratio Valuation If company “j” is “valued at historical ratios” relative to earnings: P0j P1j E1j j E 0 If company “j” is “valued at industry ratios” relative to earnings: P0i P0j E0j Avg i Industry E 0 31 Example: Wal-Mart (4/27/01) Valued at historical P/E ratio: Analysts forecast next year’s earnings for WMT at $1.58 WMT’s recent P/E was 37.7 Then: P = $1.58x37.7 = $59.57 Valued at industry average P/E ratio: This year, earnings for WMT were $1.40 The industry average P/E was 36.0 Then: P = $1.40x36.0 = $50.40 The price of Wal-Mart was actually $52.83 32 Sensitivity to P/E Multiple Model Inputs $70 Change in Earnings Stock Price from Constan $60 Growth Model $50 Change Benchmark P/E Ratio (Scale $40 shows Change / 10) $30 $20 Initial values: $10 E1 = $1.50 $0 P/E = 35 0.00 0.10 0.20 0.30 0.40 0.50 -0.50 -0.40 -0.30 -0.20 -0.10 Change in Input 33 P/S Ratio Valuation For companies w/o earnings, P/S is sometimes used If you have a sales forecast, company “j” is “valued at historical ratios” relative to sales: j P0 P1j S1j j S 0 Using current sales, a company “j” is “valued at industry ratios” relative to sales: P0i P0j S0j Avg i Industry S0 34 Example: Amazon (4/27/01) For the year ending 12/00 Sales = 2,762 million (income statement) Shares = 357.1 million (balance sheet) Sales/Share = 2762/357.1 = 7.73 Industry average P/S = 3.46 So, using industry P/S Amazon should be priced at: 3.46x7.73 = $26.76 The price of Amazon was actually $15.27 35 Sensitivity to P/S Multiple Model Inputs $70 Change in Sales Stock Price from Constan $60 Growth Model $50 Change Benchmark P/S Ratio (Scale $40 shows Change / 10) $30 $20 Initial values: $10 S1 = $3.00 $0 P/S = 15 0.00 0.10 0.20 0.30 0.40 0.50 -0.50 -0.40 -0.30 -0.20 -0.10 Change in Input 36 P/CF Ratio Valuation • For companies w/o dividends, P/CF is sometimes used • If you have a cash flow forecast, company “j” is “valued at historical ratios” relative to cash flows: P0j P1j CF1j CF j 0 • Using current cash flow, company “j” is “valued at industry ratios” relative to cash flows: P0i P0j CF0j Avg Industry CF0 i 37 Example: K-Mart (4/27/01) For the year ending 12/00 CF = 1,216 million (discussed previously) Shares = 486.5 million (balance sheet) CF/Share = 1216/486.51 = 2.50 Industry average P/CF = 21.3 Using industry P/CF K-Mart should be priced at: 21.3x2.50 = $53.24 The price of K-Mart was actually $9.82 Is K-Mart undervalued or in serious trouble? 38 Sensitivity to P/CF Multiple Model Inputs $70 Change in Cashflow Stock Price from Constan $60 Growth Model $50 Change Benchmark P/CF Ratio (Scale $40 shows Change / 10) $30 $20 Initial values: $10 CF = $1.00 $0 P/S = 30 0.00 0.10 0.20 0.30 0.40 0.50 -0.50 -0.40 -0.30 -0.20 -0.10 Change in Input 39 Summary of Market Multiples Models Valuations using historical and industry ratios Provide useful benchmarks Useful when dividends and cash flows cannot be discounted directly Can be compared to current ratios as a measure of market sentiment Weaknesses Misleading for firms that are changing rapidly or do not resemble the industry 40 Summary • Discounted Dividend • Why several w/ dividends and methods? constant expected Each has strengths (possibly zero) growth and weaknesses in dividends Different methods • Discounted Cash flow useful in different w/o dividends and situations constant expected Each gives a different (possibly zero) growth “take” on the value of in cash flows the company’s stock • P/E, P/S and P/CF Provides a range of ratios valuations instead of point estimates Comparison with past or industry 41

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