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# Stock valuation

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### Stock valuation

1. 1. 1Stock ValuationEconomics 71a: Spring 2007Mayo 11Malkiel, 5, 6 (136-144), 8Lecture notes 4.2Goals Dividend valuation model “dividend discount model” Forecasting earnings, dividends, andprices Ratio valuations Malkiel’s “Firm foundations”Dividend Discount ModelConstant Dividends Evaluate stream of dividends Stock pays the same constant dividendforever Assume some “required return” = k k = RF + RP k = RF + beta(E(Rm)-RF) Same as perpetuity formulaDividend Discount ModelConstant DividendsP = PV =d(1+ k)tt=1!" =dk
2. 2. 2Dividend Discount ModelGrowing Dividends Evaluate stream of growing dividends g = growth ratedt = (1+ g)td0More Growing DividendsPV =(1+ g)td0(1+ k)tt=1!" = d0 att=1!"a =1+ g1+ kPV =a(1# a)d0 =(1+ g)(1+ k)1#(1+ g)(1+ k)d0 =(1+ g)(1+ k)(k # g)(1+ k)d0PV =(1+ g)(k # g)d0 =1(k # g)d1Dividend Discount Must have k>g for this to make sense Otherwise, dividends growing too fast Basic feature: Very sensitive to gExamples 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 bigchanges in prices
3. 3. 3What if dividends not growingforever? Solve this by calculator or computer for d(t)P =dt(1+ k)tt=1!"Goals Dividend valuation model “dividend discount model” Forecasting earnings, dividends, andprices Ratio valuations Malkiel’s “Firm foundations”Future Price EstimatesVariable Growth Model Forecast dividends in early years In last year Estimate dividend growth Use this to estimate future pricePresent Value Calculation(End of year dividends.)P2007 =d2007(1 + k)+d2008(1 + k)2+d2009(1 + k)3+P2009(1 + k)3P2009 =(1 + g)(k ! g)d2009
4. 4. 4Forecasting Dividends Forecast sales revenue Guess revenue growth rates Sales tomorrow = (1+g) (Sales today)Sales -> EarningsNet Profit Margin =EarningsSalesEarnings = (Net profit margin) x SalesEarnings/share =EarningsTotal shares (float)Earnings->DividendsDividend/share = (payout ratio) x (earnings/share)Future Price(Guess long term growth, g.)P2009 =(1 + g)(k ! g)d2009
5. 5. 5Required 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 shouldget given its risk levelkj = RF + RPjkj = RF + !j (RM " RF )Back to Problem RF = 3% RM = 8% (difﬁcult)What You Need? Revenue (sale) forecasts Gross proﬁtability estimates Dividend payout estimates Shares CAPM inputs Future growth estimatesMicrosoft 3 year forecastsAssumptionsBeta 0.88 Market return 0.08Revenue Growth 0.1 Risk free 0.03P/E 22 Future growth 0.05Div Payout 0.32Profit Margin 0.26Shares (billions) 9.72004 2005 2006 2007 2008 2009 Price(2009)Revenue 36.00 40.00 44.00 48.40 53.24 58.56Earnings 8.10 12.25 13.00 12.58 13.84 15.23EPS 0.84 1.26 1.34 1.30 1.43 1.57Dividend/Share 0.27 0.40 0.43 0.42 0.46 0.50 21.98Required Return 0.0741 2 3 3Discounted values 0.3865 0.3959 0.4055 17.7398Present Value 18.93
6. 6. 6Connecting 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/EEt = (1+ g)tE0, dt = (1! rr)EtPV =dt(1+ k)tt=1"#PV =(1! rr)Et(1+ k)tt=1"# = (1! rr)Et(1+ k)tt=1"#PV = (1! rr)(1+ g)(k ! g)E0 =(1! rr)(k ! g)E1P/E RatiosPV = (1! rr)(1+ g)(k ! g)E0 =(1! rr)(k ! g)E1(1! rr) = div payout ratioPV/E0 = (1! rr)(1+ g)(k ! g)= P/E Ratio (curent earnings)PV/E1 =div payout ratio(k ! g)= P/E ratio (future earnings)P/E Ratios Firms with greater earnings growth willhave greater P/E ratios Firms with higher dividend payouts willhave higher P/E ratios
7. 7. 7Example: 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) = 24g, ROE, and rrg =Reinvested earningsShareholders equityg =Reinvested earningsTotal earnings*Total earningsShareholders equityg = rr * (return on equity)MSFT = (1- 0.32) * (0.29) = 0.20Goals Dividend valuation model “dividend discount model” Forecasting earnings, dividends, andprices Ratio valuations Malkiel’s “Firm foundations”Ratio Valuations Find various price ratios See if stock looks “cheap” relative toreference group Also, forecast future prices usingforecasts of ratios Necessary for nondividend payingstocks
8. 8. 8P/E Ratio Comparisons Find current P/E ratio Compare with industry Low: Buy High SellP/E Price Forecast Forecast future P/E ratio Forecast future earnings Future price = (P/E)*E Discount this back to today, andcompare with current price Can also be used along with dividendforecasts tooExample: Irobot Recent IPO Little data to work with Pays zero dividends High riskIrobot long range forecastsAssumptionsBeta 2.2 Market return 0.08Earnings Growth 0.2 Risk free 0.03P/E 94 Long run growth 0.13Div Payout 0.25Shares (millions) 14(Millions)2004 2005 2006 2010 2015 (P/E) 2015(Div discount)Earnings 0.22 2.61 3.56 7.38 18.37 18.37EPS 0.00 0.19 0.25 0.53 1.31 1.31Dividends 0.00 0.00 0.00 0.00 0.00 0.33Price 13.00 49.56 123.33 37.01Required Return 0.14PV 29.35 37.93 11.38
9. 9. 9g, ROE, and rrg =Reinvested earningsShareholders equityg =Reinvested earningsTotal earnings*Total earningsShareholders equityg = rr * (return on equity)IRBT = (1- 0.00) * (0.039) = 0.039P/E Ratios w/o dividends Remember comment about dividendsdon’t matter Value entire earnings stream, since youown this Max bound on P/E ratio Related to PEG ratios (P/E)/growthP/E (without divs)(Upper bound)Et = (1+ g)t E0PV =Et(1 + k)tt=1!" =Et(1+ k)tt=1!"PV =(1 + g)(k # g)E0 =1(k # g)E1P /E =(1 + g)(k # g)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
10. 10. 10Key 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?S&P 500 P/E RatioOther Ratios Price/Cashﬂow Price/Bookvalue Price/Sales Key problem: Find appropriate comparison ﬁrmsData Tools Stock screening software See Yahoo ﬁnance
11. 11. 11Goals Dividend valuation model “dividend discount model” Forecasting earnings, dividends, andprices 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 howmuch will unusual growth last?Determinant 2:Dividend Payout Financial Ratio Div. Payout Ratio = Divs/Earnings
12. 12. 12Determinant 3:Risk Growth rates and interest rates areuncertain Price should be higher (all things equal)the less risky the earnings stream Risk is difﬁcult to quantifyDeterminant 4:Interest rates Back to our PV formulas Higher interest rates (lower stockprices) Two ways to think about it PV formula Stock market alternatives look betterMalkiel’s Caveats Financial data is Messy Hard to predictEvidence1998(Malkiel)
13. 13. 13What does this say? Growth rates matter First hint of rationality in the stockmarket How can you tell when a P/E ratio is outof line? Look at stocks with comparable growthratesValuation Wrap Up Many tools No one right answer Some common sense, and rules ofthumb Try to stay close to sensiblegrowth/valuation ideas