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Stock Valuation Economics 71a: Spring 2007 Mayo 11 Malkiel, 5, 6 ( ), 8 Lecture notes 4.2

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Goals Dividend valuation model dividend discount model Forecasting earnings, dividends, and prices Ratio valuations Malkiels Firm foundations

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Dividend Discount Model Constant Dividends Evaluate stream of dividends Stock pays the same constant dividend forever Assume some required return = k k = RF + RP k = RF + beta(E(Rm)-RF) Same as perpetuity formula

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Dividend Discount Model Constant Dividends

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Dividend Discount Model Growing Dividends Evaluate stream of growing dividends g = growth rate

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More Growing Dividends

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Dividend Discount Must have k>g for this to make sense Otherwise, dividends growing too fast Basic feature: Very sensitive to g

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Examples Let initial d = 1, k=0.05, g=0.02 PV = 1.02/( ) = 34 k = 0.05, g = 0.03 PV = 1.03/( ) = 51.5 Why is this important? Stock prices Small changes in beliefs lead to big changes in prices

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What if dividends not growing forever? Solve this by calculator or computer for d(t)

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Goals Dividend valuation model dividend discount model Forecasting earnings, dividends, and prices Ratio valuations Malkiels Firm foundations

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Future Price Estimates Variable Growth Model Forecast dividends in early years In last year Estimate dividend growth Use this to estimate future price

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Present Value Calculation (End of year dividends.)

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Forecasting Dividends Forecast sales revenue Guess revenue growth rates Sales tomorrow = (1+g) (Sales today)

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Sales -> Earnings

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Earnings->Dividends

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Future Price (Guess long term growth, g.)

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Required Return (CAPM) Assume the CAPM is working Required return for asset j RP = risk premium Think of k as the return that a certain asset should get given its risk level

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Back to Problem RF = 3% RM = 8% (difficult)

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What Do You Need? Revenue (sales) forecasts Gross profitability estimates Dividend payout estimates Shares CAPM inputs Future growth estimates

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Connecting to P/E Ratios Define the following two terms Retention rate rr = fraction of earnings that go back to firm Dividend payout ratio (dividends/earnings) Fraction of earnings going to shareholders (1-rr) Dividends = (1-rr)(earnings)

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P/E

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P/E Ratios

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Firms with greater earnings growth will have greater P/E ratios Firms with higher dividend payouts will have higher P/E ratios

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Example: Microsoft ( Price = 27) P/E = 23 Beta = 0.88, Rm = 0.08, Rf = 0.03 k = ( ) k = Growth g = 0.05, 0.06 Div payout ratio 0.32 P/E = 0.32(1.05)/( ) = 14 P/E = 0.32(1.06)/( ) = 24

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g, ROE, and rr

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Goals Dividend valuation model dividend discount model Forecasting earnings, dividends, and prices Ratio valuations Malkiels Firm foundations

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Ratio Valuations Find various price ratios See if stock looks cheap relative to reference group Also, forecast future prices using forecasts of ratios Necessary for nondividend paying stocks

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P/E Ratio Comparisons Find current P/E ratio Compare with industry Low: Buy High Sell

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P/E Price Forecast Forecast future P/E ratio Forecast future earnings Future price = (P/E)*E Discount this back to today, and compare with current price Can also be used along with dividend forecasts too

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Example: Irobot Recent IPO Little data to work with Pays zero dividends High risk

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g, ROE, and rr

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P/E Ratios w/o dividends Remember comment about dividends dont matter Value entire earnings stream, since you own this Max bound on P/E ratio Related to PEG ratios (P/E)/growth

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P/E (without divs) (Upper bound)

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IRobot Again k = 0.14, g = 0.10 P/E = (1+0.10)/( ) P/E = 27.5 k=0.14, g = 0.13 P/E = (1+0.13)/( ) P/E = 113 Market P/E = 90

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Key Problems Estimating growth with little data What should P/E be? Earnings multiple Compare with other firms Crude dividend discount checks Lots of guesswork Negative earnings?

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S&P 500 P/E Ratio

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Other Ratios Price/Cashflow Price/Bookvalue Price/Sales Key problem: Find appropriate comparison firms

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Data Tools Stock screening software See Yahoo finance

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Goals Dividend valuation model dividend discount model Forecasting earnings, dividends, and prices Ratio valuations Malkiels Firm foundations

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Long-Run stock valuation Price = PV(dividends/earnings) Stresses uncertainty Malkiels determinants

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Determinant 1: Expected Growth Rate Remember formulas Higher expected growth -> Higher price (can be very strong) Big question: How long and by how much will unusual growth last?

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Determinant 2: Dividend Payout Financial Ratio Div. Payout Ratio = Divs/Earnings

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Determinant 3: Risk Growth rates and interest rates are uncertain Price should be higher (all things equal) the less risky the earnings stream Risk is difficult to quantify

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Determinant 4: Interest rates Back to our PV formulas Higher interest rates (lower stock prices) Two ways to think about it PV formula Stock market alternatives look better

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Malkiels Caveats Financial data is Messy Hard to predict

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Evidence 1998(Malkiel)

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What does this say? Growth rates matter First hint of rationality in the stock market How can you tell when a P/E ratio is out of line? Look at stocks with comparable growth rates

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Valuation Wrap Up Many tools No one right answer Some common sense, and rules of thumb Try to stay close to sensible growth/valuation ideas

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