Equity Valuation
 Basic Types of Models
• Balance sheet models
• Dividend discount models
• EPS (cashflow) discount models
 Modeling Framework
• Deterministicdynamics
• Stochastic dynamics
Fair Value vs Market Price

Fair Value
• Self assigned Value
• Variety of models are used for estimation

Market Price
• Consensus value assessment by all market participants

Trading Signal
• FV > MP:
• FV < MP:
• FV = MP:
Buy
Sell or Short Sell
Hold or Fairly Priced
Dividend Discount Models


Dt
Vo  
t
t  1 (1  k )
V0 = Value of Stock
Dt = Dividend
k = required return
No Growth Model

D
Vo 
k
Where the stock has earnings and dividends that are
expected to remain constant foreever.
Example: Preferred Stock
No Growth Model: Example

D
Vo 
k
E1 = D1 = $5.00
k = .15
Then, V0 = $5.00 / .15 = $33.33
Constant Growth Model

Do (1  g )
Vo 
kg
g = constant perpetual growth rate
Constant Growth Model: Example

Do (1  g )
Vo 
kg
E1 = $5.00
b = 40%
(1-b) = 60%
k = 15%
D1 = $3.00
g = 8%
(b: EPS retention ratio)
V0 = 3.00 / (.15 - .08) = $42.86
Estimating Dividend Growth Rates

g  ROE  b
 g = growth rate in dividends
 ROE = Return on Equity for the firm
 b = EPS retention rate (1- dividend payout ratio)
Partitioning Value: Growth and No Growth Components

E1
Vo 
 PVGO
k
Do (1  g )
E1
PVGO 

(k  g)
k
 PVGO = Present Value of Growth Opportunities
 E1 = Earnings Per Share for period 1
Partitioning Value: Example
ROE = 20%
b = 40%
E1 = $5.00
D1 = $3.00
g = .20 x .40 = .08
or 8%
k = 15%
Partitioning Value: Example

3
Vo 
 $42.86
(.15.08)
5
NGVo 
 $33.33
.15
PVGO  $42.86  $33.33  $9.52
• Vo = value with growth
• NGVo = no growth component value
• PVGO = Present Value of Growth Opportunities
Multi-Period Dividend-Discount Model

P
D
D
D

... 
V 
(1 k ) (1 k )
(1 k )
1
0
N
2
1
2
PN = expected sales price of stock at time N
N = number of years the stock is to be held
N
N
Practical Difficulties with DDM
 Some firms do not pay dividends
 Can you forecast future dividends?
 Can you predict the terminal liquidation
value Pn ?
 What about the discount rate k?
(perhaps, the CAPM? The APT?)
Multi-Period Earnings-Discount Model

(1  b) E N  P N
(1  b) E1 (1  b) E 2

... 
V0 
(1  k )1
(1  k ) 2
(1  k ) N
PN = expected sales price of stock at time N
N = number of years the stock is to be held
Practical Concerns with EDM
 EPS forecasts are available from I/B/E/S,
First Call, Zacks, ….
 Dividend payout ratio (1-b) can be
estimated, either based on cash dividend or dividendin-kind
 But, what about Pn
and k?
P/E Ratios
P0
d

E
k  g
d: dividend payout ratio
k: cost-of-capital (or, risk-adjusted discount rate)
g: EPS growth rate
P/E Example
k = 12.5%
Thus,
g = 9%
d = 40%
P/E = (1 - .60) / (.125 - .09) = 11.4
If E = $2.73, we have
P = 11.4 X 2.73 =$31.14
Problems with P/E Ratios
 What is
E?
• E = trailing 12-month EPS?
• E = 12-month-forward EPS?
 What is
g?
• g = average historical EPS growth?
• g = expected next-yr EPS growth?
• g = long-run EPS growth?