13
Equity Chapter Valuation
Fundamental Stock Analysis:
Models of Equity Valuation
Basic Types of Models
Balance Sheet Models
Dividend Discount Models
Price/Earnings Ratios
Free Cash Flow Models
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Models of Equity Valuation
Valuation models using comparables
Look at the relationship between price and
various determinants of value for similar firms
The internet provides a convenient way to
access firm data. Some examples are:
EDGAR
Finance.yahoo.com
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Microsoft Corporation Financial
Highlights 2009
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Valuation Methods
Book value
Value of common equity on the balance sheet
Based on historical values of assets and
liabilities, which may not reflect current values
Some assets such as brand name or
specialized skills are not on a balance sheet
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Valuation Methods
Market value
Current market value of assets minus current
market value of liabilities
Market value of assets may be difficult to
ascertain
Market value based on stock price
Better measure than book value of the worth of
the stock to the investor.
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Valuation Methods (Other Measures)
Liquidation value
Net amount realized from sale of assets and
paying off all debt
Firm becomes a takeover target if market value
stock falls below this amount, so liquidation
value may serve as floor to value
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Valuation Methods (Other Measures)
Replacement cost
Replacement cost of the assets less the
liabilities
May put a ceiling on market value in the long
run because values above replacement cost
will attract new entrants into the market.
Tobins Q = Market Value / Replacement Cost;
should tend toward 1 over time.
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Expected Holding Period Return
The return on a stock investment
comprises cash dividends and capital gains
or losses
Assuming a one-year holding period
Expected HPR= E ( r ) =
E ( D1 ) + [ E ( P ) P0
1
]
P0
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Required Return
CAPM gave us required
return, call it k:
k = market capitalization
rate
If the stock is priced
=
correctly
Required return should
equal expected return
k = rf + E (rM ) rf
Expected HPR= E (r ) =
E ( D1 ) + [ E ( P ) P0
1
]
P0
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Intrinsic Value
The present value of a firms expected future net cash
flows discounted by a risk adjusted required rate of
return.
The cash flows on a stock are
Dividends (Dt)
Sale price (Pt)
Intrinsic Value today (time 0) is denoted V0 and for ) one
E(D1 ) + E(P1 a
V0 =
year holding period may be found as: 1 + k
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Intrinsic Value and Market Price
Market Price
Consensus value of all traders
In equilibrium the current market price will equal
intrinsic value
Trading Signals
If V0 > P0
If V0 < P0
If V0 = P0
Buy
Sell or Short Sell
Hold as it is Fairly Priced
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Basic Dividend Discount Model
Intrinsic value of a stock can be found from the
following:
Dt
V0 =
t
t =1 (1 + k )
V0 = Intrinsic Value of Stock
Dt = Dividend in time t
k = required return
What happened to the expected sale price in this
formula?
Why is this an infinite sum?
Is stock price independent of the investors holding
period?
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Basic Dividend Discount Model
Intrinsic value of a stock can be found from the
following:
Dt
V0 =
(1 + k )t
t =1
V0 = Intrinsic Value of Stock
Dt = Dividend in time t
k = required return
This equation is not useable because it is an
infinite sum of variable cash flows.
Therefore we have to make assumptions about the
dividends to make the model tractable.
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No Growth Model
Use: Stocks that have earnings and
dividends that are expected to remain
constant over time (zero growth)
D
V0 =
k
Preferred Stock
A preferred stock pays a $2.00 per share
dividend and the stock has a required
return of 10%. What is the most you
should be willing to pay for the stock?
$2.00
V0 =
= $20.00
0.10
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Constant Growth Model
Use: Stocks that have earnings and dividends that
are expected to grow at a constant rate forever
D0 (1 + g )
V0 =
; g = perpetual growth rate in dividends
k -g
A common stock share just paid a $2.00 per share
dividend and the stock has a required return of
10%. Dividends are expected to grow at 6% per
year forever. What is the most you should be
willing to pay for the stock?
$2.00 1.06
V0 =
= $53.00
0.10 - 0.06
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Comparing Value and Returns
Why do you have to pay more for the
constant growth stock?
Must pay for expected growth
What is the one year rate of return for each
stock?
No Growth Stock
V0 = $20.00
D = $2.00
V1 = $2.00 / 0.10 = $20.00
k=
$20 $20 + $2
= 10%
$20
Constant Growth Stock
V0 = $53.00; D0 = $2.00
$2.00 1.06 2
V1 =
= $56.18
0.10 - 0.06
k=
$56.18 $53 + $2.12
= 10%
$53
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Comparing Value and Returns
Both stocks given an investor a pre-tax
return of 10%.
Is one stock a better buy than the other?
Not if both are actually priced at their intrinsic
value (ignoring taxes).
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Stock Prices and Investment
Opportunities
g = growth rate in dividends is a function of
two variables:
ROE = Return on Equity for the firm
b = plowback or retention percentage rate
(1- dividend payout percentage rate)
g = ROE b
g increases if a firm increases its retention
ratio and/or its ROE
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Value of Growth Opportunities
Value with 100% dividend payout
Cash Cow, Inc. (CC)
E1 = $5
D1 = $5
b = 0; therefore g = 0
k = 12.5% ; Find VCC
VCC =
$5.00
= $40
0.125
ROE = 12.5%
g = ROE b
Growth Prospects
(GP) V = $5.00 = $40
GP
0.125
E1 = $5
D1 = $5
b = 0; therefore g = 0
k = 12.5%, Find VGP
ROE = 15%
Should either or both firms retain some earnings?
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Value of Growth Opportunities
Value with 40% dividend payout
Cash Cow, Inc. (CC)
E1 = $5
b = 60%; therefore =
7.5%
D1 g = 0.40 x $5 = $2.00
k = 12.5%; Find VCC
ROE = 12.5%
CC value is the same,
2.00
VCC
= $40
why? =
0.125 - 0.075
Growth Prospects (GP)
E1 = $5
b = 60%; therefore g = 9%
D1 = 0.40 x $5 = $2.00
k = 12.5%; Find VGP
ROE = 15%
GP Value has increased,
why?
VGP =
$2.00
= $57.14
0.125 - 0.09
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Value of Growth Opportunities
Value of assets in place for GP = $40.00 (value with all
dividends paid out, with ROE = 12.5%)
Value of growth opportunities with ROE = 15% may be
inferred from the difference between the new VGP =
$57.14 and the no growth value of $40.00
Thus the present value of growth opportunities
(PVGO) = $57.14 - $40.00 = $17.14
D0 (1 + g ) E1
In general: PVGO =
(k g )
k
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Multistage Growth Models
As firms progress through their industry life cycle, earnings
and dividend growth rates (ROE) are likely to change.
A two stage growth model:
g1 = first growth rate
T (1 + g1 )t
DT (1 + g2 )
V0 = D0
+
t
(1 + k) (k g2 )(1 + k)T
t =1
g2 = second growth rate
T = number of periods of growth at g1
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Multistage 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
$2.40 $2.88 $3.46
$3.63
V0 =
+
+
+
2
3
1.15 1.15
1.15
(0.15 0.05 )(1.15)3
V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40
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Honda Motor
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Two Stage DDM for Honda
Year
Dividend
2009
0.90
2010
0.98
2011
1.06
2012
1.15
g = ROE b
From Value Line
g = 11.0% 70% = 7.70%
Assume the dividend growth rate will be
steady beyond 2012. Value Line forecasts b
= 70% and ROE of 11.0%. What should be
the long term growth rate?
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Two Stage DDM for Honda
The required rate of return:
Honda = 1.05
From Value Line
Rf in 2008 = 3.5%
Market risk premium = historical average of
8%
k Honda = R f + (RM R f )Honda
k Honda = 3.5% + (8% 1.05) = 11.90%
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Two Stage DDM for Honda
Year
k = 11.90%
g = 7.70%
Find the intrinsic value
V0 = $21.88
Divid
end
2009
0.90
2010
0.98
2011
1.06
2012
1.15
$0.90 $0.98
$1.06
$1.15
$1.15 1.077
V0 =
+
+
+
+
2
3
4
1.119 1.119
1.119
1.119
(0.119 0.077 )(1.119 )4
Value Line reported the actual price = $21.37, so
Honda was undervalued by $0.51 or about 2.4%.
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Two Stage DDM for Honda
Should we trust the valuation result?
Year
Dividen
d
What if the beta is slightly incorrect,
suppose it is 1.10 (< 5% error) rather
than 1.05?
2009
0.90
2010
0.98
2011
1.06
Now k = 12.3% and the intrinsic value
estimate V0= $19.98, reversing our
conclusion that Honda is undervalued
2012
1.15
Actual price =
$21.37
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P/E Ratio and Growth
Opportunities
P/E Ratios are a function of two factors
Required Rates of Return (k) (inverse relationship)
Expected Growth in Dividends (direct relationship)
Uses
Estimate intrinsic value of stocks
Conceptually equivalent to the constant
growth DDM
Extensively used by analysts and investors
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P/E, ROE and Growth
With positive growth:
P0 (1 b)
=
E1 k g
With zero growth:
If g = 0 then b should = 0 and the ratio
simplifies to:
P0 1
=
E1 k
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Numerical Example: No Growth
E1 = $2.50
and V0
g=0
k = 12.5%; Find P/E
P/E = 1/k = 1/.125 = 8
V0 = P/E x E1 = 8 x $2.50 = $20.00
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Numerical Example with Growth
b = 60% ROE = 15%; k = 12.5% (1-b) = 40%,
E0 = $2.50
Find the P/E and V0:
g = ROE x b = 15% x 60% = 9%
E1 = $2.50 (1.09) = $2.725
P/E = (1 - .60) / (.125 - .09) = 11.4
V0 = P/E x E1 = 11.4 x $2.73 = $31.14
13-33
P/E Ratios and Stock Risk
P0 (1 b)
=
E1 k g
Riskier firms will have higher required rates
of return (higher values of k)
Riskier stocks will have lower P/E multiples
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Pitfalls in Using P/E Ratios
Earnings management is a serious problem,
P/E should be calculated using pro forma
earnings,
A high P/E implies high expected growth, but not
necessarily high stock returns,
Simplistic, assumes the future P/E will not be lower
than the current P/E. If expected growth in
earnings fails to materialize the P/E will fall and
investors may incur large losses.
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Other Comparative Valuation
Ratios
Price-to-book
High ratio indicates a large premium over book value,
and a floor value that is often far below market price
Price-to-cash flow
P/Cash Flow instead of P/E; less subject to accounting
manipulation
Price-to-sales
Useful for firms with low or negative earnings in early
growth stage
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Free Cash Flow
Capitalize or discount the free cash flow for the firm (FCFF)
at the weighted-average cost of capital and then subtract
the existing (market) value of debt
Useful for firms that dont pay dividends,
FCFF = EBIT(1 TC ) + Depreciation Capital Expenditures Increase in NWC
where:
EBIT = earnings before interest and taxes
Tc = the corporate tax rate
NWC = net working capital
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FCFF, Firm Value & Equity Value
The free cash flow methods discount year to year cash
flows plus some estimate of the terminal value PT where
PT =
FCFFT +1
WACC g
WACC = Weighted average cost of capital
g = estimate of long run growth in free cash flow
T = time period when the firm approaches constant
growth
T
FCFF
P
t
T
Firm Value =
+
t
T
t =1 (1 + WACC ) (1 + WACC )
Equity value = Firm Value Market Value of Debt
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Comparing the Valuation
Models
In theory free cash flow approaches should provide the
same estimate of intrinsic value as the dividend growth
model
In practice the various approaches often differ substantially
Simplifying assumptions are used in all models
The models establish ranges of likely intrinsic value
Using multiple models forces rigorous thinking about the
inputs
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