AFA Module 5 Handout

1. Module 5
Dividend Discount Model

2. The Dividend Discount
Model
• Simplest and oldest present value approach to
valuing stock
• Underlying principle: When investors buy stock in
publicly listed companies, investors generally expect
to get two types of cash flows:
• Dividends during the holding period
• Expected price at the end of the holding period
Value per share of stock = ෍
𝑡=1
𝑡=∞
𝐸(𝐷𝑃𝑆)
(1 + 𝑟) 𝑡

3. The Dividend Discount
Model
• Two Basic Inputs to the Dividend Discount Model
• Expected Dividends
• Cost of Equity
Value per share of stock = ෍
𝑡=1
𝑡=∞
𝐸(𝐷𝑃𝑆)
(1 + 𝑟) 𝑡

4. Expression for Single
Holding Period
• Scenario: An investor wants to buy a share of stock
and hold it for one year and then sell it.
• To determine value of the stock, we need to
estimate:
• (1) Dividend to be received during the period,
• (2) Expected selling price at the end of the holding
period
• (3) Investor’s required rate of return

5. Expression for Single
Holding Period
• The value of the stock today is the present value of
the expected dividend to be received on the stock
plus the present value of the expected selling price
in one year, discounted at the investor’s required
rate of return.
𝑉0 =
𝐷1
(1 + 𝑟)1
+
𝑃1
(1 + 𝑟)1
=
𝐷1 + 𝑃1
(1 + 𝑟)1

6. Expression for Single
Holding Period
Checkpoint (Computation of DDM Value with a Single
Holding Period)
• Suppose that you expect UBP to pay a Php1.10
dividend next year. You expect the price of UBP
stock to be Php53.55 in one year. Suppose the
required rate of return for UBP is 9 percent. What is
the value of UBP stock today?

7. Expression for Single
Holding Period
Checkpoint (Computation of DDM Value with a Single
Holding Period)
• Suppose that you expect UBP to pay a Php1.10
dividend next year. You expect the price of UBP
stock to be Php53.55 in one year. Suppose the
required rate of return for UBP is 9 percent. What is
the value of UBP stock today?
𝑉0 =
1.10
(1+9%)1 +
53.55
(1+9%)1 =
1.10+53.55
(1+9%)1 = Php50.14

8. Expression for Multiple
Holding Periods
• Scenario: An investor wants to buy a share of stock
and hold it for two years and then sell it.
• The value of the stock today is the present value of
the expected dividend in year 1, plus the present
value of the expected dividend in year 2, plus the
present value of the expected selling price at the
end of year 2.
𝑉0 =
𝐷1
(1 + 𝑟)1
+
𝐷2
(1 + 𝑟)2
+
𝑃2
(1 + 𝑟)2
=
𝐷1
(1 + 𝑟)1
+
𝐷2 + 𝑃2
(1 + 𝑟)2

9. Expression for Multiple
Holding Periods
• The general expression for an n-period holding
period or investment horizon:
𝑉0 = ෍
𝑡=1
𝑛
𝐷𝑡
(1 + 𝑟) 𝑡
+
𝑃𝑛
(1 + 𝑟) 𝑛
𝑉0 =
𝐷1
(1 + 𝑟)1
+ ⋯ +
𝐷 𝑛
1 + 𝑟 𝑛
+
𝑃𝑛
(1 + 𝑟) 𝑛

10. Expression for Multiple
Holding Periods
Checkpoint (Computation of DDM Value with Multiple
Holding Periods)
• For the next five years, the annual dividends of a
stock are expected to be Php2.00, Php2.10, Php2.20,
Php3.50, and Php3.75. In addition, the stock price is
expected to be Php40 in five years. If the required
return on equity is 10 percent, what is the value of
this stock today?

11. Expression for Multiple
Holding Periods
Checkpoint (Computation of DDM Value with Multiple
Holding Periods)
• For the next five years, the annual dividends of a
stock are expected to be Php2.00, Php2.10, Php2.20,
Php3.50, and Php3.75. In addition, the stock price is
expected to be Php40 in five years. If the required
return on equity is 10 percent, what is the value of
this stock today?
𝑉0 =
2.00
(1+10%)1 +
2.10
(1+10%)2 +
2.20
(1+10%)3 +
3.50
(1+10%)4 +
3.75
(1+10%)5 +
40
(1+10%)5 = Php34.76

12. Expression for Infinite
Holding Periods
• Scenario: An investor wants to buy a share of stock
and holds it into the indefinite future.
• The value of the stock today is the present value of
all expected future dividends.
𝑉0 = ෍
𝑡=1
∞
𝐷𝑡
(1 + 𝑟) 𝑡
𝑉0 =
𝐷1
(1 + 𝑟)1
+
𝐷2
(1 + 𝑟)2
+ ⋯ +
𝐷 𝑛
1 + 𝑟 𝑛
+ ⋯

13. Variations of the Model
• Future dividends can be forecasted by assigning the
stream of future dividends to one of several stylized
growth patterns.
• Constant growth for an infinite period (the Gordon
growth model)
• Two distinct stages of growth (the two-stage
growth model and the H-model)
• Three distinct stages of growth (the three-stage
growth model)

14. The Gordon Growth
Model
• The simplest pattern that can be assumed in
forecasting future dividends is growth at a constant
rate where g is the expected constant growth rate in
dividends.
𝐷𝑡 = 𝐷𝑡−1(1 + 𝑔)
𝐷𝑡 = 𝐷0 (1 + 𝑔) 𝑡
--- For any time t, Dt equals the t=0 dividend
compounded at g for t periods

15. The Gordon Growth
Model
• Gordon Growth Model Equation:
𝑉0 = ෍
𝑡=1
∞
𝐷𝑡
(1 + 𝑟) 𝑡
𝑉0 =
𝐷1
(1 + 𝑟)1
+
𝐷2
(1 + 𝑟)2
+ ⋯ +
𝐷 𝑛
1 + 𝑟 𝑛
+ ⋯
𝑉0 =
𝐷0 (1 + 𝑔) 1
(1 + 𝑟)1
+
𝐷0 (1 + 𝑔) 2
(1 + 𝑟)2
+ ⋯ +
𝐷0 (1 + 𝑔) 𝑛
1 + 𝑟 𝑛
+ ⋯
𝐕𝟎 =
𝐃 𝟎(𝟏 + 𝐠)
𝐫 − 𝐠
𝐨𝐫
𝐃 𝟏
𝐫 − 𝐠
--- Gordon Growth Model

16. The Gordon Growth
Model
• Gordon Growth Model Equation:
• Required return on equity (cost of equity) must be
greater than the growth rate.
𝐕𝟎 =
𝐃 𝟎(𝟏 + 𝐠)
𝐫 − 𝐠
𝐨𝐫
𝐃 𝟏
𝐫 − 𝐠

17. The Gordon Growth
Model
Checkpoint (Computation of Gordon Growth Model)
• Suppose that an annual dividend of Php5 has just
been paid. The expected long term growth rate is 5%
and the required return on equity is 8%. What is the
Gordon growth model value per share?
• A. 65.67
• B. 166.67
• C. 175.00
• D. 180.00

18. Stable Growth Rate
• Two insights when estimating “stable” growth rate:
• Firm’s other measures of performance (i.e.,
earnings) can also be expected to grow at the
same rate with dividends
• What growth rate is reasonable as a stable
growth rate

19. Stable Growth Rate
• Estimating the growth rate:
• Industry or macroeconomic average
• Sustainable growth rate
g = b × ROE
where
g = growth rate
b = earnings retention rate or (1 – Dividend payout ratio)
ROE = return on equity

20. Stable Growth Rate
• Sustainable growth rate:
g = b × ROE
Net income Total assets
ROE =
Total assets Shareholders' equity
  
  
  
Net income Sales Total assets
ROE =
Sales Total assets Shareholders' equity
   
   
   
Net income Dividends Net income Sales Total assets
Net income Sales Total assets Equity
     −  
=         
      
g

21. Zero Growth Rate
• Fixed-Rate Perpetual Preferred Stock
• The owner of a preferred stock receives a promise to pay a
stated dividend for an infinite period.
• Example: Kansas City Southern Preferred 4% (KSU-P),
issued 2 January 1963, has a par value of $25 per share.
Thus, a share pays 0.04($25) = $1.00 in annual dividends.
The required return on this security is estimated at 5.5%.
𝑉0 =
𝐷
𝑟
𝑉0 =
1.00
5.5%
= $18.18

22. Required Rate of Return
• Frequently use the Capital Asset Pricing Model:
• Estimating a Required Return using the Gordon
Growth Model:
Required rate of return = E RFR + β[E RMkt − E RFR ]
𝑟 =
D0(1 + g)
P0
+ g =
D1
P0
+ g
P0 =
D0(1 + g)
r − g

23. Remarks of the Gordon
Growth Model
• Simplest practical implementation of discounted
dividend valuation
• Appropriate for valuing the equity of dividend
paying companies when its key assumption of a
stable future dividend and earnings growth rate is
expected to be satisfied
• Output of the model is sensitive to small changes in
the assumed growth rate and required rate of return

24. Multistage Dividend
Discount Model
• For many publicly traded companies, practitioners
assume growth falls into three stages:
• Growth Phase
• Transition Phase
• Mature Phase
• The growth phase concept provides the intuition for
multistage dividend discount models.

25. General Two-Stage
Dividend Discount Model
• Assumes high growth rate for the initial period
(Stage 1), followed by a sustainable constant growth
(usually lower growth rate) thereafter (Stage 2)
• Two-stage model is based on the multiple period
model:
𝑉0 = ෍
𝑡=1
𝑛
𝐷𝑡
(1 + 𝑟) 𝑡
+
𝑉𝑛
(1 + 𝑟) 𝑛

26. General Two-Stage
Dividend Discount Model
• General Two-Stage DDM Equation:
𝐷𝑡 = 𝐷0 (1 + 𝑔𝑠) 𝑡
𝐷 𝑛+1 = 𝐷 𝑛(1 + 𝑔 𝐿) = 𝐷0 (1 + 𝑔𝑠) 𝑛 (1 + 𝑔 𝐿)
--- Stage 1
--- Stage 2
𝑉𝑛 =
𝐷0 (1 + 𝑔𝑠) 𝑛 (1 + 𝑔 𝐿)
𝑟 − 𝑔 𝐿
𝑽 𝟎 = ෍
𝒕=𝟏
𝒏
𝑫 𝟎 (𝟏 + 𝒈 𝒔) 𝒕
(𝟏 + 𝒓) 𝒕
+
𝑫 𝟎 (𝟏 + 𝒈 𝒔) 𝒏
(𝟏 + 𝒈 𝑳)
𝟏 + 𝒓 𝒏(𝒓 − 𝒈 𝑳)
𝑉0 = ෍
𝑡=1
𝑛
𝐷𝑡
(1 + 𝑟) 𝑡
+
𝑉𝑛
(1 + 𝑟) 𝑛

27. General Two-Stage
Dividend Discount Model
Checkpoint (Computation of General Two-Stage Model)
• Consider a company that has just paid a dividend of
Php0.55. An analyst expects dividends to grow at a
rate of 9 percent per year for the next three years.
After that dividends are expected to grow at a
normal rate of 5 percent per year. Given a required
return on equity of 7 percent, what is the value of the
stock today?

28. General Two-Stage
Dividend Discount Model
Checkpoint (Computation of General Two-Stage Model)
• Consider a company that has just paid a dividend of Php0.55.
An analyst expects dividends to grow at a rate of 9 percent per
year for the next three years. After that dividends are expected
to grow at a normal rate of 5 percent per year. Required return
on equity is 7 percent.
Year Value Calculation of Dt or Vt Dt or Vt Present Value
1 D1 =0.55 x (1+0.09)^1 0.5995 0.5603
2 D2 =0.55 x (1+0.09)^2 0.6535 0.5708
3 D3 =0.55 x (1+0.09)^3 0.7123 0.5814
3 V3 =[0.55 x (1+0.09)^3 x 1.05]/(.07-.05) 37.3940 30.5246
Total 32.2371

29. Remarks of the General
Two-Stage DDM
• Since the two-stage dividend discount model is
based upon two clearly delineated growth stages,
high growth and stable growth, it is best suited for
firms which are in high growth and expect to
maintain that growth rate for a specific time period,
after which the sources of the high growth are
expected to disappear.
• Problem with the model lies in the assumption that
the growth rate is high during the initial period and
is transformed overnight to a lower stable rate at the
end of the period.

30. General Three-Stage
Dividend Discount Model
• Allows for an initial period of high growth (Stage 1),
a transitional period where growth declines (Stage
2) and a final stable growth phase (Stage 3)
Growth rate
Time
High Stable
Growth
Declining
Growth
Infinite Stable
Growth

31. General Three-Stage
Dividend Discount Model
Checkpoint (Computation of General Three-Stage
Model)
• Consider a company that has just paid a dividend of
Php1.6. Assume that dividends will grow at 14% for
the next 2 years, 12% for the following 5 years, and
10.2% thereafter. Given a required return on equity
of 12%, what is the value of the stock today?

32. General Three-Stage
Dividend Discount Model
Checkpoint (Computation of General Three-Stage
Model)
• D0 = Php1.6; Dividend growth rates: 14% for YR1-2, 12% for
YR3-7, 10.2% thereafter; r = 12%
Year Value Calculation of Dt or Vt Dt or Vt Present Value
1 D1 =1.6 x (1.14)^1 1.8240 1.6286
2 D2 =1.6 x (1.14)^2 2.0794 1.6577
3 D3 =1.6 x (1.14)^2 x (1.12)^1 2.3289 1.6577
4 D4 =1.6 x (1.14)^2 x (1.12)^2 2.6083 1.6577
5 D5 =1.6 x (1.14)^2 x (1.12)^3 2.9214 1.6577
6 D6 =1.6 x (1.14)^2 x (1.12)^4 3.2719 1.6577
7 D7 =1.6 x (1.14)^2 x (1.12)^5 3.6645 1.6577
7 V7 =[1.6 x (1.14)^2 x (1.12)^5 x 1.102]/
(0.12-0.102)
224.3515 101.4852
Total 113.0597

33. Remarks of the General
Three-Stage DDM
• This model removes many of the constraints
imposed by other versions of the dividend discount
model.
• Practically speaking, this may be the more
appropriate model to use for a firm whose earnings
are growing at very high rates, are expected to
continue growing at those rates for an initial period
but are expected to start declining towards a stable
rate as the firm become larger and loses its
competitive advantages.

34. Remarks of the DDM
• Accommodate a variety of patterns of future
streams of expected dividends
• Earnings expected to grow at a rate comparable to or
lower than the growth rate of the economy
• Earnings that are large and growing at a moderate rate
• Earnings that are small and growing at a very high rate
• Terminal stage represents more than three-quarters
of the total value of shares
• Valuing non-dividend paying or low dividend paying
stocks

35. Module 5 | End.