Stock Valuation

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 • Malkiel’s “Firm foundations”

3. Dividend Discount ModelConstant 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 ModelConstant Dividends

5. Dividend Discount ModelGrowing 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 • Malkiel’s “Firm foundations”

11. Future Price EstimatesVariable 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. 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

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 • Malkiel’s “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 don’t 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 • Malkiel’s “Firm foundations”

42. Long-Run stock valuation • Price = PV(dividends/earnings) • Stresses uncertainty • Malkiel’s “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. Malkiel’s Caveats • Financial data is • Messy • Hard to predict

48. Evidence1998(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