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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
FINN4233 Financial Policy and Planning
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
rg
P0 P Payout ratio (1 g )
EPS0 E rg
• 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 rg
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
