# stockval - Stock Valuation Economics 71a: Spring 2007 Mayo...

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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 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

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Dividend Discount Model Constant Dividends P = PV = d (1+ k ) t t =1 ¥ å = d k
Dividend Discount Model Growing Dividends Evaluate stream of growing dividends g = growth rate d t = (1+ g ) t d 0

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More Growing Dividends PV = (1+ g ) t d 0 (1+ k ) t t =1 ¥ å = d 0 a t t =1 ¥ å a = 1+ g 1+ k PV = a (1- a ) d 0 = (1+ g ) (1+ k ) 1- (1+ g ) (1+ k ) d 0 = (1+ g ) (1+ k ) ( k - g ) (1+ k ) d 0 PV = (1+ g ) ( k - g ) d 0 = 1 ( k - g ) d 1
Dividend Discount Must have k>g for this to make sense Otherwise, dividends growing too fast Basic 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 prices Small changes in beliefs lead to big changes in prices
What if dividends not growing forever? Solve this by calculator or computer for d(t) P = d t (1+ k ) t t =1 ¥ å

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Goals Dividend valuation model “dividend discount model” Forecasting earnings, dividends, and prices Ratio valuations Malkiel’s “Firm foundations”
Future Price Estimates Variable 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.) P 2007 = d 2007 (1 + k ) + d 2008 (1 + k ) 2 + d 2009 (1 + k ) 3 + P 2009 (1 + k ) 3 P 2009 = (1 + g ) ( k - g ) d 2009
Forecasting Dividends Forecast sales revenue Guess revenue growth rates Sales tomorrow = (1+g) (Sales today)

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## stockval - Stock Valuation Economics 71a: Spring 2007 Mayo...

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