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## Valuation

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**Valuation**Curriculum designed for use with the Iowa Electronic Markets by Roger Ignatius Thomas A. Rietz**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**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)**Intrinsic Valuation Procedure**• Asset Characteristics • Size of Future Cash flows • Time of Future Cash flows • Risk of Future Cash flows • Investor Characteristics • Assessment of Cash flow Riskiness • Risk Preferences Investors’ Required Rate of Return (k)**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**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%**Sensitivity to CAPM Inputs**Initial values: Rf = 3.75% RP = 8.47% Beta = 1.5**Discounted Dividend Models**• Dividends will be • Forecast directly • Assumed to be constant • Assumed to grow at a constant rate or • Some combination of the above • Stock pricing relationship:**Constant Dividend (Zero Growth Model) Model**• If Dt is constant, then it is an ordinary perpetuity: • Stock pricing relationship:**Example: Wal-Mart (4/27/01)**• The price of Wal-Mart was actually $52.83 • Can you explain the difference? • The current (annual) dividend is: $0.28 • According to the constant dividend (zero growth) model:**Sensitivity to Constant Dividend Model Inputs**Initial values: D0 = $0.50 k = 12%**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**• If Dt grows at a constant rate, g, then it is a growth perpetuity: • Stock pricing relationship:**How do You Estimate Growth (g)?**• NOTE: Must have g<k in the long run! • Historical average • Average analyst forecast • Sustainable growth • g = (1-Payout Ratio)xROE • Required return versus dividend yield:**Estimating g for Wal-Mart (4/27/01)**• What should it be? • 1st 3 are too high b/c long run must have g<k • Guess: 11%? • 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:**Example: Wal-Mart (4/27/01)**• The price of Wal-Mart was actually $52.83 • Notes: • Must have g<k in long run • As gk, the price increases without bound • Current (annual) dividend is: $0.28 • If we use estimated growth of 11%:**Sensitivity to Constant Growth Model Inputs**Initial values: D0 = $0.50 k = 12% g = 6%**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**Discounted Cash Flow Model**• Shareholders receive or “own”: • Dividends • 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**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 • Paid out in common stock dividends or • Re-invested**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**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%**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!**Estimating g for K-Mart (4/27/01)**• 5 year sales growth: 2.35% • Analysts’ 5 year earnings forecast: 10.3% • Suppose, you believe K-Mart will not grow at all! • From the historical income statement:**Example: K-Mart (4/27/01)**• The price of K-Mart was actually $9.82 • What must the market be expecting for K-Mart’s growth in the future? • 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%:**Sensitivity to Constant Growth Cash flow Model Inputs**Initial values: CF0 = $0.50 k = 12% g = 6%**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 • 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**Market Multiples**• Valuations are derived by: • Forecasting earnings, sales or cash flows • Applying the company’s historical P/E, P/S or P/CF to forecast • 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 less than 1 will grow and be valued at: • A company with a payout ratio of 1 will not grow and be valued at:**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**P/E Ratio Valuation**• If company “j” is “valued at industry ratios” relative to earnings: • If company “j” is “valued at historical ratios” relative to earnings:**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**Sensitivity to P/E Multiple Model Inputs**Initial values: E1 = $1.50 P/E = 35**P/S Ratio Valuation**• Using current sales, a company “j” is “valued at industry ratios” relative to sales: • 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:**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**Sensitivity to P/S Multiple Model Inputs**Initial values: S1 = $3.00 P/S = 15**P/CF Ratio Valuation**• Using current cash flow, company “j” is “valued at industry ratios” relative to cash flows: • 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:**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?**Sensitivity to P/CF Multiple Model Inputs**Initial values: CF = $1.00 P/S = 30**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**Discounted Dividend**w/ dividends and constant expected (possibly zero) growth in dividends Discounted Cash flow w/o dividends and constant expected (possibly zero) growth in cash flows P/E, P/S and P/CF ratios Comparison with past or industry Why several methods? Each has strengths and weaknesses Different methods useful in different situations Each gives a different “take” on the value of the company’s stock Provides a range of valuations instead of point estimates Summary