Equity Instruments & Markets: Part II
B40.3331
Relative Valuation and Private
Company Valuation
Aswath Damodaran
1
The Essence of 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
2
Relative valuation is pervasive…

Most valuations on Wall Street are relative valuations.
– Almost 85% of equity research reports are based upon a multiple and
comparables.
– More than 50% of all acquisition valuations are based upon multiples
– Rules of thumb based on multiples are not only common but are often the
basis for final valuation judgments.

While there are more discounted cashflow valuations in consulting and
corporate finance, they are often relative valuations masquerading as
discounted cash flow valuations.
– The objective in many discounted cashflow valuations is to back into a
number that has been obtained by using a multiple.
– The terminal value in a significant number of discounted cashflow
valuations is estimated using a multiple.
3
Why relative valuation?
“If you think I’m crazy, you should see the guy who lives across the hall”
Jerry Seinfeld talking about Kramer in a Seinfeld episode
“ A little inaccuracy sometimes saves tons of explanation”
H.H. Munro
“ If you are going to screw up, make sure that you have lots of company”
Ex-portfolio manager
4
So, you believe only in intrinsic value? Here’s
why you should still care about relative value



Even if you are a true believer in discounted cashflow valuation,
presenting your findings on a relative valuation basis will make it more
likely that your findings/recommendations will reach a receptive
audience.
In some cases, relative valuation can help find weak spots in
discounted cash flow valuations and fix them.
The problem with multiples is not in their use but in their abuse. If we
can find ways to frame multiples right, we should be able to use them
better.
5
Multiples are just standardized estimates of
price…


You can standardize either the equity value of an asset or the value of the asset
itself, which goes in the numerator.
You can standardize by dividing by the
– Earnings of the asset




Price/Earnings Ratio (PE) and variants (PEG and Relative PE)
Value/EBIT
Value/EBITDA
Value/Cash Flow
– Book value of the asset



Price/Book Value(of Equity) (PBV)
Value/ Book Value of Assets
Value/Replacement Cost (Tobin’s Q)
– Revenues generated by the asset


Price/Sales per Share (PS)
Value/Sales
– Asset or Industry Specific Variable (Price/kwh, Price per ton of steel ....)
6
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 more
difficult in practice than it is in theory.
7
Definitional Tests

Is the multiple consistently defined?
– Proposition 1: Both the value (the numerator) and the standardizing
variable ( the denominator) should be to the same claimholders in 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 uniformly 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.
8
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?
9
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 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.
10
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.
11
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 (though some like to use average price over last 6
months or year)
EPS:
– Time variants: EPS in most recent financial year (current), EPS in most recent four
quarters (trailing), EPS expected in next fiscal year or next four quartes (both called
forward) or EPS in some future year
– Primary, diluted or partially diluted
– Before or after extraordinary items
– Measured using different accounting rules (options expensed or not, pension fund
income counted or not…)
12
Looking at the distribution…
PE Ratio Distribution: US firms in January 2005
700
600
500
400
Current PE
Trailing PE
300
Forward PE
200
100
0
0-4
4-8
8-12
12-16
16-20
20-24
24-28 28 - 32
PE Ratio
32-36
36-40
40-50
50-75
75-100
>100
13
PE: Deciphering the Distribution
Mean
Standard Error
Median
Kurtosis
Skewness
Minimum
Maximum
Number of firms
Largest(500)
Smallest(500)
Current PE
48.12
3.69
23.21
1214.98
31.75
1.15
10081.26
4072
58.90
12.65
Trailing PE
42.86
3.39
20.65
1428.36
32.86
1.31
9713
3637
44.72
11.11
Forward PE
28.53
0.98
19.21
157.28
10.85
1.40
1017.00
2402.00
29.31
14.54
14
Comparing PE Ratios: US, Europe, Japan and
Emerging Markets
Median PE
Japan = 23.45
US = 23.21
Europe = 18.79
Em. Mkts = 16.18
PE Distributions: Comparison
18.00%
16.00%
14.00%
% of firms in market
12.00%
10.00%
US
Emerging Markets
8.00%
Europe
Japan
6.00%
4.00%
2.00%
0.00%
0-4
4-8
8-12
12-16
16-20
20-24
24-28 28 - 32
PE Ratio
32-36
36-40
40-50
50-75
75-100
>100
15
PE Ratio: Understanding the Fundamentals


To understand the fundamentals, start with a basic equity discounted
cash flow model.
With the dividend discount model,
P0 


DPS1
r  gn
Dividing both sides by the current earnings per share,
P0
Payout Ratio * (1  g n )
 PE =
EPS0
r-gn
If this had been a FCFE Model,
P0 
FCFE1
r  gn
P0
(FCFE/Earnings) * (1 gn )
 PE =
EPS 0
r-gn
16
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.
Of course, other things are difficult to hold equal since high growth
firms, tend to have risk and high reinvestment rats.
17
Using the Fundamental Model to Estimate PE
For a High Growth Firm

The price-earnings ratio for a high growth firm can also be related to
fundamentals. In the special case of the two-stage dividend discount
model, this relationship can be made explicit fairly simply:
P0 =
 (1+ g) n 
EPS 0 * Payout Ratio *(1+ g) * 1 
 (1+ r) n 
r-g
+
EPS 0 * Payout Ratio
n
*(1+ g) n *(1+ g n )
(r -g n )(1 + r)n
– For a firm that does not pay what it can afford to in dividends, substitute
FCFE/Earnings for the payout ratio.

Dividing both sides by the earnings per share:
 (1 + g)n 

Payout Ratio * (1 + g) * 1 
 (1+ r) n  Payout Ratio n *(1+ g) n * (1 + gn )
P0
=
+
EPS 0
r -g
(r - g n )(1+ r) n
18
Expanding the Model



In this model, the PE ratio for a high growth firm is a function of
growth, risk and payout, exactly the same variables that it was a
function of for the stable growth firm.
The only difference is that these inputs have to be estimated for two
phases - the high growth phase and the stable growth phase.
Expanding to more than two phases, say the three stage model, will
mean that risk, growth and cash flow patterns in each stage.
19
A Simple Example
Assume that you have been asked to estimate the PE ratio for a firm
which 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
Number of years
5 years
Forever after year 5
 Riskfree rate = T.Bond Rate = 6%
 Required rate of return = 6% + 1(5.5%)= 11.5%

 (1.25) 5 
0.2 * (1.25) * 1
5 
5
 (1.115)  0.5 * (1.25) * (1.08)
PE =
+
= 28.75
(.115 - .25)
(.115 - .08) (1.115) 5

20
PE and Growth: Firm grows at x% for 5 years,
8% thereafter
PE Ratios and Expected Growth: Interest Rate Scenarios
180
160
140
PE Ratio
120
r=4%
r=6%
r=8%
r=10%
100
80
60
40
20
0
5%
10%
15%
20%
25%
30%
35%
40%
45%
50%
Expected Grow th Rate
21
PE Ratios and Length of High Growth: 25%
growth for n years; 8% thereafter
22
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
PE Ratio
30
g=25%
g=20%
g=15%
g=8%
25
20
15
10
5
0
0.75
1.00
1.25
1.50
1.75
2.00
Beta
23
PE and Payout
24
I. Assessing Emerging Market PE Ratios Early 2000
PE: Emerging Markets
35
30
25
20
15
10
5
0
Mexico
Malaysia
Singapore
Taiwan
Hong Kong
Venezuela
Brazil
Argentina
Chile
25
Comparisons across countries




In July 2000, a market strategist is making the argument that Brazil
and Venezuela 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 than another market’s PE?
26
II. A Comparison across countries: June 2000
Country
UK
Germany
France
Switzerland
Belgium
Italy
Sweden
Netherlands
Australia
Japan
US
Canada
PE
22.02
26.33
29.04
19.6
14.74
28.23
32.39
21.1
21.69
52.25
25.14
26.14
Dividend Yield
2.59%
1.88%
1.34%
1.42%
2.66%
1.76%
1.11%
2.07%
3.12%
0.71%
1.10%
0.99%
2-yr rate
5.93%
5.06%
5.11%
3.62%
5.15%
5.27%
4.67%
5.10%
6.29%
0.58%
6.05%
5.70%
10-yr rate
5.85%
5.32%
5.48%
3.83%
5.70%
5.70%
5.26%
5.47%
6.25%
1.85%
5.85%
5.77%
10yr - 2yr
-0.08%
0.26%
0.37%
0.21%
0.55%
0.43%
0.59%
0.37%
-0.04%
1.27%
-0.20%
0.07%
27
Correlations and Regression of PE Ratios

Correlations
– 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.
28
Predicted PE Ratios
Country
UK
Germany
France
Switzerland
Belgium
Italy
Sweden
Netherlands
Australia
Japan
United States
Canada
Actual PE
Predicted PE Under or Over Valued
22.02
20.83
5.71%
26.33
25.62
2.76%
29.04
25.98
11.80%
19.6
30.58
-35.90%
14.74
26.71
-44.81%
28.23
25.69
9.89%
32.39
28.63
13.12%
21.1
26.01
-18.88%
21.69
19.73
9.96%
52.25
46.70
11.89%
25.14
19.81
26.88%
26.14
22.39
16.75%
29
III. An Example with Emerging Markets: June
2000
Country
PE Ratio
Argentina
Brazil
Chile
Hong Kong
India
Indonesia
Malaysia
Mexico
Pakistan
Peru
Phillipines
Singapore
South Korea
Thailand
Turkey
Venezuela
14
21
25
20
17
15
14
19
14
15
15
24
21
21
12
20
Interest
Rates
18.00%
14.00%
9.50%
8.00%
11.48%
21.00%
5.67%
11.50%
19.00%
18.00%
17.00%
6.50%
10.00%
12.75%
25.00%
15.00%
GDP Real
Growth
2.50%
4.80%
5.50%
6.00%
4.20%
4.00%
3.00%
5.50%
3.00%
4.90%
3.80%
5.20%
4.80%
5.50%
2.00%
3.50%
Country
Risk
45
35
15
15
25
50
40
30
45
50
45
5
25
25
35
45
30
Regression Results

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%
31
Predicted PE Ratios
Country
PE Ratio
Argentina
Brazil
Chile
Hong Kong
India
Indonesia
Malaysia
Mexico
Pakistan
Peru
Phillipines
Singapore
South Korea
Thailand
Turkey
Venezuela
14
21
25
20
17
15
14
19
14
15
15
24
21
21
12
20
Interest
Rates
18.00%
14.00%
9.50%
8.00%
11.48%
21.00%
5.67%
11.50%
19.00%
18.00%
17.00%
6.50%
10.00%
12.75%
25.00%
15.00%
GDP Real
Growth
2.50%
4.80%
5.50%
6.00%
4.20%
4.00%
3.00%
5.50%
3.00%
4.90%
3.80%
5.20%
4.80%
5.50%
2.00%
3.50%
Country
Risk
45
35
15
15
25
50
40
30
45
50
45
5
25
25
35
45
Predicted PE
13.57
18.55
22.22
23.11
18.94
15.09
15.87
20.39
14.26
16.71
15.65
23.11
19.98
20.85
13.35
15.35
32
IV. Comparisons of PE across time: PE Ratio
for the S&P 500
PE Ratio for S&P 500: 1960-2004
35
30
25
PE Ratio
20
Average over period = 16.82
15
10
5
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
0
33
Is low (high) PE cheap (expensive)?

A market strategist argues that stocks are over priced because the PE
ratio 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 higher PE ratio
today?
34
E/P Ratios , T.Bond Rates and Term Structure
EP Ratios and Interest Rates: S&P 500
16.00%
14.00%
12.00%
10.00%
8.00%
Earnings Yield
T.Bond Rate
Bond-Bill
6.00%
4.00%
2.00%
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
1968
1966
1964
1962
1960
0.00%
-2.00%
Year
35
Regression Results



There is a strong positive relationship between E/P ratios and T.Bond
rates, as evidenced by the correlation of 0.70 between the two
variables.,
In addition, there is evidence that the term structure also affects the PE
ratio.
In the following regression, using 1960-2004 data, we regress E/P
ratios against the level of T.Bond rates and a term structure variable
(T.Bond - T.Bill rate)
E/P = 2.07% + 0.746 T.Bond Rate - 0.323 (T.Bond Rate-T.Bill Rate)
(2.31)
(6.51)
(-1.28)
R squared = 51.11%
36
Estimate the E/P Ratio Today




T. Bond Rate =
T.Bond Rate - T.Bill Rate =
Expected E/P Ratio =
Expected PE Ratio =
37
V. Comparing PE ratios across firms
Company Name
Coca-Cola Bottling
Molson Inc. Ltd. 'A'
Anheuser-Busch
Corby Distilleries Ltd.
Chalone Wine Group Ltd.
Andres Wines Ltd. 'A'
Todhunter Int'l
Brown-Forman 'B'
Coors (Adolph) 'B'
PepsiCo, Inc.
Coca-Cola
Boston Beer 'A'
Whitman Corp.
Mondavi (Robert) 'A'
Coca-Cola Enterprises
Trailing PE
29.18
43.65
24.31
16.24
21.76
8.96
8.94
10.07
23.02
33.00
44.33
10.59
25.19
16.47
37.14
Expected Growth
9.50%
15.50%
11.00%
7.50%
14.00%
3.50%
3.00%
11.50%
10.00%
10.50%
19.00%
17.13%
11.50%
14.00%
27.00%
Standard Dev
20.58%
21.88%
22.92%
23.66%
24.08%
24.70%
25.74%
29.43%
29.52%
31.35%
35.51%
39.58%
44.26%
45.84%
51.34%
Hansen Natural Corp
9.70
17.00%
62.45%
38
A Question
You are reading an equity research report on this sector, and the analyst
claims that Andres Wine and Hansen Natural are under valued because
they have low PE ratios. Would you agree?
 Yes
 No
 Why or why not?
39
VI. Comparing PE Ratios across a Sector
Comp any Name
PT Indosat ADR
Te lebras ADR
Te lecom Corporati on o f New Zeala nd ADR
Te lecom Argenti na Stet - France Telecom SA ADR B
Hell enic Te lecommu nicatio n Organ ization SA ADR
Te lecomun ica cio nes de Ch ile ADR
Swisscom AG ADR
Asia Sa tell ite Telecom Holdi ngs ADR
Portugal Tel eco m SA ADR
Te lefo nos de Me xico ADR L
Mata v RT ADR
Te lstra ADR
Gila t Comm unicati ons
Deutsche Telek om AG ADR
British Tel eco mmun ica tions PL C ADR
Te le Dan mark AS ADR
Te leko muni kasi Ind onesia ADR
Cab le & Wi reless PLC ADR
APT Satel lite Holdi ngs ADR
Te lefo nica SA ADR
Royal KPN NV ADR
Te lecom Italia SPA ADR
Nippon Teleg raph & Tel epho ne ADR
Fra nce Tel eco m SA ADR
Kore a Te lecom ADR
PE
7.8
8.9
11 .2
12 .5
12 .8
16 .6
18 .3
19 .6
20 .8
21 .1
21 .5
21 .7
22 .7
24 .6
25 .7
27
28 .4
29 .8
31
32 .5
35 .7
42 .2
44 .3
45 .2
71 .3
Growth
0.06
0.075
0.11
0.08
0.12
0.08
0.11
0.16
0.13
0.14
0.22
0.12
0.31
0.11
0.07
0.09
0.32
0.14
0.33
0.18
0.13
0.14
0.2
0.19
0.44
40
PE, Growth and Risk
Dependent variable is:
R squared = 66.2%
PE
R squared (adjusted) = 63.1%
Variable
Coefficient SE
t-ratio
Constant
13.1151
3.471
3.78
Growth rate
1.21223
19.27
6.29
Emerging Market
-13.8531
3.606
-3.84
Emerging Market is a dummy: 1 if emerging market
0 if not
prob
0.0010
≤ 0.0001
0.0009
41
Is Telebras under valued?


Predicted PE = 13.12 + 1.2122 (7.5) - 13.85 (1) = 8.35
At an actual price to earnings ratio of 8.9, Telebras is slightly
overvalued.
42
Using comparable firms- Pros and Cons

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 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 fundamentals between the firm
being valued and this group.
43
Using the entire crosssection: A regression
approach


In contrast to the 'comparable firm' approach, the information in the
entire 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.
44
PE versus Growth
300
200
100
Current PE
0
-100
Rsq = 0.1500
-20
0
20
40
60
80
100
Expected Growth in EPS: next 5 years
45
PE Ratio: Standard Regression for US stocks January 2005
Mod el Su mm a ry
Mo de l
1
R
R Sq ua re
.2 3 8
.48 7 a
Adju s te d R
Sq u ar e
.2 3 6
Std . Er ror of t he Es tim ate
14 9 8.8 25 10 65 0 57 86 00 0
a. Pr e d icto r s: ( Co nst a nt ), Pa yo ut Ra tio , 3 - yr Re g re s sion Be t a, Exp e ct ed Gr o wth in EPS:
n e xt 5 ye a rs
Co ef ficien t sa ,b
Un st a nd ard iz ed
Co ef ficie nt s
Mo de l
1
B
1 4. 78 1
Std . Er r or
.97 9
.91 4
.04 0
.22 0
.64 1
- 4 .8 9 2 E- 0 2
.01 5
(Con st ant )
Ex pe c t ed Gro wt h in
EPS: n ext 5 yea r s
3- yr Re g re ss io n Bet a
Payo ut Ra tio
St and a r dize d
C oe ffic ien ts
Be t a
9 5% Co n fide n ce Int e rva l f or
B
Lo wer
Upp er
Bo u n d
Bou n d
1 2. 86 1
1 6. 70 1
t
1 5. 09 9
Sig .
. 00 0
.47 0
2 3. 11 7
. 00 0
. 83 7
.99 2
.00 7
.34 3
. 73 2
- 1. 03 8
1.4 7 7
- .06 2
- 3 .16 5
. 00 2
- . 07 9
- .01 9
a . Dep en d e nt Va riable: Cur r ent PE
b . Weig ht ed Le a s t Squ a re s Regr ess io n - We ig hte d by Mar ke t Ca p
46
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.
47
The Multicollinearity Problem
Co rre lat io ns
Ex pe c te d Gr owt h in
EPS: n e xt 5 ye a r s
3 - yr Re g r es sio n Be t a
Pa you t Ra tio
Pe a rs on Cor re la tion
Exp e c te d
Gr o wth in
EPS: n e x t 5
ye a r s
1
Sig . (2 - ta iled )
3- yr
Reg re s sion
Be ta
Pa yo ut Ra tio
.2 3 8**
- .19 1 **
.
.0 0 0
.00 0
N
25 0 9
25 0 9
2 08 7
Pe a rs on Cor re la tion
.2 3 8**
Sig . (2 - ta iled )
N
Pe a rs on Cor re la tion
1
- .08 4 **
.0 0 0
.
.00 0
25 0 9
70 2 4
3 97 9
- .1 91 **
- .0 84 **
1
Sig . (2 - ta iled )
.0 0 0
.0 0 0
.
N
20 8 7
39 7 9
3 97 9
**. Cor r e lat ion is s ig n ifica nt a t the 0 .0 1 leve l (2 - t a ile d ).
48
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 1.20 and pays no
dividends. Based upon the regression, estimate the predicted PE ratio
for Dell.
Predicted PE =

Dell is actually trading at 22 times earnings. What does the predicted
PE tell you?
49
The value of growth
Time Period
Value of extra 1% of growth
January 2005
0.914
January 2004
0.812
July 2003
1.228
January 2003
2.621
July 2002
0.859
January 2002
1.003
July 2001
1.251
January 2001
1.457
July 2000
1.761
January 2000
2.105
The value of growth is in terms of additional PE…
Equity Risk Premium
3.65%
3.69%
3.88%
4.10%
4.35%
3.62%
3.05%
2.75%
2.20%
2.05%
50
Fundamentals hold in every market: PE ratio
regression for Japan
Mod e l Su m m ary
Mo de l
1
R
R Sq u a re
.57 5
a
.33 0
Adjus t e d R
Sq ua r e
.32 5
Std . Er ro r o f th e
Es t im a te
1 91 9 8.6 0 01 5 6 50 85
a . Pr e d ict or s: ( Con st an t), Est im a te d Gr owt h in e a r nin gs pe r sh a r e,
BETA, Pa yo ut Ra tio
Co e f fic ie n t s a,b
Un s ta n da rd iz e d
Co e ffic ie n ts
Mo de l
1
B
(C on st a nt )
Pa yo ut Ra tio
BETA
Es t im a te d Gr o wth in
ea r n ing s p e r s ha r e
Sta n da r d iz e d
Coe f fic ie nt s
Std . Er r or
- 8.1 10
Be ta
t
4.2 0 7
Sig.
- 1.9 28
.0 5 5
.5 2 8
.0 6 4
.3 4 5
8.2 2 7
.0 0 0
14 .6 05
3.4 1 7
.1 7 7
4.2 7 4
.0 0 0
.7 9 9
.0 8 3
.3 9 9
9.6 5 8
.0 0 0
a . De p en d e nt Va ria ble : PE
b . Weig ht ed Le a s t Squ a re s Re gr e ss io n - We ig hte d by Ma r ke t Ca p ita liz a t io n
51
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.
52
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 will emerge as
undervalued using this approach.
53
PE Ratio versus Growth - The Effect of Interest
rates:
Average Risk firm with 25% growth for 5 years; 8% thereafter
54
PE Ratios Less Than The Expected Growth
Rate

In January 2005,
– 32% of firms had PE ratios lower than the expected 5-year growth rate
– 68% of firms had PE ratios higher than the expected 5-year growth rate

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 in
1981.
55
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
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 ADR EPS)
56
PEG Ratio: Distribution
PEG Ratio: US Companies in January 2005
300
250
200
150
100
50
0
<0.5
0.50.75
0.75-1
1-1.25
1.251.5
1.51.75
1.75-2
2-2.25
2.252.5
2.52.75
2.75-3
3-3.35
3.5-4
4-4.5
4.5-5
5-10
>10
57
PEG Ratios: The Beverage Sector
Company Name
Coca-Cola Bottling
Molson Inc. Ltd. 'A'
Anheuser-Busch
Corby Distilleries Ltd.
Chalone Wine Group Ltd.
Andres Wines Ltd. 'A'
Todhunter Int'l
Brown-Forman 'B'
Coors (Adolph) 'B'
PepsiCo, Inc.
Coca-Cola
Boston Beer 'A'
Whitman Corp.
Mondavi (Robert) 'A'
Coca-Cola Enterprises
Hansen Natural Corp
Average
Trailing PE
29.18
43.65
24.31
16.24
21.76
8.96
8.94
10.07
23.02
33.00
44.33
10.59
25.19
16.47
37.14
9.70
22.66
Growth
9.50%
15.50%
11.00%
7.50%
14.00%
3.50%
3.00%
11.50%
10.00%
10.50%
19.00%
17.13%
11.50%
14.00%
27.00%
17.00%
Std Dev
20.58%
21.88%
22.92%
23.66%
24.08%
24.70%
25.74%
29.43%
29.52%
31.35%
35.51%
39.58%
44.26%
45.84%
51.34%
62.45%
PEG
3.07
2.82
2.21
2.16
1.55
2.56
2.98
0.88
2.30
3.14
2.33
0.62
2.19
1.18
1.38
0.57
0.13
0.33
2.00
58
PEG Ratio: Reading the Numbers




The average PEG ratio for the beverage sector is 2.00. The lowest PEG
ratio 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?
59
PEG Ratio: Analysis

To understand the fundamentals that determine PEG ratios, let us
return again to a 2-stage equity discounted cash flow model
P0 =

 (1+ g) n 
EPS 0 * Payout Ratio *(1+ g) * 1 
 (1+ r) n 
r-g
+
EPS 0 * Payout Ratio
n
*(1+ g) n *(1+ g n )
(r -g n )(1 + r)n
Dividing both sides of the equation by the earnings gives us the
equation for the PE ratio. Dividing it again by the expected growth ‘g’
PEG =
 (1+ g) n 
Payout Ratio *(1 + g) * 1 
 (1 + r) n 
g(r - g)
+
Payout Ratio n * (1+ g) n * (1+ g n )
g(r - gn )(1 + r)n
60
PEG Ratios and Fundamentals

Risk and payout, which affect PE ratios, continue to affect PEG ratios
as well.
– Implication: When comparing PEG ratios across companies, we are
making implicit or explicit assumptions about these variables.

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)
61
A Simple Example
Assume that you have been asked to estimate the PEG ratio for a firm
which 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
 Riskfree rate = T.Bond Rate = 6%
 Required rate of return = 6% + 1(5.5%)= 11.5%
 The PEG ratio for this firm can be estimated as follows:

 (1.25) 5 
0.2 * (1.25) * 1
5 
0.5 * (1.25) 5 * (1.08)
 (1.115) 
PEG =
+
= 115 or 1.15
.25(.115 - .25)
.25(.115 - .08) (1.115) 5

62
PEG Ratios and Risk
63
PEG Ratios and Quality of Growth
64
PE Ratios and Expected Growth
65
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.
66
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
67
PEG Ratio: Returning to the Beverage Sector
Company Name
Coca-Cola Bottling
Molson Inc. Ltd. 'A'
Anheuser-Busch
Corby Distilleries Ltd.
Chalone Wine Group Ltd.
Andres Wines Ltd. 'A'
Todhunter Int'l
Brown-Forman 'B'
Coors (Adolph) 'B'
PepsiCo, Inc.
Coca-Cola
Boston Beer 'A'
Whitman Corp.
Mondavi (Robert) 'A'
Coca-Cola Enterprises
Hansen Natural Corp
Trailing PE
29.18
43.65
24.31
16.24
21.76
8.96
8.94
10.07
23.02
33.00
44.33
10.59
25.19
16.47
37.14
9.70
Growth
9.50%
15.50%
11.00%
7.50%
14.00%
3.50%
3.00%
11.50%
10.00%
10.50%
19.00%
17.13%
11.50%
14.00%
27.00%
17.00%
Std Dev
20.58%
21.88%
22.92%
23.66%
24.08%
24.70%
25.74%
29.43%
29.52%
31.35%
35.51%
39.58%
44.26%
45.84%
51.34%
62.45%
PEG
3.07
2.82
2.21
2.16
1.55
2.56
2.98
0.88
2.30
3.14
2.33
0.62
2.19
1.18
1.38
0.57
Average
22.66
0.13
0.33
2.00
68
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 -.0286 (Expected Growth) - .0375 (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.
69
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 - .0286 (17) - .0375 (62.45)
= 0.78
 With its actual PEG ratio of 0.57, Hansen looks undervalued,
notwithstanding its high risk.

70
Extending the Comparables


This analysis, which is restricted to firms in the 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.
71
PEG versus Growth
100
80
60
40
PEG Ratio
20
0
-20
-20
0
20
40
60
80
100
Expected Growth in EPS: next 5 years
72
Analyzing the Relationship


The relationship in not linear. In fact, the smallest firms seem to have
the highest PEG ratios and PEG ratios become relatively stable at
higher growth rates.
To make the relationship more linear, we converted the expected
growth rates in ln(expected growth rate). The relationship between
PEG ratios and ln(expected growth rate) was then plotted.
73
PEG versus ln(Expected Growth)
100
80
60
40
PEG Ratio
20
0
-20
-1
0
1
2
3
4
5
LNGROWTH
74
PEG Ratio Regression - US stocks
Mod e l Summ a ry
Mo de l
1
R
Ad jus te d R
Squ a r e
R Sq u a re
.55 7
a
.31 1
.31 0
Std . Err or o f t he
Est im a te
2 13 .1 59 6 8 22 4 16 6
a . Pr e d ict or s: ( Con sta n t), ln (Ex pe c te d Growt h), 3 - yr R e gre s s io n Be t a,
Pa you t Ra tio
Co ef ficien t sa ,b
Un st a nd ard iz ed
Co ef ficie nt s
Mo de l
1
B
(Con st ant )
Std . Er r or
Be t a
t
8.5 3 0
.26 0
.73 0
.09 0
.15 4
- 8 .3 3 8 E- 0 4
.00 2
- 2.72 7
.09 2
3- yr Re g re ss io n Bet a
Payo ut Ra tio
St and a r dize d
C oe ffic ien ts
ln (Ex pec t ed Gro wth )
Sig .
9 5% Co n fide n ce Int e rva l f or
B
Lo wer
Upp er
Bo u n d
Bou n d
3 2. 86 4
. 00 0
8. 0 2 1
8 .1 5 4
. 00 0
. 55 4
9.0 3 9
- .00 7
- .36 6
. 71 4
- . 00 5
.00 4
- .57 6
- 29 .57 1
. 00 0
- 2. 90 8
- 2.54 6
.90 6
a . Dep en d e nt Va riable: PEG Ra t io
b . Weig ht ed Le a s t Squ a re s Regr ess io n - We ig hte d by Mar ke t Ca p
75
Applying the PEG ratio regression

Consider Dell again. The stock has an expected growth rate of 10%, a
beta of 1.20 and pays out no dividends. What should its PEG ratio be?

If the stock’s actual PE ratio is 22, what does this analysis tell you
about the stock?
76
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
77
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.
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.
Relative PE ratios are also used when comparing companies across
markets with different PE ratios (Japanese versus US stocks, for
example).
78
Relative PE: Determinants

To analyze the determinants of the relative PE ratios, let us revisit the
discounted cash flow model we developed for the PE ratio. Using the 2-stage
DDM model as our basis (replacing the payout ratio with the FCFE/Earnings
Ratio, if necessary), we get
 (1+ g j )n 

Payout Ratio j *(1 + g j ) * 1 
n
 (1+ rj ) 
Relative PE j =
rj - g j
 (1+ g m ) n 

Payout Ratio m * (1+ g m )* 1 
n
 (1+ rm ) 
rm - gm
where
+
+
Payout Ratio
n
j,n
*(1 + g j ) *(1 + g j,n )
n
(rj - g j,n )(1 + rj )
Payout Ratio
m, n
* (1+ g m )n *(1 + gm, n )
n
(rm - gm, n )(1 + rm )
Payoutj, gj, rj = Payout, growth and risk of the firm
Payoutm, gm, rm = Payout, growth and risk of the market
79
Relative PE: A Simple Example
Consider the following example of a firm growing at twice the rate as
the market, while having the same growth and risk characteristics of
the 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%

80
Estimating Relative PE

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:
PE fi rm
PE market

 (1.20) 5 
0.3 * (1.20) * 1
 (1.115) 5  0.5 * (1.20)5 * (1.06)
=
+
= 15.79
(.115 - .20)
(.115 -.06) (1.115) 5

(1.10)5 
0.3 * (1.10) * 1
 (1.115)5  0.5 * (1.10) 5 *(1.06)
=
+
= 10.45
(.115 - .10)
(.115-.06) (1.115) 5
Relative PE Ratio = 15.79/10.45 = 1.51
81
Relative PE and Relative Growth
82
Relative PE: Another Example
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%

83
Estimating Relative PE

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:
PE fi rm
PE market

 (1.10) 5 
0.3 * (1.10) * 1 
 (1.17) 5  0.5 * (1.10)5 * (1.06)
=
+
= 8.33
(.17 - .10)
(.115- .06) (1.17) 5

(1.10)5 
0.3 * (1.10) * 1
 (1.115)5  0.5 * (1.10) 5 *(1.06)
=
+
= 10.45
(.115 - .10)
(.115-.06) (1.115) 5
Relative PE Ratio = 8.33/10.45 = 0.80
84
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
1.5
1
0.5
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
85
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 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.
86
Relative PE Ratios: The Auto Sector
Relative PE Ratios: Auto Stocks
1.20
1.00
0.80
Ford
Chrysler
GM
0.60
0.40
0.20
0.00
1993
1994
1995
1996
1997
1998
1999
2000
87
Using Relative PE ratios

On a relative PE basis, all of the automobile stocks looked cheap in
2000 because they were trading at their lowest relative PE ratios than
1993. Why might the relative PE ratio be lower in 2000 than in 1993?
88
Relative PE Ratios: US stocks
Mode l Su m m ary
Mo de l
1
R
R Sq u a re
.25 2
.50 2 a
Ad jus t ed R
Sq ua r e
.25 1
St d. Er ro r o f
th e Es t im at e
4 9. 22 83 8
a. Pr ed ict or s: ( Con st an t), 3 - yr Re gr e ss io n Be t a , Relative Gr o wt h
Co e f fici e n ts a,b
Uns t and ar d iz ed
Coef ficie nt s
Mo de l
1
B
. 39 2
Std . Er ro r
.02 5
. 52 2
.02 1
1 . 5 12 E- 0 2
.02 1
(Co n st ant )
Relat ive Gr o wth
3 - yr Reg res sio n Bet a
St a nd ar dize d
Co e fficien ts
Be t a
t
1 5. 84 5
Sig .
. 00 0
.49 7
2 4. 99 4
. 00 0
.01 4
.72 1
. 47 1
a . Depe n d e nt Va riable : Rela tive P E
b . Weig ht ed Le as t Squ a re s Re gre ss ion - We ig hte d by Mar ke t Cap
89
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 of the operating assets of the firm (Enterprise value or EV)
relative to operating earnings or cash flows.
 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:
EV/FCFF =
(Market Value of Equity + Market Value of Debt-Cash)
EBIT (1-t) - (Cap Ex - Deprecn) - Chg in Working Cap

90
Value of Firm/FCFF: Determinants

V =
0
Reverting back to a two-stage FCFF DCF model, we get:
n 

(1 + g)
FCFF (1 + g) 1
0
n
 (1+ WACC) 
–
–
–
–
–
FCFF (1+ g) n (1+ g )
0
n
+
WACC - g
(WACC - g )(1 + WACC)n
n
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 (first
n years)
WACC = Weighted average cost of capital
gn = Expected growth rate in FCFF in stable growth period (after n
years)
91
Value Multiples

Dividing both sides by the FCFF yields,
n

(1
+
g)

(1 + g) 1n
 (1 + WACC) 
V0
(1+ g) n (1+ gn )
=
+
FCFF0
WACC - g
(WACC - gn )(1 + WACC)n

The value/FCFF multiples is a function of
– the cost of capital
– the expected growth
92
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.
93
Value/FCFF Multiples and the Alternatives






Assume that you have computed the value of a firm, using discounted
cash flow models. Rank the following multiples in the order of
magnitude from lowest to highest?
Value/EBIT
Value/EBIT(1-t)
Value/FCFF
Value/EBITDA
What assumption(s) would you need to make for the Value/EBIT(1-t)
ratio to be equal to the Value/FCFF multiple?
94
Illustration: Using Value/FCFF Approaches to
value a firm: MCI Communications





MCI Communications had earnings before interest and taxes of $3356
million in 1994 (Its net income after taxes was $855 million).
It had capital expenditures of $2500 million in 1994 and depreciation
of $1100 million; Working capital increased by $250 million.
It expects free cashflows to the firm to grow 15% a year for the next
five years and 5% a year after that.
The cost of capital is 10.50% for the next five years and 10% after that.
The company faces a tax rate of 36%.
V0
=
FCFF0
5

 (1.15) 
(1.15) 1(1.105)5 
.105 -.15
5
(1.15) (1.05)
= 31.28
+
5
(.10 - .05)(1.105)
95
Multiple Magic

In this case of MCI there is a big difference between the FCFF and
short cut measures. For instance the following table illustrates the
appropriate multiple using short cut measures, and the amount you
would 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
96
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.
97
Enterprise 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
98
Enterprise Value/EBITDA Distribution - US
EV Multiples: US firms in January 2005
800
About 1500 firms trade at less
than 7 times EBITDA
700
600
Number of firms
500
400
EV/EBITDA
EV/EBIT
300
200
100
0
<2
2-4
4-6
6-8
8-10 10-12 12-16 16-20 20-25 25-30 30-35 35-40 40-45 45-50 50-75
75100
>100
EV Multiple
99
Value/EBITDA Multiple: Europe, Japan and
Emerging Markets in January 2005
EV/EBITDA: Market Comparison
25.00%
% of Firms in Market
20.00%
15.00%
US
Emerging Markets
Europe
10.00%
Japan
5.00%
0.00%
<2
2-4
4-6
6-8
8-10
1012
1216
1620- 25-30 30-35 35-40 40-45 45-50 50-75
20
25
EV/EBITDA
75100
>100
100
The Determinants of Value/EBITDA Multiples:
Linkage to DCF Valuation

The value of the operating assets of a firm 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 (1-t) + Depr (t) - Cex -  Working Capital
101
From Firm Value to EBITDA Multiples

Now the Value of the firm can be rewritten as,
Value =

EBITDA (1 - t) + Depr (t) - Cex -  Working Capital
WACC - g
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
102
A Simple Example

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.
103
Calculating Value/EBITDA Multiple

Value
EBITDA
In this case, the Value/EBITDA multiple for this firm can be estimated
as follows:
=
(1- .36)
.10 -.05
+
(0.2)(.36)
0.3
0
= 8.24
.10 -.05
.10 - .05
.10 - .05
104
Value/EBITDA Multiples and Taxes
105
Value/EBITDA and Net Cap Ex
106
Value/EBITDA Multiples and Return on Capital
107
Value/EBITDA Multiple: Trucking Companies
Company Name
KLLM Trans. Svcs.
Ryder System
Rollins Truck Leasing
Cannon Express Inc.
Hunt (J.B.)
Yellow Corp.
Roadway Express
Marten Transport Ltd.
Kenan Transport Co.
M.S. Carriers
Old Dominion Freight
Trimac Ltd
Matlack Systems
XTRA Corp.
Covenant Transport Inc
Builders Transport
Werner Enterprises
Landstar Sys.
AMERCO
USA Truck
Frozen Food Express
Arnold Inds.
Greyhound Lines Inc.
USFreightways
Golden Eagle Group Inc.
Arkansas Best
Airlease Ltd.
Celadon Group
Amer. Freightways
Transfinancial Holdings
Vitran Corp. 'A '
Interpool Inc.
Intrenet Inc.
Swift Transportation
Landair Services
CNF Transportation
Budget Group Inc
Caliber System
Knight Transportation Inc
Heartland Express
Greyhound CDA Transn Corp
Mark VII
Coach USA Inc
US 1 Inds Inc.
Average
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
Value
114.32
5,158.04
1,368.35
83.57
982.67
931.47
554.96
116.93
67.66
344.93
170.42
661.18
112.42
1,708.57
259.16
221.09
844.39
422.79
1,632.30
141.77
164.17
472.27
437.71
983.86
12.50
578.78
73.64
182.30
716.15
56.92
140.68
1,002.20
70.23
835.58
212.95
2,700.69
1,247.30
2,514.99
269.01
727.50
83.25
160.45
678.38
5.60
EBITDA
$
48.81
$ 1,838.26
$ 447.67
$
27.05
$ 310.22
$ 292.82
$ 169.38
$
35.62
$
19.44
$
97.85
$
45.13
$ 174.28
$
28.94
$ 427.30
$
64.35
$
51.44
$ 196.15
$
95.20
$ 345.78
$
29.93
$
34.10
$
96.88
$
89.61
$ 198.91
$
2.33
$ 107.15
$
13.48
$
32.72
$ 120.94
$
8.79
$
21.51
$ 151.18
$
10.38
$ 121.34
$
30.38
$ 366.99
$ 166.71
$ 333.13
$
28.20
$
64.62
$
6.99
$
12.96
$
51.76
$
(0.17)
Value/EBITDA
2.34
2.81
3.06
3.09
3.17
3.18
3.28
3.28
3.48
3.53
3.78
3.79
3.88
4.00
4.03
4.30
4.30
4.44
4.72
4.74
4.81
4.87
4.88
4.95
5.37
5.40
5.46
5.57
5.92
6.47
6.54
6.63
6.77
6.89
7.01
7.36
7.48
7.55
9.54
11.26
11.91
12.38
13.11
NA
5.61
108
A Test on EBITDA

Ryder System looks very cheap on a Value/EBITDA multiple basis,
relative to the rest of the sector. What explanation (other than
misvaluation) might there be for this difference?
109
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?
110
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 lead to
lower Value/EBITDA multiples)
– how high or low expected growth is in the sector (high growth sectors will
tend to have higher Value/EBITDA multiples)
111
US Market: Cross Sectional Regression
January 2005
Mod el Su mm ary
Mo de l
1
R
Adjus t ed R
Sq ua re
R Sq u are
.61 8
a
.38 2
.38 0
St d. Erro r o f th e
Es t ima te
8 00 .0 39 5 02 10 11 83 0 00
a. Pr ed ict or s: (Con st an t), Ma rk e t De bt t o Ca p it al, Eff Ta x Rat e,
Re in ve st m e nt Ra te , Ex pect ed Gro wt h in Reve n ue s : n e xt 5 ye a rs
Co ef fici ents a,b
Un s tan da rd ize d
Co efficie n ts
Mo de l
1
Stan dar d iz e d
Coe f fic ie nt s
B
8.5 5 4
Std . Er r or
.8 4 3
1.0 1 6
.0 4 5
- .1 50
.0 2 0
Reinves tmen t Ra te
- 1.88 4 E- 02
.0 0 5
Mar ket Deb t t o Cap it al
- 6.64 2 E- 02
.0 1 5
(Co n st ant )
Ex pec t ed Gro wt h in
Reven ue s: ne xt 5 ye ar s
Ef f T ax Rat e
Be ta
9 5 % Con fid en ce In terval fo r
B
Lo wer
Upp er
Bou nd
Bou nd
6.9 0 1
10 .2 07
t
10 .1 52
Sig.
.0 0 0
.5 5 2
22 .6 99
.0 0 0
.9 2 8
1.1 0 4
- .1 64
- 7.5 03
.0 0 0
- .1 90
- .1 11
- .0 79
- 3.5 32
.0 0 0
- .0 29
- .0 08
- .1 08
- 4.4 14
.0 0 0
- .0 96
- .0 37
a . Dep en d e nt Va ria ble: EV/ EBITDA
b . Weig ht ed Le a s t Squ a re s Regr ess ion - We ig hte d by Mar ke t Ca p
112
Europe: Cross Sectional Regression
January 2005
Mod e l Su m m ary
Mo de l
1
R
Adju st e d R
Sq ua re
R Sq ua re
.55 1
a
.3 0 4
St d. Er ro r of th e Estim a t e
.3 0 3
16 1 8 .3 93 59 42 0 0 67 9 00 0
a. Pr e d ic to r s: (Co nst a nt ), Ma rk e t De bt to C ap ita l, Rein ve st m e nt Ra te ,
TAX_RATE
Co e f fic ie n t s a,b
Uns t a nd ar d iz e d
Coe f fic ie nt s
Mo de l
1
(C on st a nt )
TAX_RATE
Re inve s tme n t Ra te
St a nd a r diz e d
C oe ffic ie n ts
B
1 6. 79 7
Std . Er ro r
1.0 6 6
Be t a
t
1 5. 75 5
Sig .
.00 0
- .35 6
.02 7
- .20 7
- 13 .14 7
.00 0
6 .0 93 E- 0 4
.00 1
.01 7
1 .1 06
.26 9
.51 8
.01 7
.49 0
3 1. 22 3
.00 0
Ma r ke t De b t t o Ca p it a l
a . De p en d e nt Va ria ble : EV/ EBITDA
b . Weig ht ed Le a s t Squ a re s Re gr e ss io n - We ig hte d by Mar ke t Ca p ita liz a t io n
113
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.
114
Book Value Multiples: US stocks
Book Value Multiples: US companies in January 2005
800
700
600
500
Price/BV of Equity
400
Value/ BV of Capital
EV/Invested Capital
300
200
100
0
<0.25 0.25- 0.5- 0.75- 1- 1.25- 1.5- 1.75- 2- 2.25- 2.5- 2.75- 3- 3.5-4 4-4.5 4.5-5
0.5 0.75
1
1.25 1.5 1.75
2
2.25 2.5 2.75
3
3.35
5-10
>10
115
Price to Book: Europe, Japan and Emerging
Markets
Price to Book Equity: Market Comparison
18.00%
16.00%
14.00%
% of Firms in Market
12.00%
10.00%
US
Emerging Markets
8.00%
Europe
Japan
6.00%
4.00%
2.00%
0.00%
<0.25 0.25- 0.5- 0.75- 1- 1.25- 1.5- 1.75- 2- 2.25- 2.5- 2.75- 3- 3.5-4 4-4.5 4.5-5 5-10
0.5 0.75
1 1.25 1.5 1.75
2
2.25 2.5 2.75
3 3.35
P/BV
>10
116
Price Book Value Ratio: Stable Growth Firm

Going back to a simple dividend discount model,
P0 

DPS1
r  gn
Defining the return on equity (ROE) = EPS0 / Book Value of Equity, the value
of equity can be written as:
P0 
BV0 * ROE * Payout Ratio * (1  gn )
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
117
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 =
BV0
r-gn

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.
118
Price Book Value Ratio for High Growth Firm

The Price-book ratio for a high-growth firm can be estimated
beginning with a 2-stage discounted cash flow model:
 (1+ g)n 

EPS 0 * Payout Ratio * (1 + g) * 1 
 (1+ r) n  EPS 0 * Payout Ratio n * (1+ g)n *(1+ g n )
P0 =
+
r -g
(r - g n )(1+ r) n

Dividing both sides of the equation by the book value of equity:
n



(1+ g) 

ROE * Payout Ratio *(1+ g) * 1 

 (1+ r) n 
P0
ROE n * Payout Ratio n *(1+ g) n *(1+ g n ) 
= 
+

BV0
r-g
(r - gn )(1 + r)n




where
ROE = Return on Equity in high-growth period
ROEn = Return on Equity in stable growth period
119
PBV Ratio for High Growth Firm: Example
Assume that you have been asked to estimate the PBV ratio for a firm
which has the following characteristics:
High Growth Phase Stable Growth Phase
Length of Period
5 years
Forever after year 5
Return on Equity
25%
15%
Payout Ratio
20%
60%
Growth Rate
.80*.25=.20
.4*.15=.06
Beta
1.25
1.00
Cost of Equity
12.875%
11.50%
The riskfree rate is 6% and the risk premium used is 5.5%.

120
Estimating Price/Book Value Ratio

The price/book value ratio for this firm is:

0.25 * 0.2 * (1.20) *

PBV = 
(.12875 

5

1  (1.20) 
 (1.12875) 5 
.20)

5
0.15 * 0.6 * (1.20) * (1.06) 
+
= 2.66
(.115 - .06) (1.12875) 5 


121
PBV and ROE: The Key
PBV and ROE: Risk Scenarios
4
3.5
Price/Book Value Ratios
3
2.5
Beta=0.5
Beta=1
Beta=1.5
2
1.5
1
0.5
0
10%
15%
20%
25%
30%
ROE
122
PBV/ROE: European Banks
Bank
Banca di Roma SpA
Commerzbank AG
Bayerische Hypo und Vereinsbank AG
Intesa Bci SpA
Natexis Banques Populaires
Almanij NV Algemene Mij voor Nijver
Credit Industriel et Commercial
Credit Lyonnais SA
BNL Banca Nazionale del Lavoro SpA
Banca Monte dei Paschi di Siena SpA
Deutsche Bank AG
Skandinaviska Enskilda Banken
Nordea Bank AB
DNB Holding ASA
ForeningsSparbanken AB
Danske Bank AS
Credit Suisse Group
KBC Bankverzekeringsholding
Societe Generale
Santander Central Hispano SA
National Bank of Greece SA
San Paolo IMI SpA
BNP Paribas
Svenska Handelsbanken AB
UBS AG
Banco Bilbao Vizcaya Argentaria SA
ABN Amro Holding NV
UniCredito Italiano SpA
Rolo Banca 1473 SpA
Dexia
Average
Symbol
BAHQE
COHSO
BAXWW
BAEWF
NABQE
ALPK
CIECM
CREV
BAEXC
MOGG
DEMX
SKHS
NORDEA
DNHLD
FOLG
DANKAS
CRGAL
KBCBA
SODI
BAZAB
NAGT
SAOEL
BNPRB
SVKE
UBQH
BBFUG
ABTS
UNCZA
ROGMBA
DECCT
PBV
0.60
0.74
0.82
1.12
1.12
1.17
1.20
1.20
1.22
1.34
1.36
1.39
1.40
1.42
1.61
1.66
1.68
1.69
1.73
1.83
1.87
1.88
2.00
2.12
2.15
2.18
2.21
2.25
2.37
2.76
1.60
ROE
4.15%
5.49%
5.39%
7.81%
7.38%
8.78%
9.46%
6.86%
12.43%
10.86%
17.33%
16.33%
13.69%
16.78%
18.69%
19.09%
14.34%
30.85%
17.55%
11.01%
26.19%
16.57%
18.68%
21.82%
16.64%
22.94%
24.21%
15.90%
16.67%
14.99%
14.96%
123
PBV versus ROE regression


Regressing PBV ratios against ROE for banks yields the following
regression:
PBV = 0.81 + 5.32 (ROE) R2 = 46%
For every 1% increase in ROE, the PBV ratio should increase by
0.0532.
124
Under and Over Valued Banks?
Bank
Banca di Roma SpA
Commerzbank AG
Bayerische Hypo und Vereinsbank AG
Intesa Bci SpA
Natexis Banques Populaires
Almanij NV Algemene Mij voor Nijver
Credit Industriel et Commercial
Credit Lyonnais SA
BNL Banca Nazionale del Lavoro SpA
Banca Monte dei Paschi di Siena SpA
Deutsche Bank AG
Skandinaviska Enskilda Banken
Nordea Bank AB
DNB Holding ASA
ForeningsSparbanken AB
Danske Bank AS
Credit Suisse Group
KBC Bankverzekeringsholding
Societe Generale
Santander Central Hispano SA
National Bank of Greece SA
San Paolo IMI SpA
BNP Paribas
Svenska Handelsbanken AB
UBS AG
Banco Bilbao Vizcaya Argentaria SA
ABN Amro Holding NV
UniCredito Italiano SpA
Rolo Banca 1473 SpA
Dexia
Actual
0.60
0.74
0.82
1.12
1.12
1.17
1.20
1.20
1.22
1.34
1.36
1.39
1.40
1.42
1.61
1.66
1.68
1.69
1.73
1.83
1.87
1.88
2.00
2.12
2.15
2.18
2.21
2.25
2.37
2.76
Predicted
1.03
1.10
1.09
1.22
1.20
1.27
1.31
1.17
1.47
1.39
1.73
1.68
1.54
1.70
1.80
1.82
1.57
2.45
1.74
1.39
2.20
1.69
1.80
1.97
1.69
2.03
2.10
1.65
1.69
1.61
Under or Over
-41.33%
-32.86%
-24.92%
-8.51%
-6.30%
-7.82%
-8.30%
2.61%
-16.71%
-3.38%
-21.40%
-17.32%
-9.02%
-16.72%
-10.66%
-9.01%
7.20%
-30.89%
-0.42%
31.37%
-15.06%
11.15%
11.07%
7.70%
27.17%
7.66%
5.23%
36.23%
39.74%
72.04%
125
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.
126
The Valuation Matrix
MV/BV
Overvalued
Low ROE
High MV/BV
High ROE
High MV/BV
ROE-r
Low ROE
Low MV/BV
Undervalued
High ROE
Low MV/BV
127
Price to Book vs ROE: Largest Market Cap
Firms in the United States: January 2005
18
DELL
EBAY
16
BUD
EDP
14
YHOO
12
UNH
10
D
PG
8
KO
ERICY
6
M DT
BA
DOW
IBM WYE
M RK
AMGN
FNM
4
PBV Ratio
UL
GSK
NSANY
2
TWX
VIA/B
PBR
FRE
RD
0
0
20
40
60
80
Return on Equity
128
PBV Matrix: Telecom Companies
129
PBV, ROE and Risk: Large Cap US firms
20
DELL
BUD
EBAY
EDP
YHOO
UL
PBV Ratio 10
PG
ORCL
D
ERICY
100
COP VIA/B
80
60
40
Return on Equity
20
0
0
20
40
60
80 100
120
3-yr Standard Deviation (Stock Price)
130
IBM: The Rise and Fall and Rise Again
10.00
50.00%
9.00
40.00%
8.00
30.00%
7.00
20.00%
10.00%
5.00
0.00%
Retu rn on Equity
Price to Book
6.00
4.00
-10.00%
3.00
-20.00%
2.00
-30.00%
1.00
0.00
-40.00%
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Year
PBV
ROE
131
PBV Ratio Regression: US
January 2005
Mod e l Su mm ar y
Mo de l
1
Adjus t ed R
Sq uar e
. 82 6
a
R
.90 9 b
R Sq u a re
.82 6
Std . Er r or o f th e
Es t im a te
2 01 .8 89 1 2 64 3 13 0 00 0
a. Fo r r e gr e ss io n th ro ug h t he o rig in (t he n o- in ter cep t mo de l), R Sq u a re
m ea su re s the pr op or t ion o f t he va r iab ility in th e d ep e nd e n t va ria ble
a b ou t th e o rigin e x pla ine d b y reg r e ss ion . This CANNOT b e c o mpa r ed t o
R Sq uare fo r m o dels wh ich inc lud e an in te rce p t.
b . Pr edict or s: Re tu rn on Eq uit y, Exp ec te d Gr o wth in EPS: n ext 5 ye ars ,
Payo ut Ra tio , 3 - yr R eg re ss ion Be t a
Co e f fic ie n t s a ,b ,c
Un s t a nd a rd iz e d
Co ef fic ie nt s
Mo de l
1
B
Ex pe c t ed G ro wt h in
EPS: n e xt 5 yea r s
3- yr Re g r e ss io n Bet a
Pa yo ut Ra ti o
St a nd a r diz e d
C oe ffi c ie n t s
St d . Er r or
Be t a
9 5% Co n fi de n ce Int e rva l f or
B
t
Sig .
Lo wer
Bo u n d
U pp e r
Bou n d
9 .8 3 5E- 0 2
.00 5
.31 0
2 1. 12 0
.00 0
.0 8 9
. 10 7
- .2 9 7
.07 8
- .05 8
- 3 . 80 0
.00 0
- .4 5 0
- . 14 4
- 1 .3 4 9 E- 0 2
.00 2
- .09 7
- 7 . 43 8
.00 0
- .0 1 7
- . 01 0
.2 0 2
.00 3
.80 0
5 8. 31 7
.00 0
.1 9 6
. 20 9
Re tu r n o n Eq uit y
a . D e p en d e nt Va ria ble : PBV Ra t io
b . Line a r Re g r e ss io n t hr ou gh th e Origin
c . We igh te d Le a st Squ ar e s R eg re ss io n - We ig h te d by Ma r ke t Ca p
132
PBV Ratio Regression- Europe
January 2005
Mode l Su m m ary
Mo de l
1
R
Ad jus t ed R
Sq ua r e
.24 5
R Sq u a re
.24 6
.49 6a
St d. Er ro r o f
th e Es t im at e
19 7 .91 6
a . Pr e d ict or s: ( Con st an t), Re tu rn o n Equ ity, BETA, Pa you t Rat io
Co ef ficie n t s a ,b
Uns ta n dar d ize d
C oe fficien ts
Mo de l
1
(Co n st ant )
B
2 .1 49
St d. Er ro r
.3 0 1
- .4 64
.1 7 5
1 .5 46 E- 03
.1 1 1
BETA
Payo ut Ra tio
Stan da rd ized
Co efficie nt s
Retu rn o n Equ ity
Be ta
t
Sig.
7. 1 3 4
.0 0 0
- .0 59
- 2. 6 51
.0 0 8
.0 0 3
.0 1 4
.6 09
.5 4 3
.0 0 5
.4 9 3
22 . 2 73
.0 0 0
a . De pe n d e nt Va ria ble : PBV Ra t io
b . Weig ht ed Lea s t Squ a re s Re gr ess ion - We ig hted by Mar ke t Ca p it a liz atio n
133
PBV Regression: Emerging Markets
January 2005
Mod e l Su m m ary
Mo de l
1
R
.52 5 a
R Sq u a re
.27 6
Ad jus t ed R
Sq ua r e
.27 2
St d. Er ro r o f
th e Es t im at e
2.5 2 5
a . Pr e d ict or s: ( Con st an t), ROE, Pa you t Ra tio , IBES Es t 5 ye a r
g ro wth , BETA
Co e f fic ie n t s a
Un st a nd a rd iz e d
Co ef fic ie nt s
Mo de l
1
(C on st a nt )
IBES Es t 5 yea r g ro wth
BETA
Pa yo ut Ra tio
ROE
St a nd a r diz e d
C oe ffic ie n ts
B
1.3 3 7
Std . Er r or
.38 3
2 .2 86 E- 0 2
.00 4
Be t a
t
3.4 9 0
Sig.
.00 1
.16 2
5.2 6 7
.00 0
- .83 9
.33 3
- .07 8
- 2.51 9
.01 2
5 .3 96 E- 0 4
.00 1
.02 3
.76 6
.44 4
.10 9
.00 7
.50 2
1 6. 29 2
.00 0
a. De p en d e n t Va ria ble : PBV
134
PBV Ratio: Japan in January 2005
Mod el Su mm a ry
Mo de l
1
R
Adjus t e d R
Sq ua r e
R Sq u a re
.74 4
a
.55 3
Std . Er r or o f t he
Est im a te
.54 9
1 49 4.29 8 0 88 5 2 61 39 0 0
a . Pr e d ict or s: ( Con st an t), ROE, Es tim a t ed Gro wth in e a r n in g s p er s ha r e ,
Pa you t Ra tio, BETA
Co e f fic ie n t s a,b
Un s ta n da rd iz e d
Co e ffic ie n ts
Mo de l
1
B
(C on st a nt )
Pa yo ut Ra tio
BETA
Es t im a te d Gr o wth in
ea r n ing s p e r s ha r e
ROE
Sta n da r d iz e d
Coe f fic ie nt s
Std . Er r or
- 6 .19 4 E- 02
.3 3 5
8.6 5 5E- 04
.0 0 5
- .6 49
Be ta
t
Sig.
- .1 85
.8 5 3
.0 0 6
.1 6 1
.8 7 2
.2 9 1
- .0 83
- 2.2 32
.0 2 6
4.7 8 0E- 02
.0 0 7
.2 5 1
7.3 3 0
.0 0 0
.2 1 7
.0 1 1
.7 8 7
19 .4 18
.0 0 0
a . De p en d e nt Va ria ble : PBV
b . Weig ht ed Le a s t Squ a re s Re gr e ss io n - We ig hte d by Ma r ke t Ca p ita liz a t io n
135
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
136
Determinants of Value/Book Ratios

To see the determinants of the value/book ratio, consider the simple
free cash flow to the firm model:
FCFF1
V0 =
WACC - g

Dividing both sides by the book value, we get:

If we replace, FCFF = EBIT(1-t) - (g/ROC) EBIT(1-t),we get
V0
FCFF1 /BV
=
BV
WACC - g
V0
ROC - g
=
BV
WACC - g
137
Value/Book Ratio: An Example

Consider a stable growth firm with the following characteristics:
– Return on Capital = 12%
– Cost of Capital = 10%
– Expected Growth = 5%


The value/BV ratio for this firm can be estimated as follows:
Value/BV = (.12 - .05)/(.10 - .05) = 1.40
The effects of ROC on growth will increase if the firm has a high
growth phase, but the basic determinants will remain unchanged.
138
Value/Book and the Return Spread
139
Value/Book Capital Regression - US - January
2005
Mod e l Su m m ary
Mo de l
1
R
Adju st e d R
Sq ua r e
R Sq uare
.70 8
a
.5 0 1
St d. Er ro r o f th e Est im a te
.4 9 9
15 9 .34 83 4 35 5 3 44 48 00
a. Pr e d ic to r s: ( Co nst a nt ), Re tu rn o n Ca p ita l, Ex pec te d Gr owt h in Reve nu e s: n ex t 5 ye a rs ,
Re in ve st m e n t Ra te, Mar ke t De b t to Ca p ita l
Co e f fici e n ts a,b
Un s ta n da rd iz e d
Co e ffic ie n ts
Mo de l
1
(Co n st a nt )
Sta n da r d iz e d
Coe f fic ie nt s
B
1.8 5 1
Std . Er r or
.1 4 2
Be ta
t
13 .0 47
Sig .
.0 0 0
9 5 % Con fid en c e In te rva l fo r
B
Lo we r
Upp e r
Bou nd
Bou nd
1.5 7 3
2. 1 2 9
Ex pe c t ed Gro wt h in
Re ve n ue s: ne xt 5 ye ar s
Re inve s tm e n t Ra te
.1 4 9
.0 0 8
.3 8 0
17 .5 86
.0 0 0
.1 3 3
.166
- 2.6 0 6 E- 03
.0 0 1
- .0 50
- 2.5 08
.0 1 2
- .0 05
- . 0 01
Ma r ke t De b t t o Ca p it a l
- 4.1 3 9 E- 02
.0 0 3
- .2 97
- 1 2.9 1 5
.0 0 0
- .0 48
- . 0 35
4.0 6 0E- 02
.0 0 3
.2 9 7
14 .0 97
.0 0 0
.0 3 5
.046
Re tu r n o n Ca p it a l
a . De p en d e nt Va ria ble : Va lu e / BV o f Ca p it a l
b . Weig ht ed Le a s t Squ a re s Re gr e ss ion - We ig hte d by Mar ke t Ca p
140
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.
141
Price/Sales Ratio: US stocks
Revenue Multiples: US companies in January 2005
700
600
500
400
Price/Sales
EV/Sales
300
200
100
0
<0.1
0.10.2
0.20.3
0.30.4
0.40.5
0.5- 0.75-1 1-1.25 1.250.75
1.5
1.5- 1.75-2 2-2.5
1.75
2.5-3
3-3.5
3.5-4
4-5
5-10
>10
142
Price to Sales: Europe, Japan and Emerging
Markets
Price to Sales: Market Comparisons
18.00%
16.00%
14.00%
% of Firms in Market
12.00%
10.00%
US
Emerging Markets
8.00%
Europe
Japan
6.00%
4.00%
2.00%
0.00%
<0.1
0.10.2
0.20.3
0.30.4
0.40.5
0.5- 0.75- 1- 1.25- 1.5- 1.75- 2-2.5 2.5-3 3-3.5 3.5-4
0.75
1 1.25 1.5 1.75
2
Price to Sales Ratio
4-5
5-10
>10
143
Price/Sales Ratio: Determinants

The price/sales ratio of a stable growth firm can be estimated
beginning with a 2-stage equity valuation model:
P0 

DPS1
r  gn
Dividing both sides by the sales per share:
P0
Sales 0
 PS =
Net Profit Margin * Payout Ratio *(1 g n )
r-gn
144
Price/Sales Ratio for High Growth Firm

When the growth rate is assumed to be high for a future period, the
dividend discount model can be written as follows:
 (1+ g)n 

EPS 0 * Payout Ratio * (1 + g) * 1 
 (1+ r) n  EPS 0 * Payout Ratio n * (1+ g)n *(1+ g n )
P0 =
+
r -g
(r - g n )(1+ r) n

Dividing both sides by the sales per share:



(1+ g) n 

Net Margin * Payout Ratio * (1+ g) * 1 
n

 (1+ r)n 
P0
Net Margin n * Payout Ratio n * (1+ g) *(1 + gn ) 
=
+

Sales 0 
r -g
(r - gn )(1 + r)n




where Net Marginn = Net Margin in stable growth phase
145
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.
Expected growth rate = Retention ratio * Return on Equity
= Retention Ratio *(Net Profit / Sales) * ( Sales / BV of Equity)
= Retention Ratio * Profit Margin * Sales/BV of Equity
146
Price/Sales Ratio: An Example
Length of Period
Net Margin
Sales/BV of Equity
Beta
Payout Ratio
Expected Growth
Riskless Rate =6%
High Growth Phase
5 years
10%
2.5
1.25
20%
(.1)(2.5)(.8)=20%
Stable Growth
Forever after year 5
6%
2.5
1.00
60%
(.06)(2.5)(.4)=.06
5



(1.20)

0.10 * 0.2 * (1.20) * 1 

 (1.12875)5  0.06 * 0.60 * (1.20) 5 * (1.06) 
PS = 
+
 = 1.06
(.12875 - .20)
(.115 -.06) (1.12875) 5




147
Effect of Margin Changes
Price/Sales Ratios and Net Margins
1.8
1.6
1.4
PS Ratio
1.2
1
0.8
0.6
0.4
0.2
0
2%
4%
6%
8%
10%
12%
14%
16%
Net Margin
148
PS/Margins: US Retailers - January 2005
10
COH
CTHR
8
6
CHS
BEBE
M RLN
4
NUCO
QGLYCWTR
2
LTD
SGB.TO
PS Ratio
FRDM
0
-2
0
10
20
30
Net Margin
149
Regression Results: PS Ratios and Margins



Regressing PS ratios against net margins,
PS = -.972 + 0.415 (Net Margin) R2 = 86%
Thus, a 1% increase in the margin results in an increase of 0.415 in the
price sales ratios.
The regression also allows us to get predicted PS ratios for these firms
150
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.
151
A Case Study: Internet Stocks in January 2000
30
PKSI
LCOS
20
A
d
j
P
S
INTM
SPYG
MMXI
SCNT
FFIV
MQST
CNET
INTW
RAMP
CSGP
10
NETO
PSIX
EDGR
-0
ABTL
FATB
RMII
-0.8
CLKS
AMZN
ATHY
BIDS
BIZZ
ONEM
CBIS
APNT
SPLN
ATHM
DCLK
ALOY
IIXL
INFO
TURF
-0.6
PPOD
GSVI
-0.4
NTPA
SONEPCLN
ACOM EGRP
ITRA
ANET
TMNT GEEK
ELTX
BUYX
ROWE
-0.2
AdjMargin
152
PS Ratios and Margins are not highly
correlated

Regressing PS ratios against current margins yields the following
PS = 81.36

- 7.54(Net Margin) R2 = 0.04
(0.49)
This is not surprising. These firms are priced based upon expected
margins, rather than current margins.
153
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.
154
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
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 earnings or
revenues to estimate the value of your firm 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 current value.
155
An Example of Forward Multiples: Global
Crossing



Global Crossing lost $1.9 billion in 2001 and is expected to continue to lose
money for the next 3 years. In a discounted cashflow valuation (see notes on
DCF valuation) of Global Crossing, we estimated an expected EBITDA for
Global Crossing in five years of $ 1,371 million.
The average enterprise value/ EBITDA multiple for healthy telecomm firms is
7.2 currently.
Applying this multiple to Global Crossing’s EBITDA in year 5, yields a value
in year 5 of
– Enterprise Value in year 5 = 1371 * 7.2 = $9,871 million
– Enterprise Value today = $ 9,871 million/ 1.1385 = $5,172 million
(The cost of capital for Global Crossing is 13.80%)
– The probability that Global Crossing will not make it as a going concern is 77%
and the distress sale value is only a $ 1 billion (1/2 of book value of assets).
– Adjusted Enterprise value = 5172 * .23 + 1000 (.77) = 1,960 million
156
PS Regression: United States - January 2005
Mo d e l Su mm a ry
Mo de l
1
a
R
R Sq u a re
.74 2
.86 1 b
Adjus t e d R
Sq ua r e
.74 1
Std . Er ror of t he Estim a t e
1.9 4 08 24 3 4 58 2 28 51
a . Fo r r e gr e ss io n th ro ug h t he o rig in (th e n o- in te r c ep t m o d e l) , R Sq u a re m e as u re s th e
p r op or tio n o f th e va ria b ility in t he de pe n d e nt va r ia b le a bo ut th e o rigin e x p la ine d b y
r e g re s sion . This CANNO T b e c o m p a r ed to R Sq ua r e fo r m o de ls wh ic h inclu de a n
in te rc e pt .
b . Pr e dict or s: Ne t Ma r gin, Pa yo ut Ra tio , 3 - yr R eg re ss ion Be t a, Exp ec t e d Gro wth in EPS:
ne x t 5 ye a rs
Co e f fic ie n t s a ,b
Un s t a nd a rd iz e d
Co ef fic ie nt s
Mo de l
1
B
Ex pe c t ed G ro wt h in
EPS: n e xt 5 yea r s
3- yr Re g r e ss io n Bet a
Pa yo ut Ra ti o
St a nd a r diz e d
C oe ffi c ie n t s
St d . Er r or
Be t a
t
Sig .
9 5% Co n fi de n ce Int e rva l f or
B
Lo wer
U pp e r
Bo u n d
Bou n d
5 .1 6 4E- 0 2
.00 4
.26 5
1 4. 50 1
.00 0
.0 4 5
7 .0 5 0E- 0 2
.05 4
.02 3
1.304
.19 2
- .0 3 6
. 17 7
- 6 .8 7 7 E- 0 3
.00 1
- .06 3
- 4 . 73 4
.00 0
- .0 1 0
- . 00 4
.2 1 9
.00 5
.68 3
4 3. 06 6
.00 0
.2 0 9
. 22 9
Ne t Ma r g in
. 05 9
a . D e p en d e nt Va ria ble : PS Ra tio
b . Line a r Re g r e ss io n t hr ou gh th e Origin
157
PS Regression: Emerging Markets in January
2005
Mod e l Su m m ary
Mo de l
1
R
.71 3 a
R Sq u a re
.50 9
Ad jus t ed R
Sq ua r e
.50 6
St d. Er ro r o f
th e Es t im at e
2.2 3 7
a . Pr e d ict or s: ( Con st an t), Ne t Ma rg in , BETA, Pa you t Ra tio , IBES
Es t 5 ye a r gr owt h
Co e f fic ie n t s a
Un st a nd a rd iz e d
Co ef fic ie nt s
Mo de l
1
St a nd a r diz e d
C oe ffic ie n ts
(C on st a nt )
B
5 .3 06 E- 0 2
Std . Er r or
.31 7
IBES Es t 5 yea r g ro wth
2 .3 15 E- 0 2
.00 4
- .30 7
BETA
Pa yo ut Ra tio
Ne t Ma r g in
Be t a
t
.16 8
Sig.
.86 7
.15 2
5.9 8 9
.00 0
.29 2
- .02 7
- 1.05 1
.29 4
6 .7 06 E- 0 4
.00 1
.02 7
1.0 7 7
.28 2
.15 5
.00 5
.71 8
2 8. 45 9
.00 0
a. De p en d e n t Va ria ble : PS
158
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-Cash
Total Revenues
159
Value/Sales Ratios: Analysis of Determinants

If pre-tax operating margins are used, the appropriate value estimate is
that of the firm. In particular, if one makes the assumption that
– Free Cash Flow to the Firm = EBIT (1 - tax rate) (1 - Reinvestment Rate)

Then the Value of the Firm can be written as a function of the after-tax
operating margin= (EBIT (1-t)/Sales
n




(1 + g)
(1 - RIR growth )(1 + g)* 1

n 
n
Value
 (1+ WACC)  (1- RIR stable)(1 + g) *(1+ g n ) 

= After - tax Oper. Margin *
+

Sales 0
WACC - g
(WACC - g n )(1+ WACC) n 




g = Growth rate in after-tax operating income for the first n years
gn = Growth rate in after-tax operating income after n years forever (Stable
growth rate)
RIRGrowth, Stable = Reinvestment rate in high growth and stable periods
WACC = Weighted average cost of capital
160
Value/Sales Ratio: An Example

Consider, for example, the Value/Sales ratio of Coca Cola. The
company had the following characteristics:
After-tax Operating Margin =18.56%
Sales/BV of Capital = 1.67
Return on Capital = 1.67* 18.56% = 31.02%
Reinvestment Rate= 65.00% in high growth; 20% in stable growth;
Expected Growth = 31.02% * 0.65 =20.16% (Stable Growth Rate=6%)
Length of High Growth Period = 10 years
Cost of Equity =12.33%
E/(D+E) = 97.65%
After-tax Cost of Debt = 4.16%
D/(D+E) 2.35%
Cost of Capital= 12.33% (.9765)+4.16% (.0235) =
12.13%
Value of Firm
Sales 0
0


 (1.2016) 10 
(1- .65)(1.2016) * 1

10 
10
 (1.1213)  (1 - .20)(1.2016) * (1.06) 

= .1856 *
+
= 6.10

.1213 - .2016
(.1213 - .06)(1.1213) 10 




161
Value Sales Ratios and Operating Margins
162
Grocery Stores: EV/Sales Ratios and Margins
2.5
TEO.TO
2.0
WFM I
1.5
1.0
SWY
CASYWMKARDNA
RDK
KRABS
SE
AHO
OATS
SMF
FSM PTMK
FRSH M
MARSA
ARSB
VLGEA
GAP
WIN
EV/Sales
.5
0.0
Rsq = 0.6332
0
2
4
6
8
10
12
Pre-tax Operating Margin
163
Brand Name Premiums in 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
premium added on to reflect the value of the brand name. Do you
agree?
Yes
No
Explain.
164
The value of a brand name




One of the critiques of traditional valuation is that is fails to consider
the value of brand names and other intangibles.
The approaches used by analysts to value brand names are often adhoc 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
165
Illustration: Valuing a brand name: Coca Cola
AT Operating Margin
Sales/BV of Capital
ROC
Reinvestment Rate
Expected Growth
Length
Cost of Equity
E/(D+E)
AT Cost of Debt
D/(D+E)
Cost of Capital
Value/Sales Ratio
Coca Cola
18.56%
1.67
31.02%
65.00% (19.35%)
20.16%
10 years
12.33%
97.65%
4.16%
2.35%
12.13%
6.10
Generic Cola Company
7.50%
1.67
12.53%
65.00% (47.90%)
8.15%
10 yea
12.33%
97.65%
4.16%
2.35%
12.13%
0.69
166
Value of Coca Cola’s Brand Name



Value of Coke’s Brand Name= ( 6.10 - 0.69) ($18,868 million)
= $102 billion
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
167
Value/Sales Ratio Regression: US in January
2005
Mo d e l Su m m ary
Mo de l
1
Adjus t ed R
Sq uar e
. 79 8
a
R
R Sq u a re
. 79 9
.89 4 b
St d. Er ro r o f th e
Es tim a te
17 7 .49 55 6 4 22 3 41 12 0
a . Fo r r egr e ss io n th ro ug h t he o rig in (the n o- in te rc ep t m o de l) , R Sq u a re
m ea su re s the pr op or t ion o f t he var iab ility in th e d ep e nd e n t va ria ble
a b ou t th e o rigin e x pla ine d b y r eg r ess ion . This CANNOT b e c o m pa r ed
t o R Sq u a re fo r m od e ls wh ich inc lud e a n in te r ce pt .
b . Pr e dict or s: Ma r ke t De bt to C ap ita l, Re in ve st m en t Ra te, Ex p ec t ed
Gr o wth in Revenu e s: ne xt 5 ye ar s , P re - ta x Op er at ing Ma rg in
Co e f fici e n ts a,b ,c
Un s ta n da rd iz e d
Co e ffic ie n ts
Mo de l
1
B
Ex pe c t ed Gro wt h in
Re ve n ue s: ne xt 5 ye ar s
Re inve s tm e n t Ra te
Pr e - t ax O p e ra tin g
Ma r g in
Ma r ke t De b t t o Ca p it a l
Sta n da r d iz e d
Coe f fic ie nt s
Std . Er r or
Be ta
t
Sig .
9 5 % Con fid en c e In te rva l fo r
B
Lo we r
Upp e r
Bou nd
Bou nd
.1 8 2
.0 0 7
.4 3 9
24 .5 88
.0 0 0
.1 6 8
.197
- 1.2 6 8 E- 03
.0 0 1
- .0 14
- 1.0 67
.2 8 6
- .0 04
.001
8.6 1 2E- 02
.0 0 3
.6 2 0
29 .4 85
.0 0 0
.0 8 0
.092
- 2.5 6 4 E- 02
.0 0 3
- .1 51
- 9.1 09
.0 0 0
- .0 31
- . 0 20
a . De p en d e nt Va ria ble : EV/ Sa le s
b . Lin e a r Re g r e s s io n t hr ou g h the Orig in
c . We igh te d Le a s t Sq u ar e s Re g re ss ion - We ig h te d by Ma r ke t Ca p
168
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 nmber of
different multiples
– Choose one of the multiples and base your valuation on that multiple
169
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 different ways of thinking
about relative valuation.
170
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.
171
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.
172
Self Serving … But all too common




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:
– Why was this multiple chosen?
– What would the value be if a different multiple were used? (You pick the
specific multiple that you want to see tried.)
173
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.
174
A More Intuitive Approach

Managers in every sector tend to focus on specific variables when
analyzing strategy and performance. The multiple used will generally
reflect this focus. Consider three examples.
– In retailing: The focus is usually on same store sales (turnover) and profit
margins. Not surprisingly, the revenue multiple is most common in this
sector.
– In financial services: The emphasis is usually on return on equity. Book
Equity is often viewed as a scarce resource, since capital ratios are based
upon it. Price to book ratios dominate.
– In technology: Growth is usually the dominant theme. PEG ratios were
invented in this sector.
175
Conventional Usage: A Summary

As a general rule of thumb, the following table provides a way of
picking a multiple for a sector
Sector
Cyclical Manufacturing
High Tech, High Growth
Multiple Used
PE, Relative PE
PEG
High Growth/No Earnings
Heavy Infrastructure
PS, VS
VEBITDA
REIT
P/CF
Financial Services
Retailing
PBV
PS
VS
Rationale
Often with normalized earnings
Big differences in growth across
firms
Assume future margins will be good
Firms in sector have losses in early
years and earnings can vary
depending on depreciation method
Generally no cap ex investments
from equity earnings
Book value often marked to market
If leverage is similar across firms
If leverage is different
176
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.
177
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?

178
Reviewing: The Four Steps to Understanding
Multiples

Define the multiple
– Check for consistency
– Make sure that they are estimated uniformly

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
– Identify the companion variable that drives the multiple
– Examine the nature of the relationship

Apply the multiple
179