stock valuation economics 71a: spring 2007 mayo 11 malkiel, 5, 6 (136-144), 8 lecture notes 4.2
TRANSCRIPT
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Stock Valuation
Economics 71a: Spring 2007
Mayo 11
Malkiel, 5, 6 (136-144), 8
Lecture notes 4.2
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Goals
Dividend valuation model “dividend discount model”
Forecasting earnings, dividends, and prices
Ratio valuationsMalkiel’s “Firm foundations”
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Dividend Discount ModelConstant Dividends
Evaluate stream of dividendsStock pays the same constant dividend
foreverAssume some “required return” = k
k = RF + RP k = RF + beta(E(Rm)-RF)
Same as perpetuity formula
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Dividend Discount ModelConstant Dividends
€ €
P = PV =d
(1+ k)tt=1
∞
∑ =dk
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Dividend Discount ModelGrowing Dividends
Evaluate stream of growing dividends
g = growth rate€
dt = (1+ g)td0
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More Growing Dividends
€
PV =(1+ g) t d0
(1+ k) tt=1
∞
∑ = d0 a t
t=1
∞
∑
a =1+ g1+ k
PV =a
(1− a)d0 =
(1+ g)(1+ k)
1−(1+ g)(1+ k)
d0 =
(1+ g)(1+ k)(k − g)(1+ k)
d0
PV =(1+ g)(k − g)
d0 =1
(k − g)d1
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Dividend Discount
Must have k>g for this to make senseOtherwise, dividends growing too fastBasic feature: Very sensitive to g
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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 pricesSmall changes in beliefs lead to big
changes in prices
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What if dividends not growing forever?
Solve this by calculator or computer for d(t)
€
P =dt
(1+ k)tt=1
∞
∑
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Goals
Dividend valuation model “dividend discount model”
Forecasting earnings, dividends, and prices
Ratio valuationsMalkiel’s “Firm foundations”
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Future Price EstimatesVariable Growth Model
Forecast dividends in early years In last year
Estimate dividend growth Use this to estimate future price
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Present Value Calculation(End of year dividends.)
€
P2007 =d2007(1 + k)
+d2008
(1 + k)2+d2009
(1 + k)3+P2009
(1 + k)3
P2009 =(1 + g)
(k − g)d2009
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Forecasting Dividends
Forecast sales revenueGuess revenue growth ratesSales tomorrow = (1+g) (Sales today)
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Sales -> Earnings
€
Net Profit Margin =Earnings
SalesEarnings = (Net profit margin) x Sales
Earnings/share = Earnings
Total shares
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Earnings->Dividends
€
Dividend/share = (payout ratio) x (earnings/share)
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Future Price(Guess long term growth, g.)
€
P2009 =(1 + g)
(k − g)d2009
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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€
k j = RF + RPjk j = RF +β j (RM − RF )
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Back to Problem
RF = 3%RM = 8% (difficult)
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What Do You Need?
Revenue (sales) forecastsGross profitability estimatesDividend payout estimatesSharesCAPM inputsFuture growth estimates
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Microsoft 3 year forecasts
AssumptionsBeta 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) 9.7
2004 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 21.98
Required Return 0.0741 2 3 3
Discounted values 0.3865 0.3959 0.4055 17.7398
Present Value 18.93
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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)
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P/E
€
E t = (1+ g) t E0 , d t = (1− rr)E t
PV =d t
(1+ k) tt=1
∞
∑
PV =(1− rr)E t
(1+ k) tt=1
∞
∑ = (1− rr)E t
(1+ k) tt=1
∞
∑
PV = (1− rr)(1+ g)(k − g)
E0 =(1− rr)(k − g)
E1
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P/E Ratios
€
PV = (1− rr)(1+ g)(k − g)
E0 =(1− rr)(k − g)
E1
(1− rr) = div payout ratio
PV/E0 = (1− rr)(1+ g)(k − g)
= P/E Ratio (curent earnings)
PV/E1 =div payout ratio
(k − g)= P/E ratio (future earnings)
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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
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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
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g, ROE, and rr
€
g =Reinvested earnings
Shareholders equity
g =Reinvested earnings
Total earnings*
Total earnings
Shareholders equity
g = rr * (return on equity)
MSFT = (1- 0.32) * (0.29) = 0.20
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Goals
Dividend valuation model “dividend discount model”
Forecasting earnings, dividends, and prices
Ratio valuationsMalkiel’s “Firm foundations”
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Ratio Valuations
Find various price ratiosSee if stock looks “cheap” relative to
reference groupAlso, forecast future prices using
forecasts of ratiosNecessary for nondividend paying
stocks
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P/E Ratio Comparisons
Find current P/E ratioCompare with industryLow:
BuyHigh
Sell
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P/E Price Forecast
Forecast future P/E ratioForecast future earningsFuture price = (P/E)*EDiscount this back to today, and
compare with current priceCan also be used along with dividend
forecasts too
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Example: Irobot
Recent IPO Little data to work with
Pays zero dividendsHigh risk
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Irobot long range forecasts
AssumptionsBeta 2.2 Market return 0.08Earnings Growth 0.2 Risk free 0.03P/E 94 Long run growth 0.13Div Payout 0.25
Shares (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 37.01
Required Return 0.14PV 29.35 37.93 11.38
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g, ROE, and rr
€
g =Reinvested earnings
Shareholders equity
g =Reinvested earnings
Total earnings*
Total earnings
Shareholders equity
g = rr * (return on equity)
IRBT = (1- 0.00) * (0.039) = 0.039
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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 ratioRelated to PEG ratios (P/E)/growth
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P/E (without divs)(Upper bound)
€
Et = (1 + g)t E0
PV =Et
(1 + k)tt=1
∞
∑ =Et
(1 + k)tt=1
∞
∑
PV =(1 + g)
(k − g)E0 =
1
(k − g)E1
P /E =(1 + g)
(k − g)
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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
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Key Problems
Estimating growth with little dataWhat should P/E be?
“Earnings multiple” Compare with other firms Crude dividend discount checks
Lots of guesswork Negative earnings?
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S&P 500 P/E Ratio
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Other Ratios
Price/CashflowPrice/BookvaluePrice/SalesKey problem:
Find appropriate comparison firms
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Data Tools
Stock screening software See Yahoo finance
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Goals
Dividend valuation model “dividend discount model”
Forecasting earnings, dividends, and prices
Ratio valuationsMalkiel’s “Firm foundations”
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Long-Run stock valuation
Price = PV(dividends/earnings)Stresses uncertainty Malkiel’s “determinants”
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Determinant 1: Expected Growth Rate
Remember formulasHigher expected growth -> Higher price
(can be very strong)Big question: How long and by how
much will unusual growth last?
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Determinant 2:Dividend Payout
Financial Ratio Div. Payout Ratio = Divs/Earnings
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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
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Determinant 4:Interest rates
Back to our PV formulasHigher interest rates (lower stock
prices)Two ways to think about it
PV formula Stock market alternatives look better
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Malkiel’s Caveats
Financial data is Messy Hard to predict
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Evidence1998(Malkiel)
0
10
20
30
40
50
Ford IBM Microsoft
Growth Rate P/E Ratio
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What does this say?
Growth rates matterFirst hint of rationality in the stock
marketHow can you tell when a P/E ratio is out
of line?Look at stocks with comparable growth
rates
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Valuation Wrap Up
Many toolsNo one right answerSome common sense, and rules of
thumbTry to stay close to sensible
growth/valuation ideas