# Relative Valuation by alicejenny

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• pg 1
```									       Relative Valuation

1

Why relative valuation?
“If you think I’m crazy, you should see the
h lives across th h ll”
guy who li             the hall”
Jerry Seinfeld talking about Kramer in a
Seinfeld episode

“ A little inaccuracy sometimes saves tons of
explanation”
H.H. Munro
2
What is relative valuation?
• In relative valuation, the value of an asset is compared to the values
assessed by the market for similar or comparable assets.
• 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
absolute prices cannot be compared This process of
standardizing creates price multiples.
– compare the standardized value or multiple for the asset being
analyzed to the standardized values for comparable asset,
controlling for any differences between the firms that might affect
the multiple, to judge whether the asset is under or over valued

3

Standardizing Value
•   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 ....)   4
The Four Steps to
Understanding Multiples
•   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, it is critical that we understand how the multiples have been
estimated
•   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 of a multiple is, it is difficult to look at a number and pass
judgment on whether it is too high or low.
•   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.
•   Apply the multiple
– Defining the comparable universe and controlling for differences is far        5
more difficult in practice than it is in theory.

Definitional Tests
• Is the multiple consistently defined?
– Proposition 1: Both the value (the numerator) and the
p                            (              )
standardizing variable ( the denominator) should be to the
same claimholders in the firm. In other words, the value of
equity should be divided by equity earnings or equity book
value, and firm value should be divided by firm earnings or
book value.
• 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
measure earnings should be applied consistently across assets.
The same rule applies with book-value based multiples.

6
Descriptive Tests
• What is the average and standard deviation for this multiple, across
the universe (market)?
• What is the median for this multiple?
– The median for this multiple is often a more reliable comparison
point.
• How large are the outliers to the distribution, and how do we deal
with the 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 large positive numbers), this can lead to a biased estimate.
• Are there cases where the multiple cannot be estimated? Will
ignoring these cases lead to a biased estimate of the multiple?
• How has this multiple changed over time?

7

Analytical Tests
•   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 flow
patterns.
– In fact, using a simple discounted cash flow model and basic algebra
should yield the fundamentals that drive a multiple
•   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
g                     ,        g       y
growth rate of firm B, it will generally not trade at twice its PE ratio
– Proposition 3: It is impossible to properly compare firms on a
multiple, if we do not know the nature of the relationship between
fundamentals and the multiple.

8
Application Tests
•   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 a
comparable firm is one which is similar to the one being analyzed in
terms of fundamentals.
– Proposition 4: There is no reason why a firm cannot be compared
with another firm in a very different business, if the two firms have
the same risk, growth and cash flow characteristics.
•   Given the comparable firms, how do we adjust for differences across firms
on the fundamentals?
– Proposition 5: It is impossible to find an exactly identical firm to
the one you are valuing.

9

Price Earnings Ratio: Definition
PE = Market Price per Share / Earnings per Share
•   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.
•   Price:        is usually the current price
is sometimes the average price for the year
•   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

10
PE Ratio: Descriptive Statistics
Distribution of PE Ratios - September 2001

1200

1000

800

Current PE
600                                                                                                                                Trailing PE
Forward PE

400

200

0
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

11

PE: Deciphering the Distribution
Current PE     Trailing PE     Forward PE
Mean                   30.93
30 93           30.33
30 33         21 13
21.13
Standard Error           2.70            2.74          0.73
Median                 15.27           15.20         13.71
Mode                       10               0            14
Standard Devia       157.30           150.65         38.22
Kurtosis             795.82         1615.73         224.85
Skewness               26.28           36.04         12.97
Range               5370.00         7090.50         864.91
Maximum             5370.00         7090.50         865.00
Count                   3387            3021          2737
12
PE Ratio: Understanding the
Fundamentals
model.
basic equity discounted cash flow model
• With the dividend discount model,
DPS1
P0 
r  gn

• Dividing both sides by the earnings per share,
P0          Payout Ratio * (1  g n )
 PE =
EPS 0                r-gn

• If this had been a FCFE Model,
FCFE 1       P0         (FCFE/Earnings) * (1  g n )
P0                      PE =
r  gn      EPS0                 r-g n                 13

PE Ratio and Fundamentals
• Proposition: Other things held equal, higher growth
firms will have higher PE ratios than lower growth
firms.
• Proposition: Other things held equal, higher risk
firms will have lower PE ratios than lower risk firms
• Proposition: Other things held equal, firms with
lower reinvestment needs will have higher PE ratios
than firms with higher reinvestment rates.rates
• Of course, other things are difficult to hold equal since
high growth firms, tend to have risk and high
reinvestment rats.

14
PE and Risk: Effects of Changing Betas on
PE Ratio:
Firm with x% growth for 5 years; 8% thereafter

PE Ratios and Beta: Growth Scenarios

50

45

40

35

30
g=25%
g=20%
25
g=15%
g=8%
20

15

10

5

0
0.75       1.00         1.25          1.50         1.75     2.00
Beta

15

PE: Emerging Markets

35

30

25

20

15

10

5

0
Mexico        Malaysia   Singapore    Taiwan       Hong Kong    Venezuela   Brazil   Argentina   Chile
16
Comparisons across countries
• In July 2000, a market strategist is making
the          t th t B il d Venezuela
th argument that Brazil and V          l
are cheap relative to Chile, because they
have much lower PE ratios. Would you
agree?
Yes
No
• What are some of the factors that may
cause one market’s PE ratios to be lower
17
than another market’s PE?

Correlations and Regression of
PE Ratios
• Correlations
g
– Correlation between PE ratio and long term interest rates = -
0.733
– Correlation between PE ratio and yield spread = 0.706
• 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 for Japan 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.

18
Predicted PE Ratios
Country             Actual PE      Predicted PE Under or Over V
UK                          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
21 1         26.01
26 01     18 88%
-18.88%
Australia                   21.69          19.73       9.96%
Japan                       52.25          46.70     11.89%
United States               25.14          19.81     26.88%
19

An Example with Emerging
Markets: June 2000
Country       PE Ratio   Interest   GDP Real   Country
Rates      Growth     Risk
Argentina          14       18.00%      2.50%      45
Brazil             21       14.00%      4.80%      35
Chile              25       9.50%       5.50%      15
Hong Kong          20       8.00%       6.00%      15
India              17       11.48%      4.20%      25
Indonesia          15       21.00%      4.00%      50
Malaysia           14       5.67%       3.00%      40
Mexico             19       11.50%      5.50%      30
Pakistan           14       19.00%      3.00%      45
Peru               15       18.00%      4.90%      50
Phillipines        15       17.00%      3.80%      45
Singapore          24       6.50%       5.20%       5
South Korea        21       10.00%      4.80%      25
Thailand           21       12.75%      5.50%      25
Turkey             12       25.00%      2.00%      35
Venezuela          20       15.00%      3.50%      45

20
Regression Results
• The regression of PE ratios on these
i bl       id the following
variables provides th f ll i –
PE = 16.16 - 7.94 Interest Rates
+ 154.40 Growth in GDP
- 0.1116 Country Risk
R Squared = 73%

21

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

22
Comparisons of PE across time:
PE Ratio for the S&P 500
PE Ratio: 1960-2000

35.00

30.00

25.00

20.00

15.00

10.00

5.00

0.00
60

62

64

66

68

70

72

74

76

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80

82

84

86

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Is low (high) PE cheap
(expensive)?
• A market strategist argues that stocks are
i d because th PE ratio t d i
over priced b          the      ti today is
too high relative to the average PE ratio
across time. Do you agree?
Yes
No
• If you do not agree, what factors might
explain the higer PE ratio today?

24
E/P Ratios , T.Bond Rates and
Term Structure
16.00%

14.00%
14 00%

12.00%

10.00%

8.00%
Earnings Yield
T.Bond Rate
Bond-Bill
6.00%

4.00%
4 00%

2.00%

0.00%
60

62

64

66

68

70

72

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82

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00
19

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20
-2.00%

25

Comparing PE ratios across firms
Company Name                                    Trailing PE                         Expected Growth                     Standard Dev
Coca-Cola Bottling                              29.18                               9.50%                               20.58%
Molson Inc. Ltd. 'A'                            43.65                               15.50%                              21.88%
Anheuser Busch
Anheuser-Busch                                  24.31
24 31                               11 00%
11.00%                              22 92%
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%
26
A Question
You are reading an equity research report
this   t      d the  l t l i     that
on thi sector, and th analyst claims th t
Andres Wine and Hansen Natural are
under valued because they have low PE
ratios. Would you agree?
Yes
No
• Why or why not?
27

Comparing PE Ratios across a
Sector
Company Name                  PE      Growth
Telecom Corporation of New Zealand ADR
p                                     11.2       0.11
Telecom Argentina Stet - France Telecom SA ADR B    12.5       0.08
Hellenic Telecommunication Organization SA ADR      12.8       0.12
Telecomunicaciones de Chile ADR                     16.6       0.08
Asia Satellite Telecom Holdings ADR                 19.6       0.16
Portugal Telecom SA ADR                             20.8       0.13
Telefonos de Mexico ADR L                           21.1       0.14
Gilat Communications                                22.7       0.31
Deutsche Telekom AG ADR                             24.6       0.11
British Telecommunications PLC ADR                  25.7       0.07
Tele Danmark AS ADR                                   27       0.09
Cable & Wireless PLC ADR                            29.8       0.14
APT Satellite Holdings ADR                            31       0.33
Royal KPN NV ADR                                    35.7       0.13
Telecom Italia SPA ADR                              42.2       0.14
Nippon Telegraph & Telephone ADR                    44.3         0.2
France Telecom SA ADR                               45.2       0.19

28
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

29

Is Telebras under valued?
• Predicted PE = 13.12 + 121.22 (.075) -
13.85       8.35
13 85 (1) = 8 35
• At an actual price to earnings ratio of 8.9,
Telebras is slightly overvalued.

30
Using comparable firms- Pros
and Cons
• The most common approach to estimating the PE ratio for a firm is
g p            p
– 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 being valued and the comparable firms.
• 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 a solution because firms within the same industry can
have very different business 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 fundamentals31
between the firm being valued and this group.

Using the entire crosssection: A
regression approach
• In contrast to the 'comparable firm'
h the information i th entire
approach, th i f       ti in the ti
cross-section of firms can be used to
predict PE ratios.
• The simplest way of summarizing this
information is with a multiple regression,
with the PE ratio as the dependent
variable, and proxies for risk, growth and
payout forming the independent variables.
32
PE versus Growth
120

100

80

60

40

20

0

-20
-20                0          20             40                60           80         100

Expected Growth in EPS: next 5 years

33

PE Ratio: Standard Regression
Model Summary

Std Error of
Model                    R                R Square                Square                 the Estimate
1                             .478   a         .229                    .227                 803.9541
a. Predictors: (Constant), Expected Growth in EPS: next 5 y,
PAYOUT1, Beta

Coefficients      a,b

Standar
Unstandardized                 dized
Coefficients
Coe c e ts                 Coe c e ts
Coefficients
Model                                    B          Std. Error           Beta           t              Sig.
1             (Constant)                13.090            1.164                        11.242             .000
Beta                      -3.392            .908                -.089     -3.737           .000
PAYOUT1                    4.938           1.190                 .098      4.150           .000
Expected Growth
.880              .040              .527     22.115            .000
in EPS: next 5 y
a. Dependent Variable: Current PE
b. Weighted Least Squares Regression - Weighted by Market Cap

34
Second Thoughts?
• Based on this regression, estimate the PE ratio for a firm
with no growth, no payout and no risk.

• Is there a problem with your prediction?

35

PE Regression- No Intercept
Model Summary

a
Model               R                    q
R Square                q
Square               the Estimate
1                       .912   b           .832                   .832               833.0224
a. For regression through the origin (the no-intercept
model), R Square measures the proportion of the
variability in the dependent variable about the origin
explained by regression. This CANNOT be compared to R
Square for models which include an intercept.
b. Predictors: Expected Growth in EPS: next 5 y, PAYOUT1,
Beta

Coefficients        a,b,c

Standar
Unstandardized                   dized
Coefficients                 Coefficients
Model                                      B           Std. Error               Beta            t         Sig.
1        Beta                              4.389              .609                 .188         7.212        .000
PAYOUT1                           13.299                .962              .189        13.823       .000
Expected Growth
1.014                .039              .608        25.786       .000
in EPS: next 5 y
a. Dependent Variable: Current PE
b. Linear Regression through the Origin
c. Weighted Least Squares Regression - Weighted by Market Cap

36
Problems with the regression
methodology
• The basic regression assumes a linear relationship
between PE ratios and the financial proxies, and that
might not be appropriate.
• The basic relationship between PE ratios and financial
variables itself might not be stable, and if it shifts from
year to year, the predictions from the model may not be
reliable.
• The independent variables are correlated with each
other. For example, high growth firms tend to have high
risk. This multi-collinearity makes the coefficients of the
regressions unreliable and may explain the large
changes in these coefficients from period to period.
37

The Multicollinearity Problem
Correlations

Expected
Growth in EPS:
Current PE            next 5 y          Beta       Payout Ratio
Current PE              Pearson Correlation             1.000                    .342 **      .130 **         .009
Sig. (2-tailed)                           .              .000         .000            .594
N                                 3303                  2085         3027            3290
Expected Growth         Pearson Correlation                .342 **             1.000          .397 **        -.078 **
in EPS: next 5 y        Sig. (2-tailed)                    .000                        .      .000            .000
N                                 2085                  2675         2393            2143
Beta                    Pearson Correlation                .130 **               .397 **     1.000           -.213 **
Sig (2-tailed)
Sig.                                000
.000                  .000
000                .         000
.000
N                                 3027                  2393         4534            3114
Payout Ratio            Pearson Correlation                .009                -.078 **      -.213 **       1.000
Sig. (2-tailed)                    .594                 .000          .000                   .
N                                 3290                 2143          3114            3388
**. Correlation is significant at the 0.01 level (2-tailed).

38
Using the PE ratio regression
• Assume that you were given the following information for Dell. The
firm has an expected growth rate of 10%, a beta of 1.40 and pays no
dividends. Based upon the regression, estimate the predicted PE
ratio for Dell.
Predicted PE =
(Work with absolute values in regression - 10 for 10% etc.)

• Dell is actually trading at 18 times earnings. What does the
predicted PE tell you?

39

Investment Strategies that
compare PE to the expected
•
growth rate
If we assume that all firms within a sector have similar
growth rates and risk, a strategy of picking the lowest PE
ratio stock in each sector will yield undervalued stocks.
• Portfolio managers and analysts sometimes compare PE
ratios to the expected 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 a measure of relative value.

40
Problems with comparing PE
ratios to expected growth
• In its simple form, there is no basis for believing that a
firm is undervalued just because it has a PE ratio less
than expected growth.
• This relationship may be consistent with a fairly valued
or even an overvalued firm, if interest rates are high, or if
a firm is high risk.
• As interest rate decrease (increase), fewer (more) stocks
approach.
will emerge as undervalued using this approach

41

PE Ratio versus Growth - The Effect of Interest rates:
Average Risk firm with 25% growth for 5 years; 8% thereafter

Figure 14.2: PE Ratios and T.Bond Rates

45

40

35

30

25

20

15

10

5

0
5%      6%          7%           8%            9%   10%
T.Bond Rate

42
PEG Ratio: Definition
•   The PEG ratio is the ratio of price earnings to expected growth in earnings
per share.
PEG = PE / Expected Growth Rate in Earnings
•   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 growth
t      ti t ?
rate estimate?
• No double counting: If the estimate of growth in earnings per share
is from the current 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
ratio consistent with the growth rate estimate? (US analysts use the

PEG Ratio: Distribution
400

300

200

100

Std Dev = 1 05
Std. D    1.05
Mean = 1.55

0                                  N = 2084.00

Price/ Expected Growth RAte
44
PEG Ratios: The Beverage Sector
Company Name              Trailing PE   Growth   Std Dev   PEG
Coca-Cola Bottling        29.18         9.50%    20.58%    3.07
Molson Inc. Ltd. 'A'      43.65         15.50%   21.88%    2.82
Anheuser-Busch            24.31         11.00%   22.92%    2.21
Corby Distilleries Ltd.
y                     16.24         7.50%    23.66%    2.16
Chalone Wine Group Ltd.     21.76       14.00%   24.08%    1.55
Andres Wines Ltd. 'A'     8.96          3.50%    24.70%    2.56
Todhunter Int'l           8.94          3.00%    25.74%    2.98
Brown-Forman 'B'          10.07         11.50%   29.43%    0.88
Coors (Adolph) 'B'        23.02         10.00%   29.52%    2.30
PepsiCo, Inc.             33.00         10.50%   31.35%    3.14
Coca-Cola                 44.33         19.00%   35.51%    2.33
A
Boston Beer 'A'           10.59         17.13%   39.58%    0.62
Whitman Corp.             25.19         11.50%   44.26%    2.19
Mondavi (Robert) 'A'      16.47         14.00%   45.84%    1.18
Coca-Cola Enterprises        37.14      27.00%   51.34%    1.38
Hansen Natural Corp          9.70       17.00%   62.45%    0.57

Average                   22.66         0.13     0.33      2.00
45

Numbers
• The average PEG ratio for the beverage
t i 2.00. The lowest PEG ratio i th
sector is 2 00 Th l      t        ti in the
group belongs to Hansen Natural, which
has a PEG ratio of 0.57. Using this
measure of value, Hansen Natural is
the most under valued stock in the group
the most over valued stock in the group
• What other explanation could there be for
Hansen’s low PEG ratio?
46
PEG Ratios and Fundamentals
• Risk and payout, which affect PE ratios,
ti    to ff t        ti         ll
continue t affect PEG ratios as well.
– Implication: When comparing PEG ratios
across companies, we are making implicit or
• Dividing PE by expected growth does not
neutralize the effects of expected growth,
since the relationship between growth and
value is not linear and fairly complex (even
in a 2-stage model)                        47

PEG Ratios and Risk
PEG Ratios and Beta: Different Growth Rates

3

2.5

2

g =25%
g=20%
1.5
g=15%
g=8%

1

0.5

0
0.75     1.00            1.25           1.50             1.75   2.00
Beta

48
PEG Ratios and Quality of
Growth
PEG Ratios and Retention Ratios

1.4

1.2

1

0.8

PEG

0.6

0.4

0.2

0
1                  0.8                0.6                 0.4               0.2          0
Retention Ratio

49

PE Ratios and Expected Growth
PEG Ratios, Expected Growth and Interest Rates

2.50

2.00

1.50
r=6%
r=8%
r=10%

1.00

0.50

0.00
5%       10%      15%           20%       25%        30%             35%   40%         45%   50%
Expected Growth Rate

50
PEG Ratios and Fundamentals:
Propositions
• Proposition 1: High risk companies will trade at much lower PEG
ratios 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
• Proposition 2: Companies that can attain growth more efficiently by
investing less in better return projects will have higher PEG ratios
than companies 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.
• Proposition 3: Companies with very low or very high growth rates
will tend 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.
51

PE, PEG Ratios and Risk
45                                            2.5

40

2
35

30

1.5
25
PE
PEG Ratio
20
1

15

10
0.5

5

0                                            0
Lowest   2       3       4     Highest

52
PEG Ratio: Returning to the Beverage Sector
Company Name                   Trailing PE   Growth   Std Dev   PEG
Coca-Cola Bottling             29.18         9.50%    20.58%    3.07
Molson Inc. Ltd. 'A'           43.65         15.50%   21.88%    2.82
Anheuser-Busch                 24.31         11.00%   22.92%    2.21
Corby Distilleries Ltd.        16.24         7.50%    23.66%    2.16
Chalone Wine Group Ltd  Ltd.    21.76
21 76        14 00%
14.00%   24 08%
24.08%    1 55
1.55
Andres Wines Ltd. 'A'          8.96          3.50%    24.70%    2.56
Todhunter Int'l                8.94          3.00%    25.74%    2.98
Brown-Forman 'B'               10.07         11.50%   29.43%    0.88
Coors (Adolph) 'B'             23.02         10.00%   29.52%    2.30
PepsiCo, Inc.                  33.00         10.50%   31.35%    3.14
Coca-Cola                      44.33         19.00%   35.51%    2.33
Boston Beer 'A'                10.59         17.13%   39.58%    0.62
Corp.
Whitman Corp                   25.19
25 19         11.50%
11 50%   44.26%
44 26%    2 19
2.19
Mondavi (Robert) 'A'           16.47         14.00%   45.84%    1.18
Coca-Cola Enterprises          37.14         27.00%   51.34%    1.38
Hansen Natural Corp            9.70          17.00%   62.45%    0.57

Average                        22.66         0.13     0.33      2.00
53

Analyzing PE/Growth
• Given that the PEG ratio is still determined by the expected growth
rates, risk and cash flow patterns, it is necessary that we control for
differences in these variables.
• 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%
• In other words,
– PEG ratios will be lower for high growth companies
– PEG ratios will be lower for high risk companies
• We also ran the regression using the deviation of the actual growth
rate from the industry-average growth rate as the independent
variable, with mixed results.
54
Estimating the PEG Ratio for
Hansen
• Applying this regression to Hansen, the predicted PEG ratio for the
firm can be estimated using Hansen’s measures for the independent
variables:
– Expected Growth Rate = 17.00%
– Standard Deviation in Stock Prices = 62.45%
• Plugging in,
Expected PEG Ratio for Hansen = 3.61 - 2.86 (.17) - 3.75 (.6245)
= 0.78
0 57               undervalued,
• With its actual PEG ratio of 0.57, Hansen looks undervalued
notwithstanding its high risk.

55

Extending the Comparables
• This analysis, which is restricted to firms in
the ft             t        b        d dt
th software sector, can be expanded to
include all firms in the firm, as long as we
control for differences in risk, growth and
payout.
• To look at the cross sectional relationship,
we first plotted PEG ratios against
expected growth rates.

56
A Variant on PEG Ratio: The PEGY ratio

• The PEG ratio is biased against low growth firms
because the relationship between value and growth is
non-linear. One variant that has been devised to
consolidate the growth rate and the expected dividend
yield:
PEGY = PE / (Expected Growth Rate + Dividend Yield)
• As an example, Con Ed has a PE ratio of 16, an
expected growth rate of 5% in earnings and a dividend
yield of 4.5%.
– PEG = 16/ 5 = 3.2
– PEGY = 16/(5+4.5) = 1.7
57

Relative PE: Definition
• The relative PE ratio of a firm is the ratio of the PE of the
firm to the PE of the market.
Relative PE = PE of Firm / PE of Market
• While the PE can be defined in terms of current
earnings, trailing earnings or forward earnings,
consistency requires that it be estimated using the same
measure of earnings for both the firm and the market.
time. Thus,
• Relative PE ratios are usually compared over time Thus
a firm or sector 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.

58
Relative PE and Relative Risk
Relative PE and Relative Risk: Stable Beta Scenarios

4.5

4

3.5

3

2.5
Beta stays at current level
Beta drops to 1 in stable phase
2

15
1.5

1

0.5

0
0.25   0.5     0.75      1      1.25      1.5     1.75         2

59

Relative PE: Summary of
Determinants
• The relative PE ratio of a firm is determined by two variables. In
particular, 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 growth rate, with much greater changes
when the market growth rate is higher. In other words, a firm or
sector with a growth rate twice that of the market will have a
much higher relative PE when the market growth rate is 10%
than when it is 5%.
– decrease as the f firm’s risk relative to the market increases. The
extent of the decrease depends upon how long the firm is
expected to stay at this level of relative risk. If the different is
permanent, the effect is much greater.
• Relative PE ratios seem to be unaffected by the level of rates,
which might give them a decided advantage over PE ratios.               60
Relative PE Ratios: The Auto
Sector
Relative PE Ratios: Auto Stocks

1.20

1.00

0.80

Ford
0.60                                                                           Chrysler
GM

0.40
0 40

0.20

0.00
1993   1994   1995         1996        1997        1998   1999   2000

61

Relative PEs: Why do they
change?
• Historically, GM has traded at the highest
l ti         ti f the three auto
relative PE ratio of th th       t
companies, and Chrysler has traded at the
lowest. In the last two or three years, this
historical relationship has been upended
with Ford and Chrysler now trading at the
higher ratios than GM. Analyst projections
for earnings growth at the three
companies are about the same. How
would you explain the shift?                 62
Value/Earnings and
Value/Cashflow Ratios
•  While Price earnings ratios look at the market value of equity relative to
earnings to equity investors, Value earnings ratios look at the market value
f th fi      l ti to         ti
of the firm relative t operating earnings. V l t cash fl
i     Value to              ti     dif
h flow ratios modify
the earnings number to make it a cash flow number.
• The form of value to cash flow ratios that has the closest parallels in DCF
valuation 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
• Consistency Tests:
used
– 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 in the numerator. If only long term debt is considered, only long
term interest should be added back.

63

Value/FCFF Distribution
800

600

400

200

Std.      21.77
Std Dev = 21 77
Mean = 20.6
0                               N = 3063.00

Enterprise Value/FCFF

64
Alternatives to FCFF - EBIT and
EBITDA
• Most analysts find FCFF to complex or messy to use in multiples
(partly because capital expenditures and working capital have to be
estimated). They use modified versions of the multiple with the
following 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
operating income, where any non-operating expenses and
income is removed from the EBIT
– EBITDA, which is earnings before interest, taxes, depreciation
and amortization.

65

Reasons for Increased Use of
Value/EBITDA
1. The multiple can be computed even for firms that are reporting net losses,
since earnings before interest, taxes and depreciation are usually positive.
2. For firms in certain industries, such as cellular, which require a substantial
investment in infrastructure and long gestation periods, this multiple seems
to be more appropriate than the price/earnings ratio.
3. In leveraged buyouts, where the key factor is cash generated by the firm
prior to all discretionary expenditures, the EBITDA is the measure of cash
flows from operations that can be used to support debt payment at least in
the short term.
4. By looking at cashflows prior to capital expenditures, it may provide a better
estimate of “optimal value”, especially if the capital expenditures are unwise
or earn substandard returns.
5. By looking at the value of the firm and cashflows to the firm it allows for
comparisons across firms with different financial leverage.

66
Value/EBITDA Multiple
•   The Classic Definition

Value   Market Value of Equity + Market Value of Debt

EBITDA   Earnings before Interest, Taxes and Depreciation
•   The No-Cash Version

Enterprise Value Market Value of Equity + Market Value of Debt - Cash

EBITDA          Earnings before Interest, Taxes and Depreciation

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

67

The Determinants of Value/EBITDA
• Firm value can be written as:
FCFF1
V0 =
WACC - g
• The numerator can be written as follows:
FCFF    = EBIT (1-t) - (Cex - Depr) -  Working Capital
= (EBITDA - Depr) (1-t) - (Cex - Depr) -  Working
Capital
= EBITDA ( ) + Depr ( ) - C -  Working C
(1-t)         (t) Cex            Capital

68
From Firm Value to EBITDA
Multiples
• Now the Value of the firm can be rewritten
as,

EBITDA (1 - t) + Depr (t) - Cex -  Working Capital
Value =
WACC - g

f
• Dividing both sides of the equation by
EBITDA,
Value    (1- t)    Depr (t)/EBITDA   CEx/EBITDA    Working Capital/EBITDA
=          +                 -            -
EBITDA   WACC - g      WACC -g         WACC - g            WACC - g
69

A Simple Example
• Consider a firm with the following
h    t i ti
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.
70
Calculating Value/EBITDA
Multiple
• In this case, the Value/EBITDA multiple for
this fi       b    ti t d    follows:
thi firm can be estimated as f ll

Value       (1 - .36)               (0.2)(.36)                          0.3          0
=                     +                                 -              -           = 8.24
EBITDA       .10 - .05                .10 - .05                       .10 - .05   .10 - .05

71

Value/EBITDA Multiple:
Trucking Companies
Company Name             Value         EBITDA       Value/EBITDA
KLLM Trans. Svcs.           \$      114.32    \$     48.81         2.34
Ryder System                \$   5,158.04     \$ 1,838.26          2.81
Rollins Truck Leasing       \$   1,368.35     \$    447.67         3.06
Cannon Express Inc.         \$       83.57    \$     27.05         3.09
Hunt (J.B.)                 \$      982.67    \$    310.22         3.17
Yellow Corp.                \$      931.47    \$    292.82         3.18
Roadway Express             \$      554.96    \$    169.38         3.28
Marten Transport Ltd.       \$      116.93    \$     35.62         3.28
Kenan Transport Co.         \$       67.66    \$     19.44         3.48
M.S. Carriers               \$      344.93    \$     97.85         3.53
Old Dominion Freight        \$      170.42    \$     45.13         3.78
Trimac Ltd                  \$      661.18    \$    174.28         3.79
Matlack Systems             \$      112.42    \$     28.94         3.88
XTRA Corp.                  \$   1,708.57     \$    427.30         4.00
Covenant Transport Inc      \$      259.16    \$     64.35         4.03
Builders Transport          \$      221.09    \$     51.44         4.30
Werner Enterprises          \$      844.39    \$    196.15         4.30
Landstar Sys.               \$      422.79    \$     95.20         4.44
AMERCO                      \$   1,632.30     \$    345.78         4.72
USA Truck                   \$      141.77    \$     29.93         4.74
Frozen Food Express         \$      164.17    \$     34.10         4.81
Arnold Inds.                \$      472.27    \$     96.88         4.87
Greyhound Lines Inc.        \$      437.71    \$     89.61         4.88
USFreightways               \$      983.86    \$    198.91         4.95
Golden Eagle Group Inc.     \$       12.50    \$       2.33        5.37
Arkansas Best               \$      578.78    \$    107.15         5.40
Airlease Ltd.               \$       73.64    \$     13.48         5.46
Celadon Group               \$      182.30    \$     32.72         5.57
Amer. Freightways           \$      716.15    \$    120.94         5.92
Transfinancial Holdings     \$       56 92
56.92    \$       8 79
8.79        6 47
6.47
Vitran Corp. 'A'            \$      140.68    \$     21.51         6.54
Interpool Inc.              \$   1,002.20     \$    151.18         6.63
Intrenet Inc.               \$       70.23    \$     10.38         6.77
Swift Transportation        \$      835.58    \$    121.34         6.89
Landair Services            \$      212.95    \$     30.38         7.01
CNF Transportation          \$   2,700.69     \$    366.99         7.36
Budget Group Inc            \$   1,247.30     \$    166.71         7.48
Caliber System              \$   2,514.99     \$    333.13         7.55
Knight Transportation Inc   \$      269.01    \$     28.20         9.54
Heartland Express           \$      727.50    \$     64.62        11.26
Greyhound CDA Transn Corp   \$       83.25    \$       6.99       11.91
Mark VII                    \$      160.45    \$     12.96        12.38
Coach USA Inc               \$      678.38    \$     51.76        13.11
US 1 Inds Inc.              \$         5.60   \$     (0.17)         NA
Average                                                         5.61

72
A Test on EBITDA
• Ryder System looks very cheap on a
Value/EBITDA        lti l basis, l ti to
V l /EBITDA multiple b i relative t
the rest of the sector. What explanation
(other than misvaluation) might there be
for this difference?

73

Analyzing the Value/EBITDA
Multiple
• While low value/EBITDA multiples may be a symptom of
undervaluation, 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 the trucking 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 the sector?
– Does the firm face a much higher tax rate than other firms in the
sector?

74
Value/EBITDA Multiples: Market
• The multiple of value to EBITDA varies widely across firms in the
market, 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 needed to keep the business going and create
growth
– how high or low the cost of capital is (higher costs of capital will
– how high or low expected growth is in the sector (high growth
sectors will tend to have higher Value/EBITDA multiples)

75

Price-Book Value Ratio:
Definition
• The price/book value ratio is the ratio of the market value of equity to
the book value of equity, i.e., the measure of shareholders’ equity in
the balance sheet.
• Price/Book Value = Market Value of Equity
Book Value of Equity
• 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 be used in the denominator.
– If there is more that one class of common stock outstanding, the
market values of all classes (even the non-traded classes) needs
to be factored in.

76
Price to Book Value: Distribution
1000

800

600

400

200
Std. Dev = 2.36
Mean = 2.39
0                                                      N = 4866.00

PBV Ratio

77

Price Book Value Ratio: Stable
Growth Firm
• Going back to a simple dividend discount model,

DPS1
P0 
r  gn
• Defining the return on equity (ROE) = EPS0 / Book Value of Equity,
the value of equity can be written as:

BV 0 * ROE * Payout Ratio * (1  gn )
P0 
r-gn

P0          ROE * Payout Ratio * (1  g n )
 PBV =
BV 0                    r-g        n

• If the return on equity is based upon expected earnings in the next
time period, this can be simplified to,
P0          ROE * Payout Ratio
 PBV =
BV 0                r-g    n

78
Price Book Value Ratio: Stable
Growth Firm
Another Presentation
•  This formulation can be simplified even further by relating growth to
the return on equity:
g = (1 - Payout ratio) * ROE
• Substituting back into the P/BV equation,
P0             ROE - gn
 PBV =
BV 0                 r-g      n

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

79

PBV/ROE: Oil Companies
Company 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
1 45   13.41%
13 41%
USX-Marathon Group                    MRO    1.59     13.42%
Lakehead Pipe Line                    LHP    1.72     13.28%
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
2 64   17 92%
17.92%
Chevron Corp.             CHV         3.03   15.69%
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%         80
Average                               2.30   12.23%
PBV versus ROE regression
• Regressing PBV ratios against ROE for oil
i    i ld the following
companies yields th f ll i regression:  i
PBV = 1.04 + 10.24 (ROE)        R2 = 49%
• For every 1% increase in ROE, the PBV
ratio should increase by 0.1024.

81

Valuing Pemex
• Assume that you have been asked to
l             f th M i
value a PEMEX for the Mexican
Government; All you know is that it has
earned a return on equity of 10% last year.
The appropriate P/BV ratio can be
estimated
P/BV Ratio (based upon regression) = 1.04
+ 10.24 * 0.1 = 2.06

82
Looking for undervalued
securities - PBV Ratios and
•
ROE
Given the relationship between price-book value ratios
and returns on equity, it is not surprising to see firms
which have high returns on equity selling for well above
book value and firms which have low returns on equity
selling at or below book value.
• The firms which should draw attention from investors are
those which provide 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.

83

The Valuation Matrix
MV/BV

Overvalued
Low ROE              High ROE
High MV/BV           High MV/BV

ROE-r

Undervalued
Low ROE                High ROE
Low MV/BV              Low MV/BV

84
Value/Book Value Ratio:
Definition
•   While the price to book ratio is a equity multiple, both the market value and
the book value can be stated in terms of the firm.
•   Value/Book Value = Market Value of Equity + Market Value of Debt
Book Value of Equity + Book Value of Debt

85

Price Sales Ratio: Definition
• The price/sales ratio is the ratio of the market value of
equity to the sales.
• Price/ Sales=      Market Value of Equity
Total Revenues
• Consistency Tests
– The price/sales ratio is internally inconsistent, since
the market value of equity is divided by the total
revenues of the firm.

86
PS Ratios: The Inconsistency
Test
• Assume that you are comparing
i / l       ti          firms i a sector,
price/sales ratios across fi    in      t
and that there are differences in financial
leverage across firms. What type of firms
will emerge with the lowest price/sales
ratios?
Low Leverage Firms
Average Leverage Firms
High Leverage Firms
87

Price/Sales Ratio: Cross
Sectional Distribution
1400

1200

1000

800

600

400

Std. Dev = 2.55
200
Mean = 1.87
0                  N = 4634.00

PS RATIO

88
Price Sales Ratios and Profit
Margins
• The key determinant of price-sales ratios is the profit
margin.
• 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 lower price-sales ratios.
E     t d     th t      Retention ti
Expected growth rate = R t ti ratio * R t             Equity
Return on E it
= Retention Ratio *(Net Profit / Sales) * ( Sales / BV of Equity)
= Retention Ratio * Profit Margin * Sales/BV of Equity

89

Effect of Margin Changes
Price/Sales Ratios and Net Margins

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0
2%      4%         6%          8%                10%   12%   14%   16%
Net Margin

90
PS/Margins: Greek Retailers
Company           PS           Net Margin
SPAKIANAKIS 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
1.71         5 04%
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%
91

Regression Results: PS Ratios
and Margins
• Regressing PS ratios against net margins,
PS = -.10 + 36 29 (N t M i )
10 36.29 (Net Margin)        R2 = 78%
• Thus, a 1% increase in the margin results in an
increase of 0.36 in the price sales ratios.
• The regression also allows us to get predicted
PS ratios for these firms

92
Predicted PS Ratios
Symbol        Company     PS                Predicted PS Under or Over V
SFA           SPAKIANAKIS            0.25            0.94    73.28%
-73.28%
KOTSV         KOTSOVOLOS             0.48            0.59   -18.47%
SANYO         SANYO HELLA            1.12            1.74   -35.37%
IKONA         IMAGE-SOV2V            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 N            1 71
1.71            1.73
1 73     -1 38%
-1.38%
GOODY         GOODY'S                2.24            2.36     -5.01%
HDF           HELLENIC DUT           5.60            6.97   -19.72%
ASCO          AS COMPANY             7.02            2.89   143.07%
FOLLI         FOLLX-FOLLXE          10.82           10.45      3.51%

93

Current versus Predicted
Margins
• One of the limitations of the analysis we did in these last few pages
is the focus on current margins. Stocks are priced based upon
expected margins rather than current margins.
• For most firms, current margins and predicted margins are highly
correlated, making the analysis still relevant.
• For firms where current margins have little or no correlation with
expected margins, regressions of price to sales ratios against
current margins (or price to book against current return on equity)
will not provide much explanatory power.
• In these cases, it makes more sense to run the regression using
either predicted margins or some proxy for predicted margins.

94
A Case Study: The Internet
Stocks
30

PKSI

LCOS                                 SPYG
20
INTM                                                           MMXI
SCNT

MQST                                         FFIV     ATHM
A
CNET                                                DCLK
d
j                                        RAMP
INTW
P   10                                                                 CSGP                    CBIS           NTPA
S          NETO                                                                                    SONE
APNT                                          CLKS               PCLN
PSIX
EDGR                                           ATHY         AMZN
SPLN                  BIDS
ALOY                                ACOM EGRP
BIZZ                             IIXL
ITRA              ANET
ONEM      FATB                             ABTL           INFO                         TMNT GEEK
RMII
GSVI                            ROWE

-0.8                    -0.6                  -0.4                   -0.2

95

PS Ratios and Margins are not
highly correlated
• Regressing PS ratios against current margins yields the following
PS = 81.36        - 7.54(Net Margin)
(        g )            R2 = 0.04
(0.49)
• This is not surprising. These firms are priced based upon expected
margins, rather than current margins.

96
Solution 1: Use proxies for survival and
growth: Amazon in early 2000
• Hypothesizing that firms with higher revenue growth and higher cash
balances should have a greater chance of surviving and becoming
profitable, we ran the following regression: (The level of revenues
was used 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.

97

Solution 2: Use forward
multiples
• You can always estimate price (or value) as a multiple of revenues,
earnings or book value in a future year. These multiples are called
multiples.
forward multiples
• For young and evolving firms, the values of fundamentals in future
years may provide a much better picture of the true value potential
of the 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 the average of this multiple in conjunction with your
firm’s      i                  to ti t the l           f
fi ’ earnings or revenues t estimate th value of your firm    fi
today.
– Estimate value as a multiple of current revenues or earnings for
more mature firms in the group and apply this multiple to the
forward earnings or revenues to the forward earnings for your
firm. This will yield the expected value for your firm in the forward
year and will have to be discounted back to the present to get 98
current value.
An Example of Forward
Multiples: Amazon in early 2000
•   Amazon.com lost \$0.63 per share in 2000 but is expected to earn \$ 1.50 per
share in 2005. At its current price of \$ 49 per share, this would translate into
32.67.
a price/future earnings per share of 32 67
•   In the first approach, this multiple of earnings can be compared to the
price/future earnings ratios of comparable firms. If you define comparable
firms to be e-tailers, Amazon looks reasonably attractive since the average
price/future earnings per share of e-tailers is 65. If, on the other hand, you
compared Amazon’s price to future earnings per share to the average price
to future 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 to a conclusion that Amazon is over valued.
•                    approach,
In the second approach the current price to earnings ratio for specialty
retailers, which is estimated to be 20.31 to the earnings per share of
Amazon in 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 of equity 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.
99

PS Regression
Model Summary

Model              R               R Square        Square      the Estimate
1                      .851   a         .723            .723        88.1869
a. Predictors: (Constant), Beta, MARGIN, PAYOUT, Expected
Growth in EPS: next 5 y
Coefficients a,b,c

Standar
Unstandardized                            dized
Coefficients                          Coefficients
Model                                 B                Std. Error                Beta                 t       Sig.
1       Expected Growth
4.392E-02                          .005               .199             9.210      .000
in EPS: next 5 y
PAYOUT                            .807                    .115               .087             7.007      .000
MARGIN                     23.747                         .466               .876           50.955       .000
Beta                         -.607                        .085              -.187           -7.110       .000
a. Dependent Variable: PS RATIO
b. Linear Regression through the Origin
c. Weighted Least Squares Regression - Weighted by Market Cap

100
Value/Sales Ratio: Definition
•   The value/sales ratio is the ratio of the market value of the firm to the sales.
•   Value/ Sales= Market Value of Equity + Market Value of Debt-Cas
Total Revenues

101

Value/Sales Ratio: Cross
Sectional Distribution
1400

1200

1000

800

600

400

Std.      2.48
Std Dev = 2 48
200
Mean = 2.01
0                               N = 4644.00

EV/SALES

102
Valuation
• You have been hired to value Coca Cola for an analyst
reports and you have valued the firm at 6.10 times
revenues, using the model described in the last few
pages. Another analyst is arguing that there should be a
name. Do you agree?
 Yes
 No
• Explain.

103

The value of a brand name
• One of the critiques of traditional valuation is that it fails to consider
the value of brand names and other intangibles.
• The approaches used by analysts to value brand names are often
ad-hoc and may significantly overstate or understate their value.
• One of the benefits of having a well-known and respected brand
name is that firms can charge higher prices for the same products,
leading to higher profit margins and hence to higher price-sales
ratios and firm value. The larger the price premium that a firm can
charge, the greater is the value of the brand name.
• 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                                                              104
Illustration: Valuing a brand
name: Coca Cola
Coca Cola         Generic Cola Company
O      ti    M
AT Operating Margin i   18.56%
18 56%            7.50%
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)
E/(D+E)                 97.65%
97 65%            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
105

Value of Coca Cola’s Brand
Name
• Value of Coke’s Brand Name = ( 6.10 - 0.69)
(\$18 868 million) = \$102 billion
(\$18,868
• Value of Coke as a company = 6.10 (\$18,868)
million) = \$ 115 Billion
• Approximately 88.69% of the value of the
company can be traced to brand name value

106
Choosing Between the Multiples
• As presented in this section, there are dozens of multiples that can
be potentially used to value an individual firm.
• In addition, relative valuation can be relative to a sector (or
comparable firms) or to the entire market (using the regressions, for
instance)
• Since there can be only one final estimate of value, there are three
choices 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
number of different multiples
– Choose one of the multiples and base your valuation on that
multiple

107

Averaging Across Multiples
• This procedure involves valuing a firm using five or six or
more multiples and then taking an average of the
valuations across these multiples.
• This is completely inappropriate since it averages good
estimates with poor ones equally.
• If some of the multiples are “sector based” and some are
“market based”, this will also average across two
valuation.
different ways of thinking about relative valuation

108
Weighted Averaging Across
Multiples
• In this approach, the estimates obtained from using different
multiples are averaged, with weights on each based upon the
precision of each estimate. The more precise estimates are
weighted more and the less precise ones weighted less.
• The precision of each estimate can be estimated fairly simply for
those estimated based upon regressions as follows:
Precision of Estimate = 1 / Standard Error of Estimate
where the standard error of the predicted value is used in the
denominator.
• This approach is more difficult to use when some of the estimates
are subjective and some are based upon more quantitative
techniques.

109

Picking one Multiple
• This is usually the best way to approach this issue. While a range of
values can be obtained from a number of multiples, the “best
estimate” value is obtained using one multiple.
• 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 highest value.
– Use the multiple that has the highest R-squared in the sector
when regressed against fundamentals. Thus, if you have tried
PE, PBV, PS, etc. and run regressions of these multiples against
fundamentals, use the multiple that works best at explaining
differences across firms in that sector.
– Use the multiple that seems to make the most sense for that
sector, given how value is measured and created.
110
Self Serving Multiple Choice
• When a firm is valued using several multiples, some will yield really
high values and some really low ones.
• If there is a significant bias in the valuation towards high or low
values, it is tempting to pick the multiple that best reflects this bias.
Once the multiple that works best is picked, the other multiples can
be abandoned and never brought up.
• This approach, while yielding very biased and often absurd
valuations, may serve other purposes very well.
• As a user of valuations, it is always important to look at the biases of
the entity doing the valuation, and asking some questions:
– What would the value be if a different multiple were used? (You
pick the specific multiple that you want to see tried.)

111

The Statistical Approach
• One of the advantages of running regressions of multiples against
fundamentals across firms in a sector is that you get R-squared
values on the regression (that provide information on how well
fundamentals explain differences across multiples in that sector).
• As a rule, it is dangerous to use multiples where valuation
fundamentals (cash flows, risk and growth) do not explain a
significant portion of the differences across firms in the sector.
• As a caveat, however, it is not necessarily true that the multiple that
has the highest R-squared provides the best estimate of value for
firms in a sector.

112
A More Intuitive Approach
•    As a general rule of thumb, the following table provides a way of picking 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 early
years 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
R t ili                       PS                              l        i i il            firms
If leverage is similar across fi
VS                           If leverage is different

113

Sector or Market Multiples
•    The conventional approach to using multiples is to look at the sector or
comparable firms.
•    Whether sector or market based multiples make the most sense depends
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 will
use sector-based valuation only,
– If you think that markets make mistakes on entire sectors, but is
generally right on the overall market level, you will use only market-
based valuation
•    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 persists
once you correct for sector under or over valuation.
114
A Test
• You have valued Earthlink Networks, an internet service provider,
relative to other internet companies using Price/Sales ratios and find
it to be under valued almost 50% .When you value it relative to the
market, using the market regression, you find it to be overvalued by
almost 50%. How would you reconcile the two findings?
 One of the two valuations must be wrong. A stock cannot be under
and over valued at the same time.
 It is possible that both valuations are right.
What has to be true about valuations in the sector for the second
statement to be true?

115

Reviewing: The Four Steps to
Understanding Multiples
• Define the multiple
– Check for consistency  y
– Make sure that they are estimated uniformally
• 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
• Analyze the multiple
f
– Identify the companion variable that drives the multiple
– Examine the nature of the relationship
• Apply the multiple

116

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