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Chapter 13
EquityValuation
Copyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
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Fundamental Stock Analysis:Models of Equity Valuation
Basic Types of Models
Balance Sheet Models
Dividend Discount Models
Price/Earnings Ratios
Free Cash Flow Models
13-3
Models of Equity Valuation
Valuation models using comparables
Look at the relationship between price andvarious determinants of value for similar firms
The internet provides a convenient way toaccess firm data. Some examples are:
EDGAR Electronic Data-Gathering, Analysis, and Retrieval system
Finance.yahoo.com
Factset, Reuters (Thompson), Bloomberg, etc
Aside) 10-K, 10-Q 13-4
Table 13.1 Microsoft CorporationFinancial 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 orspecialized skills are not on a balance sheet
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Valuation Methods
Market value
Current market value of assets minus currentmarket value of liabilities
Market value of assets may be difficult to ascertain
Market value based on stock price =>basically, price rather than value
Better measure than book value of the worthof the stock to the investor.
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Valuation Methods (Other Measures)
Liquidation value
Net amount realized from sale of assets andpaying off all debt
Firm becomes a takeover target if marketvalue stock falls below this amount, soliquidation value may serve as floor to value
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Valuation Methods (Other Measures)
Replacement cost
Replacement cost of the assets less theliabilities
May put a ceiling on market value in the longrun because values above replacement costwill attract new entrants into the market.
Cost; should tend toward 1 over time.
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13.2 Intrinsic Value VersusMarket Price
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Expected Holding Period Return
1 1 0
0
( ) ( )Expected HPR= ( )
E D E P PE r
P
The return on a stock investmentcomprises cash dividends and capitalgains or losses
Assuming a one-year holding period
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Required ReturnCAPM gave us requiredreturn, call it k:
k = market capitalizationrate
If the stock is pricedcorrectly (EMH)
Required return shouldequal expected return
1 1 0
0
( ) ( )Expected HPR= ( )
E D E P PE r
P=
( )f M f
k r E r r
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Intrinsic Value
Intrinsic Value
The present value
required rate of return (e.g., CAPM).
The cash flows on a stock are?Dividends (Dt)
Sale price (Pt)
Intrinsic Value today (time 0) is denoted V0 and for a oneyear holding period may be found as:
k1
)P(E)D(EV 110
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Intrinsic Value and Market Price
Market Price
Consensus value of all traders
Given to small investors like you and me
In equilibrium, the current market price willequal intrinsic value (EMH)
Trading Signals
If V0 > P0If V0 < P0If V0 = P0
Buy for me. But then what happens?
Sell or Short Sell for me. But then?
Indifferent at it is fairly priced
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Basic Dividend Discount Model
Intrinsic value of a stock can be found from thefollowing:
What happened to the expected sale price in thisformula?
Why is this an infinite sum?
holding period?
1tt
t
0 )k1(
D
V
V0 = Intrinsic Value of Stock
Dt = Dividend in time tk = required return
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Basic Dividend Discount Model
Intrinsic value of a stock can be found from thefollowing:
This equation is not useable because it is aninfinite sum of variable cash flows.
Therefore we have to make assumptions aboutthe dividends to make the model tractable.
1t
tt
0
)k1(
DV
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No Growth ModelUse: Stocks that have earnings anddividends that are expected to remainconstant over time (zero growth)
Preferred Stock
A preferred stock pays a $2.00 per share dividendand the stock has a required return of 10%. Whatis the most you should be willing to pay for thestock?
k
D
V0
00.20$0.10
$2.00V0
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Constant Growth Model
Use: Stocks that have earnings and dividendsthat are expected to grow at a constant rateforever
A common stock share just paid a $2.00 pershare dividend and the stock has a requiredreturn of 10%. Dividends are expected to growat 6% per year forever. What is the most youshould be willing to pay for the stock?
dividendsinrategrowthperpetual;g-k
D
V
1
0 g
00.53$0.06-0.10
1.06$2.00V0
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Comparing Value and ReturnsWhy do you have to pay more for theconstant growth stock?
Must pay for expected growth
What is the one year rate of return foreach stock?
No Growth Stock
V0 = $20.00; D = $2.00
E(V1)=
%1020$
2$20$20$)(ROIE
Constant Growth Stock
V0 = $53.00; D0 = $2.00
18.56$0.06-0.10
1.06$2.00)E(V
2
1
%1053$
12.2$53$18.56$)(ROIE
$2.00 / 0.10 = $20.00
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Comparing Value and Returns
Both stocks give an investor a pre-taxreturn of 10%.
Is one stock a better buy than the other?Not if both are actually priced at their intrinsicvalue (ignoring taxes).
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Stock Prices and InvestmentOpportunities
g = growth rate in dividends is a function oftwo variables:
ROE = Return on Equity for the firm
b = plowback or retention percentage rate
= (1- dividend payout percentage rate)
g increases if a firm increases its retentionratio and/or its ROE
bROEg
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Value of Growth Opportunities
Cash Cow, Inc.(CC)
E1 = $5, ROE=12.5%
D1 = $5
b = ; therefore g =
k = 12.5% ; Find VCC
Growth Prospects(GP)
E1 = $5, ROE=15%
D1 = $5
b =0; therefore g = 0
k = 12.5%, Find VGP
00
40$0.125
$5.00VCC 40$
0.125
$5.00VGP
Should either or both firms retain some earnings?
bROEgValue with 100% dividend payout
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Value of Growth Opportunities
Cash Cow, Inc.(CC)
E1 = $5, ROE=12.5%
b = 60%; therefore g =
D1 = 0.40 x $5 = $2.00
k = 12.5%; Find VCCCC value is the same, why?
Growth Prospects (GP)
E1 = $5, ROE=15%
b = 60%; therefore g = 9%
D1 = 0.40 x $5 = $2.00
k = 12.5%; Find VGPGP Value has increased,
why?
7.5%
40$0.075-0.125
$2.00VCC 14.57$
0.09-0.125
$2.00V
GP
bROEgValue with 40% dividend payout
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Value of Growth Opportunities
Value of assets in place for GP = $40.00 (value with alldividends paid out, with ROE = 12.5%)
Value of growth opportunities with ROE = 15% may beinferred from the difference between the new VGP =
$57.14 and the no growth value of $40.00Thus the present value of growth opportunities
(PVGO) = $57.14 - $40.00 = $17.14
0 1(1 )
( )
D g EPVGO
k g kIn general:
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Figure 13.1 Dividend Growth forTwo Earnings Reinvestment
Policies
(for a given ROE)
High reinvestment increases stockprice only if ROE > k
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Multistage Growth Models
As firms progress through their industry life cycle,earnings and dividend growth rates (ROE) are likely tochange.
A two stage growth model:
g1 = first growth rate
g2 = second growth rate
T = number of periods of growth at g1
T
2
2TT
1tt
t
100
k))(1g(k
)g(1D
k)(1
)g(1DV
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Multistage Growth RateModel: 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 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40
3320 )15.1)(05.015.0(
63.3$
15.1
46.3$
15.1
88.2$
15.1
40.2$V
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Two Stage DDM for Honda
Dividends:
Assume the dividend growth rate will besteady beyond 2012. Value Line forecastsb = 70% and ROE of 11%. What shouldbe the long term growth rate?
Year Dividend
2009 0.90
2010 0.98
2011 1.06
2012 1.15
bROEg %7.77.0%11g
From Value Line
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Two Stage DDM for Honda
The required rate of return:
Honda = 1.05
Rf in 2008 = 3.5%
Market risk premium=historical average of 8%
HondafMfHonda )RR(Rk
%9.1105.1%8%5.3Hondak
From Value Line
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Two Stage DDM for Honda
k = 11.90%
g = 7.70%
Find the intrinsic value
Value Line reported the actual price = $21.37, soHonda was undervalued by $0.51 or about 2.4%.
44320 )119.1)(077.0119.0(
077.115.1$
119.1
15.1$
119.1
06.1$
119.1
98.0$
119.1
90.0$V
Year Dividend
2009 0.90
2010 0.98
2011 1.06
2012 1.15
88.21$V0
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Two Stage DDM for HondaShould we trust the valuation result?
What if the beta is slightly incorrect,suppose it is 1.10 (< 5% error) rather than 1.05?
Now k = 12.3% and the intrinsic value estimate V0=$19.98, reversing our conclusion that Honda isundervalued
Recall that the actual price = $21.37
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13.4 Price-Earnings (P/E) Ratios
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P/E Ratio and GrowthOpportunities
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 stocksConceptually equivalent to the constant growthDDM
Extensively used by analysts and investors
Aside) k = required r/r, discount rate, opportunity, canbe given, or needs to be estimated. As k increases,the (present) value decreases.
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P/E, ROE and Growth
With positive growth:
With zero growth:
If b = 0 then g should = 0 and the ratiosimplifies to:
bROEg
gk
b
E
P )1(
1
0
k
1
E
P
1
0
The P/E here is not the actual P/Eyou get with P0 and trailing EPS.The elements of the V0/E1 ratiohere (theoretical P/E) are similar tothe constant growth DDM.
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Numerical Example: No GrowthE(E1)= $2.50 g = 0 k = 12.5%; Find P/Eand V0
P/E = 1/k = 1/.125 = 8
V0
= P/E x E(E1
)= 8 x $2.50 = $20.00 or= $2.50/(.125-0)= $20.00Then, the theoretical P/E= $20/$2.5= 8
V0 = P/E x E(E1) is called P/E multiple.Typically, we use current industry P/E andprojected E(EPS1) of the firm instead ofthis hypothetcal situation.
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Numerical Example with Growthb = 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%
E(E1)= $2.50 (1.09) = $2.725, E(D1)=$2.725 (0.4) = $1.09
P/E = (1 - 0.60) / (0.125 - 0.09) = 11.4
V0 = P/E x E(E1)= 11.4 x $2.73 = $31.14 or
= $1.09/(.125 - .09) = $31.14
Then => the theoretical P/E = 31.14/2.725 = 11.4
Again, V0 = P/E x E(E1) Is using data (current industry P/Efrom Yahoo Finance! and the projected E(E1) from I/B/E/Sor pro forma I/S)
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ROE and b and growth and P/E
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P/E Ratios and Stock Risk
Riskier firms will have higher requiredrates of return (higher values of k)
Riskier stocks will have lower P/Emultiples
gk
b
E
P )1(
1
0
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Pitfalls in Using Actual P/E1 RatiosNot often, but E(EPS1) can be negative,
Earnings management is a serious problem,
E(EPS1) should be calculated using pro formaearnings, or obtained from data services which
A high P/E implies high expected growth, but notnecessarily high stock returns,
It assumes that the future P/E will be steady. If theexpected growth in earnings fails to materialize, theP/E will fall and investors may incur (large) losses.
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Figure 13.3 Actual P/E Ratiosand Inflation
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Figure 13.4 Earnings Growthfor Two Companies
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Figure 13.5 Price-Earnings Ratios
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Figure 13.6 P/E Ratios
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Other Comparative ValuationRatios
Price-to-book
High ratio indicates a large premium over book value,
Price-to-cash flow
P/Cash Flow instead of P/E; less subject toaccounting manipulation
Price-to-sales
Useful for firms with low or negative earnings in earlygrowth stage
Be creative
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Figure 13.7 Valuation Ratios for theS&P 500
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Free Cash Flow Valuation Approach
Capitalize or discount the free cash flow for the firm(FCFF) at the weighted-average cost of capital and thensubtract the existing (market) value of debt
Helpful to understand sources and uses of cash
where:
EBIT = earnings before interest and taxes
Tc = the corporate tax rate
NWC = net working capital
NWCinIncreaseesExpenditurCapitalonDepreciati)TEBIT(1FCFF C
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FCFF, Firm Value & Equity ValueThe free cash flow methods discount year to year cash flowsplus some estimate of the terminal value PT where
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
Equity value =
gWACC
FCFFP 1TT
T
TT
tt
t
WACC
P
WACC
FCFFValueFirm
)1()1(
1
Firm Value Market Value of Debt
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Free Cash Flow (cont.)
Another approach calculates the free cash flowto the equity holders (FCFE) and discounts thecash flows directly at the cost of equity, kE.
Equity value can then be estimated as:
DebtNetinIncrease)TExpense(1InterestFCFFFCFE C
gk
FCFEP
E
1TT T
E
TT
1tt
E
t
)k1(
P
)k1(
FCFEValuequityE
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FCF Valuation Example
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Comparing the Valuation Models
In theory free cash flow approaches should provide the sameestimate 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 theinputs
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13.6 The Aggregate StockMarket
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Earnings Multiplier Approach
1. Forecast corporate profits for the coming period for anindex such as the S&P 500.
2. Derive an estimate for the aggregate P/E ratio using
long-term interest rates
10 year Treasuries
3. Product of the two forecasts is the estimate of the end-of-period level of the market
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Figure 13.8 Earnings Yield of the S&P500 Versus 10-year Treasury Bond Yield
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Earnings Multiplier Approach2009 Data: Starting S&P500 level = 900
Treasury yield = 3.2%
Implied Earnings Yield = 2.5% + 3.2% = 5.7%
If E/P = 5.7% then P/E = 1 / 0.057 = 17.54
If forecast EPS = $55 what is the expected forecast forthe S&P500 one year later and the % gain or loss?
2.5%spreadTreasuryyr10?P500&SyieldEarningsExpected
7.2%900
900965turnExpectedRe
9655517.54P500&S 1
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Table 13.4 S&P 500 IndexForecasts
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