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Aswath Damodaran 1
Earnings Multiples
Aswath Damodaran
Aswath Damodaran 2
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 3
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 4
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 5
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 6
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 7
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 8
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 9
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 10
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 11
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 12
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 13
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%
Aswath Damodaran 14
PE: Emerging Markets
0
5
10
15
20
25
30
35
Mexico Malaysia Singapore Taiwan Hong Kong Venezuela Brazil Argentina Chile
Aswath Damodaran 15
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 16
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 17
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 18
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 19
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 20
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 21
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 22
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 23
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 24
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 25
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 26
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 27
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 28
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 29
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 30
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 31
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 32
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 33
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 34
PE versus Growth
Expected Growth in EPS: next 5 years
100806040200-20
120
100
80
60
40
20
0
-20
Aswath Damodaran 35
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 36
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 37
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
UnstandardizedCoefficients
Beta
Standardized
Coefficientst Sig.
Dependent Variable: Current PEa.
Linear Regression through the Originb.
Weighted Least Squares Regression - Weighted by Market Capc.
Aswath Damodaran 38
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 39
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 40
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 41
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 42
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 43
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 44
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 45
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 46
PEG Ratio: Distribution
Price/ Expected Growth RAte
400
300
200
100
0
Std. Dev = 1.05
Mean = 1.55
N = 2084.00
Aswath Damodaran 47
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 48
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 49
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 50
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 51
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%
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%
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 52
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 53
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 54
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 55
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 56
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 57
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 58
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 59
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 60
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 61
PEG versus Growth
Expected Growth in EPS: next 5 years
100806040200-20
6
5
4
3
2
1
0
-1
Aswath Damodaran 62
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 63
PEG versus ln(Expected Growth)
Ln(Expected Growth)
543210-1
6
5
4
3
2
1
0
-1
Aswath Damodaran 64
Market PEG Ratio Regression
Model Summary
.587a .344 .343 56.7746Model1
R R SquareAdjusted R
SquareStd. Error ofthe Estimate
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
UnstandardizedCoefficients
Beta
Standardized
Coefficientst Sig.
Dependent Variable: PEG1a.
Weighted Least Squares Regression - Weighted by Market Capb.
Aswath Damodaran 65
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 66
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 67
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 68
Relative PE: Cross Sectional Distribution
Relative PE
1000
800
600
400
200
0
Std. Dev = .77
Mean = 1.00
N = 3303.00
Aswath Damodaran 69
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 70
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 71
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 72
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 73
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 74
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 75
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 76
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 77
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 78
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 79
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 80
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 81
Relative PE Ratios: Market Analysis
Model Summary
.478a .229 .227 41.4196Model1
R R SquareAdjusted R
SquareStd. Error ofthe Estimate
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
UnstandardizedCoefficients
Beta
Standardized
Coefficientst Sig.
Dependent Variable: RELPEa.
Weighted Least Squares Regression - Weighted by Market Capb.
Aswath Damodaran 82
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 83
Value/FCFF Distribution
Enterprise Value/FCFF
800
600
400
200
0
Std. Dev = 21.77
Mean = 20.6
N = 3063.00
Aswath Damodaran 84
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 85
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 86
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 87
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 88
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 89
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 90
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 91
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 92
Value/EBITDA Distribution
EV/EBITDA
1200
1000
800
600
400
200
0
Std. Dev = 8.06
Mean = 8.0
N = 3630.00
Aswath Damodaran 93
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
Aswath Damodaran 94
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
Aswath Damodaran 95
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.
Aswath Damodaran 96
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
Aswath Damodaran 97
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
Aswath Damodaran 98
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
Aswath Damodaran 99
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%
Aswath Damodaran 100
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
Aswath Damodaran 101
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?
Aswath Damodaran 102
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?
Aswath Damodaran 103
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)
