The Dividend Discount and the Flows to Equity Models

1
The Dividend Discount and the Flows to Equity
Models
Where We Are Going
We begin our detailed study of valuation
models with two of the five cash flow models

Chapter 8
2
Third and Fourth Phases of
Security Analysis
Business Analysis
GAAP Financial Statements
Financial Statement Analysis
Forecast Assumptions
Valuation
Time
Historical Periods
Valuation Date
Forecast Periods
3
Dividend Discount Model

• Is the only model that makes a direct link
  between the value of the firm's equity and the
  payoff to investors in that equity
• Two sources of returns by holding a stock
  dividends and capital appreciations
• Easy to understand and intuitive
• Express the value of equity as the present value
  of the cash flows the equityholder expect to
  receive

4
Dividend Discount Model Continued

• Value of Common Equity

Present value of stock at end of holding period
Present value of future dividends during the
holding period
means the Cost of Equity
5
Dividend Discount Model Continued

• This equation shows the value of equity is the
  present value of all the expected future
  dividends

6
Dividend Discount Model Continued

• Therefore, the value of the firm's equity is
  independent of the investor's investment horizon
• The model is simple
• But forecasting the dividend stream correctly is
  complicated

7
Dividend Discount Model Assumptions

• DDM requires a forecast for an infinite number of
  yeas
• Which is infeasible
• Analysts must make a simplifying assumption about
  the dividend streams pattern
• Using the assumption that dividends will grow at
  a constant rate (g), the dividend discount model
  can be adapted to the Gordon Growth Model

8
Dividend Discount Model Assumptions Continued

• The Gordon Growth Model

9
Gordon Growth Model

• The reasonableness of a Gordon Model valuation
  depends on three assumptions
• Initial Dividend (DIV1)
• Cost of Equity (ke)
• Dividend Growth Rate (g)

10
Gordon Growth Model Continued

• Initial Dividend
• Actually, it is the expected dividend in the
  first year of the future dividend stream
• It is determined by
• Newspapers
• Annual reports
• Other public sources

11
Gordon Growth Model Continued

• Cost of Equity
• Estimated with the aid of an asset pricing model
  such as the Capital Asset Pricing Model (CAPM)

12
Gordon Growth Model Continued

• Dividend growth rate
• Valuation is very sensitive to the growth rate
  assumption
• Introduce the concept of a just barely
  sustainable dividend growth rate, which is the
  appropriate growth rate to use in the model

13
Equity Value as a Function of Dividend Growth Rate
g5, v42.86 g4, v37.50 g6, v50.00
14
The Just Barely Sustainable Dividend Growth Rate
"g"

• So which is right growth rate?
• Just barely sustainable growth rate (g)
• The rate of growth in the dividend over the long
  run for which the firm would have sufficient
  resources to pay the specified dividend but would
  build up no excess cash

15
The Just Barely Sustainable Dividend Growth Rate
"g"

• If g is greater than g
• Then at some point, the firm will not generate
  enough cash to fund the dividend stream, so it
  has to borrow to make dividend payments
• If the firm keeps borrowing to fund ever
  increasing debt, theoretically, this will drive
  debt to an infinite level

16
The Just Barely Sustainable Dividend Growth Rate
"g"

• If g is less than g
• Eventually the firm will build up an infinite
  amount of cash, which would never be paid out
• By assuming this cash would grow within the firm,
  rather than being paid out as dividend, we
  exclude its value from the valuation under DDM.
  This is problematic.

17
The Just Barely Sustainable Dividend Growth Rate
"g" Cont.

• g is the dividend growth rate that makes excess
  cash trend toward zero over the long run
• The following equation represents the condition
  that must be true for g to represent the just
  barely sustainable dividend growth rate

18
The Just Barely Sustainable Dividend Growth Rate
"g" Cont.
Cash flow before dividends
means the firm's cash on hand at
time 0
means the free cash flow in
period t
means the debt service in period
t
19
The Just Barely Sustainable Dividend Growth Rate
"g" Cont.

• Implications of the equation of g
• We should forecast cash flows before considering
  dividends
• However, once the right hand side of the equation
  is computed, we have the value of the firms
  equity and there is no longer any need to know
  g. So DDM is somewhat impractical
• Why not just estimate g?
• Because g will depend on the relation between
  the initial dividend and the firm value
• See ex. 8.4 and the example

20
Variants of the Dividend Discount Model

• The two-stage model
• Assumes dividends grow at one rate for a period
  of time, followed by a different growth rate that
  is sustainable indefinitely

21
The Two-Stage Model
Value of dividends during supernormal growth
period
Value of dividend beyond
supernormal growth period
22
Example of DDM

• Data for Unitil Corp Ex. 8.6
• Valuation under different growth rates Ex. 8.7
• Valuation under different supernormal and normal
  growth rates Ex. 8.8
• Compare case 1 and 2 (under market value per
  share)
• Compare case 1 and 3
• Compare case 1 and 4

23
Flows to Equity Model

• Discounts the cash flows available to
  equityholders
• The flows to equity model is simply considering
  all cash flow except dividends (see Ex. 8.9)
• Is equivalent to the dividend discount model
• See example on p. 179

24
Flows to Equity Model Continued
means flows to
equity in period t and is the cost of equity
25
Flows to Equity Model

• All just barely sustainable dividend streams have
  the same value, no matter how management alters
  the dividend stream
• Dividends are distribution of value
• We can thus measure the value that can be
  distributed by measuring how much has been created

26
Summary

• We have learned
• The dividend discount model
• The assumptions of the dividend discount model
• The concept of a just barely sustainable dividend
  stream
• The flows to equity model