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Chapter 12
Equity Valuation
Fundamental Stock
Analysis: Models of
Equity Valuation
• Basic Types of Models
• Balance Sheet Models
• Dividend Discount Models
• Price/Earning Ratios
• Estimating Growth Rates and
Opportunities
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Intrinsic Value and
Market Price
• Intrinsic Value
• Self assigned Value
• Variety of models are used for estimation
• Market Price
• Consensus value of all potential traders
• Trading Signal
• IV > MP Buy
• IV < MP Sell or Short Sell
• IV = MP Hold or Fairly Priced
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Dividend Discount Models:
General Model

Dt
Vo = 
t
t = 1 (1 + k )
• V0 = Value of Stock
• Dt = Dividend
• k = required return
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No Growth Model
D
Vo =
k
• Stocks that have earnings and dividends that
are expected to remain constant
• Preferred Stock
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No Growth Model:
Example
D
Vo =
k
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33
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Constant Growth Model
Do(1 + g)
Vo =
k-g
• g = constant perpetual growth rate
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Constant Growth Model:
Example
Do(1 + g)
Vo =
k-g
E1 = $5.00 b = 40%
k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / (.15 - .08) = $42.86
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Estimating Dividend
Growth Rates
g = ROE  b
• g = growth rate in dividends
• ROE = Return on Equity for the firm
• b = plowback or retention percentage rate
• (1- dividend payout percentage rate)
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Shifting Growth Rate
Model
(1+ g1)
DT (1+ g2)
+
V o = Do
t
T
( k - g2)(1+ k )
t =1 (1 + k )
T
t
• g1 = first growth rate
• g2 = second growth rate
• T = number of periods of growth at g1
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Shifting Growth Rate
Model: Example
D0 = $2.00 g1 = 20% g2 = 5%
k = 15% T = 3 D1 = 2.40
D2 = 2.88 D3 = 3.46 D4 = 3.63
V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +
D4 / (.15 - .05) ( (1.15)3
V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40
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Specified Holding Period
Model
=
V0
D + D
(1+ k ) (1+ k )
1
2
1
+
...
2
+
DN
P
(1+ k )
N
N
• PN = the expected sales price for the stock at
time N
• N = the specified number of years the stock is
expected to be held
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Partitioning Value: Growth
and No Growth Components
E1
+ PVGO
Vo =
k
D o (1 + g )
E1
PVGO =
(k - g)
k
• PVGO = Present Value of Growth
Opportunities
• E1 = Earnings Per Share for period 1
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Partitioning Value:
Example
• ROE = 20% d = 60% b = 40%
• E1 = $5.00 D1 = $3.00 k = 15%
• g = .20 x .40 = .08 or 8%
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Partitioning Value: Example
3
= $42.86
Vo =
(.15-.08)
5
= $33.33
NGV o =
.15
PVGO = $42.86 - $33.33 = $9.52
Vo = value with growth
NGVo = no growth component value
PVGO = Present Value of Growth Opportunities
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Price Earnings Ratios
• P/E Ratios are a function of two factors
• Required Rates of Return (k)
• Expected growth in Dividends
• Uses
• Relative valuation
• Extensive Use in industry
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P/E Ratio: No expected
growth
E1
P0 =
k
P0
1
=
E1
k
• E1 - expected earnings for next year
• E1 is equal to D1 under no growth
• k - required rate of return
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P/E Ratio with Constant
Growth
D1
E 1(1 - b)
=
P0 =
k - g k - (b  ROE )
P0
1- b
=
E 1 k - (b  ROE )
• b = retention ration
• ROE = Return on Equity
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Numerical Example: No
Growth
E0 = $2.50
g=0
k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
PE = 1/k = 1/.125 = 8
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Numerical Example with
Growth
b = 60% ROE = 15% (1-b) = 40%
E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
k = 12.5% g = 9%
P0 = 1.09/(.125-.09) = $31.14
PE = 31.14/2.73 = 11.4
PE = (1 - .60) / (.125 - .09) = 11.4
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Pitfalls in Using PE Ratios
• Flexibility in reporting makes choice of
earnings difficult
• Pro forma earnings may give a better
measure of operating earnings
• Problem of too much flexibility
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Other Valuation Ratios &
Approaches
•
•
•
•
Price-to-book
Price-to-cash flow
Price-to-sales
Present Value of Free Cash Flow
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