經濟,財務,統計學,數理科學與政治評論

Hello there:

  這個部份主要是談企業在面臨自身成長與衰退到穩定期間,企業的現金股利發放對於企業價值的影響與計算!!

 1.先談Gordon Growth Model (GGM): Constant growth rate g with the required rate of return(r) > growth rate(g)

   Po = [Do*(1+g)/(1+r) + Do*(1+g)/(1+r)*(1+g)/(1+r)+ ......]

      = Do*(1+g)/(r-g)

    r = D1/Po + g as D1 = Do*(1+g)

 小應用:

  (1) (V(t+1) - V(t))/V(t) = [D(t+2)/(r-g) - D(t+1)/(r-g)]/[D(t+1)/(r-g)] = (D(t+2) - D(t+1))/D(t+1) = (1 + g) - 1 = g (growth rate)

  (2) 若今天企業在考量到沒有成長性之後,將所有的盈餘都發放成股利:

       g = 0 => Po = D1/r = E1/r = E/r

  (3) 回頭談企業成長與企業價值的關係:

      Present Value of Growth Opportunities (PVGO)

          Po = E/r + PVGO

     a. leading Po/E1 = (1-b)/(r-g) 其中 b is the retention rate and (1-b) is the Earnings' payout rate

     b. 若今天Dividends/Earnings is a constant (1-b), 則

     trailing Po/Eo = (1-b)*(1+g)/(r-g).....

  so... GGM只適用於成長性固定且會配發穩定現金股利的企業,對於unstable-growth, non-dividend-paying firm則無用!!

 2. Two-Stage DDM

    A constant grwoth T periods of g(S)

      and then a constant growth g(L) thereafter forever

    The firm value is 

    Vo = Sum of (t=1,2,3,...T; D(t)/(1+r)**t) + V(T)/(1+r)**T

    where

         D(t) = Do*[(1+g(S))**t] for t = 1,2,3,....,T

         V(T) = Do*[(1+g(S))**T]*(1+g(L))/[r-g(L)]

         S is for the supernormal period and L is for the stable normal period hereafter

 3. The H-Model

   H for the Horizon which is the half of decreasing period

   from g(S) to g(L), H = T/2,

   Then the firm value is

   Vo = Do*(1+g(L))/(r-g(L)) + Do*H*(g(S)-g(L))/(r-g(L))

       = Do *[(1+g(L)) + T/2*(g(S)-g(L)]/[r-g(L)]

 4. Three-Stage DDM

   We have to backward calculate to the end of two-stage for the V(2-stage),

      and then use the 2-stage DDM for the calculation !!!

 5. The decomposition of ROE for the growth rate

   Recall that

   ROE = NI/Average Equity

      = (NI/Sales) * (Sales/Average Total Assets) * (Average Total Assets/Average Equity)

   then we have the growth rate as

    g  = Rentention Rate (RR) * ROE

       = [(Net Income - Dividends)/Net Income] * ROE

       = [(NI - Dividends)/NI]*[(NI/Sales) * (Sales/Average Total Assets) * (Average Total Assets/Average Equity)]