# Goals. Stock Valuation. Dividend Discount Model Constant Dividends. Dividend Discount Model Constant Dividends

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1 Stock Valuation Economics 71a: Spring 2007 Mayo 11 Malkiel, 5, 6 ( ), 8 Lecture notes 4.2 Goals Dividend valuation model dividend discount model Forecasting earnings, dividends, and prices Ratio valuations Malkiel s Firm foundations 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 Dividend Discount Model Constant Dividends! d P = PV = " = d (1 + k) t k t =1 1

2 Dividend Discount Model Growing Dividends Evaluate stream of growing dividends g = growth rate d t = t d 0 More Growing Dividends! t d PV = " 0 = d (1 + k) t 0 " a t t =1! t =1 a = 1 + g 1 + k a PV = (1# a) d (1 + k) 0 = d 0 = 1# (1 + k) PV = (k # g) d 0 = 1 (k # g) d 1 (1 + k) (k # g) (1 + k) d 0 Dividend Discount Must have k>g for this to make sense Otherwise, dividends growing too fast Basic feature: Very sensitive to g 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 2

3 What if dividends not growing forever? Solve this by calculator or computer for d(t) P =! " t =1 d t (1 + k) t Goals Dividend valuation model dividend discount model Forecasting earnings, dividends, and prices Ratio valuations Malkiel s Firm foundations Future Price Estimates Variable Growth Model Forecast dividends in early years In last year Estimate dividend growth Use this to estimate future price Present Value Calculation (End of year dividends.) P 2007 = d 2007 (1 + k) + d 2008 (1 + k) 2 + d 2009 (1 + k) 3 + P 2009 (1 + k) 3 P 2009 = (k! g) d

4 Forecasting Dividends Forecast sales revenue Guess revenue growth rates Sales tomorrow = (1+g) (Sales today) Sales -> Earnings Net Profit Margin = Earnings Sales Earnings = (Net profit margin) x Sales Earnings/share = Earnings Total shares (float) Earnings->Dividends Future Price (Guess long term growth, g.) Dividend/share = (payout ratio) x (earnings/share) P 2009 = (k! g) d

5 Required Return (CAPM) Back to Problem Assume the CAPM is working Required return for asset j RF = 3% RM = 8% (difficult) k j = R F + RP j k j = R F +! j (R M " R F ) RP = risk premium Think of k as the return that a certain asset should get given its risk level What You Need? Revenue (sale) forecasts Gross profitability estimates Dividend payout estimates Shares CAPM inputs Future growth estimates Microsoft 3 year forecasts Assumptions Beta 0.88 Market return 0.08 Revenue Growth 0.1 Risk free 0.03 P/E 22 Future growth 0.05 Div Payout 0.32 Profit Margin 0.26 Shares (billions) Price(2009) Revenue Earnings EPS Dividend/Share Required Return Discounted values Present Value

6 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) P/E E t = t E 0, d t = (1! rr)e t " # d t PV = t =1(1 + k) t " (1! rr)e PV = t E # = (1! rr) # t (1 + k) t t =1 t =1(1 + k) t PV = (1! rr) (k! g) E (1! rr) 0 = (k! g) E 1 " P/E Ratios PV = (1! rr) (k! g) E (1! rr) 0 = (k! g) E 1 (1! rr) = div payout ratio PV/E 0 = (1! rr) = P/E Ratio (curent earnings) (k! g) PV/E 1 = div payout ratio = P/E ratio (future earnings) (k! g) P/E Ratios Firms with greater earnings growth will have greater P/E ratios Firms with higher dividend payouts will have higher P/E ratios 6

7 P/E = 23 Example: Microsoft ( Price = 27) 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 g, ROE, and rr Reinvested earnings g = Shareholders equity Reinvested earnings Total earnings g = * Total earnings Shareholders equity g = rr * (return on equity) MSFT = (1-0.32) * (0.29) = 0.20 Goals Dividend valuation model dividend discount model Forecasting earnings, dividends, and prices Ratio valuations Malkiel s Firm foundations 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 7

8 P/E Ratio Comparisons Find current P/E ratio Compare with industry Low: Buy High Sell 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 Example: Irobot Recent IPO Little data to work with Pays zero dividends High risk Irobot long range forecasts Assumptions Beta 2.2 Market return 0.08 Earnings Growth 0.2 Risk free 0.03 P/E 94 Long run growth 0.13 Div Payout 0.25 Shares (millions) 14 (Millions) (P/E) 2015(Div discount) Earnings EPS Dividends Price Required Return 0.14 PV

9 g, ROE, and rr Reinvested earnings g = Shareholders equity Reinvested earnings Total earnings g = * Total earnings Shareholders equity g = rr * (return on equity) IRBT = (1-0.00) * (0.039) = P/E Ratios w/o dividends Remember comment about dividends don t matter Value entire earnings stream, since you own this Max bound on P/E ratio Related to PEG ratios (P/E)/growth P/E (without divs) (Upper bound) E t = t E 0!! PV = Et " = Et " t =1 (1 + k)t t =1 (1 + k)t PV = (k # g) E 0 = 1 (k # g) E 1 P /E = (k # g) k = 0.14, g = 0.10 IRobot Again 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 9

10 Key Problems S&P 500 P/E Ratio 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? Other Ratios Price/Cashflow Price/Bookvalue Price/Sales Key problem: Find appropriate comparison firms Data Tools Stock screening software See Yahoo finance 10

11 Goals Dividend valuation model dividend discount model Forecasting earnings, dividends, and prices Ratio valuations Malkiel s Firm foundations Long-Run stock valuation Price = PV(dividends/earnings) Stresses uncertainty Malkiel s determinants 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? Determinant 2: Dividend Payout Financial Ratio Div. Payout Ratio = Divs/Earnings 11

12 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 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 Malkiel s Caveats Evidence 1998(Malkiel) Financial data is Messy Hard to predict 12

13 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 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 13

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