1. Stock Valuation Economics 71a: Spring 2007 Mayo 11 Malkiel, 5, 6 (136-144), 8 Lecture notes 4.2

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

3. 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

4. Dividend Discount Model Constant Dividends

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

6. More Growing Dividends

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

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

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

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

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

12. Present Value Calculation (End of year dividends.)

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

14. Sales -> Earnings

15. Earnings->Dividends

16. Future Price (Guess long term growth, g.)

17. 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

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

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

21. 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)

22. P/E

23. P/E Ratios

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

25. Example: Microsoft ( Price = 27) P/E = 23 Beta = 0.88, Rm = 0.08, Rf = 0.03 k = 0.03 + 0.88(0.08-0.03) k = 0.074 Growth g = 0.05, 0.06 Div payout ratio 0.32 P/E = 0.32(1.05)/(0.074-0.05) = 14 P/E = 0.32(1.06)/(0.074-0.06) = 24

26. g, ROE, and rr

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

28. 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

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

30. 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

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

33. g, ROE, and rr

34. 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

35. P/E (without divs) (Upper bound)

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

37. 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?

38. S&P 500 P/E Ratio

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

40. Data Tools Stock screening software See Yahoo finance

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

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

43. 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?

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

45. 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

46. 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

47. Malkiels Caveats Financial data is Messy Hard to predict

48. Evidence 1998(Malkiel)

49. 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

50. 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