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Equity Valuation
CHAPTER 12
1
Fundamental analysis
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Identify stocks that are mispriced relative to true value
Compare the actual market price and the true price estimated
from various models using publicly available information
The true price estimated from models is the intrinsic value
(IV)
Market price (MP): consensus value of all potential trades
(buyers and sellers)
Trading signal



IV > MP: underpriced, buy
IV < MP: overpriced, sell
IV = MP: fairly priced, hold
Determine underpriced/overpriced stocks
(calculate alpha)
estimated E(r) 
E D1   E P1   P0 
P0
• If estimated E(r) > Required Return, the stock is undervalued.
• If estimated E(r) < required return, the stock is overvalued
• required return is from a pricing model, e.g. CAPM:
E (rXYZ )  rf   XYZ ( E (rm )  rf )
Determine underpriced/overpriced stocks
(calculate alpha)
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example: stock ABC, the current price Po = 48, expected price
in 1 year E(P1) = 52, expected dividend in 1 year E(D1) = 4
rf = 6, RPm = 5, beta = 1.2
Is this stock overpriced or underpriced?
Step 1: calculate the estimated expected return
estimated E(R) = (52+4-48)/48 = 16.7%
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Step 2: calculate required return from CAPM
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required E(R) = 6 + 1.2(5) = 12
Step 3: calculate alpha
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alpha = 16.7 – 12 = 4.7 > 0
stock is undervalued
Determine underpriced/overpriced stocks
(calculate intrinsic value)
Intrinsic value --The present value of a firm’s expected future
net cash flows discounted by the required rate of return.
E ( D1 )  E ( P1 )
V0 
1 k
•V0 (intrinsic value) > P0 (market price)  buy (undervalued)
•V0 (intrinsic value) < P0 (market price)  sell or sell short
(overvalued)
•In market equilibrium, V0 = P0 (fairly priced)
•k is required return
Determine underpriced/overpriced stocks
(calculate intrinsic value)

Previous example
E ( D1 )  E ( P1 ) 4  52
V0 

 50
1 k
1.12

Vo = 50 > Po = 48, the current market price is undervalued
compared with the intrinsic value
Estimate intrinsic value
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Dividend discount model (DDM)
P/E ratios approach
Dividend discount model (DDM)
Dividend discount model (infinite horizon):
the intrinsic value is the present value of all
futures dividends discounted by the required
return
D3
D1
D2
V0 


...
2
3
1  k 1  k 
1  k 
Dividend discount model (DDM)

No growth model: The same amount of dividend every year
(perpetuity)
D
V0 
k
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Example: a preferred stock, D = 5, required return k = 15%. What
is the value of this stock

Vo = 5/.15 = 33.33
Dividend discount model (DDM): constant growth rate

Constant growth model: dividend grows at a constant rate g
D1  D0 (1  g )
D2  D1 (1  g )  D0 (1  g ) 2
D3  D2 (1  g )  D0 (1  g ) 3
................................................
D0 1  g  D0 1  g 
D0 1  g 
V0 


...
2
3
1 k
1  k 
1  k 
D 1  g 
D1
 0

kg
kg
2
3
Dividend discount model (DDM): constant
growth rate
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Example 1: stock ABC, next year
dividend = 3, required return k =
15%, constant growth rate = 8%.
What is the value of the stock
Example 2: stock ABC, just paid
dividend = 0.50, required return k
= 15%, constant growth rate =
2%. What is the value of the stock
V0 
V0 
D1
3

 42.86
k  g .15  .08
Do (1  g ) 0.5(1  .02)

 3.92
kg
.15  .02
Implications of constant growth DDM
D1
V0 
k g
• If expected dividend D1 increases, then V0 increases.
• If k decreases, then V0 increases.
• If g increases, then V0 increases.
• Price grows at the same rate as dividend
D1  D0 (1  g )
P1  P0 (1  g )
Implications of constant growth DDM

Required return k:
V0 

D1
kg
In equilibrium, the intrinsic value = market price i.e. Vo = Po, therefore,
D1
P0 
kg
D1
k 
g
P0
Dividend
Yield
Capital
Gains Yield
Estimate growth rate g
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Company A: 2 scenarios


No investment opportunities: the expected return of all projects in the
company < required return k. In this case, the company would choose
to pay 100% of the earning as dividends and let the stockholders invest
in the market by themselves
Has investment opportunities: if the company has investment
opportunity, expected return of projects is higher than required return k,
then the company would choose low dividend payout policy, (a smaller
fraction of earning goes to dividend) say
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
40% dividend (dividend payout ratio)
60% retained earning to be used for reinvestment (plow-back ratio or
earning retention ratio)
Dividend Payout Ratio and Plowback Ratio
 Dividend
Payout Ratio: Percentage of
earnings paid out as dividends
 Plowback
(or Earning Retention) Ratio:
Fraction of earnings retained and
reinvested in the firm
Estimate growth rate g
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Company A, total asset 100 mil, all equity financed. ROE =
15%.
Total earning = 15% (100) = 15 mil
If 60% of earning is reinvested, new additional capital is
60%(15) = 9 mil
Old capital = 100, new capital = 9, total capital = 109
Growth rate g is the growth rate in value of capital (stock)

g = (109-100)/100 = 9%
Plowback Ratio and Growth
g  ROE  b
Where:
ROE = Return on Equity
b
= Plowback Ratio
(or Earning Retention Ratio)
Example: g = 15% (0.6) = 9%
Partitioning value
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Example, Company A, expected earning E1=5, k = 12.5%
No growth: pay all earnings as dividend, D = 5
With growth: ROE = 15%, b = 0.6 so g = ?
No growth: P*0= E1/k = D/k = 40
with growth: P0 = D1/(k-g) = 5(.4)/(0.15-0.125) = 57.14
Why the price with growth is higher than the price with no
growth?
Price (with growth) = P*0 (no growth) + PVGO (present value
of growth opportunities)
PVGO is reward to growth opportunities
57.14 = 40 + 17.14
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

Partitioning Value: Growth and No Growth
Components
Example: Takeover Target has a dividend payout ratio of 60%
and an ROE of 20%. If it expects earnings to be $ 5 per share,
the appropriate capitalization rate is 15%? What is the intrinsic
value, what is PVGO, what is NGVo?
Partitioning Value: Example
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ROE = 20% d = 60% b = 40%

E1 = $5.00 D1 = $3.00 k = 15%

g = .20 x .40 = .08 or 8%
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
Growth opportunity: another example

Takeover Target is run by entrenched
management that insists on reinvesting 60% of
its earnings in projects that provide an ROE of
10% despite the fact that the firm’s required
return k = 15%. The firm’s next year dividend =
$2 per share, paid out of earnings of $5 per
share. At what price should the firm sell? what is
the present value of growth opportunities? Can
we increase the firm’s value?
Shifting growth rate model (multistage growth model)
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In constant growth DDM, g is constant over time
In practice, there are some periods g is high (when more
investment opportunities), some periods g is low (when less
investment opportunities)
Shifting growth rate model (multistage
growth model)
Changing growth rates:
V0 
D1
1 k

D2
1  k 
2
temporary high
(or low) growth
 ... 
DH
1  k 
H

DH  1
1  k 
H 1
permanent
constant growth
 . ..
Shifting growth rate model (multistage growth
model)
Example: Whitewater Rapids Company is expected to have
dividends grow at a rate of 20% for the next three years. In
three years, the dividends will settle down to a more
sustainable growth rate of 5% which is expected to last
“forever.” If Whitewater just paid a dividend of $2.00 and its
level of risk requires a discount rate of 15%, what is the
intrinsic value of Whitewater stock?
Shifting growth rate model (multistage growth
model)
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Compute the dividends until growth levels off
 D1 = 2(1.2) = $2.40
 D2 = 2.4(1.2) = $2.88
 D3 = 2.88(1.2) = $3.46
Find the expected future price at the year growth leves off
 P3 = D3(1+g) / (k – g) = 3.46(1.05) / (.15 - .05) = 36.3
Find the intrinsic value which is the present value of the all
expected future cash flows
 V0 = 2.4 / (1.15) + (2.88) / (1.15)2 + (3.46) / (1.15)3
+ (36.3) / (1.15)3 = 30.40
Price-Earning (P/E) Ratios
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Ratio of Stock price to its earnings per share
Useful for firm valuation:
P
P  E
E
in practice
 Forecasts of E
 Forecasts of P/E
Price-Earning (P/E) Ratios and growth
P0 
E1
 PVGO
k
P0 1 PVGO 1  PVGO 

 
 1 
E1 k
E1
k
E1 / k 
When PVGO  0, P0  E1/k (no growth price). P0/E1  1/k (constant)
PVGO increases, and dominates no growth price, P/E ratio can rise dramatical ly
PVGO component of firm value reflecting growth opportunit ies

E1 / k
component of firm value already in place (no growth)
If a firm has high P/E ratio, the firm might have good growth opportunit ies
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 )
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b = retention ration
ROE = Return on Equity
Price-Earning (P/E) Ratio
Plowback ratio (b) (k = 12%)
0
0.25
A. Growth rate g
ROE
10
0
2.5
12
0
3
14
0
3.5
B. P/E ratio
ROE
10
8.33
7.89
12
8.33
8.33
14
8.33
8.82
0.50
0.75
5
6
7
7.5
9
10.5
7.14
8.33
10.00
5.56
8.33
16.67
Some comments with P/E Ratios
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High plowback ratio (b)
= ROE*b)
High Growth Rate (g) (g
BUT
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High g (if due to high b)

higher b
High P/E ratio
higher P/E only when ROE > k
P/E ratio and Risk
P 1 b

E kg
Holding everything equal:
High risk (k), Low P/E.
P/E ratios in practice
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P/E ratio proxies for expected growth in dividends or earnings.
If the stock is correctly priced, the rule of thumb is
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P/E ≈ g or PEG ≈ 1
PEG > 1 then overpriced
PEG < 1 then underpriced
PEG: no theoretical explanation but works very well
Peter Lynch, the famous portfolio manager, said in this book
One Up on Wall Street
The P/E ratio of any company that is fairly priced will equal its growth
rate. I am talking here about growth rate of earnings.... If the P/E ratio of
Coca-Cola is 15, you’d expect the company to be growing at 15% per year,
etc. But if the P/E ratio is less than the growth rate, you may have found
yourself a bargain.
Pitfalls in P/E Analysis
• Earnings are based on accounting data
Current price and current earnings
Future expected earnings is more appropriate
• In P/E formula, E is an expected trend
• In financial pages, E is the actual past period's earnings
• Different accounting methods will give different earnings
Other Valuation Ratios & Approaches

Price-to-book: price per share/book value per
share
 How
aggressively the market values the firm
Price-to-cash flow: price per share/cash flow
per share
 Price-to-sales: price per share/sales per share

 Some
start-up firms do not have earnings so sale is
more appropriate.

Be creative: depending on particular situation
to design your own ratio
16. Janet Ludlow’s firm requires all its analysts to use a two-stage DDM and the CAPM to
value stocks. Using these measures, Ludlow has valued QuickBrush Company at $63 per
share. She now must value SmileWhite Corporation.
a.
Calculate the required rate of return for SmileWhite using the information in the
following table:
(K)
b.
Ludlow estimates the following EPS and dividend growth rates for SmileWhite:
(K)
Estimate the intrinsic value of SmileWhite using the table above, and the twostage DDM. Dividends per share in 2007 were $1.72.
c.
d.
Recommend QuickBrush or SmileWhite stock for purchase by comparing each
company’s intrinsic value with its current market price.
Describe one strength of the two-stage DDM in comparison with the constant
growth DDM. Describe one weakness inherent in all DDMs.
Summary
• Valuation approaches:
-Balance sheet values (P/E ratio)
-Present value of expected future dividends
• DDM states that the price of a share of stock is equal to the
present value of all future dividends discounted at the appropriate
required rate of return
D1
V

• Constant growth model DDM:
0
kg
• P/E ratio is an indication of the firm's future
growth opportunities