Damodaran on Relval

Aswath Damodaran 1

Equity Instruments & Markets: Part IIB40.3331

Relative ValuationAswath Damodaran

Aswath Damodaran 2

Why relative valuation?

“If you think I’m crazy, you should see the guy who lives across the hall”

Jerry Seinfeld talking about Kramer in a Seinfeld episode

“ A little inaccuracy sometimes saves tons of explanation”

H.H. Munro

Aswath Damodaran 3

What is relative valuation?

n In relative valuation, the value of an asset is compared to the valuesassessed by the market for similar or comparable assets.

n To do relative valuation then,• we need to identify comparable assets and obtain market values for these

assets

• convert these market values into standardized values, since the absoluteprices cannot be compared This process of standardizing creates pricemultiples.

• compare the standardized value or multiple for the asset being analyzed tothe standardized values for comparable asset, controlling for anydifferences between the firms that might affect the multiple, to judgewhether the asset is under or over valued

Aswath Damodaran 4

Standardizing Value

n Prices can be standardized using a common variable such as earnings,cashflows, book value or revenues.• Earnings Multiples

– Price/Earnings Ratio (PE) and variants (PEG and Relative PE)

– Value/EBIT

– Value/EBITDA

– Value/Cash Flow

• Book Value Multiples– Price/Book Value(of Equity) (PBV)

– Value/ Book Value of Assets

– Value/Replacement Cost (Tobin’s Q)

• Revenues– Price/Sales per Share (PS)

– Value/Sales

• Industry Specific Variable (Price/kwh, Price per ton of steel ....)

Aswath Damodaran 5

The Four Steps to Understanding Multiples

n Define the multiple• In use, the same multiple can be defined in different ways by different

users. When comparing and using multiples, estimated by someone else, itis critical that we understand how the multiples have been estimated

n Describe the multiple• Too many people who use a multiple have no idea what its cross sectional

distribution is. If you do not know what the cross sectional distribution ofa multiple is, it is difficult to look at a number and pass judgment onwhether it is too high or low.

n Analyze the multiple• It is critical that we understand the fundamentals that drive each multiple,

and the nature of the relationship between the multiple and each variable.

n Apply the multiple• Defining the comparable universe and controlling for differences is far

more difficult in practice than it is in theory.

Aswath Damodaran 6

Definitional Tests

n Is the multiple consistently defined?• Proposition 1: Both the value (the numerator) and the standardizing

variable ( the denominator) should be to the same claimholders in thefirm. In other words, the value of equity should be divided by equityearnings or equity book value, and firm value should be divided byfirm earnings or book value.

n Is the multiple uniformally estimated?• The variables used in defining the multiple should be estimated uniformly

across assets in the “comparable firm” list.

• If earnings-based multiples are used, the accounting rules to measureearnings should be applied consistently across assets. The same ruleapplies with book-value based multiples.

Aswath Damodaran 7

Descriptive Tests

n What is the average and standard deviation for this multiple, across theuniverse (market)?

n What is the median for this multiple?• The median for this multiple is often a more reliable comparison point.

n How large are the outliers to the distribution, and how do we deal withthe outliers?• Throwing out the outliers may seem like an obvious solution, but if the

outliers all lie on one side of the distribution (they usually are largepositive numbers), this can lead to a biased estimate.

n Are there cases where the multiple cannot be estimated? Will ignoringthese cases lead to a biased estimate of the multiple?

n How has this multiple changed over time?

Aswath Damodaran 8

Analytical Tests

n What are the fundamentals that determine and drive these multiples?• Proposition 2: Embedded in every multiple are all of the variables that

drive every discounted cash flow valuation - growth, risk and cash flowpatterns.

• In fact, using a simple discounted cash flow model and basic algebrashould yield the fundamentals that drive a multiple

n How do changes in these fundamentals change the multiple?• The relationship between a fundamental (like growth) and a multiple

(such as PE) is seldom linear. For example, if firm A has twice the growthrate of firm B, it will generally not trade at twice its PE ratio

• Proposition 3: It is impossible to properly compare firms on amultiple, if we do not know the nature of the relationship betweenfundamentals and the multiple.

Aswath Damodaran 9

Application Tests

n Given the firm that we are valuing, what is a “comparable” firm?• While traditional analysis is built on the premise that firms in the same

sector are comparable firms, valuation theory would suggest that acomparable firm is one which is similar to the one being analyzed in termsof fundamentals.

• Proposition 4: There is no reason why a firm cannot be comparedwith another firm in a very different business, if the two firms havethe same risk, growth and cash flow characteristics.

n Given the comparable firms, how do we adjust for differences acrossfirms on the fundamentals?• Proposition 5: It is impossible to find an exactly identical firm to the

one you are valuing.

Aswath Damodaran 10

Price Earnings Ratio: Definition

PE = Market Price per Share / Earnings per Sharen There are a number of variants on the basic PE ratio in use. They are

based upon how the price and the earnings are defined.

n Price: is usually the current price

is sometimes the average price for the year

n EPS: earnings per share in most recent financial year

earnings per share in trailing 12 months (Trailing PE)

forecasted earnings per share next year (Forward PE)

forecasted earnings per share in future year

Aswath Damodaran 11

PE Ratio: Descriptive Statistics

Distribution of PE Ratios - September 2001

0

200

400

600

800

1000

1200

0-4 4 - 6 6 - 8 8 - 10 10 - 15 15-20 20-25 25-30 30-35 35-40 40 - 45 45- 50 50 -75 75 -100

> 100

PE ratio

Num

ber

of

firm

s

Current PE

Trailing PE

Forward PE

Aswath Damodaran 12

PE: Deciphering the Distribution

Current PE Trailing PE Forward PEMean 30.93 30.33 21.13Standard Error 2.70 2.74 0.73Median 15.27 15.20 13.71Mode 10 0 14Standard Deviation 157.30 150.65 38.22Kurtosis 795.82 1615.73 224.85Skewness 26.28 36.04 12.97Range 5370.00 7090.50 864.91Maximum 5370.00 7090.50 865.00Count 3387 3021 2737

Aswath Damodaran 13

PE Ratio: Understanding the Fundamentals

n To understand the fundamentals, start with a basic equity discountedcash flow model.

n With the dividend discount model,

n Dividing both sides by the earnings per share,

n If this had been a FCFE Model,

P0 =DPS1

r − gn

P0

EPS0= PE =

Payout Ratio *(1 + gn )

r - gn

P0 =FCFE1

r − gn

P0

EPS0

= PE = (FCFE/Earnings)*(1 + gn )

r-g n

Aswath Damodaran 14

PE Ratio and Fundamentals

n Proposition: Other things held equal, higher growth firms willhave higher PE ratios than lower growth firms.

n Proposition: Other things held equal, higher risk firms will havelower PE ratios than lower risk firms

n Proposition: Other things held equal, firms with lowerreinvestment needs will have higher PE ratios than firms withhigher reinvestment rates.

n Of course, other things are difficult to hold equal since high growthfirms, tend to have risk and high reinvestment rats.

Aswath Damodaran 15

Using the Fundamental Model to Estimate PE For aHigh Growth Firm

n The price-earnings ratio for a high growth firm can also be related tofundamentals. In the special case of the two-stage dividend discountmodel, this relationship can be made explicit fairly simply:

• For a firm that does not pay what it can afford to in dividends, substituteFCFE/Earnings for the payout ratio.

n Dividing both sides by the earnings per share:

P0 =

EPS0 *Payout Rat io*(1+g)* 1 −(1+g)n

(1+r)n

r - g

+ EPS0 *Payout Ration * ( 1 +g)n * ( 1 +gn )

(r - gn )(1+r)n

P0

EPS0=

Payout Ratio *(1 + g )* 1 − (1+ g )n

(1+ r)n

r - g+

Payout Ration * ( 1 + g )n *(1 + gn )

(r - gn )(1+ r)n

Aswath Damodaran 16

Expanding the Model

n In this model, the PE ratio for a high growth firm is a function ofgrowth, risk and payout, exactly the same variables that it was afunction of for the stable growth firm.

n The only difference is that these inputs have to be estimated for twophases - the high growth phase and the stable growth phase.

n Expanding to more than two phases, say the three stage model, willmean that risk, growth and cash flow patterns in each stage.

Aswath Damodaran 17

A Simple Example

n Assume that you have been asked to estimate the PE ratio for a firmwhich has the following characteristics:

Variable High Growth Phase Stable Growth Phase

Expected Growth Rate 25% 8%

Payout Ratio 20% 50%

Beta 1.00 1.00

n Riskfree rate = T.Bond Rate = 6%

n Required rate of return = 6% + 1(5.5%)= 11.5%

PE =

0 . 2 * (1.25) * 1−(1.25)5

(1.115) 5

(.115 - .25)+

0.5 * (1.25)5 *(1.08)

(.115-.08) (1.115) 5 = 28.75

Aswath Damodaran 18

PE and Growth: Firm grows at x% for 5 years, 8%thereafter

PE Ratios and Expected Growth: Interest Rate Scenarios

0

20

40

60

80

100

120

140

160

180

5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Expected Growth Rate

PE R

atio

r=4%r=6%r=8%r=10%

Aswath Damodaran 19

PE Ratios and Length of High Growth: 25% growthfor n years; 8% thereafter

PE Ratios and Length of High Growth Period

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8 9 10

Length of High Growth Period

PE R

atio

g=25%g=20%g=15%g=10%

Aswath Damodaran 20

PE and Risk: Effects of Changing Betas on PERatio:

Firm with x% growth for 5 years; 8% thereafter

PE Ratios and Beta: Growth Scenarios

0

5

10

15

20

25

30

35

40

45

50

0.75 1.00 1.25 1.50 1.75 2.00

Beta

PE R

atio

g=25%g=20%g=15%g=8%

Aswath Damodaran 21

PE and Payout

PE Ratios and Payour Ratios: Growth Scenarios

0

5

10

15

20

25

30

35

0% 20% 40% 60% 80% 100%

Payout Ratio

PE

g=25%g=20%g=15%g=10%

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PE: Emerging Markets

0

5

10

15

20

25

30

35

Mexico Malaysia Singapore Taiwan Hong Kong Venezuela Brazil Argentina Chile

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Comparisons across countries

n In July 2000, a market strategist is making the argument that Braziland Venezuela are cheap relative to Chile, because they have muchlower PE ratios. Would you agree?

o Yes

o No

n What are some of the factors that may cause one market’s PE ratios tobe lower than another market’s PE?

Aswath Damodaran 24

A Comparison across countries: June 2000

Country PE Dividend Yield 2-yr rate 10-yr rate 10yr - 2yrUK 22.02 2.59% 5.93% 5.85% -0.08%Germany 26.33 1.88% 5.06% 5.32% 0.26%France 29.04 1.34% 5.11% 5.48% 0.37%Switzerland 19.6 1.42% 3.62% 3.83% 0.21%Belgium 14.74 2.66% 5.15% 5.70% 0.55%Italy 28.23 1.76% 5.27% 5.70% 0.43%Sweden 32.39 1.11% 4.67% 5.26% 0.59%Netherlands 21.1 2.07% 5.10% 5.47% 0.37%Australia 21.69 3.12% 6.29% 6.25% -0.04%Japan 52.25 0.71% 0.58% 1.85% 1.27%US 25.14 1.10% 6.05% 5.85% -0.20%Canada 26.14 0.99% 5.70% 5.77% 0.07%

Aswath Damodaran 25

Correlations and Regression of PE Ratios

n Correlations• Correlation between PE ratio and long term interest rates = -0.733

• Correlation between PE ratio and yield spread = 0.706

n Regression Results

PE Ratio = 42.62 - 3.61 (10’yr rate) + 8.47 (10-yr - 2 yr rate) R2 = 59%

Input the interest rates as percent. For instance, the predicted PE ratio forJapan with this regression would be:

PE: Japan = 42.62 - 3.61 (1.85) + 8.47 (1.27) = 46.70

At an actual PE ratio of 52.25, Japanese stocks are slightly overvalued.

Aswath Damodaran 26

Predicted PE Ratios

Country Actual PE Predicted PE Under or Over ValuedUK 22.02 20.83 5.71%Germany 26.33 25.62 2.76%France 29.04 25.98 11.80%Switzerland 19.6 30.58 -35.90%Belgium 14.74 26.71 -44.81%Italy 28.23 25.69 9.89%Sweden 32.39 28.63 13.12%Netherlands 21.1 26.01 -18.88%Australia 21.69 19.73 9.96%Japan 52.25 46.70 11.89%United States 25.14 19.81 26.88%Canada 26.14 22.39 16.75%

Aswath Damodaran 27

An Example with Emerging Markets: June 2000

Country PE Ratio Interest Rates

GDP Real Growth

Country Risk

Argentina 14 18.00% 2.50% 45Brazil 21 14.00% 4.80% 35Chile 25 9.50% 5.50% 15Hong Kong 20 8.00% 6.00% 15India 17 11.48% 4.20% 25Indonesia 15 21.00% 4.00% 50Malaysia 14 5.67% 3.00% 40Mexico 19 11.50% 5.50% 30Pakistan 14 19.00% 3.00% 45Peru 15 18.00% 4.90% 50Phillipines 15 17.00% 3.80% 45Singapore 24 6.50% 5.20% 5South Korea 21 10.00% 4.80% 25Thailand 21 12.75% 5.50% 25Turkey 12 25.00% 2.00% 35Venezuela 20 15.00% 3.50% 45

Aswath Damodaran 28

Regression Results

n The regression of PE ratios on these variables provides the following –PE = 16.16 - 7.94 Interest Rates

+ 154.40 Growth in GDP

- 0.1116 Country Risk

R Squared = 73%

Aswath Damodaran 29

Predicted PE Ratios

Country PE Ratio Interest Rates

GDP Real Growth

Country Risk

Predicted PE

Argentina 14 18.00% 2.50% 45 13.57Brazil 21 14.00% 4.80% 35 18.55Chile 25 9.50% 5.50% 15 22.22Hong Kong 20 8.00% 6.00% 15 23.11India 17 11.48% 4.20% 25 18.94Indonesia 15 21.00% 4.00% 50 15.09Malaysia 14 5.67% 3.00% 40 15.87Mexico 19 11.50% 5.50% 30 20.39Pakistan 14 19.00% 3.00% 45 14.26Peru 15 18.00% 4.90% 50 16.71Phillipines 15 17.00% 3.80% 45 15.65Singapore 24 6.50% 5.20% 5 23.11South Korea 21 10.00% 4.80% 25 19.98Thailand 21 12.75% 5.50% 25 20.85Turkey 12 25.00% 2.00% 35 13.35Venezuela 20 15.00% 3.50% 45 15.35

Aswath Damodaran 30

Comparisons of PE across time: PE Ratio for theS&P 500

PE Ratio: 1960-2000

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

Aswath Damodaran 31

Is low (high) PE cheap (expensive)?

n A market strategist argues that stocks are over priced because the PEratio today is too high relative to the average PE ratio across time. Doyou agree?q Yes

q No

n If you do not agree, what factors might explain the higer PE ratiotoday?

Aswath Damodaran 32

E/P Ratios , T.Bond Rates and Term Structure

-2.00%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

Earnings YieldT.Bond RateBond-Bill

Aswath Damodaran 33

Regression Results

n There is a strong positive relationship between E/P ratios and T.Bondrates, as evidenced by the correlation of 0.685 between the twovariables.,

n In addition, there is evidence that the term structure also affects the PEratio.

n In the following regression, using 1960-2000 data, we regress E/Pratios against the level of T.Bond rates and a term structure variable(T.Bond - T.Bill rate)E/P = 1 .88% + 0.776 T.Bond Rate - 0.407 (T.Bond Rate-T.Bill Rate)

(2.84) (6.08) (-2.37)

R squared = 50%

Aswath Damodaran 34

Estimate the E/P Ratio Today

n T. Bond Rate =

n T.Bond Rate - T.Bill Rate =

n Expected E/P Ratio =

n Expected PE Ratio =

Aswath Damodaran 35

Comparing PE ratios across firms

Company Name Trailing PE Expected Growth Standard DevCoca-Cola Bottling 29.18 9.50% 20.58%Molson Inc. Ltd. 'A' 43.65 15.50% 21.88%Anheuser-Busch 24.31 11.00% 22.92%Corby Distilleries Ltd. 16.24 7.50% 23.66%Chalone Wine Group Ltd. 21.76 14.00% 24.08%Andres Wines Ltd. 'A' 8.96 3.50% 24.70%Todhunter Int'l 8.94 3.00% 25.74%Brown-Forman 'B' 10.07 11.50% 29.43%Coors (Adolph) 'B' 23.02 10.00% 29.52%PepsiCo, Inc. 33.00 10.50% 31.35%Coca-Cola 44.33 19.00% 35.51%Boston Beer 'A' 10.59 17.13% 39.58%Whitman Corp. 25.19 11.50% 44.26%Mondavi (Robert) 'A' 16.47 14.00% 45.84%Coca-Cola Enterprises 37.14 27.00% 51.34%

Hansen Natural Corp 9.70 17.00% 62.45%

Aswath Damodaran 36

A Question

You are reading an equity research report on this sector, and the analystclaims that Andres Wine and Hansen Natural are under valued becausethey have low PE ratios. Would you agree?

o Yes

o No

n Why or why not?

Aswath Damodaran 37

Comparing PE Ratios across a Sector

Company Name PE GrowthPT Indosat ADR 7.8 0.06Telebras ADR 8.9 0.075Telecom Corporation of New Zealand ADR 11.2 0.11Telecom Argentina Stet - France Telecom SA ADR B 12.5 0.08Hellenic Telecommunication Organization SA ADR 12.8 0.12Telecomunicaciones de Chile ADR 16.6 0.08Swisscom AG ADR 18.3 0.11Asia Satellite Telecom Holdings ADR 19.6 0.16Portugal Telecom SA ADR 20.8 0.13Telefonos de Mexico ADR L 21.1 0.14Matav RT ADR 21.5 0.22Telstra ADR 21.7 0.12Gilat Communications 22.7 0.31Deutsche Telekom AG ADR 24.6 0.11British Telecommunications PLC ADR 25.7 0.07Tele Danmark AS ADR 27 0.09Telekomunikasi Indonesia ADR 28.4 0.32Cable & Wireless PLC ADR 29.8 0.14APT Satellite Holdings ADR 31 0.33Telefonica SA ADR 32.5 0.18Royal KPN NV ADR 35.7 0.13Telecom Italia SPA ADR 42.2 0.14Nippon Telegraph & Telephone ADR 44.3 0.2France Telecom SA ADR 45.2 0.19Korea Telecom ADR 71.3 0.44

Aswath Damodaran 38

PE, Growth and Risk

Dependent variable is: PE

R squared = 66.2% R squared (adjusted) = 63.1%

Variable Coefficient SE t-ratio prob

Constant 13.1151 3.471 3.78 0.0010

Growth rate 121.223 19.27 6.29 ≤ 0.0001

Emerging Market -13.8531 3.606 -3.84 0.0009

Emerging Market is a dummy: 1 if emerging market

0 if not

Aswath Damodaran 39

Is Telebras under valued?

n Predicted PE = 13.12 + 121.22 (.075) - 13.85 (1) = 8.35

n At an actual price to earnings ratio of 8.9, Telebras is slightlyovervalued.

Aswath Damodaran 40

Using comparable firms- Pros and Cons

n The most common approach to estimating the PE ratio for a firm is• to choose a group of comparable firms,

• to calculate the average PE ratio for this group and

• to subjectively adjust this average for differences between the firm beingvalued and the comparable firms.

n Problems with this approach.• The definition of a 'comparable' firm is essentially a subjective one.

• The use of other firms in the industry as the control group is often not asolution because firms within the same industry can have very differentbusiness mixes and risk and growth profiles.

• There is also plenty of potential for bias.

• Even when a legitimate group of comparable firms can be constructed,differences will continue to persist in fundamentals between the firmbeing valued and this group.

Aswath Damodaran 41

Using the entire crosssection: A regression approach

n In contrast to the 'comparable firm' approach, the information in theentire cross-section of firms can be used to predict PE ratios.

n The simplest way of summarizing this information is with a multipleregression, with the PE ratio as the dependent variable, and proxies forrisk, growth and payout forming the independent variables.

Aswath Damodaran 42

PE versus Growth

Expected Growth in EPS: next 5 years

100806040200-20

120

100

80

60

40

20

0

-20

Aswath Damodaran 43

PE Ratio: Standard Regression

Model Summary

.478a .229 .227 803.9541Model1

R R SquareAdjusted R

SquareStd. Error ofthe Estimate

Predictors: (Constant), Expected Growth in EPS: next 5 y,PAYOUT1, Beta

a.

Coefficients a,b

13.090 1.164 11.242 .000-3.392 .908 -.089 -3.737 .0004.938 1.190 .098 4.150 .000

.880 .040 .527 22.115 .000

(Constant)BetaPAYOUT1Expected Growthin EPS: next 5 y

Model1

B Std. Error

UnstandardizedCoefficients

Beta

Standardized

Coefficientst Sig.

Dependent Variable: Current PEa.

Weighted Least Squares Regression - Weighted by Market Capb.

Aswath Damodaran 44

Second Thoughts?

n Based on this regression, estimate the PE ratio for a firm with nogrowth, no payout and no risk.

n Is there a problem with your prediction?

Aswath Damodaran 45

PE Regression- No Intercept

Model Summary

.912b .832 .832 833.0224Model1

R R Squarea

Adjusted RSquare

Std. Error ofthe Estimate

For regression through the origin (the no-interceptmodel), R Square measures the proportion of thevariability in the dependent variable about the originexplained by regression. This CANNOT be compared to RSquare for models which include an intercept.

a.

Predictors: Expected Growth in EPS: next 5 y, PAYOUT1,Beta

b.

Coefficients a,b,c

4.389 .609 .188 7.212 .00013.299 .962 .189 13.823 .000

1.014 .039 .608 25.786 .000

BetaPAYOUT1Expected Growthin EPS: next 5 y

Model1

B Std. Error


Beta

Standardized

Coefficientst Sig.

Dependent Variable: Current PEa.

Linear Regression through the Originb.

Weighted Least Squares Regression - Weighted by Market Capc.

Aswath Damodaran 46

Problems with the regression methodology

n The basic regression assumes a linear relationship between PE ratiosand the financial proxies, and that might not be appropriate.

n The basic relationship between PE ratios and financial variables itselfmight not be stable, and if it shifts from year to year, the predictionsfrom the model may not be reliable.

n The independent variables are correlated with each other. For example,high growth firms tend to have high risk. This multi-collinearity makesthe coefficients of the regressions unreliable and may explain the largechanges in these coefficients from period to period.

Aswath Damodaran 47

The Multicollinearity Problem

Correlations

1.000 .342** .130** .009. .000 .000 .594

3303 2085 3027 3290.342** 1.000 .397** -.078**.000 . .000 .000

2085 2675 2393 2143.130** .397** 1.000 -.213**.000 .000 . .000

3027 2393 4534 3114.009 -.078** -.213** 1.000.594 .000 .000 .

3290 2143 3114 3388

Pearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)N

Current PE

Expected Growthin EPS: next 5 y

Beta

Payout Ratio

Current PE

ExpectedGrowth in EPS:

next 5 y Beta Payout Ratio

Correlation is significant at the 0.01 level (2-tailed).**.

Aswath Damodaran 48

Using the PE ratio regression

n Assume that you were given the following information for Dell. Thefirm has an expected growth rate of 10%, a beta of 1.40 and pays nodividends. Based upon the regression, estimate the predicted PE ratiofor Dell.Predicted PE =

(Work with absolute values in regression - 10 for 10% etc.)

n Dell is actually trading at 18 times earnings. What does the predictedPE tell you?

Aswath Damodaran 49

Investment Strategies that compare PE to theexpected growth rate

n If we assume that all firms within a sector have similar growth ratesand risk, a strategy of picking the lowest PE ratio stock in each sectorwill yield undervalued stocks.

n Portfolio managers and analysts sometimes compare PE ratios to theexpected growth rate to identify under and overvalued stocks.• In the simplest form of this approach, firms with PE ratios less than their

expected growth rate are viewed as undervalued.

• In its more general form, the ratio of PE ratio to growth is used as ameasure of relative value.

Aswath Damodaran 50

Problems with comparing PE ratios to expectedgrowth

n In its simple form, there is no basis for believing that a firm isundervalued just because it has a PE ratio less than expected growth.

n This relationship may be consistent with a fairly valued or even anovervalued firm, if interest rates are high, or if a firm is high risk.

n As interest rate decrease (increase), fewer (more) stocks will emerge asundervalued using this approach.

Aswath Damodaran 51

PE Ratio versus Growth - The Effect of Interestrates:

Average Risk firm with 25% growth for 5 years; 8% thereafter

Figure 14.2: PE Ratios and T.Bond Rates

0

5

10

15

20

25

30

35

40

45

5% 6% 7% 8% 9% 10%

T.Bond Rate

Aswath Damodaran 52

PE Ratios Less Than The Expected Growth Rate

n In September 2001,• 33% of firms had PE ratios lower than the expected 5-year growth rate

• 67% of firms had PE ratios higher than the expected 5-year growth rate

n In comparison,• 38.1% of firms had PE ratios less than the expected 5-year growth rate in

September 1991

• 65.3% of firm had PE ratios less than the expected 5-year growth rate in1981.

Aswath Damodaran 53

PEG Ratio: Definition

n The PEG ratio is the ratio of price earnings to expected growth inearnings per share.

PEG = PE / Expected Growth Rate in Earnings

n Definitional tests:• Is the growth rate used to compute the PEG ratio

– on the same base? (base year EPS)

– over the same period?(2 years, 5 years)

– from the same source? (analyst projections, consensus estimates..)

• Is the earnings used to compute the PE ratio consistent with the growthrate estimate?

– No double counting: If the estimate of growth in earnings per share is from thecurrent year, it would be a mistake to use forward EPS in computing PE

– If looking at foreign stocks or ADRs, is the earnings used for the PE ratioconsistent with the growth rate estimate? (US analysts use the ADR EPS)

Aswath Damodaran 54

PEG Ratio: Distribution

Price/ Expected Growth RAte

400

300

200

100

0

Std. Dev = 1.05

Mean = 1.55

N = 2084.00

Aswath Damodaran 55

PEG Ratios: The Beverage Sector

Company Name Trailing PE Growth Std Dev PEGCoca-Cola Bottling 29.18 9.50% 20.58% 3.07Molson Inc. Ltd. 'A' 43.65 15.50% 21.88% 2.82Anheuser-Busch 24.31 11.00% 22.92% 2.21Corby Distilleries Ltd. 16.24 7.50% 23.66% 2.16Chalone Wine Group Ltd. 21.76 14.00% 24.08% 1.55Andres Wines Ltd. 'A' 8.96 3.50% 24.70% 2.56Todhunter Int'l 8.94 3.00% 25.74% 2.98Brown-Forman 'B' 10.07 11.50% 29.43% 0.88Coors (Adolph) 'B' 23.02 10.00% 29.52% 2.30PepsiCo, Inc. 33.00 10.50% 31.35% 3.14Coca-Cola 44.33 19.00% 35.51% 2.33Boston Beer 'A' 10.59 17.13% 39.58% 0.62Whitman Corp. 25.19 11.50% 44.26% 2.19Mondavi (Robert) 'A' 16.47 14.00% 45.84% 1.18Coca-Cola Enterprises 37.14 27.00% 51.34% 1.38Hansen Natural Corp 9.70 17.00% 62.45% 0.57

Average 22.66 0.13 0.33 2.00

Aswath Damodaran 56

PEG Ratio: Reading the Numbers

n The average PEG ratio for the beverage sector is 2.00. The lowestPEG ratio in the group belongs to Hansen Natural, which has a PEGratio of 0.57. Using this measure of value, Hansen Natural is

o the most under valued stock in the group

o the most over valued stock in the group

n What other explanation could there be for Hansen’s low PEG ratio?

Aswath Damodaran 57

PEG Ratio: Analysis

n To understand the fundamentals that determine PEG ratios, let usreturn again to a 2-stage equity discounted cash flow model

n Dividing both sides of the equation by the earnings gives us theequation for the PE ratio. Dividing it again by the expected growth ‘g’

P0 =

EPS0 *Payout Rat io*(1+g)* 1 −(1+g)n

(1+r)n

r - g

+ EPS0 *Payout Ration * ( 1 +g)n * ( 1 +gn )

(r - gn )(1+r)n

PEG =

Payout Ratio*(1+ g) * 1 −(1+g)n

(1 + r)n

g(r - g)

+ Payout Ration * (1+g)n * ( 1 +gn )

g(r - gn )(1 + r)n

Aswath Damodaran 58

PEG Ratios and Fundamentals

n Risk and payout, which affect PE ratios, continue to affect PEG ratiosas well.• Implication: When comparing PEG ratios across companies, we are

making implicit or explicit assumptions about these variables.

n Dividing PE by expected growth does not neutralize the effects ofexpected growth, since the relationship between growth and value isnot linear and fairly complex (even in a 2-stage model)

Aswath Damodaran 59

A Simple Example

n Assume that you have been asked to estimate the PEG ratio for a firmwhich has the following characteristics:

Variable High Growth Phase Stable Growth Phase

Expected Growth Rate 25% 8%


Beta 1.00 1.00

n Riskfree rate = T.Bond Rate = 6%

n Required rate of return = 6% + 1(5.5%)= 11.5%

n The PEG ratio for this firm can be estimated as follows:

PEG =

0.2 * (1.25) * 1 −(1.25) 5

(1.115) 5

.25(.115 - .25)+

0.5 * (1.25)5 *(1.08)

.25(.115-.08) (1.115)5 = .115 or 1.15

Aswath Damodaran 60

PEG Ratios and Risk

PEG Ratios and Beta: Different Growth Rates

0

0.5

1

1.5

2

2.5

3

0.75 1.00 1.25 1.50 1.75 2.00

Beta

PEG R

atio g =25%

g=20%g=15%g=8%

Aswath Damodaran 61

PEG Ratios and Quality of Growth

PEG Ratios and Retention Ratios

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 0.8 0.6 0.4 0.2 0

Retention Ratio

PEG R

atio

PEG

Aswath Damodaran 62

PE Ratios and Expected Growth

PEG Ratios, Expected Growth and Interest Rates

0.00

0.50

1.00

1.50

2.00

2.50

5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Expected Growth Rate

PEG R

atio r=6%

r=8%r=10%

Aswath Damodaran 63

PEG Ratios and Fundamentals: Propositions

n Proposition 1: High risk companies will trade at much lower PEGratios than low risk companies with the same expected growth rate.• Corollary 1: The company that looks most under valued on a PEG ratio

basis in a sector may be the riskiest firm in the sector

n Proposition 2: Companies that can attain growth more efficiently byinvesting less in better return projects will have higher PEG ratios thancompanies that grow at the same rate less efficiently.• Corollary 2: Companies that look cheap on a PEG ratio basis may be

companies with high reinvestment rates and poor project returns.

n Proposition 3: Companies with very low or very high growth rates willtend to have higher PEG ratios than firms with average growth rates.This bias is worse for low growth stocks.• Corollary 3: PEG ratios do not neutralize the growth effect.

Aswath Damodaran 64

PE, PEG Ratios and Risk

0

5

10

15

20

25

30

35

40

45

Lowest 2 3 4 Highest

0

0.5

1

1.5

2

2.5

PEPEG Ratio

Aswath Damodaran 65

PEG Ratio: Returning to the Beverage Sector

Company Name Trailing PE Growth Std Dev PEGCoca-Cola Bottling 29.18 9.50% 20.58% 3.07Molson Inc. Ltd. 'A' 43.65 15.50% 21.88% 2.82Anheuser-Busch 24.31 11.00% 22.92% 2.21Corby Distilleries Ltd. 16.24 7.50% 23.66% 2.16Chalone Wine Group Ltd. 21.76 14.00% 24.08% 1.55Andres Wines Ltd. 'A' 8.96 3.50% 24.70% 2.56Todhunter Int'l 8.94 3.00% 25.74% 2.98Brown-Forman 'B' 10.07 11.50% 29.43% 0.88Coors (Adolph) 'B' 23.02 10.00% 29.52% 2.30PepsiCo, Inc. 33.00 10.50% 31.35% 3.14Coca-Cola 44.33 19.00% 35.51% 2.33Boston Beer 'A' 10.59 17.13% 39.58% 0.62Whitman Corp. 25.19 11.50% 44.26% 2.19Mondavi (Robert) 'A' 16.47 14.00% 45.84% 1.18Coca-Cola Enterprises 37.14 27.00% 51.34% 1.38Hansen Natural Corp 9.70 17.00% 62.45% 0.57

Average 22.66 0.13 0.33 2.00

Aswath Damodaran 66

Analyzing PE/Growth

n Given that the PEG ratio is still determined by the expected growthrates, risk and cash flow patterns, it is necessary that we control fordifferences in these variables.

n Regressing PEG against risk and a measure of the growth dispersion,we get:

PEG = 3.61 - 2.86 (Expected Growth) - 3.75 (Std Deviation in Prices)

R Squared = 44.75%

n In other words,• PEG ratios will be lower for high growth companies

• PEG ratios will be lower for high risk companies

n We also ran the regression using the deviation of the actual growth ratefrom the industry-average growth rate as the independent variable,with mixed results.

Aswath Damodaran 67

Estimating the PEG Ratio for Hansen

n Applying this regression to Hansen, the predicted PEG ratio for thefirm can be estimated using Hansen’s measures for the independentvariables:• Expected Growth Rate = 17.00%

• Standard Deviation in Stock Prices = 62.45%

n Plugging in,

Expected PEG Ratio for Hansen = 3.61 - 2.86 (.17) - 3.75 (.6245)

= 0.78

n With its actual PEG ratio of 0.57, Hansen looks undervalued,notwithstanding its high risk.

Aswath Damodaran 68

Extending the Comparables

n This analysis, which is restricted to firms in the software sector, can beexpanded to include all firms in the firm, as long as we control fordifferences in risk, growth and payout.

n To look at the cross sectional relationship, we first plotted PEG ratiosagainst expected growth rates.

Aswath Damodaran 69

PEG versus Growth

Expected Growth in EPS: next 5 years

100806040200-20

6

5

4

3

2

1

0

-1

Aswath Damodaran 70

Analyzing the Relationship

n The relationship in not linear. In fact, the smallest firms seem to havethe highest PEG ratios and PEG ratios become relatively stable athigher growth rates.

n To make the relationship more linear, we converted the expectedgrowth rates in ln(expected growth rate). The relationship betweenPEG ratios and ln(expected growth rate) was then plotted.

Aswath Damodaran 71

PEG versus ln(Expected Growth)

Ln(Expected Growth)

543210-1

6

5

4

3

2

1

0

-1

Aswath Damodaran 72

Market PEG Ratio Regression

Model Summary

.587a .344 .343 56.7746Model1



Predictors: (Constant), LNGROWTH, PAYOUT1, Betaa.

Coefficients a,b

3.935 .112 35.175 .000-7.249E-02 .064 -.025 -1.140 .255

.575 .084 .149 6.873 .000-.867 .037 -.509 -23.522 .000

(Constant)BetaPAYOUT1LNGROWTH

Model1

B Std. Error


Beta

Standardized

Coefficientst Sig.

Dependent Variable: PEG1a.


Aswath Damodaran 73

Applying the PEG ratio regression

n Consider Dell again. The stock has an expected growth rate of 10%, abeta of 1.40 and pays out no dividends. What should its PEG ratio be?

n If the stock’s actual PE ratio is 18, what does this analysis tell youabout the stock?

Aswath Damodaran 74

A Variant on PEG Ratio: The PEGY ratio

n The PEG ratio is biased against low growth firms because therelationship between value and growth is non-linear. One variant thathas been devised to consolidate the growth rate and the expecteddividend yield:

PEGY = PE / (Expected Growth Rate + Dividend Yield)

n As an example, Con Ed has a PE ratio of 16, an expected growth rateof 5% in earnings and a dividend yield of 4.5%.• PEG = 16/ 5 = 3.2

• PEGY = 16/(5+4.5) = 1.7

Aswath Damodaran 75

Relative PE: Definition

n The relative PE ratio of a firm is the ratio of the PE of the firm to thePE of the market.

Relative PE = PE of Firm / PE of Market

n While the PE can be defined in terms of current earnings, trailingearnings or forward earnings, consistency requires that it be estimatedusing the same measure of earnings for both the firm and the market.

n Relative PE ratios are usually compared over time. Thus, a firm orsector which has historically traded at half the market PE (Relative PE= 0.5) is considered over valued if it is trading at a relative PE of 0.7.

Aswath Damodaran 76

Relative PE: Cross Sectional Distribution

Relative PE

1000

800

600

400

200

0

Std. Dev = .77

Mean = 1.00

N = 3303.00

Aswath Damodaran 77

Relative PE: Distributional Statistics

n The average relative PE is always one.

n The median relative PE is much lower, since PE ratios are skewedtowards higher values. Thus, more companies trade at PE ratios lessthan the market PE and have relative PE ratios less than one.

Aswath Damodaran 78

Relative PE: Determinants

n To analyze the determinants of the relative PE ratios, let us revisit thediscounted cash flow model we developed for the PE ratio. Using the2-stage DDM model as our basis (replacing the payout ratio with theFCFE/Earnings Ratio, if necessary), we get

where Payoutj, gj, rj = Payout, growth and risk of the firm

Payoutm, gm, rm = Payout, growth and risk of the market

Relative PE j =

Payout Ratio j * ( 1+ g j) * 1 −( 1 +g j)

n

( 1 +rj)n

rj - g j

+ Payout Ratio j,n * ( 1+ g j)

n * ( 1+ g j,n )

(rj - g j,n )(1 + rj)n

Payout Ratiom * ( 1 +gm ) * 1 −( 1 +gm)n

( 1 +rm )n

rm - gm

+ Payout Ratiom,n * ( 1 +gm )n * ( 1+ gm,n )

(rm - gm,n ) (1+rm )n

Aswath Damodaran 79

Relative PE: A Simple Example

n Consider the following example of a firm growing at twice the rate asthe market, while having the same growth and risk characteristics ofthe market:

Firm Market

Expected growth rate 20% 10%

Length of Growth Period 5 years 5 years

Payout Ratio: first 5 yrs 30% 30%

Growth Rate after yr 5 6% 6%

Payout Ratio after yr 5 50% 50%

Beta 1.00 1.00

Riskfree Rate = 6%

Aswath Damodaran 80

Estimating Relative PE

n The relative PE ratio for this firm can be estimated in two steps. First,we compute the PE ratio for the firm and the market separately:

n Relative PE Ratio = 15.79/10.45 = 1.51

PE firm =

0 .3 * (1.20) * 1− (1.20)5

(1.115)5

(.115 - .20)

+ 0.5 * (1.20)5 * (1.06)

(.115 -.06) (1.115)5 = 15.79

PEmarket =

0 .3 * (1.10) * 1− (1.10)5

(1.115)5

(.115 - .10)

+ 0.5 * (1.10)5 *(1.06)

(.115-.06) (1.115)5 = 10.45

Aswath Damodaran 81

Relative PE and Relative Growth

Relative PE and Relative Growth Rates: Market Growth Scenarios

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0% 50% 100% 150% 200% 250% 300%

Firm's Growth Rate/Market Growth Rate

Rela

tive

PE Market g=5%

Market g=10%Market g=15%

Aswath Damodaran 82

Relative PE: Another Example

n In this example, consider a firm with twice the risk as the market,while having the same growth and payout characteristics as the firm:

Firm Market

Expected growth rate 10% 10%

Length of Growth Period 5 years 5 years

Payout Ratio: first 5 yrs 30% 30%

Growth Rate after yr 5 6% 6%

Payout Ratio after yr 5 50% 50%

Beta in first 5 years 2.00 1.00

Beta after year 5 1.00 1.00

Riskfree Rate = 6%

Aswath Damodaran 83

Estimating Relative PE

n The relative PE ratio for this firm can be estimated in two steps. First,we compute the PE ratio for the firm and the market separately:

n Relative PE Ratio = 8.33/10.45 = 0.80

PE firm =

0.3 * (1.10) * 1 −(1.10) 5

(1.17) 5

(.17 - .10)

+ 0 . 5 * (1.10)5 * (1.06)

(.115-.06) (1.17)5 = 8.33

PEmarket =

0 .3 * (1.10) * 1− (1.10)5

(1.115)5

(.115 - .10)

+ 0.5 * (1.10)5 *(1.06)

(.115-.06) (1.115)5 = 10.45

Aswath Damodaran 84

Relative PE and Relative Risk

Relative PE and Relative Risk: Stable Beta Scenarios

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.25 0.5 0.75 1 1.25 1.5 1.75 2

Beta stays at current levelBeta drops to 1 in stable phase

Aswath Damodaran 85

Relative PE: Summary of Determinants

n The relative PE ratio of a firm is determined by two variables. Inparticular, it will• increase as the firm’s growth rate relative to the market increases. The rate

of change in the relative PE will itself be a function of the market growthrate, with much greater changes when the market growth rate is higher. Inother words, a firm or sector with a growth rate twice that of the marketwill have a much higher relative PE when the market growth rate is 10%than when it is 5%.

• decrease as the firm’s risk relative to the market increases. The extent ofthe decrease depends upon how long the firm is expected to stay at thislevel of relative risk. If the different is permanent, the effect is muchgreater.

n Relative PE ratios seem to be unaffected by the level of rates, whichmight give them a decided advantage over PE ratios.

Aswath Damodaran 86

Relative PE Ratios: The Auto Sector

Relative PE Ratios: Auto Stocks

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1993 1994 1995 1996 1997 1998 1999 2000

FordChryslerGM

Aswath Damodaran 87

Using Relative PE ratios

n On a relative PE basis, all of the automobile stocks look cheap becausethey are trading at their lowest relative PE ratios in five years. Whymight the relative PE ratio be lower today than it was 5 years ago?

Aswath Damodaran 88

Relative PEs: Why do they change?

n Historically, GM has traded at the highest relative PE ratio of the threeauto companies, and Chrysler has traded at the lowest. In the last twoor three years, this historical relationship has been upended with Fordand Chrysler now trading at the higher ratios than GM. Analystprojections for earnings growth at the three companies are about thesame. How would you explain the shift?

Aswath Damodaran 89

Relative PE Ratios: Market Analysis

Model Summary

.478a .229 .227 41.4196Model1



Predictors: (Constant), Beta, RELPYT, RELGRa.

Coefficients a,b

.674 .060 11.242 .000

.835 .038 .527 22.115 .0004.431E-02 .011 .098 4.150 .000

-.175 .047 -.089 -3.737 .000

(Constant)RELGRRELPYTBeta

Model1

B Std. Error


Beta

Standardized

Coefficientst Sig.

Dependent Variable: RELPEa.


Aswath Damodaran 90

Value/Earnings and Value/Cashflow Ratios

n While Price earnings ratios look at the market value of equity relative toearnings to equity investors, Value earnings ratios look at the market value ofthe firm relative to operating earnings. Value to cash flow ratios modify theearnings number to make it a cash flow number.

n The form of value to cash flow ratios that has the closest parallels in DCFvaluation is the value to Free Cash Flow to the Firm, which is defined as:

Value/FCFF = (Market Value of Equity + Market Value of Debt-Cash)

EBIT (1-t) - (Cap Ex - Deprecn) - Chg in WC

n Consistency Tests:• If the numerator is net of cash (or if net debt is used, then the interest income from

the cash should not be in denominator

• The interest expenses added back to get to EBIT should correspond to the debt inthe numerator. If only long term debt is considered, only long term interest shouldbe added back.

Aswath Damodaran 91

Value/FCFF Distribution

Enterprise Value/FCFF

800

600

400

200

0

Std. Dev = 21.77

Mean = 20.6

N = 3063.00

Aswath Damodaran 92

Value of Firm/FCFF: Determinants

n Reverting back to a two-stage FCFF DCF model, we get:

• V0 = Value of the firm (today)

• FCFF0 = Free Cashflow to the firm in current year

• g = Expected growth rate in FCFF in extraordinary growth period (firstn years)

• WACC = Weighted average cost of capital

• gn = Expected growth rate in FCFF in stable growth period (after nyears)

V0 =

FCFF0 (1 + g) 1 -

(1 + g)n

( 1 +WACC)n

WACC - g +

FCFF0 ( 1 +g)n ( 1 +gn)

(WACC - gn

)(1 + WACC)n

Aswath Damodaran 93

Value Multiples

n Dividing both sides by the FCFF yields,

n The value/FCFF multiples is a function of• the cost of capital

• the expected growth

V0

FCFF0

=

(1 + g) 1 -(1 + g)n

(1 + WACC)n

WACC - g

+ ( 1 +g)n ( 1 +gn )

(WACC - gn )(1 + WACC)n

Aswath Damodaran 94

Alternatives to FCFF - EBIT and EBITDA

n Most analysts find FCFF to complex or messy to use in multiples(partly because capital expenditures and working capital have to beestimated). They use modified versions of the multiple with thefollowing alternative denominator:• after-tax operating income or EBIT(1-t)

• pre-tax operating income or EBIT

• net operating income (NOI), a slightly modified version of operatingincome, where any non-operating expenses and income is removed fromthe EBIT

• EBITDA, which is earnings before interest, taxes, depreciation andamortization.

Aswath Damodaran 95

Value/FCFF Multiples and the Alternatives

n Assume that you have computed the value of a firm, using discountedcash flow models. Rank the following multiples in the order ofmagnitude from lowest to highest?

o Value/EBIT

o Value/EBIT(1-t)

o Value/FCFF

o Value/EBITDA

n What assumption(s) would you need to make for the Value/EBIT(1-t)ratio to be equal to the Value/FCFF multiple?

Aswath Damodaran 96

Illustration: Using Value/FCFF Approaches to valuea firm: MCI Communications

n MCI Communications had earnings before interest and taxes of $3356million in 1994 (Its net income after taxes was $855 million).

n It had capital expenditures of $2500 million in 1994 and depreciationof $1100 million; Working capital increased by $250 million.

n It expects free cashflows to the firm to grow 15% a year for the nextfive years and 5% a year after that.

n The cost of capital is 10.50% for the next five years and 10% afterthat.

n The company faces a tax rate of 36%.

V0

FCFF0

=

(1.15) 1-(1.15)5

(1.105)5

.105 -.15 +

(1.15)5(1.05)

(.10 - .05)(1.105)5 = 31.28

Aswath Damodaran 97

Multiple Magic

n In this case of MCI there is a big difference between the FCFF andshort cut measures. For instance the following table illustrates theappropriate multiple using short cut measures, and the amount youwould overpay by if you used the FCFF multiple.Free Cash Flow to the Firm

= EBIT (1-t) - Net Cap Ex - Change in Working Capital

= 3356 (1 - 0.36) + 1100 - 2500 - 250 = $ 498 million

$ Value Correct Multiple

FCFF $498 31.28382355

EBIT (1-t) $2,148 7.251163362

EBIT $ 3,356 4.640744552

EBITDA $4,456 3.49513885

Aswath Damodaran 98

Reasons for Increased Use of Value/EBITDA

1. The multiple can be computed even for firms that are reporting netlosses, since earnings before interest, taxes and depreciation areusually positive.

2. For firms in certain industries, such as cellular, which require asubstantial investment in infrastructure and long gestation periods, thismultiple seems to be more appropriate than the price/earnings ratio.

3. In leveraged buyouts, where the key factor is cash generated by the firmprior to all discretionary expenditures, the EBITDA is the measure ofcash flows from operations that can be used to support debt payment atleast in the short term.

4. By looking at cashflows prior to capital expenditures, it may provide abetter estimate of “optimal value”, especially if the capitalexpenditures are unwise or earn substandard returns.

5. By looking at the value of the firm and cashflows to the firm it allowsfor comparisons across firms with different financial leverage.

Aswath Damodaran 99

Value/EBITDA Multiple

n The Classic Definition

n The No-Cash Version

n When cash and marketable securities are netted out of value, none ofthe income from the cash and securities should be reflected in thedenominator.

Value

EBITDA=

Market Value of Equity + Market Value of Debt

Earnings before Interest, Taxes and Depreciation

Enterprise Value

EBITDA=

Market Value of Equity + Market Value of Debt - Cash

Earnings before Interest, Taxes and Depreciation

Aswath Damodaran 100

Value/EBITDA Distribution

EV/EBITDA

1200

1000

800

600

400

200

0

Std. Dev = 8.06

Mean = 8.0

N = 3630.00


The Determinants of Value/EBITDA Multiples:Linkage to DCF Valuation

n Firm value can be written as:

n The numerator can be written as follows:FCFF = EBIT (1-t) - (Cex - Depr) - ∆ Working Capital

= (EBITDA - Depr) (1-t) - (Cex - Depr) - ∆ Working Capital

= EBITDA (1-t) + Depr (t) - Cex - ∆ Working Capital

V0 = FCFF1

WACC - g


From Firm Value to EBITDA Multiples

n Now the Value of the firm can be rewritten as,

n Dividing both sides of the equation by EBITDA,

Value = EBITDA (1-t) + Depr (t) - Cex - ∆ Working Capital

WACC - g

Value

EBITDA =

(1- t)

WACC-g +

Depr (t)/EBITDA

WACC - g -

CEx/EBITDA

WACC - g -

∆ Working Capital/EBITDA

WACC - g


A Simple Example

n Consider a firm with the following characteristics:• Tax Rate = 36%

• Capital Expenditures/EBITDA = 30%

• Depreciation/EBITDA = 20%

• Cost of Capital = 10%

• The firm has no working capital requirements

• The firm is in stable growth and is expected to grow 5% a year forever.


Calculating Value/EBITDA Multiple

n In this case, the Value/EBITDA multiple for this firm can be estimatedas follows:

Value

EBITDA =

(1 -.36)

.10 - .05 +

(0.2)(.36)

.10 - .05 -

0.3

.10 - .05 -

0

.10 - .05 = 8.24


Value/EBITDA Multiples and Taxes

VEBITDA Multiples and Tax Rates

0

2

4

6

8

10

12

14

16

0% 10% 20% 30% 40% 50%

Tax Rate

Val

ue/E

BIT

DA


Value/EBITDA and Net Cap Ex

Value/EBITDA and Net Cap Ex Ratios

0

2

4

6

8

10

12

0% 5% 10% 15% 20% 25% 30%

Net Cap Ex/EBITDA

Val

ue/E

BIT

DA


Value/EBITDA Multiples and Return on Capital

Value/EBITDA and Return on Capital

0

2

4

6

8

10

12

6% 7% 8% 9% 10% 11% 12% 13% 14% 15%

Return on Capital

Val

ue/E

BIT

DA

WACC=10%WACC=9%WACC=8%


Value/EBITDA Multiple: Trucking Companies

Company Name Value EBITDA Value/EBITDAKLLM Trans. Svcs. 114.32$ 48.81$ 2.34Ryder System 5,158.04$ 1,838.26$ 2.81Rollins Truck Leasing 1,368.35$ 447.67$ 3.06Cannon Express Inc. 83.57$ 27.05$ 3.09Hunt (J.B.) 982.67$ 310.22$ 3.17Yellow Corp. 931.47$ 292.82$ 3.18Roadway Express 554.96$ 169.38$ 3.28Marten Transport Ltd. 116.93$ 35.62$ 3.28Kenan Transport Co. 67.66$ 19.44$ 3.48M.S. Carriers 344.93$ 97.85$ 3.53Old Dominion Freight 170.42$ 45.13$ 3.78Trimac Ltd 661.18$ 174.28$ 3.79Matlack Systems 112.42$ 28.94$ 3.88XTRA Corp. 1,708.57$ 427.30$ 4.00Covenant Transport Inc 259.16$ 64.35$ 4.03Builders Transport 221.09$ 51.44$ 4.30Werner Enterprises 844.39$ 196.15$ 4.30Landstar Sys. 422.79$ 95.20$ 4.44AMERCO 1,632.30$ 345.78$ 4.72USA Truck 141.77$ 29.93$ 4.74Frozen Food Express 164.17$ 34.10$ 4.81Arnold Inds. 472.27$ 96.88$ 4.87Greyhound Lines Inc. 437.71$ 89.61$ 4.88USFreightways 983.86$ 198.91$ 4.95Golden Eagle Group Inc. 12.50$ 2.33$ 5.37Arkansas Best 578.78$ 107.15$ 5.40Airlease Ltd. 73.64$ 13.48$ 5.46Celadon Group 182.30$ 32.72$ 5.57Amer. Freightways 716.15$ 120.94$ 5.92Transfinancial Holdings 56.92$ 8.79$ 6.47Vitran Corp. 'A' 140.68$ 21.51$ 6.54Interpool Inc. 1,002.20$ 151.18$ 6.63Intrenet Inc. 70.23$ 10.38$ 6.77Swift Transportation 835.58$ 121.34$ 6.89Landair Services 212.95$ 30.38$ 7.01CNF Transportation 2,700.69$ 366.99$ 7.36Budget Group Inc 1,247.30$ 166.71$ 7.48Caliber System 2,514.99$ 333.13$ 7.55Knight Transportation Inc 269.01$ 28.20$ 9.54Heartland Express 727.50$ 64.62$ 11.26Greyhound CDA Transn Corp 83.25$ 6.99$ 11.91Mark VII 160.45$ 12.96$ 12.38Coach USA Inc 678.38$ 51.76$ 13.11US 1 Inds Inc. 5.60$ (0.17)$ NAAverage 5.61


A Test on EBITDA

n Ryder System looks very cheap on a Value/EBITDA multiple basis,relative to the rest of the sector. What explanation (other thanmisvaluation) might there be for this difference?


Analyzing the Value/EBITDA Multiple

n While low value/EBITDA multiples may be a symptom ofundervaluation, a few questions need to be answered:• Is the operating income next year expected to be significantly lower than

the EBITDA for the most recent period? (Price may have dropped)

• Does the firm have significant capital expenditures coming up? (In thetrucking business, the life of the trucking fleet would be a good indicator)

• Does the firm have a much higher cost of capital than other firms in thesector?

• Does the firm face a much higher tax rate than other firms in the sector?


Value/EBITDA Multiples: Market

n The multiple of value to EBITDA varies widely across firms in themarket, depending upon:• how capital intensive the firm is (high capital intensity firms will tend to

have lower value/EBITDA ratios), and how much reinvestment is neededto keep the business going and create growth

• how high or low the cost of capital is (higher costs of capital will lead tolower Value/EBITDA multiples)

• how high or low expected growth is in the sector (high growth sectors willtend to have higher Value/EBITDA multiples)


US Market: Cross Sectional Regression

Model Summary

.526a .277 .276 426.8390Model1



Predictors: (Constant), Eff Tax Rate, ROC1, ExpectedGrowth in EPS: next 5 y

a.

Coefficients a,b

7.221 .617 11.707 .000

.287 .016 .344 17.739 .000

11.123 .670 .319 16.610 .000-.110 .014 -.155 -7.917 .000

(Constant)

Expected Growthin EPS: next 5 yROC1Eff Tax Rate

Model1

B Std. Error


Beta

Standardized

Coefficientst Sig.

Dependent Variable: EV/EBITDAa.



Price-Book Value Ratio: Definition

n The price/book value ratio is the ratio of the market value of equity tothe book value of equity, i.e., the measure of shareholders’ equity inthe balance sheet.

n Price/Book Value = Market Value of Equity

Book Value of Equity

n Consistency Tests:• If the market value of equity refers to the market value of equity of

common stock outstanding, the book value of common equity should beused in the denominator.

• If there is more that one class of common stock outstanding, the marketvalues of all classes (even the non-traded classes) needs to be factored in.


Price to Book Value: Distribution

PBV Ratio

1000

800

600

400

200

0

Std. Dev = 2.36

Mean = 2.39

N = 4866.00


Price Book Value Ratio: Stable Growth Firm

n Going back to a simple dividend discount model,

n Defining the return on equity (ROE) = EPS0 / Book Value of Equity,the value of equity can be written as:

n If the return on equity is based upon expected earnings in the next timeperiod, this can be simplified to,

P0 =DPS1

r − gn

P 0 = BV0 *ROE*Payout Ratio*(1 + gn )

r -gn

P 0

BV 0= PBV =

ROE*Payout Ratio*(1 + gn )

r-gn

P 0

BV 0= PBV =

ROE *Payout Ratio

r-gn


Price Book Value Ratio: Stable Growth FirmAnother Presentation

n This formulation can be simplified even further by relating growth tothe return on equity:

g = (1 - Payout ratio) * ROE

n Substituting back into the P/BV equation,

n The price-book value ratio of a stable firm is determined by thedifferential between the return on equity and the required rate of returnon its projects.

P 0

BV0= PBV =

R O E - gn

r -gn


Price Book Value Ratio for a Stable Growth Firm:Example

n Jenapharm was the most respected pharmaceutical manufacturer inEast Germany.

n Jenapharm was expected to have revenues of 230 million DM andearnings before interest and taxes of 30 million DM in 1991.

n The firm had a book value of assets of 110 million DM, and a bookvalue of equity of 58 million DM. The interest expenses in 1991 isexpected to be 15 million DM. The corporate tax rate is 40%.

n The firm was expected to maintain sales in its niche product, acontraceptive pill, and grow at 5% a year in the long term, primarily byexpanding into the generic drug market.

n The average beta of pharmaceutical firms traded on the FrankfurtStock exchange was 1.05.

n The ten-year bond rate in Germany at the time of this valuation was7%; the risk premium for stocks over bonds is assumed to be 5.5%.


Estimating a Price/Book Ratio for Jenapharm

n Expected Net Income = (EBIT - Interest Expense)*(1-t)* 1+g) = (30 -15) *(1-0.4)* (1.05) = 9.45 mil DM

n Return on Equity = Expected Net Income / Book Value of Equity =9.45 / 58 = 16.29%

n Cost on Equity = 7% + 1.05 (5.5%) = 12.775%

n Price/Book Value Ratio = (ROE - g) / (r - g) = (.1629 - .05) / (.12775 -.05) = 1.46

n Estimated MV of equity = BV of Equity * Price/BV ratio = 58 * 1.46= $ 84.50 mil DM


Price Book Value Ratio for High Growth Firm

n The Price-book ratio for a high-growth firm can be estimatedbeginning with a 2-stage discounted cash flow model:

n Dividing both sides of the equation by the book value of equity:

where ROE = Return on Equity in high-growth period

ROEn = Return on Equity in stable growth period

P 0 =

EPS0 *Payout Ratio *(1 + g )* 1 − (1+ g)n

( 1 +r)n

r - g+

EPS0 * Payout Ration * ( 1 + g )n * ( 1 + gn )

( r- gn )(1+ r)n

P0

BV0

=

ROE* Payout Ratio*(1+g)* 1 −(1+g)n

(1+r)n

r - g

+ ROE n * Payout Ration * ( 1 +g)n * ( 1 +gn )

(r - gn )(1+r)n


PBV Ratio for High Growth Firm: Example

n Assume that you have been asked to estimate the PBV ratio for a firmwhich has the following characteristics:

High Growth Phase Stable Growth Phase

Length of Period 5 years Forever after year 5

Return on Equity 25% 15%


Growth Rate .80*.25=.20 .4*.15=.06

Beta 1.25 1.00

Cost of Equity 12.875% 11.50%

The riskfree rate is 6% and the risk premium used is 5.5%.


Estimating Price/Book Value Ratio

n The price/book value ratio for this firm is:

PBV =

0.25 * 0.2 * (1.20) * 1 −(1.20)5

(1.12875)5

(.12875 - .20)

+ 0.15 * 0.6 * (1.20)5 * (1.06)

(.115 - .06) (1.12875)5

= 2.66


PBV and ROE: The Key

PBV and ROE: Risk Scenarios

0

0.5

1

1.5

2

2.5

3

3.5

4

10% 15% 20% 25% 30%

ROE

Pric

e/Boo

k V

alue

Rat

ios

Beta=0.5Beta=1Beta=1.5


PBV/ROE: Oil CompaniesCompany Name Ticker Symbol PBV ROE

Crown Cent. Petr.'A' CNPA 0.29 -14.60%

Giant Industries GI 0.54 7.47%

Harken Energy Corp. HEC 0.64 -5.83%

Getty Petroleum Mktg. GPM 0.95 6.26%

Pennzoil-Quaker State PZL 0.95 3.99%

Ashland Inc. ASH 1.13 10.27%

Shell Transport SC 1.45 13.41%

USX-Marathon Group MRO 1.59 13.42%

Lakehead Pipe Line LHP 1.72 13.28%

Amerada Hess AHC 1.77 16.69%

Tosco Corp. TOS 1.95 15.44%

Occidental Petroleum OXY 2.15 16.68%

Royal Dutch Petr. RD 2.33 13.41%

Murphy Oil Corp. MUR 2.40 14.49%

Texaco Inc. TX 2.44 13.77%

Phillips Petroleum P 2.64 17.92%

Chevron Corp. CHV 3.03 15.69%

Repsol-YPF ADR REP 3.24 13.43%

Unocal Corp. UCL 3.53 10.67%

Kerr-McGee Corp. KMG 3.59 28.88%

Exxon Mobil Corp. XOM 4.22 11.20%

BP Amoco ADR BPA 4.66 14.34%

Clayton Williams Energy CWEI 5.57 31.02%

Average 2.30 12.23%


PBV versus ROE regression

n Regressing PBV ratios against ROE for oil companies yields thefollowing regression:

PBV = 1.04 + 10.24 (ROE) R2 = 49%

n For every 1% increase in ROE, the PBV ratio should increase by0.1024.


Valuing Pemex

n Assume that you have been asked to value a PEMEX for the MexicanGovernment; All you know is that it has earned a return on equity of10% last year. The appropriate P/BV ratio can be estimated

P/BV Ratio (based upon regression) = 1.04 + 10.24 * 0.1 = 2.06


Looking for undervalued securities - PBV Ratiosand ROE

n Given the relationship between price-book value ratios and returns onequity, it is not surprising to see firms which have high returns onequity selling for well above book value and firms which have lowreturns on equity selling at or below book value.

n The firms which should draw attention from investors are those whichprovide mismatches of price-book value ratios and returns on equity -low P/BV ratios and high ROE or high P/BV ratios and low ROE.


The Valuation Matrix

MV/BV

ROE-r

High ROEHigh MV/BV

Low ROELow MV/BV

OvervaluedLow ROEHigh MV/BV

UndervaluedHigh ROELow MV/BV


Large Market Cap Firms: PBV vs ROE: January 2001

ROE

.5.4.3.2.10.0

12

10

8

6

4

2

0

XOM

C

CSCO

WMT

INTC

AIG

BP

SBC

IBM

VZ

JNJ

RD

HD

TYCMWD

NT

DT

JPM

PG

T

WFC

BLS

TXN

BAC

FNM

SC

ERICY

TEF

PHA

SNEBTY

PEP

ABT

DIS

AXP

HWP

WCOM

LU

AVE

QCOM

BA

AEG

GS

PHG

ENE

CHVSTD

MC

BBV

DD

F

MOT

ONEJDSU

SLB

MMM

FRE

DCX

WAG

FBF

ADP

HMC

HON

AMAT

BUD

KMB

TOC.TO

DNA

UTX

TX

EMR

UN

KRB

FTU

TGT

CPQ

MMC

AA

GMALL

SWYFITBCAH

WMDUK

TMX

EDS

A BAX

HI

AES

SLR

AHO

FSR

MELFDC

USB

UL

BCE

CVS

DOW

BBDB.TO

FON

MU

BNS.TO

AT

REP

PNCHCA


Company Symbols

Company Name Ticker SymbolCompany Name Ticker SymbolCompany Name Ticker Symbol Company Name Ticker SymbolMatsushita Elec. ADR MC British Telecom ADR BTY Merrill Lynch & Co. MER Int'l Business Mach. IBMCompaq Computer CPQ Amer. Int'l Group AIG Fannie Mae FNM Abbott Labs. ABTNews Corp. Ltd. ADR NWS Chevron Corp. CHV Tyco Int'l Ltd. TYC Morgan S. Dean Witter MWDAT&T Corp. T AEGON Ins. Group AEG Amer. Express AXP Amgen AMGNSchlumberger Ltd. SLB Sprint Corp. FON Corning Inc. GLW Dell Computer DELLDisney (Walt) DIS Boeing BA EMC Corp. EMC Amer. Home Products AHPKoninklijke Philips NV PHG Hewlett-Packard HWP Gen'l Electric GE Procter & Gamble PGTime Warner TWX Banco Bilbao Vis. ADR BBV Intel Corp. INTC Pfizer, Inc. PFEDeutsche Telekom ADR DT Wells Fargo WFC Ford Motor F Schering-Plough SGPWorldCom Inc. WCOM Ericsson ADR ERICY BellSouth Corp. BLS Merck & Co. MRKMotorola, Inc. MOT Texas Instruments TXN Johnson & Johnson JNJ Bristol-Myers Squibb BMYTelefonica SA ADR TEF Micron Technology MU Lucent Technologies LU Philip Morris MOBanco Santander ADR STD Bank of America BAC PepsiCo, Inc. PEP Lilly (Eli) LLYSony Corp. ADR SNE Home Depot HD Cisco Systems CSCO Oracle Corp. ORCLExxon Mobil Corp. XOM McDonald's Corp. MCD Goldman Sachs GSAventis ADR AVE SBC Communications SBC Medtronic, Inc. MDTEnron Corp. ENE Wal-Mart Stores WMT Sun Microsystems SUNWPharmacia Corp. PHA Du Pont DD Applied Materials AMATShell Transport SC Citigroup Inc. C Schwab (Charles) SCHRoyal Dutch Petr. RD Qualcomm Inc. QCOM Microsoft Corp. MSFTDaimlerChrysler AG DCX SmithKline Beecham SBH Nokia Corp. ADR NOKBP Amoco ADR BPA Chase Manhattan Corp. CMB Coca-Cola KO


PBV Matrix: Telecom Companies

TelAzteca

TelNZ VimpleCarlton

Cable&WTeleglobeFranceTel

DeutscheTelBritTelTelItalia AsiaSatPortugal HongKong

RoyalBCE Hellenic

ChinaTelNipponDanmarkEspana Indast

TelevisasTelmexTelArgFrancePhilTelTelArgentina TelIndoTelPeru

GrupoCentroAPTCallNetAnonima

ROE

6050403020100

12

10

8

6

4

2

0


WABC

OV

NBAK

BWE

HU

PFGI

BOH

CBC

TRMK

SKYF

WL

VLY

CBH

CFR

FULT

FVB

CYN

MRBK

CBSSBPOP

FSCO

UB

ZION

UPC SOTRRGBK

SNV

ASO

KEY

BBT

WB

PNC

STI

MEL

FTU

FBF

CMB

WFC

BAC

1.25

2.50

3.75

5.00

0.12 0.16 0.20 0.24

ROE

PBV

U.S. Banks: Market Cap > $ 1 billion


Company Name Ticker Symbol Company Name Ticker Symbol Company Name Ticker SymbolWestamerica Bancorp WABC Fulton Fin'l FULT Regions Financial RGBKKeystone Fin'l KSTN First Va. Banks FVB Synovus Financial SNVColonial BncGrp. 'A' CNB City National Corp. CYN AmSouth Bancorp. ASOOne Valley Bancorp OV Hibernia Corp. `A' HIB KeyCorp KEYNational BanCorp. of Alaska,In NBAK Silicon Valley Bncsh SIVB BB&T Corp. BBTBancWest Corp. BWE Mercantile Bankshares MRBK Wachovia Corp. WBHudson United Bancorp HU Compass Bancshares CBSS PNC Financial Serv. PNCProvident Finl Group PFGI Popular Inc BPOP SunTrust Banks STIPacific Century Fin'l BOH First Security FSCO State Street Corp. STTCentura Banks CBC No. Fork Bancorp NFB Mellon Financial Corp. MELTrustmark Corp. TRMK Natl Commerce Bancrp NCBC Morgan (J.P.) & Co JPMSky Finl Group Inc SKYF UnionBancal Corp UB First Union Corp. FTUWilmington Trust WL M&T Bank Corp. MTB FleetBoston Fin'l FBFValley Natl Bancp NJ VLY Zions Bancorp. ZION Bank of New York BKCommerce Bancorp NJ CBH Union Planters UPC Chase Manhattan Corp. CMBCullen/Frost Bankers CFR SouthTrust Corp. SOTR Wells Fargo WFC

Summit Bancorp SUB Bank of America BAC


IBM: The Rise and Fall and Rise Again

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

Year

Pric

e to

Boo

k

-40.00%

-30.00%

-20.00%

-10.00%

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

Ret

urn

on E

quity

PBV ROE


PBV Ratio Regression

Model Summary

.686a .470 .469 167.8482Model1



Predictors: (Constant), Beta, ROE1, Expected Growth inEPS: next 5 y

a.

Coefficients a,b

2.719 .199 13.678 .000

6.325E-02 .008 .159 8.302 .000

9.656 .253 .667 38.183 .000-1.438 .183 -.150 -7.862 .000

(Constant)

Expected Growthin EPS: next 5 yROE1Beta

Model1

B Std. Error


Beta

Standardized

Coefficientst Sig.

Dependent Variable: PBV Ratioa.



PBV Ratio Regression: Brazil - September 2000

n Regressing PBV against ROE for 177 Brazilian firms (The betas aremissing for a lot of firms and meaningless for the rest, and there are noexpected growth rate estimates over the long term)

PBV = 0.77 + 3.78 (ROE) R squared = 17.3%

n To run this regression, we used• Only firms with positive returns on equity

• Only firms with positive book values of equity


Cross Sectional Regression for Greece: May 2001

Coefficients a

2.106 .280 7.531 .000

11.631 1.535 .418 7.579 .000

(Constant)

ROE

Model1

B Std. Error


Beta

Standardized

Coefficients

t Sig.

Dependent Variable: PBVa.

R squared = 22%Number of firms in sample = 272


Value/Book Value Ratio: Definition

n While the price to book ratio is a equity multiple, both the marketvalue and the book value can be stated in terms of the firm.

n Value/Book Value = Market Value of Equity + Market Value of Debt

Book Value of Equity + Book Value of Debt


Value/Book Ratio: Description

Value/BV of Capital

1400

1200

1000

800

600

400

200

0

Std. Dev = 2.63

Mean = 2.53

N = 4813.00


Determinants of Value/Book Ratios

n To see the determinants of the value/book ratio, consider the simplefree cash flow to the firm model:

n Dividing both sides by the book value, we get:

n If we replace, FCFF = EBIT(1-t) - (g/ROC) EBIT(1-t),we get

V0 = FCFF1

WACC - g

V0

BV=

FCFF1/BV

WACC - g

V0

BV=

ROC - g

WACC - g


Value/Book Ratio: An Example

n Consider a stable growth firm with the following characteristics:• Return on Capital = 12%

• Cost of Capital = 10%

• Expected Growth = 5%

n The value/BV ratio for this firm can be estimated as follows:

Value/BV = (.12 - .05)/(.10 - .05) = 1.40

n The effects of ROC on growth will increase if the firm has a highgrowth phase, but the basic determinants will remain unchanged.


Value/Book and the Return Spread

Value/BV Ratios and Return Spreads

-

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50-2

%

-1% 0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10

%

ROC - WACC

Val

ue/B

V R

atio

WACC=8%WACC=10%WACC=12%


Price Sales Ratio: Definition

n The price/sales ratio is the ratio of the market value of equity to thesales.

n Price/ Sales= Market Value of Equity

Total Revenues

n Consistency Tests• The price/sales ratio is internally inconsistent, since the market value of

equity is divided by the total revenues of the firm.


PS Ratios: The Inconsistency Test

n Assume that you are comparing price/sales ratios across firms in asector, and that there are differences in financial leverage across firms.What type of firms will emerge with the lowest price/sales ratios?

o Low Leverage Firms

o Average Leverage Firms

o High Leverage Firms


Price/Sales Ratio: Cross Sectional Distribution

PS RATIO

1400

1200

1000

800

600

400

200

0

Std. Dev = 2.55

Mean = 1.87

N = 4634.00


Price/Sales Ratio: Determinants

n The price/sales ratio of a stable growth firm can be estimatedbeginning with a 2-stage equity valuation model:

n Dividing both sides by the sales per share:

P0 =DPS1

r − gn

P0

Sales0

= PS = Net Profit Margin*Payout Ratio * ( 1+ gn )

r-gn


Price/Sales Ratio for High Growth Firm

n When the growth rate is assumed to be high for a future period, thedividend discount model can be written as follows:

n Dividing both sides by the sales per share:

where Net Marginn = Net Margin in stable growth phase

P 0 =

EPS0 *Payout Ratio*(1 + g )* 1 − (1+ g)n

( 1 +r)n

r - g+

EPS0 * Payout Ration * ( 1 + g )n * ( 1 + gn )

( r- gn )(1+ r)n

P0

Sales0

=

Net Margin * Payout Ratio*( 1 +g ) * 1 −(1+g) n

(1+r)n

r - g

+ Net Marginn * Payout Ration * ( 1 +g) n *(1 + gn )

(r - gn )(1 + r)n


Price Sales Ratios and Profit Margins

n The key determinant of price-sales ratios is the profit margin.

n A decline in profit margins has a two-fold effect.• First, the reduction in profit margins reduces the price-sales ratio directly.

• Second, the lower profit margin can lead to lower growth and hence lowerprice-sales ratios.

Expected growth rate = Retention ratio * Return on Equity

= Retention Ratio *(Net Profit / Sales) * ( Sales / BV of Equity)

= Retention Ratio * Profit Margin * Sales/BV of Equity


Price/Sales Ratio: An Example

High Growth Phase Stable Growth

Length of Period 5 years Forever after year 5

Net Margin 10% 6%

Sales/BV of Equity 2.5 2.5

Beta 1.25 1.00


Expected Growth (.1)(2.5)(.8)=20% (.06)(2.5)(.4)=.06

Riskless Rate =6%

PS =

0.10 * 0.2 * (1.20) * 1 −(1.20)5

(1.12875)5

(.12875 - .20)

+ 0.06 * 0.60 * (1.20) 5 * (1.06)

(.115 -.06) (1.12875)5

= 1.06


Effect of Margin Changes

Price/Sales Ratios and Net Margins

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2% 4% 6% 8% 10% 12% 14% 16%

Net Margin

PS R

atio


PS/Margins: Greek Retailers

Company PS Net MarginSPAKIANAKIS SA 0.25 2.88%KOTSOVOLOS SA 0.48 1.91%SANYO HELLAS 1.12 5.07%IMAGE-SOV2VD SA 1.31 2.86%GERMAN0S 1.49 6.94%ELEKTRONIKI 1.61 6.29%JUMBO 1.68 6.08%PHiLIPPOS NAKAS 1.71 5.04%GOODY'S 2.24 6.77%HELLENIC DUTY 5.60 19.49%AS COMPANY 7.02 8.23%FOLLI-FOLLIE 10.82 29.08%


Regression Results: PS Ratios and Margins

n Regressing PS ratios against net margins,

PS = -.10 + 36.29 (Net Margin) R2 = 78%

n Thus, a 1% increase in the margin results in an increase of 0.36 in theprice sales ratios.

n The regression also allows us to get predicted PS ratios for these firms


Predicted PS Ratios

Symbol Company PS Predicted PS Under or Over ValuedSFA SPAKIANAKIS SA 0.25 0.94 -73.28%KOTSV KOTSOVOLOS SA 0.48 0.59 -18.47%SANYO SANYO HELLAS 1.12 1.74 -35.37%IKONA IMAGE-SOV2VD SA 1.31 0.94 39.82%GERM GERMAN0S 1.49 2.42 -38.41%ELATH ELEKTRONIKI 1.61 2.18 -26.47%BABY JUMBO 1.68 2.11 -20.39%NAKAS PHXLXPPOS NAKAS 1.71 1.73 -1.38%GOODY GOODY'S 2.24 2.36 -5.01%HDF HELLENIC DUTY 5.60 6.97 -19.72%ASCO AS COMPANY 7.02 2.89 143.07%FOLLI FOLLX-FOLLXE 10.82 10.45 3.51%


Current versus Predicted Margins

n One of the limitations of the analysis we did in these last few pages isthe focus on current margins. Stocks are priced based upon expectedmargins rather than current margins.

n For most firms, current margins and predicted margins are highlycorrelated, making the analysis still relevant.

n For firms where current margins have little or no correlation withexpected margins, regressions of price to sales ratios against currentmargins (or price to book against current return on equity) will notprovide much explanatory power.

n In these cases, it makes more sense to run the regression using eitherpredicted margins or some proxy for predicted margins.


A Case Study: The Internet Stocks

ROWEGSVIPPODTURF BUYX ELTXGEEKRMIIFATB TMNTONEM ABTL INFO ANETITRAIIXLBIZZ EGRPACOMALOYBIDSSPLN EDGRPSIX ATHY AMZNCLKS PCLNAPNT SONENETO

CBIS NTPACSGPINTW RAMP

DCLKCNETATHMMQST FFIV

SCNT MMXIINTMSPYGLCOS

PKSI

-0

10

20

30

-0.8 -0.6 -0.4 -0.2

AdjMargin

AdjPS


PS Ratios and Margins are not highly correlated

n Regressing PS ratios against current margins yields the followingPS = 81.36 - 7.54(Net Margin) R2 = 0.04

(0.49)

n This is not surprising. These firms are priced based upon expectedmargins, rather than current margins.


Solution 1: Use proxies for survival and growth:Amazon in early 2000

n Hypothesizing that firms with higher revenue growth and higher cashbalances should have a greater chance of surviving and becomingprofitable, we ran the following regression: (The level of revenues wasused to control for size)

PS = 30.61 - 2.77 ln(Rev) + 6.42 (Rev Growth) + 5.11 (Cash/Rev)

(0.66) (2.63) (3.49)

R squared = 31.8%

Predicted PS = 30.61 - 2.77(7.1039) + 6.42(1.9946) + 5.11 (.3069) =30.42

Actual PS = 25.63

Stock is undervalued, relative to other internet stocks.


Solution 2: Use forward multiples

n You can always estimate price (or value) as a multiple of revenues,earnings or book value in a future year. These multiples are calledforward multiples.

n For young and evolving firms, the values of fundamentals in futureyears may provide a much better picture of the true value potential ofthe firm. There are two ways in which you can use forward multiples:• Look at value today as a multiple of revenues or earnings in the future

(say 5 years from now) for all firms in the comparable firm list. Use theaverage of this multiple in conjunction with your firm’s earnings orrevenues to estimate the value of your firm today.

• Estimate value as a multiple of current revenues or earnings for moremature firms in the group and apply this multiple to the forward earningsor revenues to the forward earnings for your firm. This will yield theexpected value for your firm in the forward year and will have to bediscounted back to the present to get current value.


An Example of Forward Multiples: Amazon in early2000

n Amazon.com lost $0.63 per share in 2000 but is expected to earn $ 1.50 pershare in 2005. At its current price of $ 49 per share, this would translate into aprice/future earnings per share of 32.67.

n In the first approach, this multiple of earnings can be compared to theprice/future earnings ratios of comparable firms. If you define comparablefirms to be e-tailers, Amazon looks reasonably attractive since the averageprice/future earnings per share of e-tailers is 65. If, on the other hand, youcompared Amazon’s price to future earnings per share to the average price tofuture earnings per share (in 2004) of specialty retailers, the picture is bleaker.The average price to future earnings for these firms is 12, which would lead toa conclusion that Amazon is over valued.

n In the second approach, the current price to earnings ratio for specialtyretailers, which is estimated to be 20.31 to the earnings per share of Amazonin 2004 (which is estimated to be $1.50). This would yield a target price of$30.46. Discounting this price back to the present using Amazon’s cost ofequity of 12.94% results in a value per share:

Value per share = Target price in five years/ (1 + Cost of equity)5

= $30.46/1.12945 = $16.58.


PS Regression

Model Summary

.851a .723 .723 88.1869Model1



Predictors: (Constant), Beta, MARGIN, PAYOUT, ExpectedGrowth in EPS: next 5 y

a.

Coefficients a,b,c

4.392E-02 .005 .199 9.210 .000

.807 .115 .087 7.007 .00023.747 .466 .876 50.955 .000

-.607 .085 -.187 -7.110 .000

Expected Growthin EPS: next 5 yPAYOUTMARGINBeta

Model1

B Std. Error


Beta

Standardized

Coefficientst Sig.

Dependent Variable: PS RATIOa.

Linear Regression through the Originb.

Weighted Least Squares Regression - Weighted by Market Capc.


Cross Sectional Regression for Portugal in June1999

n Using data on 74 Portuguese companies from 1999, we regressed PSratios against profit margins:

PS = 0.98 + 6.96 Margin

(4.34) (3.07) R2 = 45.29%


Value/Sales Ratio: Definition

n The value/sales ratio is the ratio of the market value of the firm to thesales.

n Value/ Sales= Market Value of Equity + Market Value of Debt-Cash

Total Revenues


Value/Sales Ratio: Cross Sectional Distribution

EV/SALES

1400

1200

1000

800

600

400

200

0

Std. Dev = 2.48

Mean = 2.01

N = 4644.00


Value/Sales Ratios: Analysis of Determinants

n If pre-tax operating margins are used, the appropriate value estimate isthat of the firm. In particular, if one makes the assumption that• Free Cash Flow to the Firm = EBIT (1 - tax rate) (1 - Reinvestment Rate)

n Then the Value of the Firm can be written as a function of the after-taxoperating margin= (EBIT (1-t)/Sales

g = Growth rate in after-tax operating income for the first n yearsgn = Growth rate in after-tax operating income after n years forever (Stable

growth rate)

RIRGrowth, Stable = Reinvestment rate in high growth and stable periods

WACC = Weighted average cost of capital

Value

Sales0

= After - tax Oper. Margin *

(1 - RIRgrowth )(1 + g)* 1− (1 + g )n

(1+ WACC)n

WACC - g+

(1- RIR stable)(1 + g)n * ( 1 +gn )

(WACC - gn ) (1+WACC)n


Value/Sales Ratio: An Example

n Consider, for example, the Value/Sales ratio of Coca Cola. Thecompany had the following characteristics:After-tax Operating Margin =18.56% Sales/BV of Capital = 1.67

Return on Capital = 1.67* 18.56% = 31.02%

Reinvestment Rate= 65.00% in high growth; 20% in stable growth;

Expected Growth = 31.02% * 0.65 =20.16% (Stable Growth Rate=6%)

Length of High Growth Period = 10 years

Cost of Equity =12.33% E/(D+E) = 97.65%

After-tax Cost of Debt = 4.16% D/(D+E) 2.35%

Cost of Capital= 12.33% (.9765)+4.16% (.0235) = 12.13%

Value of Firm 0

Sales0

= .1856*

( 1 -.65)(1.2016)* 1− (1.2016)10

(1.1213)10

.1213-.2016+

( 1 -.20)(1.2016)10 * (1.06)(.1213-.06)(1.1213)10

= 6.10


Value Sales Ratios and Operating Margins

Coca Cola: The Operating Margin Effect

0

2

4

6

8

10

12

6% 8% 10% 12% 14% 16% 18% 20%

Operating Margin

Val

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ales

Rat

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0

50

100

150

200

250

$ V

alue Value/Sales

$ Value


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Operating Margin

V/Sales

U.S. Specialty Retailers: V/S vs Operating Margin


Brand Name Premiums in Valuation

n You have been hired to value Coca Cola for an analyst reports andyou have valued the firm at 6.10 times revenues, using the modeldescribed in the last few pages. Another analyst is arguing that thereshould be a premium added on to reflect the value of the brand name.Do you agree?

o Yes

o No

n Explain.


The value of a brand name

n One of the critiques of traditional valuation is that is fails to considerthe value of brand names and other intangibles.

n The approaches used by analysts to value brand names are often ad-hoc and may significantly overstate or understate their value.

n One of the benefits of having a well-known and respected brand nameis that firms can charge higher prices for the same products, leading tohigher profit margins and hence to higher price-sales ratios and firmvalue. The larger the price premium that a firm can charge, the greateris the value of the brand name.

n In general, the value of a brand name can be written as:Value of brand name ={(V/S)b-(V/S)g }* Sales

(V/S)b = Value of Firm/Sales ratio with the benefit of the brand name

(V/S)g = Value of Firm/Sales ratio of the firm with the generic product


Illustration: Valuing a brand name: Coca Cola

Coca Cola Generic Cola Company

AT Operating Margin 18.56% 7.50%Sales/BV of Capital 1.67 1.67

ROC 31.02% 12.53%

Reinvestment Rate 65.00% (19.35%) 65.00% (47.90%)

Expected Growth 20.16% 8.15%

Length 10 years 10 yea

Cost of Equity 12.33% 12.33%

E/(D+E) 97.65% 97.65%

AT Cost of Debt 4.16% 4.16%

D/(D+E) 2.35% 2.35%

Cost of Capital 12.13% 12.13%

Value/Sales Ratio 6.10 0.69


Value of Coca Cola’s Brand Name

n Value of Coke’s Brand Name = ( 6.10 - 0.69) ($18,868 million) =$102 billion

n Value of Coke as a company = 6.10 ($18,546 million) = $ 115 Billion

n Approximately 88.69% of the value of the company can be traced tobrand name value


Value/Sales Ratio Regression: Market

Model Summary

.615a .379 .378 110.8277Model1



Predictors: (Constant), Expected Growth in EPS: next 5 y,OPMGN

a.

Coefficients a,b

.107 .090 1.196 .23211.854 .340 .583 34.903 .000

6.041E-02 .004 .238 14.274 .000

(Constant)OPMGNExpected Growthin EPS: next 5 y

Model1

B Std. Error


Beta

Standardized

Coefficientst Sig.

Dependent Variable: EV/SALESa.



Choosing Between the Multiples

n As presented in this section, there are dozens of multiples that can bepotentially used to value an individual firm.

n In addition, relative valuation can be relative to a sector (orcomparable firms) or to the entire market (using the regressions, forinstance)

n Since there can be only one final estimate of value, there are threechoices at this stage:• Use a simple average of the valuations obtained using a number of

different multiples

• Use a weighted average of the valuations obtained using a nmber ofdifferent multiples

• Choose one of the multiples and base your valuation on that multiple


Averaging Across Multiples

n This procedure involves valuing a firm using five or six or moremultiples and then taking an average of the valuations across thesemultiples.

n This is completely inappropriate since it averages good estimates withpoor ones equally.

n If some of the multiples are “sector based” and some are “marketbased”, this will also average across two different ways of thinkingabout relative valuation.


Weighted Averaging Across Multiples

n In this approach, the estimates obtained from using different multiplesare averaged, with weights on each based upon the precision of eachestimate. The more precise estimates are weighted more and the lessprecise ones weighted less.

n The precision of each estimate can be estimated fairly simply for thoseestimated based upon regressions as follows:

Precision of Estimate = 1 / Standard Error of Estimate

where the standard error of the predicted value is used in thedenominator.

n This approach is more difficult to use when some of the estimates aresubjective and some are based upon more quantitative techniques.


Picking one Multiple

n This is usually the best way to approach this issue. While a range ofvalues can be obtained from a number of multiples, the “best estimate”value is obtained using one multiple.

n The multiple that is used can be chosen in one of two ways:• Use the multiple that best fits your objective. Thus, if you want the

company to be undervalued, you pick the multiple that yields the highestvalue.

• Use the multiple that has the highest R-squared in the sector whenregressed against fundamentals. Thus, if you have tried PE, PBV, PS, etc.and run regressions of these multiples against fundamentals, use themultiple that works best at explaining differences across firms in thatsector.

• Use the multiple that seems to make the most sense for that sector, givenhow value is measured and created.


Self Serving Multiple Choice

n When a firm is valued using several multiples, some will yield reallyhigh values and some really low ones.

n If there is a significant bias in the valuation towards high or lowvalues, it is tempting to pick the multiple that best reflects this bias.Once the multiple that works best is picked, the other multiples can beabandoned and never brought up.

n This approach, while yielding very biased and often absurd valuations,may serve other purposes very well.

n As a user of valuations, it is always important to look at the biases ofthe entity doing the valuation, and asking some questions:• Why was this multiple chosen?

• What would the value be if a different multiple were used? (You pick thespecific multiple that you want to see tried.)


The Statistical Approach

n One of the advantages of running regressions of multiples againstfundamentals across firms in a sector is that you get R-squared valueson the regression (that provide information on how well fundamentalsexplain differences across multiples in that sector).

n As a rule, it is dangerous to use multiples where valuationfundamentals (cash flows, risk and growth) do not explain a significantportion of the differences across firms in the sector.

n As a caveat, however, it is not necessarily true that the multiple thathas the highest R-squared provides the best estimate of value for firmsin a sector.


A More Intuitive Approach

n As a general rule of thumb, the following table provides a way ofpicking a multiple for a sector

Sector Multiple Used Rationale

Cyclical Manufacturing PE, Relative PE Often with normalized earnings

High Tech, High Growth PEG Big differences in growth across firms

High Growth/No Earnings PS, VS Assume future margins will be good

Heavy Infrastructure VEBITDA Firms in sector have losses in earlyyears and reported earnings can vary

depending on depreciation method

REITa P/CF Generally no cap ex investments

from equity earnings

Financial Services PBV Book value often marked to market

Retailing PS If leverage is similar across firms

VS If leverage is different


Sector or Market Multiples

n The conventional approach to using multiples is to look at the sector orcomparable firms.

n Whether sector or market based multiples make the most sensedepends upon how you think the market makes mistakes in valuation• If you think that markets make mistakes on individual firm valuations but

that valuations tend to be right, on average, at the sector level, you willuse sector-based valuation only,

• If you think that markets make mistakes on entire sectors, but is generallyright on the overall market level, you will use only market-basedvaluation

n It is usually a good idea to approach the valuation at two levels:• At the sector level, use multiples to see if the firm is under or over valued

at the sector level

• At the market level, check to see if the under or over valuation persistsonce you correct for sector under or over valuation.


A Test

n You have valued Earthlink Networks, an internet service provider,relative to other internet companies using Price/Sales ratios and find itto be under valued almost 50% .When you value it relative to themarket, using the market regression, you find it to be overvalued byalmost 50%. How would you reconcile the two findings?

o One of the two valuations must be wrong. A stock cannot be under andover valued at the same time.

o It is possible that both valuations are right.

What has to be true about valuations in the sector for the second statementto be true?


Reviewing: The Four Steps to UnderstandingMultiples

n Define the multiple• Check for consistency

• Make sure that they are estimated uniformally

n Describe the multiple• Multiples have skewed distributions: The averages are seldom good

indicators of typical multiples

• Check for bias, if the multiple cannot be estimated

n Analyze the multiple• Identify the companion variable that drives the multiple

• Examine the nature of the relationship

n Apply the multiple

Documents

Damodaran on Relval