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The dividend discount model

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					                  FINN4233   Financial Policy and Planning




The dividend discount model
                                    FINN4233       Financial Policy and Planning



Dividend Growth Models
•   The value of a stock is the present value of dividends through infinity:
                                                   t 
                                                        E ( DPS ) t
                     Value per share of stock =     (1  k )t
                                                   t 1       e

                     where,    E(DPSt) = expected dividends per share
                               ke = required rate of return

•   The required rate of return on a stock is determined by its riskiness
     – More about this later, but think about the CAPM

•   To estimate expected dividends, we need to make assumptions about:
     – Expected future growth rates
     – Payout ratios
                                FINN4233        Financial Policy and Planning



Aside: Payout ratios

                                                    (1)
                  (2)
    Firm‘s                                                 Financial
    operations:                 Financial    (4a)          markets:
    e.g.                        manager                    e.g.
    projects                                               investors

                  (3)                            (4b)

                        (1) Cash raised from investors
                        (2) Cash invested in firm
                        (3) Cash generated by operations
                        (4a) Cash reinvested
                        (4b) Cash returned to investors
                                     FINN4233       Financial Policy and Planning



    What determines growth?
•   Dividends are related to earnings
•   Usually: Dividends=Dividend payout ratio*Earnings=
    =(1-Retention ratio)*Earnings
•   So: growth rate in dividends = growth rate in earnings
•   For a firm to grow, net investment must be positive
     – Will only happen if some earnings are retained

•   Earnings next year = Earnings this year + Retained Earnings this year *
    Return on equity
•   Divide both sides by the earnings this year:
     1 + g = 1 + Retention Ratio * Return on equity
     Where g is the growth rate in earnings

•   Growth rate = Retention Ratio * Return on Equity
                                    FINN4233      Financial Policy and Planning



The Gordon Growth Model
•    Can be used to value a firm in a “steady state”
      – Dividends growing at a rate that can be sustained forever

•    We have the following situation:

0                 1                     2             3               

D0            D1=D0 (1+g)      D2=D0 (1+g)2    D3=D0 (1+g)3     D¥=D0 (1+g)¥


                         DPS 1
•    Value of stock = ke  g
•    It‟s just the growing perpetuity formula
•    Maximal long-term stable growth rate g should correspond to expected
     inflation + real growth rate in the economy = ~6%
                                 FINN4233      Financial Policy and Planning



Example: Consolidated Edison in May 2001
•   Background: An electric utility that supplies power to homes
    and businesses in New York City. It is a monopoly whose
    prices and profits are regulated by the state. Its rates are also
    regulated; It is unlikely that the regulators will allow profits to
    grow at extraordinary rates.
•   Firm Characteristics are consistent with stable, DDM model firm
•   Background information needed for valuation:
     – Earnings per share in 2000 = $3.13
     – Dividend payout ratio in 2000 = 69.97%
     – Dividends per share in 2000 = $2.19
     – Return on equity = 11.63%
     – Beta=0.9, rf=5.40%, market risk premium = 4%
                              FINN4233     Financial Policy and Planning



Example: Consolidated Edison in May 2001
•   ke = 5.4%+0.9*4%=9%
•   Expected g=(1-payout ratio)*ROE=(1-.6997)*.1163=3.49%
•   P=DPS2001/(ke-g)=$2.19*(1.0349)/(0.09-0.0349) = $41.15
•   Consolidated Edison was trading at $36.59 on May 14, 2001.
    The stock seems to be undervalued.
                                 FINN4233     Financial Policy and Planning



Why the difference?
•   Our valuation is different from the market price
     – Almost always will be the case

•   Three possible reasons:
     – You are right and the market is wrong
     – The market is right and you are wrong
     – Difference is too small to draw any conclusions

•   Need to examine the magnitude of the difference
     – Hold the other variables constant
     – Change the growth rate until value converges to market
       price
                                FINN4233     Financial Policy and Planning



Implied growth rate
•   Pt = DPSt*(1+g)/(re-g)
•   we can solve for g if we know the true price.
•   For example, $36.59 = $2.19*(1+g)/(0.09-g)
•   implied g = 2.84%
•   So, growth rate in dividends would have to be 2.84% to justify a
    $36.59
•   Also ROE = g/b, so
•   implied ROE = 0.0284/(1-0.6997) = 9.47%
                                                        FINN4233                     Financial Policy and Planning



Value per share versus growth rate
                $70.00




                $60.00




                $50.00




                $40.00
Current Price




                $30.00




                $20.00




                $10.00




                  $-
                         -3.00%   -2.00%   -1.00%   0.00%          1.00%           2.00%   3.00%   4.00%   5.00%
                                                            Expected growth rate
                 FINN4233   Financial Policy and Planning



Con Ed Value over Time
                                  FINN4233       Financial Policy and Planning



Two-stage growth model
•   Firms rarely grow at a stable rate forever



•   More typical:
    – Initial high growth period
    – Followed by more stable growth period



•   This possibility is easy to control for
                                                     FINN4233         Financial Policy and Planning



The model
•   Based on two stages of growth:
     – High growth (hg ) phase that lasts n years
     – A stable growth (st) rate that lasts forever
•   Value of the stock = PV of dividends during extraordinary phase
                                            + PV of terminal price

                  t n
                            DPSt              Pn
           P0                         
                  t 1   (1  ke ,hg ) t (1  ke ,hg ) n
                                   DPSn 1
           where          Pn 
                                 (ke , st  g n )
           DPSt  Expected dividends per share in year t
           ke  cost of equity
           Pn  price at the end of year n
           g  extraordinary growth rate for the first n years
           g n  growth rate forever after year n
                                        FINN4233          Financial Policy and Planning



Simplified Formula
•   If growth rate (g) and payout ratio are unchanged for first n
    years, then

                                    (1  g ) n 
           DPS 0  (1  g )  1                 
                              
                                  (1  ke,hg ) n 
                                                            DPS n 1
      P0 
                        ke,hg  g                    (ke, st  g n )(1  ke,hg ) n
                                  FINN4233      Financial Policy and Planning



Example: ABN Amro (December 2000)
•   Background: Holland's #1 purely banking company, ABN AMRO and its
    subsidiaries operate more than 800 offices at home and another 2,600
    in 75 other countries. Other lines include investment banking services
    (corporate advisory, finance, and asset management), leasing, and
    growing operations in pan-European real estate development,
    financing, and management. In the US, the company owns Chicago-
    based LaSalle Bank and Standard Federal Bank, one of Michigan's
    largest banks.
•   Why use a two-stage model?
      – ABN Amro has strong brand names and impressive track record of
        growth, however
      – The expected growth rate based upon the current return on equity
        of 15.56% and a retention ratio of 62.5% is 9.73%. This is higher
        than what would be a stable growth rate (roughly 5% in Euros)
                               FINN4233      Financial Policy and Planning



Background information on ABN Amro
•  Market Inputs
    – Long Term Riskfree Rate (in Euros) = 5.02%
    – Risk Premium = 4% (U.S. premium : Netherlands is AAA rated)
• Current Earnings Per Share = €1.60; Current DPS = €0.60;
Variable          High Growth Phase Stable Growth Phase
Length            5 years            Forever after yr 5
Return on Equity 15.56%              15% (Industry average)
Payout Ratio      37.5% (0.6/1.6)    66.67%
Retention Ratio   62.5%              33.33% (b=g/ROE)
Expected growth   .1556*.625=.0973 5% (Assumed)
Beta              0.95               1.00
Cost of Equity    5.02%+0.95(4%) 5.02%+1.00(4%)
                  =8.82%             =9.02%
                               FINN4233     Financial Policy and Planning



ABN Amro: Valuation
Year     EPS                DPS                PV of DPS
1        1.76 (1.60*1.0973) 0.66(1.76*0.375)   0.60[0.66/(1.0882)]
2        1.93               0.72               0.61
3        2.11               0.79               0.62
4        2.32               0.87               0.62
5        2.54               0.95               0.63
Expected EPS in year 6 = 2.54(1.05) = €2.67
Expected DPS in year 6 = 2.67*0.667= €1.78
Terminal Price (in year 5) = 1.78/(.0902-.05) = €42.41
PV of Terminal Price = 42.41/(1.0882)5 = €27.79
  Value Per Share = 0.60 + 0.61+0.62+0.62+0.63+27.79 = €30.87
     The stock was trading at €24.33 on December 31, 2000
                               FINN4233     Financial Policy and Planning



Extensions
•   We could also use a three-stage model
    – Allows for an initial period of high growth
    – Transitional period where growth declines
    – Final stable growth phase
                                   FINN4233      Financial Policy and Planning



Issues in using the DDM
•   Primary attraction is its simplicity and intuitive logic

•   Practitioners claim it is not really useful:
     – Only works for stable, high-dividend paying firms
     – Too conservative in estimating value
                              FINN4233    Financial Policy and Planning



How well does it work in practice?
•   Topic of a study by Sorensen and Williamson (1985)
     – Valued 150 stocks in December 1980
     – Used difference between the market price and the model
       value to firm portfolios based on degree of under/over-
       valuation
     – Made a number of other assumptions to estimate the model
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Result
                              FINN4233    Financial Policy and Planning



Interpretation
•   Undervalued stocks tended to have good future performance

•   Overvalued stocks tended to have bad future performance

•   Seems to support the use of the DDM
                                 FINN4233      Financial Policy and Planning



A first pass at relative valuation
•   In the DDM the objective is to find value given:
     – Dividends
     – Growth
     – Risk characteristics

•   In relative valuation, valueis derived from the pricing of „comparable
    assets‟
     – A notable example is the Price/Earnings (P/E ratio)

•   Most commonly used technique in practice
                                 FINN4233           Financial Policy and Planning



Determinants of multiples
•   Let‟s start with the dividend discount model again
                                      t 
                                           E ( DPS ) t
    Value per share of stock =         (1  k )t
                                      t 1       e



                   where, E(DPSt) = expected dividends per share
                          ke = required rate of return



•   If dividends grow at a constant rate, we have the Gordon Growth
    Model:
                               DPS 1
                       P0 
                              (ke  g )
                                     FINN4233     Financial Policy and Planning



The Price/Earnings Ratio
•   We can substitute EPS 0  Payout Ratio  (1  g )         for DPS1
                           EPS0  Payout ratio  (1  g )
•   We then have: P0 
                                     rg


                      P0  P Payout ratio  (1  g )
                          
                     EPS0 E        rg


•   If the P/E ratio is stated in terms of expected earnings next time
    period, then we have: P Payout Ratio
                         P
                       0
                                    
                     EPS1       E1        rg
                                 FINN4233     Financial Policy and Planning



What are the implications?
•   P/E ratio formed from today‟s stock price P0 and next year‟s
    expected earnings

•   P/E ratio is connected to growth, dividend policy, and required
    rate of return
     – Same factors as the Gordon Growth Model

•   The higher the payout ratio, the higher the P/E ratio

•   The higher the growth rate, the higher the P/E ratio

•   The higher the required rate of return, the lower the P/E ratio
                           FINN4233   Financial Policy and Planning



Some sample problems to consider
• Damodaran: Chapter 13 pg. 349
   – 13.2
   – 13.3

				
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