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# Stock Valuation

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### Stock Valuation

1. 1. Goals Stock Valuation  Dividend valuation model  “dividend discount model” Economics 71a: Spring 2007  Forecasting earnings, dividends, and Mayo 11 prices  Ratio valuations Malkiel, 5, 6 (136-144), 8  Malkiel’s “Firm foundations” Lecture notes 4.2 Dividend Discount Model Dividend Discount Model Constant Dividends Constant Dividends  Evaluate stream of dividends  Stock pays the same constant dividend ! forever P = PV = " d d =  Assume some “required return” = k t=1 (1+ k)t k  k = RF + RP  k = RF + beta(E(Rm)-RF)  Same as perpetuity formula 1
2. 2. Dividend Discount Model More Growing Dividends Growing Dividends ! ! (1 + g) t d 0 PV = " = d0 " a t t=1 (1 + k) t  Evaluate stream of growing dividends t=1 1+ g a= dt = (1+ g)t d0 1+ k (1 + g) (1 + g) g = growth rate a (1 + k) (1 + k) PV = d0 = d = d (1 # a) (1 + g) 0 (k # g) 0 1# (1 + k) (1 + k) (1 + g) 1 PV = d0 = d1 (k # g) (k # g) Dividend Discount Examples  Must have k>g for this to make sense  Let initial d = 1, k=0.05, g=0.02  Otherwise, dividends growing too fast  PV = 1.02/(0.05-0.02) = 34 k = 0.05, g = 0.03  Basic feature: Very sensitive to g  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 2
3. 3. What if dividends not growing Goals forever?  Solve this by calculator or computer for d(t)  Dividend valuation model  “dividend discount model”  Forecasting earnings, dividends, and ! P =" dt prices t=1 (1+ k)t  Ratio valuations  Malkiel’s “Firm foundations” Future Price Estimates Present Value Calculation Variable Growth Model (End of year dividends.)  Forecast dividends in early years  In last year d d d P  Estimate dividend growth P2007 = 2007 + 2008 + 2009 + 2009 (1 + k) (1 + k) 2 (1 + k) 3 (1 + k) 3  Use this to estimate future price (1 + g) P2009 = d (k ! g) 2009 3
4. 4. Forecasting Dividends Sales -> Earnings  Forecast sales revenue Earnings  Guess revenue growth rates Net Profit Margin = Sales  Sales tomorrow = (1+g) (Sales today) Earnings = (Net profit margin) x Sales Earnings Earnings/share = Total shares (float) Future Price Earnings->Dividends (Guess long term growth, g.) Dividend/share = (payout ratio) x (earnings/share) (1 + g) P2009 = d (k ! g) 2009 4
5. 5. Required Return (CAPM) Back to Problem  Assume the CAPM is working  RF= 3%  Required return for asset j  RM = 8% (difﬁcult) k j = RF + RPj k j = RF + ! j (RM " RF )  RP = risk premium  Think of k as the return that a certain asset should get given its risk level What You Need? Microsoft 3 year forecasts Assumptions Beta 0.88 Market return 0.08 Revenue Growth 0.1 Risk free 0.03  Revenue (sale) forecasts P/E Div Payout 22 Future growth 0.32 0.05 Profit Margin 0.26 Shares (billions) 9.7  Gross proﬁtability estimates 2004 2005 2006 2007 2008 2009 Price(2009) Revenue 36.00 40.00 44.00 48.40 53.24 58.56  Dividend payout estimates Earnings 8.10 12.25 13.00 12.58 13.84 15.23 EPS 0.84 1.26 1.34 1.30 1.43 1.57 Dividend/Share 0.27 0.40 0.43 0.42 0.46 0.50 21.98  Shares Required Return 0.074 1 2 3 3  CAPM inputs Discounted values 0.3865 0.3959 0.4055 17.7398 Present Value 18.93  Future growth estimates 5
6. 6. Connecting to P/E Ratios P/E E t = (1+ g) t E 0 , d t = (1 ! rr)E t  Deﬁne the following two terms " dt  Retention rate PV = #  rr = fraction of earnings that go back to ﬁrm t=1 (1 + k) t  Dividend payout ratio (dividends/earnings) " (1 ! rr)E t " Et  Fraction of earnings going to shareholders PV = # = (1 ! rr)#  (1-rr) t=1 (1+ k) t t=1 (1 + k) t (1 + g) (1 ! rr)  Dividends = (1-rr)(earnings) PV = (1 ! rr) E0 = E1 (k ! g) (k ! g) P/E Ratios P/E Ratios (1 + g) (1 ! rr)  Firms with greater earnings growth will PV = (1 ! rr) E0 = E1 (k ! g) (k ! g) have greater P/E ratios (1! rr) = div payout ratio  Firms with higher dividend payouts will (1 + g) have higher P/E ratios PV/E 0 = (1! rr) = P/E Ratio (curent earnings) (k ! g) div payout ratio PV/E1 = = P/E ratio (future earnings) (k ! g) 6
7. 7. Example: Microsoft g, ROE, and rr ( Price = 27)  P/E = 23 Reinvested earnings  Beta = 0.88, Rm = 0.08, Rf = 0.03 g = Shareholders equity  k = 0.03 + 0.88(0.08-0.03) Reinvested earnings Total earnings g= *  k = 0.074 Total earnings Shareholders equity  Growth g = rr * (return on equity)  g = 0.05, 0.06 MSFT = (1- 0.32) * (0.29) = 0.20  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 Goals Ratio Valuations  Dividend valuation model  Find various price ratios  “dividend discount model”  See if stock looks “cheap” relative to  Forecasting earnings, dividends, and reference group prices  Also, forecast future prices using  Ratio valuations forecasts of ratios  Malkiel’s “Firm foundations”  Necessary for nondividend paying stocks 7
8. 8. P/E Ratio Comparisons P/E Price Forecast  Find current P/E ratio  Forecast future P/E ratio  Compare with industry  Forecast future earnings  Low:  Future price = (P/E)*E  Buy  Discount this back to today, and  High compare with current price  Sell  Can also be used along with dividend forecasts too Example: Irobot Irobot long range forecasts  Recent IPO Assumptions Beta 2.2 Market return 0.08 Earnings Growth 0.2 Risk free 0.03  Little data to work with P/E Div Payout 94 Long run growth 0.25 0.13  Pays zero dividends Shares (millions) 14 (Millions) 2004 2005 2006 2010 2015 (P/E) 2015(Div discount)  High risk Earnings EPS 0.22 0.00 2.61 0.19 3.56 0.25 7.38 0.53 18.37 1.31 18.37 1.31 Dividends 0.00 0.00 0.00 0.00 0.00 0.33 Price 13.00 49.56 123.33 37.01 Required Return 0.14 PV 29.35 37.93 11.38 8
9. 9. g, ROE, and rr P/E Ratios w/o dividends  Remember comment about dividends Reinvested earnings g = Shareholders equity don’t matter Reinvested earnings Total earnings g= *  Value entire earnings stream, since you Total earnings Shareholders equity g = rr * (return on equity) own this IRBT = (1 - 0.00) * (0.039) = 0.039  Max bound on P/E ratio  Related to PEG ratios (P/E)/growth P/E (without divs) IRobot Again (Upper bound) k = 0.14, g = 0.10 E t = (1 + g) t E 0  P/E = (1+0.10)/(0.14-0.10) ! !  P/E = 27.5 Et Et PV = " ="  k=0.14, g = 0.13 t =1 (1 + k) t t =1(1 + k) t  P/E = (1+0.13)/(0.14-0.13) (1 + g) 1 PV = E = E  P/E = 113 (k # g) 0 (k # g) 1  Market P/E = 90 (1 + g) P /E = (k # g) 9
10. 10. S&P 500 P/E Ratio Key Problems  Estimatinggrowth with little data  What should P/E be?  “Earnings multiple”  Compare with other ﬁrms  Crude dividend discount checks  Lotsof guesswork  Negative earnings? Other Ratios Data Tools  Price/Cashﬂow  Stock screening software  Price/Bookvalue  See Yahoo ﬁnance  Price/Sales  Key problem:  Find appropriate comparison ﬁrms 10
11. 11. Goals Long-Run stock valuation  Dividend valuation model  Price= PV(dividends/earnings)  “dividend discount model”  Stresses uncertainty  Forecasting earnings, dividends, and  Malkiel’s “determinants” prices  Ratio valuations  Malkiel’s “Firm foundations” Determinant 1: Determinant 2: Expected Growth Rate Dividend Payout  Remember formulas  Financial Ratio  Higher expected growth -> Higher price  Div. Payout Ratio = Divs/Earnings (can be very strong)  Big question: How long and by how much will unusual growth last? 11
12. 12. Determinant 3: Determinant 4: Risk Interest rates  Growth rates and interest rates are  Back to our PV formulas uncertain  Higher interest rates (lower stock  Price should be higher (all things equal) prices) the less risky the earnings stream  Two ways to think about it  Risk is difﬁcult to quantify  PV formula  Stock market alternatives look better Evidence Malkiel’s Caveats 1998(Malkiel)  Financial data is  Messy  Hard to predict 12
13. 13. What does this say? Valuation Wrap Up  Growth rates matter  Many tools  First hint of rationality in the stock  No one right answer market  Some common sense, and rules of  How can you tell when a P/E ratio is out thumb of line?  Try to stay close to sensible  Look at stocks with comparable growth growth/valuation ideas rates 13