stock valuation

g, ROE, and rr
Reinvested earnings Shareholders equity Reinvested earnings Total earnings g= * Total earnings Shareholders equity g = rr * (return on equity) MSFT = (1- 0.32) * (0.29) = 0.20 g =
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)
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Forecasting Dividends
Forecast
sales revenue Guess revenue growth rates Sales tomorrow = (1+g) (Sales today)
Sales -> Earnings
Earnings Net Profit Margin = Sales Earnings = (Net profit margin) x Sales Earnings Earnings/share = Total shares
Back to Problem
RF
= 3% RM = 8% (difficult)
What Do You Need?
Revenue
(sales) forecasts Gross profitability estimates Dividend payout estimates Shares CAPM inputs Future growth estimates

Goals
Dividend

valuation model earnings, dividends, and
“dividend discount model”
Forecasting
prices Ratio valuations Malkiel’s “Firm foundations”

Estimate dividend growth Use this to estimate future price
Present Value Calculation (End of year dividends.)
d d d P P2007 2007 2008 2009 2009 (1 k) (1 k ) 2 (1 k ) 3 (1 k ) 3 (1 g) P2009 d 2009 (k g)
P/E = 23 Beta = 0.88, Rm = 0.08, = 0.03



k = 0.03 + 0.88(0.08-0.03) k = 0.074 g = 0.05, 0.06

Growth

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
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
Example: Microsoft ( Price = 27)
What if dividends not growing forever?

Solve this by calculator or computer for d(t)
P
dt t (1 k ) t 1


Goals
Dividend

valuation model earnings, dividends, and
Stock Valuation
Economics 71a: Spring 2007 Mayo 11 Malkiel, 5, 6 (136-144), 8 Lecture notes 4.2
Goals
Dividend

valuation model earnings, dividends, and
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
Fraction of earnings going to shareholders (1-rr)

Dividends
= (1-rr)(earnings)
P/E
E t (1 g) t E 0 , d t (1 rr)E t dt PV t (1 k) t 1
(1 rr)E t Et PV (1 rr) t t t 1 (1 k) t 1 (1 k) (1 g) (1 rr) PV (1 rr) E0 E1 (k g) (k g)
Dividend Discount
Must
have k>g for this to make sense Otherwise, dividends growing too fast Basic feature: Very sensitive to g
Examples
Let

initial d = 1, k=0.05, g=0.02
Evaluate
stream of growing dividends
d t (1 g )t d0
g
= growth rate

More Growing Dividends
(1 g) t d 0 t PV d0 a t t 1 (1 k ) t 1 1 g a 1 k (1 g) (1 g) a (1 k ) (1 k ) PV d0 d0 d0 (1 g) (k g) (1 a) 1 (1 k ) (1 k ) (1 g) 1 PV d0 d1 (k g) (k g)
“dividend discount model”
Forecasting
prices Ratio valuations Malkiel’s “Firm foundations”
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
Dividend Discount Model Constant Dividends
P PV d d t (1 k ) k t 1



Dividend Discount Model Growing Dividends
P/E Ratio Comparisons
Find
current P/E ratio Compare with industry Low:

Buy Sell
High

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

Earnings->Dividends
Dividend/share = (payout ratio) x (earnings/share)
Future Price (Guess long term growth, g.)
(1 g) P2009 d 2009 (k g)

Required Return (CAPM)
2 0 0 9P ric e(2 0 0 9 ) 5 8 .5 6 1 5 .2 3 1 .5 7 0 .5 0 2 1 .9 8
Required Return D is c ounted values P res ent V alue
0 .0 7 4 1 0 .3 8 6 5 1 8 .9 3 2 0 .3 9 5 9 3 0 .4 0 5 5 3 1 7 .7 3 9 8
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
“dividend discount model”
Forecasting
prices Ratio valuations Malkiel’s “Firm foundations”
Future Price Estimates Variable Growth Model
Forecast
dividends in early years In last year
P/E Ratios
(1 g) (1 rr) PV (1 rr) E0 E1 (k g) (k g) (1 rr) div payout ratio (1 g) PV/E 0 (1 rr) P/E Ratio (curent earnings) (k g) div payout ratio PV/E1 P/E ratio (future earnings) (k g)

Assume the CAPM is working Required return for asset j
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
0 .0 8 0 .0 3 0 .0 5
Revenue E arnings EPS D ividend/Share
2006 4 4 .0 0 1 3 .0 0 1 .3 4 0 .4 3
2007 4 8 .4 0 1 2 .5 8 1 .3 0 0 .4 2
2008 5 3 .2 4 1 3 .8 4 1 .4 3 0 .4 6
M ic ros oft 3 year forec as ts A s s umptions Beta Revenue G rowth P /E D iv P ayout P rofit M argin S hares (billions )
0 .8 8 M arket return 0 .1 Ris k free 2 2 Future growth 0 .3 2 0 .2 6 9 .7 2004 3 6 .0 0 8 .1 0 0 .8 4 0 .2 7 2005 4 0 .0 0 1 2 .2 5 1 .2 6 0 .4 0