20190402 我的另類高登成長模型(Gordon Growth Model, GGM)

GGM是股利折現模型(dividend discount model, DDM)的一個特例，即假設股利會永遠以固定的成長率來成長。公式如下：

P = D*(1+G)/(K-G) ~= D/(K-G)

P：股價(合理價)

D：每股現金股利

K：折現率(discount rate)，或者期望報酬率

G：成長率，可以用G = ROA(或ROE) × RR(保留盈餘率)

為了消除G，我嘗試用K=價差回報率+股利回報率

=(賣出價-買入價)/(買入價) + G (股利回報率用成長率代表)  

假設用P0買入，P賣出，則：

P=D/((P-P0)/P0 + G - G) = D*P0/(P-P0)

∴P^2 - P0*P - D*P0 = 0 (P的二次方程式)

∴P = (P0±SQRT(P0^2 + 4*D*P0 ) / 2

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例：領展估值

現價P0=92.5，D=2.5, 

P=(92.5+SQRT(92.5*92.5+4*2.5*92.5)/2 = 94.93

註：K=(P-P0)/P0 + Y% 
所以領展的期望報酬率大約為=(94.93-92.5)/92.5 + 2.8% = 5.4%
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後記：A Note on the Gordon Growth Model with Earnings per Share 
https://download.atlantis-press.com/article/25856081.pdf
另一個消除G的GGM的估值方法為以上的論文所推導：
E1 = P0∗ k
D1 = E1∗ a= P0∗ k∗ a      a=派息比率(Dividend Payout Ratio DPR)
ΔP1 = E1 − D1 = P0∗ k∗(1− a)    ΔP1 is part of profit that is reinvested.
P1 = P0+ ΔP1 = P0∗ (1+ k∗ (1− a))
E2 = P1∗ k= P0∗ k∗ (1+ k∗ (1− a))
E2 = E1∗ (1+ g)  where  g is EPS/dividend growth rate
g= k∗ (1− a)= k− k∗a
k− g= k∗ a
therefore P = D*(1+G)/(K-G) ~= D/(K-G) = D/(k*a) = D/(E1/P0)*a
P=D/(a/PE)
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例：領展估值

現價P0=93.05, PE=4.29，D=2.5, a=20.06% (五年geomean平均)
P=D/(a/PE)=2.5/((20.06/100)/4.29)=53.46
註：K=(a/PE) + dg , 若dg=10.79% (四年geomean平均)
所以領展的期望報酬率約為=(20.06/100)/4.29+10.79/100=15.5%