damodaran valuation

Aswath Damodaran 1

Equity Instruments & Markets: Part IIB40.3331

Relative Valuation and Private CompanyValuation

Aswath Damodaran

Aswath Damodaran 2

The Essence of relative valuation?

In relative valuation, the value of an asset is compared to the values assessedby 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 betweenthe firms that might affect the multiple, to judge whether the asset is under or overvalued

Aswath Damodaran 3

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 asdiscounted cash flow valuations.

• The objective in many discounted cashflow valuations is to back into a number thathas been obtained by using a multiple.

• The terminal value in a significant number of discounted cashflow valuations isestimated using a multiple.

Aswath Damodaran 4

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

Aswath Damodaran 5

So, you believe only in intrinsic value? Here’s why youshould still care about relative value

Even if you are a true believer in discounted cashflow valuation, presentingyour findings on a relative valuation basis will make it more likely that yourfindings/recommendations will reach a receptive audience.

In some cases, relative valuation can help find weak spots in discounted cashflow valuations and fix them.

The problem with multiples is not in their use but in their abuse. If we canfind ways to frame multiples right, we should be able to use them better.

Aswath Damodaran 6

Multiples are just standardized estimates of price…

You can standardize either the equity value of an asset or the value of theasset 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 ....)

Aswath Damodaran 7

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 themultiples 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 anumber 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 inpractice than it is in theory.

Aswath Damodaran 8

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 otherwords, the value of equity should be divided by equity earnings or equity bookvalue, 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.

Aswath Damodaran 9

Descriptive Tests

What is the average and standard deviation for this multiple, across theuniverse (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 theoutliers?

• Throwing out the outliers may seem like an obvious solution, but if the outliers alllie on one side of the distribution (they usually are large positive numbers), thiscan lead to a biased estimate.

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

How has this multiple changed over time?

Aswath Damodaran 10

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 willgenerally not trade at twice its PE ratio

• Proposition 3: It is impossible to properly compare firms on a multiple, if wedo not know the nature of the relationship between fundamentals and themultiple.

Aswath Damodaran 11

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 onewhich is similar to the one being analyzed in terms of fundamentals.

• Proposition 4: There is no reason why a firm cannot be compared withanother 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 onthe fundamentals?

• Proposition 5: It is impossible to find an exactly identical firm to the one youare valuing.

Aswath Damodaran 12

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 insome 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…)

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PE Ratio: Distribution for the US: January 2004

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PE: Deciphering the Distribution

Current PE Trailing PE Forward PE

Mean 41.41 41.53 30.90

Standard Error 2.42 3.64 1.10

Median 20.76 19.39 19.21

Kurtosis 1062.81 700.63 252.62

Skewness 27.78 24.21 12.48

Minimum 0.40 1.22 2.57

Maximum 6841.25 7184.00 1430.00

Count 4032 3492 2281

500th largest 54.50 43.98 31.13

500th smallest 11.31 11.13 14.29

Aswath Damodaran 15

Comparing PE Ratios: US, Europe, Japan and EmergingMarkets Median PE

Japan = 24.74US = 20.76

Em. Mkts = 18.87 Europe = 15.99

Aswath Damodaran 16

PE Ratio: Understanding the Fundamentals

To understand the fundamentals, start with a basic equity discounted cashflow model.

With the dividend discount model,

Dividing both sides by the current earnings per share,

If this had been a FCFE Model,

P0 =DPS1

r ! gn

P0

EPS0

= PE = Payout Ratio * (1 + gn )

r-gn

P0 =FCFE1

r ! gn

!

P0

EPS0

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

r-gn

Aswath Damodaran 17

PE Ratio and Fundamentals

Proposition: Other things held equal, higher growth firms will havehigher PE ratios than lower growth firms.

Proposition: Other things held equal, higher risk firms will have lowerPE ratios than lower risk firms

Proposition: Other things held equal, firms with lower reinvestmentneeds will have higher PE ratios than firms with higher reinvestmentrates.

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

Aswath Damodaran 18

Using the Fundamental Model to Estimate PE For a HighGrowth Firm

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

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

Dividing both sides by the earnings per share:

P0 =

EPS0 * Payout Ratio *(1+ g)* 1 !(1+ g)

n

(1+ r)n

"

# $ %

&

r - g+

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

(r -gn )(1+ r)n

P0

EPS0

=

Payout Ratio * (1 + g) * 1 !(1 + g)n

(1+ r)n

"

# $ %

& '

r - g+

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

(r - gn )(1+ r)n

Aswath Damodaran 19

Expanding the Model

In this model, the PE ratio for a high growth firm is a function of growth, riskand payout, exactly the same variables that it was a function of for the stablegrowth 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 thatrisk, growth and cash flow patterns in each stage.

Aswath Damodaran 20

A Simple Example

Assume that you have been asked to estimate the PE ratio for a firm whichhas the following characteristics:Variable High Growth Phase Stable Growth Phase

Expected Growth Rate 25% 8%Payout Ratio 20% 50%Beta 1.00 1.00Number of years 5 years Forever after year 5 Riskfree rate = T.Bond Rate = 6% Required rate of return = 6% + 1(5.5%)= 11.5%

!

PE =

0.2 * (1.25) * 1"(1.25)

5

(1.115)5

#

$ %

&

' (

(.115 - .25)+

0.5 * (1.25)5* (1.08)

(.115 - .08) (1.115)5

= 28.75

Aswath Damodaran 21

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

PE Ratios and Expected Growth: Interest Rate Scenarios

0

20

40

60

80

100

120

140

160

180

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

Expected Growth Rate

PE

Rati

o r=4%

r=6%

r=8%

r=10%

Aswath Damodaran 22

PE Ratios and Length of High Growth: 25% growth for nyears; 8% thereafter

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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

0

5

10

15

20

25

30

35

40

45

50

0.75 1.00 1.25 1.50 1.75 2.00

Beta

PE

Rati

o g=25%

g=20%

g=15%

g=8%

Aswath Damodaran 24

PE and Payout

Aswath Damodaran 25

I. Assessing Emerging Market PE Ratios - Early 2000

PE: Emerging Markets

0

5

10

15

20

25

30

35

Mexico Malaysia Singapore Taiwan Hong Kong Venezuela Brazil Argentina Chile

Aswath Damodaran 26

Comparisons across countries

In July 2000, a market strategist is making the argument that Brazil andVenezuela are cheap relative to Chile, because they have much lower PEratios. 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?

Aswath Damodaran 27

II. A Comparison across countries: June 2000

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

Aswath Damodaran 28

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 ResultsPE 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) = 46.70At an actual PE ratio of 52.25, Japanese stocks are slightly overvalued.

Aswath Damodaran 29

Predicted PE Ratios

Country Actual PE Predicted PE Under or Over Valued

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 26.01 -18.88%

Australia 21.69 19.73 9.96%

Japan 52.25 46.70 11.89%

United States 25.14 19.81 26.88%

Canada 26.14 22.39 16.75%

Aswath Damodaran 30

III. An Example with Emerging Markets: June 2000

Country PE Ratio Interest Rates

GDP Real Growth

Country 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

Aswath Damodaran 31

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%

Aswath Damodaran 32

Predicted PE Ratios

Country PE Ratio Interest Rates

GDP Real Growth

Country Risk

Predicted PE

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

Aswath Damodaran 33

IV. Comparisons of PE across time: PE Ratio for the S&P500

Aswath Damodaran 34

Is low (high) PE cheap (expensive)?

A market strategist argues that stocks are over priced because the PE ratiotoday 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?

Aswath Damodaran 35

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

Aswath Damodaran 36

Regression Results

There is a strong positive relationship between E/P ratios and T.Bond rates, asevidenced by the correlation of 0.69 between the two variables.,

In addition, there is evidence that the term structure also affects the PE ratio. In the following regression, using 1960-2003 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 = 2.03% + 0.753 T.Bond Rate - 0.355 (T.Bond Rate-T.Bill Rate) (2.19) (6.38) (-1.38)

R squared = 50.85%

Aswath Damodaran 37

Estimate the E/P Ratio Today

T. Bond Rate = T.Bond Rate - T.Bill Rate = Expected E/P Ratio = Expected PE Ratio =

Aswath Damodaran 38

V. Comparing PE ratios across firms

Company Name Trailing PE Expected Growth Standard DevCoca-Cola Bottling 29.18 9.50% 20.58%Molson Inc. Ltd. 'A' 43.65 15.50% 21.88%Anheuser-Busch 24.31 11.00% 22.92%Corby Distiller ies 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 Enterpr ises 37.14 27.00% 51.34%

Hansen Natural Corp 9.70 17.00% 62.45%

Aswath Damodaran 39

A Question

You are reading an equity research report on this sector, and the analyst claimsthat Andres Wine and Hansen Natural are under valued because they havelow PE ratios. Would you agree?

Yes No Why or why not?

Aswath Damodaran 40

VI. Comparing PE Ratios across a Sector

Company Name PE Growth

PT Indosat ADR 7.8 0.06

Telebras ADR 8.9 0.075

Telecom Corporation of New Zealand ADR 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

Swisscom AG ADR 18.3 0.11

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

Matav RT ADR 21.5 0.22

Telstra ADR 21.7 0.12

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

Telekomunikasi Indonesia ADR 28.4 0.32

Cable & Wireless PLC ADR 29.8 0.14

APT Satellite Holdings ADR 31 0.33

Telefonica SA ADR 32.5 0.18

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

Korea Telecom ADR 71.3 0.44

Aswath Damodaran 41

PE, Growth and Risk

Dependent variable is: PE

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

Variable Coefficient SE t-ratio probConstant 13.1151 3.471 3.78 0.0010Growth rate 1.21223 19.27 6.29 ≤ 0.0001Emerging Market -13.8531 3.606 -3.84 0.0009Emerging Market is a dummy: 1 if emerging market

0 if not

Aswath Damodaran 42

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.

Aswath Damodaran 43

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 andrisk 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 thisgroup.

Aswath Damodaran 44

Using the entire crosssection: A regression approach

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

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

Aswath Damodaran 45

PE versus Growth

Current PE vs Expected Growth in EPS

January 2004: US Companies

Expected Growth in EPS: next 5 years

806040200-20

Curr

ent

PE

120

100

80

60

40

20

0

Aswath Damodaran 46

PE Ratio: Standard Regression for US stocks - January 2004

Model Summary

.467a .218 .217 1049.7506205340

Model

1

R R SquareAdjusted R

SquareStd. Error of the

Estimate

Predictor s: (Constant), PAYOUT, Regression Be ta, ExpectedGrowth in EPS: next 5 years

a.

Coeffici entsa,b

9.475 .961 9.862 .000

.814 .046 .375 17.558 .000

6.283 .437 .298 14.375 .000

6.E-02 .014 .092 4.161 .000

(Constant)

Expected G rowth inEPS: next 5 years

Regression Beta

PAYOUT

Model

1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: Current PEa.

Weighted Least Squares Regression - Weighted by Market Capb.

Aswath Damodaran 47

Problems with the regression methodology

The basic regression assumes a linear relationship between PE ratios and thefinancial proxies, and that might not be appropriate.

The basic relationship between PE ratios and financial variables itself mightnot be stable, and if it shifts from year to year, the predictions from the modelmay not be reliable.

The independent variables are correlated with each other. For example, highgrowth firms tend to have high risk. This multi-collinearity makes thecoefficients of the regressions unreliable and may explain the large changes inthese coefficients from period to period.

Aswath Damodaran 48

The Multicollinearity Problem

Correlations

1 .031 -.325**

. .228 .000

1472 1472 1185

.031 1 -.183**

.228 . .000

1472 6933 4187

-.325** -.183** 1

.000 .000 .

1185 4187 4187

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Expected G rowth inRevenues: next 5 year s

Regression Beta

PAYOUT

ExpectedGrowth inRevenues:

next 5 yearsRegression

Beta PAYOUT

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

Aswath Damodaran 49

Using the PE ratio regression

Assume that you were given the following information for Dell. The firm hasan expected growth rate of 10%, a beta of 1.20 and pays no dividends. Basedupon the regression, estimate the predicted PE ratio for Dell.

Predicted PE =

Dell is actually trading at 22 times earnings. What does the predicted PE tellyou?

Aswath Damodaran 50

The value of growth

Time Period Value of extra 1% of growth Equity Risk PremiumJanuary 2004 0.812 3.69%July 2003 1.228 3.88%January 2003 2.621 4.10%July 2002 0.859 4.35%January 2002 1.003 3.62%July 2001 1.251 3.05%January 2001 1.457 2.75%July 2000 1.761 2.20%January 2000 2.105 2.05%The value of growth is in terms of additional PE…

Aswath Damodaran 51

Investment Strategies that compare PE to the expectedgrowth 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 yieldundervalued stocks.

Portfolio managers and analysts sometimes compare PE ratios to the expectedgrowth rate to identify under and overvalued stocks.

• In the simplest form of this approach, firms with PE ratios less than their expectedgrowth rate are viewed as undervalued.

• In its more general form, the ratio of PE ratio to growth is used as a measure ofrelative value.

Aswath Damodaran 52

Problems with comparing PE ratios to expected growth

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

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

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

Aswath Damodaran 53

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

Aswath Damodaran 54

PE Ratios Less Than The Expected Growth Rate

In January 2004,• 33% of firms had PE ratios lower than the expected 5-year growth rate• 67% of firms had PE ratios higher than the expected 5-year growth rate

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.

Aswath Damodaran 55

PEG Ratio: Definition

The PEG ratio is the ratio of price earnings to expected growth in earnings pershare.

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 rateestimate?

– No double counting: If the estimate of growth in earnings per share is from the currentyear, 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 withthe growth rate estimate? (US analysts use the ADR EPS)

Aswath Damodaran 56

PEG Ratio: Distribution

Aswath Damodaran 57

PEG Ratios: The Beverage Sector

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

Average 22.66 0.13 0.33 2.00

Aswath Damodaran 58

PEG Ratio: Reading the Numbers

The average PEG ratio for the beverage sector is 2.00. The lowest PEG ratioin the group belongs to Hansen Natural, which has a PEG ratio of 0.57. Usingthis 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?

Aswath Damodaran 59

PEG Ratio: Analysis

To understand the fundamentals that determine PEG ratios, let us return againto a 2-stage equity discounted cash flow model

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

P0 =

EPS0 * Payout Ratio *(1+ g)* 1 !(1+ g)

n

(1+ r)n

"

# $ %

&

r - g+

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

(r -gn )(1+ r)n

PEG =

Payout Ratio *(1 + g) * 1 !(1+ g)n

(1 + r)n

"

# $ %

&

g(r - g)+

Payout Ration * (1+ g)n

* (1+ gn )

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

Aswath Damodaran 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 andfairly complex (even in a 2-stage model)

Aswath Damodaran 61

A Simple Example

Assume that you have been asked to estimate the PEG ratio for a firm whichhas the following characteristics:

Variable High Growth Phase Stable Growth PhaseExpected 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:

!

PEG =

0.2 * (1.25) * 1"(1.25)

5

(1.115)5

#

$ %

&

' (

.25(.115 - .25)+

0.5 * (1.25)5* (1.08)

.25(.115 - .08) (1.115)5

= 115 or 1.15

Aswath Damodaran 62

PEG Ratios and Risk

Aswath Damodaran 63

PEG Ratios and Quality of Growth

Aswath Damodaran 64

PE Ratios and Expected Growth

Aswath Damodaran 65

PEG Ratios and Fundamentals: Propositions

Proposition 1: High risk companies will trade at much lower PEG ratios thanlow risk companies with the same expected growth rate.

• Corollary 1: The company that looks most under valued on a PEG ratio basis in asector may be the riskiest firm in the sector

Proposition 2: Companies that can attain growth more efficiently by investingless in better return projects will have higher PEG ratios than companies thatgrow at the same rate less efficiently.

• Corollary 2: Companies that look cheap on a PEG ratio basis may be companieswith high reinvestment rates and poor project returns.

Proposition 3: Companies with very low or very high growth rates will tend tohave higher PEG ratios than firms with average growth rates. This bias isworse for low growth stocks.

• Corollary 3: PEG ratios do not neutralize the growth effect.

Aswath Damodaran 66

PE, PEG Ratios and Risk

0

5

10

15

20

25

30

35

40

45

Lowest 2 3 4 Highest

0

0.5

1

1.5

2

2.5

PE

PEG Ratio

Aswath Damodaran 67

PEG Ratio: Returning to the Beverage Sector

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

Average 22.66 0.13 0.33 2.00

Aswath Damodaran 68

Analyzing PE/Growth

Given that the PEG ratio is still determined by the expected growth rates, riskand cash flow patterns, it is necessary that we control for differences in thesevariables.

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 fromthe industry-average growth rate as the independent variable, with mixedresults.

Aswath Damodaran 69

Estimating the PEG Ratio for Hansen

Applying this regression to Hansen, the predicted PEG ratio for the firm canbe 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.

Aswath Damodaran 70

Extending the Comparables

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

To look at the cross sectional relationship, we first plotted PEG ratios againstexpected growth rates.

Aswath Damodaran 71

PEG versus Growth

PEG Ratio vs Expected Growth in EPS


Expected Growth in EPS: next 5 years

100806040200-20

PEG

Rati

o10

8

6

4

2

0

Aswath Damodaran 72

Analyzing the Relationship

The relationship in not linear. In fact, the smallest firms seem to have thehighest PEG ratios and PEG ratios become relatively stable at higher growthrates.

To make the relationship more linear, we converted the expected growth ratesin ln(expected growth rate). The relationship between PEG ratios andln(expected growth rate) was then plotted.

Aswath Damodaran 73

PEG versus ln(Expected Growth)

PEG vs ln (Expected Growth)


ln(Expected Growth Rate)

543210

PEG

Rati

o10

8

6

4

2

0

Aswath Damodaran 74

PEG Ratio Regression - US stocks in January 2004

Model Summary

.492 a .242 .241 91.242648963259

Model

1



Estimate

Predictors: (Constant), LNGROWTH, Regression Beta,PAYOUT

a.

Coef fici entsa,b

4.308 .155 27.774 .000

.539 .038 .293 14.249 .000

6.E-03 .001 .116 5.262 .000

-1.042 .055 -.404 -18.86 .000

(Constant)

Regression Beta

PAYOUT

LNGROWTH

Model

1

B Std. Error

Unstandard izedCoefficients

Beta


t Sig.

Dependent Variable: PEG Ratioa.


Aswath Damodaran 75

Applying the PEG ratio regression

Consider Dell again. The stock has an expected growth rate of 10%, a beta of1.20 and pays out no dividends. What should its PEG ratio be?

If the stock’s actual PE ratio is 23, what does this analysis tell you about thestock?

Aswath Damodaran 76

A Variant on PEG Ratio: The PEGY ratio

The PEG ratio is biased against low growth firms because the relationshipbetween value and growth is non-linear. One variant that has been devised toconsolidate 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

Aswath Damodaran 77

Relative PE: Definition

The relative PE ratio of a firm is the ratio of the PE of the firm to the PE ofthe 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 samemeasure of earnings for both the firm and the market.

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

Relative PE ratios are also used when comparing companies across marketswith different PE ratios (Japanese versus US stocks, for example).

Aswath Damodaran 78

Relative PE: Determinants

To analyze the determinants of the relative PE ratios, let us revisit the discounted cashflow 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

where Payoutj, gj, rj = Payout, growth and risk of the firm Payoutm, gm, rm = Payout, growth and risk of the market

Relative PEj =

Payout Ratioj *(1 + gj) * 1 !(1+ gj)

n

(1+ rj)n

"

# $

%

& '

rj - gj

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

n*(1 + gj,n )

(rj - gj,n )(1 + rj)n

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

(1+ rm )n

"

# $ %

& '

rm - gm

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

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

Aswath Damodaran 79

Relative PE: A Simple Example

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

Firm MarketExpected growth rate 20% 10%Length of Growth Period 5 years 5 yearsPayout Ratio: first 5 yrs 30% 30%Growth Rate after yr 5 6% 6%Payout Ratio after yr 5 50% 50%Beta 1.00 1.00Riskfree Rate = 6%

Aswath Damodaran 80

Estimating Relative PE

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

Relative PE Ratio = 15.79/10.45 = 1.51

PEfirm =

0.3 * (1.20) * 1!(1.20)

5

(1.115)5

"

# $ %

&

(.115 - .20)+

0.5 * (1.20)5 * (1.06)

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

PEmarket =

0.3 * (1.10) * 1!(1.10)

5

(1.115)5

"

# $ %

&

(.115 - .10)+

0.5 * (1.10)5 *(1.06)

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

Aswath Damodaran 81

Relative PE and Relative Growth

Aswath Damodaran 82

Relative PE: Another Example

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

Firm MarketExpected growth rate 10% 10%Length of Growth Period 5 years 5 yearsPayout 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 1.00Beta after year 5 1.00 1.00Riskfree Rate = 6%

Aswath Damodaran 83

Estimating Relative PE

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

Relative PE Ratio = 8.33/10.45 = 0.80

PEfirm =

0.3 * (1.10) * 1 !(1.10)5

(1.17)5

"

# $ %

&

(.17 - .10)+

0.5 * (1.10)5

* (1.06)

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

PEmarket =

0.3 * (1.10) * 1!(1.10)

5

(1.115)5

"

# $ %

&

(.115 - .10)+

0.5 * (1.10)5 *(1.06)

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

Aswath Damodaran 84

Relative PE and Relative Risk

Relative PE and Relative Risk: Stable Beta Scenarios

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.25 0.5 0.75 1 1.25 1.5 1.75 2

Beta stays at current level

Beta drops to 1 in stable phase

Aswath Damodaran 85

Relative PE: Summary of Determinants

The relative PE ratio of a firm is determined by two variables. In particular, itwill

• increase as the firm’s growth rate relative to the market increases. The rate ofchange in the relative PE will itself be a function of the market growth rate, withmuch greater changes when the market growth rate is higher. In other words, afirm or sector with a growth rate twice that of the market will have a much higherrelative 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 thedecrease depends upon how long the firm is expected to stay at this level ofrelative risk. If the different is permanent, the effect is much greater.

Relative PE ratios seem to be unaffected by the level of rates, which mightgive them a decided advantage over PE ratios.

Aswath Damodaran 86

Relative PE Ratios: The Auto Sector

Relative PE Ratios: Auto Stocks

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1993 1994 1995 1996 1997 1998 1999 2000

Ford

Chrysler

GM

Aswath Damodaran 87

Using Relative PE ratios

On a relative PE basis, all of the automobile stocks looked cheap in 2000because they were trading at their lowest relative PE ratios than 1993. Whymight the relative PE ratio be lower in 2000 than in 1993?

Aswath Damodaran 88

Relative PE Ratios: US stocks

Model Summary

.467a .218 .217 41.97324

Model

1


SquareStd. Error ofthe Estimate

Predictors: (Constant), Regression Beta, RELGR,RELPAYOU

a.

Coef fici entsa,b

.379 .038 9.862 .000

4.E-02 .009 .092 4.161 .000

.506 .029 .375 17.558 .000

.251 .017 .298 14.375 .000

(Constant)

RELPAYOU

RELGR

Regression Beta

Model

1

B Std. Error

Unstandard izedCoefficients

Beta


t Sig.

Dependent Variable: RELPEa.


Aswath Damodaran 89

Value/Earnings and Value/Cashflow Ratios

While Price earnings ratios look at the market value of equity relative toearnings to equity investors, Value earnings ratios look at the market value ofthe operating assets of the firm (Enterprise value or EV) relative to operatingearnings or cash flows.

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

EV/FCFF = (Market Value of Equity + Market Value of Debt-Cash)EBIT (1-t) - (Cap Ex - Deprecn) - Chg in Working Cap

Aswath Damodaran 90

Value of Firm/FCFF: Determinants

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

• V0 = Value of the firm (today)• FCFF0 = Free Cashflow to the firm in current year• g = Expected growth rate in FCFF in extraordinary growth period (first n years)• WACC = Weighted average cost of capital• gn = Expected growth rate in FCFF in stable growth period (after n years)

V0

=

FCFF0

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

n

(1+ WACC)n

!

" #

$

% &

WACC - g +

FCFF0

(1+ g)n

(1+ gn

)

(WACC - gn

)(1 + WACC)n

Aswath Damodaran 91

Value Multiples

Dividing both sides by the FCFF yields,

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

V0

FCFF0

=

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

(1 + WACC)n

!

" # $

%

WACC - g +

(1+ g)n (1+ gn )

(WACC - gn )(1 + WACC)n

Aswath Damodaran 92

Alternatives to FCFF - EBIT and EBITDA

Most analysts find FCFF to complex or messy to use in multiples (partlybecause capital expenditures and working capital have to be estimated). Theyuse modified versions of the multiple with the following alternativedenominator:

• 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.

Aswath Damodaran 93

Value/FCFF Multiples and the Alternatives

Assume that you have computed the value of a firm, using discounted cashflow models. Rank the following multiples in the order of magnitude fromlowest 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?

Aswath Damodaran 94

Illustration: Using Value/FCFF Approaches to value a firm:MCI Communications

MCI Communications had earnings before interest and taxes of $3356 millionin 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 yearsand 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=

(1.15) 1- (1.15)5

(1.105)5

.105 -.15 + (1.15)5(1.05)

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

Aswath Damodaran 95

Multiple Magic

In this case of MCI there is a big difference between the FCFF and short cutmeasures. For instance the following table illustrates the appropriate multipleusing short cut measures, and the amount you would overpay by if you usedthe 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 MultipleFCFF $498 31.28382355EBIT (1-t) $2,148 7.251163362EBIT $ 3,356 4.640744552EBITDA $4,456 3.49513885

Aswath Damodaran 96

Reasons for Increased Use of Value/EBITDA

1. The multiple can be computed even for firms that are reporting net losses, sinceearnings before interest, taxes and depreciation are usually positive.

2. For firms in certain industries, such as cellular, which require a substantialinvestment in infrastructure and long gestation periods, this multiple seems tobe more appropriate than the price/earnings ratio.

3. In leveraged buyouts, where the key factor is cash generated by the firm priorto all discretionary expenditures, the EBITDA is the measure of cash flowsfrom operations that can be used to support debt payment at least in the shortterm.

4. By looking at cashflows prior to capital expenditures, it may provide a betterestimate of “optimal value”, especially if the capital expenditures are unwiseor earn substandard returns.

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

Aswath Damodaran 97

Enterprise Value/EBITDA Multiple

The Classic Definition

The No-Cash Version

Value

EBITDA=

Market Value of Equity + Market Value of Debt

Earnings before Interest, Taxes and Depreciation

!

Enterprise Value

EBITDA=

Market Value of Equity + Market Value of Debt - Cash

Earnings before Interest, Taxes and Depreciation

Aswath Damodaran 98

Enterprise Value/EBITDA Distribution - US in January 2004

Aswath Damodaran 99

Value/EBITDA Multiple: Europe, Japan and EmergingMarkets in January 2004

Aswath Damodaran 100

The Determinants of Value/EBITDA Multiples: Linkage toDCF Valuation

The value of the operating assets of a firm can be written as:

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

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

V0 = FCFF1

WACC - g


From Firm Value to EBITDA Multiples

Now the Value of the firm can be rewritten as,

Dividing both sides of the equation by EBITDA,

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

WACC - g

Value

EBITDA =

(1- t)

WACC- g +

Depr (t)/EBITDA

WACC -g -

CEx/EBITDA

WACC - g -

! Working Capital/EBITDA

WACC - g


A Simple Example

Consider a firm with the following characteristics:• Tax Rate = 36%• Capital Expenditures/EBITDA = 30%• Depreciation/EBITDA = 20%• Cost of Capital = 10%• The firm has no working capital requirements• The firm is in stable growth and is expected to grow 5% a year forever.


Calculating Value/EBITDA Multiple

In this case, the Value/EBITDA multiple for this firm can be estimated asfollows:

Value

EBITDA =

(1- .36)

.10 -.05 +

(0.2)(.36)

.10 -.05 -

0.3

.10 - .05 -

0

.10 - .05 = 8.24


Value/EBITDA Multiples and Taxes


Value/EBITDA and Net Cap Ex


Value/EBITDA Multiples and Return on Capital


Value/EBITDA Multiple: Trucking Companies

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

Average 5 .61


A Test on EBITDA

Ryder System looks very cheap on a Value/EBITDA multiple basis, relativeto the rest of the sector. What explanation (other than misvaluation) mightthere be for this difference?


Analyzing the Value/EBITDA Multiple

While low value/EBITDA multiples may be a symptom of undervaluation, afew questions need to be answered:

• Is the operating income next year expected to be significantly lower than theEBITDA for the most recent period? (Price may have dropped)

• Does the firm have significant capital expenditures coming up? (In the truckingbusiness, 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?


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 havelower value/EBITDA ratios), and how much reinvestment is needed to keep thebusiness going and create growth

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

• how high or low expected growth is in the sector (high growth sectors will tend tohave higher Value/EBITDA multiples)


US Market: Cross Sectional RegressionJanuary 2004

Model Summary

.583a

.340 .338 653 .80185507239

Model

1


SquareStd. Er ror of the

Estimate

Predictor s: ( Constant), Reinvestment Rate, Expected Growth

in Revenues: next 5 years, Eff Tax Rat e

a.

Coef fici entsa,b

10.073 .768 13.121 .000

-.152 .022 -.174 -6.878 .000

.907 .039 .563 23.464 .000

-.015 .006 -.062 -2.420 .016

(Constant)

Eff Tax Rate

Expected G rowth inRevenues: next 5 years

Reinvestment Rate

Model

1

B Std. Er ror


Be ta


t Sig.

Dependent Variable: EV/EBITDAa.



Europe: Cross Sectional RegressionJanuary 2004

Model Summary

.542a .293 .292 1581.333005721082000

Model

1


Square Std. Er ror of the Estimate

Predictors: (Constant), Tax Rate , Reinv Rate , Market Debt to Capitala.

Coefficientsa,b

8.419 1.279 6.580 .000

.589 .021 .511 28.035 .000

-.051 .009 -.099 -5.472 .000

-.152 .029 -.095 -5.236 .000

(Constant)

Market Debt to Capital

Reinv Rate

Tax Rat e

Model

1

B Std. Er ror


Beta


t Sig.

Dependent Variable: EV/EBITDAa.

Weighted Least Squares Regression - Weighted by Market Capitalizationb.


Price-Book Value Ratio: Definition

The price/book value ratio is the ratio of the market value of equity to thebook value of equity, i.e., the measure of shareholders’ equity in the balancesheet.

Price/Book Value = Market Value of EquityBook 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.


Price to Book Value: US stocks


Price to Book: Europe, Japan and Emerging Markets


Price Book Value Ratio: Stable Growth Firm

Going back to a simple dividend discount model,

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

If the return on equity is based upon expected earnings in the next time period, this canbe simplified to,

P0 =DPS1

r ! gn

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

r-gn

P 0

BV 0

= PBV = ROE * Payout Ratio * (1 + gn )

r-gn

P 0

BV 0

= PBV = ROE * Payout Ratio

r-gn


Price Book Value Ratio: Stable Growth FirmAnother Presentation

This formulation can be simplified even further by relating growth to thereturn on equity:

g = (1 - Payout ratio) * ROE Substituting back into the P/BV equation,

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

P0

BV0

= PBV = ROE - gn

r-gn


Price Book Value Ratio for High Growth Firm

The Price-book ratio for a high-growth firm can be estimated beginning witha 2-stage discounted cash flow model:

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

where ROE = Return on Equity in high-growth periodROEn = Return on Equity in stable growth period

P 0 =

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

(1+ r)n

"

# $ %

& '

r - g+

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

(r - gn )(1+ r)n

P0

BV0

=

ROE* Payout Ratio *(1+ g)* 1 !(1+ g)

n

(1+ r)n

"

# $ %

&

r - g+

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

(r - gn )(1+ r)n

'

(

)

)

)

*

+

,

,

,


PBV Ratio for High Growth Firm: Example

Assume that you have been asked to estimate the PBV ratio for a firm whichhas the following characteristics:

High Growth Phase Stable Growth PhaseLength of Period 5 years Forever after year 5Return on Equity 25% 15%Payout Ratio 20% 60%Growth Rate .80*.25=.20 .4*.15=.06Beta 1.25 1.00Cost of Equity 12.875% 11.50%

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


Estimating Price/Book Value Ratio

The price/book value ratio for this firm is:

PBV =

0.25 * 0.2 * (1.20) * 1 !(1.20)5

(1.12875)5

"

# $ %

&

(.12875 - .20)+

0.15 * 0.6 * (1.20)5

* (1.06)

(.115 - .06) (1.12875)5

'

(

)

)

)

*

+

,

,

,

= 2.66


PBV and ROE: The Key

PBV and ROE: Risk Scenarios

0

0.5

1

1.5

2

2.5

3

3.5

4

10% 15% 20% 25% 30%

ROE

Pric

e/B

oo

k

Valu

e

Ratio

s

Beta=0.5

Beta=1

Beta=1.5


PBV/ROE: European Banks

Bank Symbol PBV ROE

Banca di Roma SpA BAHQE 0.60 4.15%

Commerzbank AG COHSO 0.74 5.49%

Bayerische Hypo und Vereinsbank AG BAXWW 0.82 5.39%

Intesa Bci SpA BAEWF 1.12 7.81%

Natexis Banques Populaires NABQE 1.12 7.38%

Almanij NV Algemene Mij voor Nijver ALPK 1.17 8.78%

Credit Industriel et Commercial CIECM 1.20 9.46%

Credit Lyonnais SA CREV 1.20 6.86%

BNL Banca Nazionale del Lavoro SpA BAEXC 1.22 12.43%

Banca Monte dei Paschi di Siena SpA MOGG 1.34 10.86%

Deutsche Bank AG DEMX 1.36 17.33%

Skandinaviska Enskilda Banken SKHS 1.39 16.33%

Nordea Bank AB NORDEA 1.40 13.69%

DNB Holding ASA DNHLD 1.42 16.78%

ForeningsSparbanken AB FOLG 1.61 18.69%

Danske Bank AS DANKAS 1.66 19.09%

Credit Suisse Group CRGAL 1.68 14.34%

KBC Bankverzekeringsholding KBCBA 1.69 30.85%

Societe Generale SODI 1.73 17.55%

Santander Central Hispano SA BAZAB 1.83 11.01%

National Bank of Greece SA NAGT 1.87 26.19%

San Paolo IMI SpA SAOEL 1.88 16.57%

BNP Paribas BNPRB 2.00 18.68%

Svenska Handelsbanken AB SVKE 2.12 21.82%

UBS AG UBQH 2.15 16.64%

Banco Bilbao Vizcaya Argentaria SA BBFUG 2.18 22.94%

ABN Amro Holding NV ABTS 2.21 24.21%

UniCredito Italiano SpA UNCZA 2.25 15.90%

Rolo Banca 1473 SpA ROGMBA 2.37 16.67%

Dexia DECCT 2.76 14.99%

Average 1.60 14.96%


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.


Under and Over Valued Banks?

Bank Actual Predicted Under or Over

Banca di Roma SpA 0.60 1.03 -41.33%

Commerzbank AG 0.74 1.10 -32.86%

Bayerische Hypo und Vereinsbank AG 0.82 1.09 -24.92%

Intesa Bci SpA 1.12 1.22 -8.51%

Natexis Banques Populaires 1.12 1.20 -6.30%

Almanij NV Algemene Mij voor Nijver 1.17 1.27 -7.82%

Credit Industriel et Commercial 1.20 1.31 -8.30%

Credit Lyonnais SA 1.20 1.17 2.61%

BNL Banca Nazionale del Lavoro SpA 1.22 1.47 -16.71%

Banca Monte dei Paschi di Siena SpA 1.34 1.39 -3.38%

Deutsche Bank AG 1.36 1.73 -21.40%

Skandinaviska Enskilda Banken 1.39 1.68 -17.32%

Nordea Bank AB 1.40 1.54 -9.02%

DNB Holding ASA 1.42 1.70 -16.72%

ForeningsSparbanken AB 1.61 1.80 -10.66%

Danske Bank AS 1.66 1.82 -9.01%

Credit Suisse Group 1.68 1.57 7.20%

KBC Bankverzekeringsholding 1.69 2.45 -30.89%

Societe Generale 1.73 1.74 -0.42%

Santander Central Hispano SA 1.83 1.39 31.37%

National Bank of Greece SA 1.87 2.20 -15.06%

San Paolo IMI SpA 1.88 1.69 11.15%

BNP Paribas 2.00 1.80 11.07%

Svenska Handelsbanken AB 2.12 1.97 7.70%

UBS AG 2.15 1.69 27.17%

Banco Bilbao Vizcaya Argentaria SA 2.18 2.03 7.66%

ABN Amro Holding NV 2.21 2.10 5.23%

UniCredito Italiano SpA 2.25 1.65 36.23%

Rolo Banca 1473 SpA 2.37 1.69 39.74%

Dexia 2.76 1.61 72.04%


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 forwell above book value and firms which have low returns on equity selling ator below book value.

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


The Valuation Matrix

MV/BV

ROE-r

High ROEHigh MV/BV

Low ROELow MV/BV

Overvalued

Low ROEHigh MV/BV

Undervalued

High ROELow MV/BV


Price to Book vs ROE: Largest Market Cap Firms in theUnited States: September 2003

ROE

706050403020100

PBV

Rati

o

20

10

0

WMT

PFE

JNJ

GSK

MRK

PG

DELL

MO

AZN

SC

ORCL

MDT

FNM

MMM

ULBMY

BUD

D

SAP

EBAY

AMAT

G

QCOM

ABN

BSX

KMB


PBV Matrix: Telecom Companies

TelAzteca

TelNZ Vimple

Carlton

Cable&WTeleglobeFranceTel

DeutscheTelBritTelTelItalia

AsiaSatPortugal HongKongRoyalBCE Hellenic

ChinaTelNipponDanmark

Espana IndastTelevisasTelmexTelArgFrancePhilTelTelArgentina TelIndo

TelPeru

GrupoCentroAPTCallNetAnonima

ROE

6050403020100

12

10

8

6

4

2

0


PBV, ROE and Risk: Large Cap US firms

470

PBV Ratio

2

4

TSM

60

6

FNM

ORCL

UL

8

3

BUD

10

AMAT

AOL

50

MRK

12PFE

14

G

PG

16

VIA/B

40

FRE

MMM

SC

2

EBAY

KMB

ROERegression Beta

QCOMWMT

MDT

30

D

120 10 00


IBM: The Rise and Fall and Rise Again

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

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

Year

Pri

ce t

o B

ook

-40.00%

-30.00%

-20.00%

-10.00%

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

Ret

urn

on

Eq

uit

y

PBV ROE


PBV Ratio Regression: USJanuary 2004

Model Summary

.943b .889 .889 117.0574933200291

Model

1

R R Squarea

Adjusted RSquare

Std. Er ror of theEstimate

For regression through the origin (the no-intercept model) , RSquare measures the proportion of the variability in thedependent variable about the origin explained by regression.This CANNOT be compared to R Squar e for models whichinclude an intercept.

a.

Predictors: ROE, Regression Beta, PAYOU T, Expected Growth

in EPS: next 5 years

b.

Coeffici entsa,b,c

8.E-02 .004 .256 21.935 .000

2.E-03 .001 .017 1.551 .121

.599 .042 .151 14.249 .000

.140 .003 .628 50.731 .000


PAYOUT

Regression Beta

ROE

Model

1

B Std. Error


Beta


t Sig.

Dependent Variable: PBV Ratioa.

Linear Regression through the Originb.

Weighted Least Squares Regression - Weighted by Market Capc.


PBV Ratio Regression- EuropeJanuary 2004

Model Summary

.830b .689 .689 154.44047748882220

Model

1

R R Squarea

Adjusted RSquare Std. Error of the Estimate

For regression through the origin (the no-intercept model) , R Squaremeasures the propor tion of the variability in the dependent variableabout the origin explained by regression. This CANNOT be comparedto R Square for models which include an inter cept.

a.

Predictors: ROE, Payout Ra tio, B ETAb.

Coefficientsa ,b,c

8.E-03 .002 .074 3.667 .000

1.399 .114 .291 12.279 .000

.104 .004 .537 28.148 .000

Payout Ratio

BETA

ROE

Model

1

B Std. Er ror


Beta


t Sig.

Dependent Variable: PBVa.


Weighted Least Squares Regression - Weighted by Market Capitalizationc.


PBV Regression: Emerging MarketsJanuary 2004

Model Summary

.795b .631 .631 2.070869461234543

Model

1

R R Squarea

Adjusted RSquare Std. Error of the Estimate

For regression through the origin (the no-intercept model) , R Squaremeasures the proportion of the variability in the dependent variableabout the origin explained by regression. This CANNOT becompared to R Square f or models which include an inter cept.

a.

Predictors: ROE, Payout Ratio, BETAb.

Coefficientsa ,b

5.E-03 .001 .076 4.148 .000

.805 .088 .213 9.164 .000

9.E-02 .003 .579 29.414 .000

Payout Ratio

BETA

ROE

Model

1

B Std. Er ror


Beta


t Sig.




PBV Ratio: Japan in January 2004

Model Summary

.815b

.664 .664 848.865237162549000

Model

1

Net Income> 0

(Selected)

R

R SquareaAdjusted R


Estimate

For regression through the origin (the no-intercept model) , R Squaremeasures the propor tion of the variability in the depende nt variableabout the origin explained by regression. This CANNOT be compare dto R Square for models which include an intercept.

a.

Predictors: B ETA, ROEb. Coef fici entsa,b,c,d

.189 .007 .597 28.912 .000

.973 .073 .276 13.359 .000

ROE

BETA

Model

1

B Std. Er ror


Be ta


t Sig.



Weighted Least Squares Regression - Weighted by Mar ketCapitalization

c.

Selecting only cases for which Net Income > 0d.


Value/Book Value Ratio: Definition

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

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


Determinants of Value/Book Ratios

To see the determinants of the value/book ratio, consider the simple free cashflow to the firm model:

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

WACC - g

V0

BV=

FCFF1/BV

WACC - g

V0

BV=

ROC - g

WACC - g


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 growthphase, but the basic determinants will remain unchanged.


Value/Book and the Return Spread


Value/Book Capital Regression - US

Model Summary

.758a

.575 .574 135.062398927610600

Model

1


Square Std. Error of the Estimate

Predictors: (Constant), Market Debt to Cap ital, Expected Growth

in Revenues: next 5 years, ROC

a.

Coef fici entsa,b

3.041 .133 22.838 .000

1.E-02 .008 .026 1.330 .184

9.E-02 .004 .446 22.992 .000

-.066 .003 -.473 -23.04 .000

(Constant)


ROC


Model

1

B Std. Er ror


Be ta


t Sig.

Dependent Variable: Value/BV of Capitala.



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 isdivided by the total revenues of the firm.


Price/Sales Ratio: US stocks

0

100

200

300

400

500

600

<0.1 0.1-

0.2

0.2-

0.3

0.3-

0.4

0.4-

0.5

0.5-

0.75

0.75-1 1-1.25 1.25-

1.5

1.5-

1.75

1.75-2 2-2.5 2.5-3 3-3.5 3.5-4 4-5 5-10 >10

Revenue Multiples: US Companies in January 2004

Price to Sales

EV/Sales


Price to Sales: Europe, Japan and Emerging Markets


Price/Sales Ratio: Determinants

The price/sales ratio of a stable growth firm can be estimated beginning with a2-stage equity valuation model:

Dividing both sides by the sales per share:

P0 =DPS1

r ! gn

P0

Sales0

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

r-gn


Price/Sales Ratio for High Growth Firm

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

Dividing both sides by the sales per share:

where Net Marginn = Net Margin in stable growth phase

P 0 =

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

(1+ r)n

"

# $ %

& '

r - g+

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

(r - gn )(1+ r)n

P0

Sales0

=

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

(1+ r)n

"

# $ %

&

r - g+

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

*(1 + gn )

(r - gn )(1 + r)n

'

(

)

)

)

*

+

,

,

,


Price Sales Ratios and Profit Margins

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


Price/Sales Ratio: An Example

High Growth Phase Stable GrowthLength of Period 5 years Forever after year 5Net Margin 10% 6%Sales/BV of Equity 2.5 2.5Beta 1.25 1.00Payout Ratio 20% 60%Expected Growth (.1)(2.5)(.8)=20% (.06)(2.5)(.4)=.06Riskless Rate =6%

PS =

0.10 * 0.2 * (1.20) * 1 !(1.20)5

(1.12875)5

"

# $ %

&

(.12875 - .20)+

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

(.115 -.06) (1.12875)5

'

(

)

)

)

*

+

,

,

,

= 1.06


Effect of Margin Changes

Price/Sales Ratios and Net Margins

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

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

Net Margin

PS

Rati

o


PS/Margins: European Retailers - September 2003


Regression Results: PS Ratios and Margins

Regressing PS ratios against net margins,PS = -.39 + 0.6548 (Net Margin) R2 = 43.5%

Thus, a 1% increase in the margin results in an increase of 0.6548 in the pricesales ratios.

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


Current versus Predicted Margins

One of the limitations of the analysis we did in these last few pages is thefocus on current margins. Stocks are priced based upon expected marginsrather 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 expectedmargins, regressions of price to sales ratios against current margins (or priceto book against current return on equity) will not provide much explanatorypower.

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


A Case Study: The Internet Stocks

ROWEGSVIPPODTURF BUYX ELTXGEEKRMIIFATB TMNTONEM ABTL INFO ANETITRAIIXLBIZZ EGRPACOMALOYBIDSSPLN EDGRPSIX ATHY AMZN

CLKS PCLNAPNT SONENETO

CBIS NTPACSGPINTW RAMP

DCLKCNETATHMMQST FFIV

SCNT MMXIINTM

SPYGLCOS

PKSI

-0

10

20

30

-0.8 -0.6 -0.4 -0.2

AdjMargin

AdjPS


PS Ratios and Margins are not highly correlated

Regressing PS ratios against current margins yields the followingPS = 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.


Solution 1: Use proxies for survival and growth: Amazon inearly 2000

Hypothesizing that firms with higher revenue growth and higher cashbalances should have a greater chance of surviving and becoming profitable,we ran the following regression: (The level of revenues was used to controlfor 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) = 30.42Actual PS = 25.63Stock is undervalued, relative to other internet stocks.


Solution 2: Use forward multiples

You can always estimate price (or value) as a multiple of revenues, earningsor book value in a future year. These multiples are called forward multiples.

For young and evolving firms, the values of fundamentals in future years mayprovide a much better picture of the true value potential of the firm. There aretwo ways in which you can use forward multiples:

• Look at value today as a multiple of revenues or earnings in the future (say 5 yearsfrom now) for all firms in the comparable firm list. Use the average of this multiplein conjunction with your firm’s earnings or revenues to estimate the value of yourfirm today.

• Estimate value as a multiple of current revenues or earnings for more mature firmsin the group and apply this multiple to the forward earnings or revenues to theforward earnings for your firm. This will yield the expected value for your firm inthe forward year and will have to be discounted back to the present to get currentvalue.


An Example of Forward Multiples: Global Crossing

Global Crossing lost $1.9 billion in 2001 and is expected to continue to lose money forthe next 3 years. In a discounted cashflow valuation (see notes on DCF valuation) ofGlobal Crossing, we estimated an expected EBITDA for Global Crossing in five yearsof $ 1,371 million.

The average enterprise value/ EBITDA multiple for healthy telecomm firms is 7.2currently.

Applying this multiple to Global Crossing’s EBITDA in year 5, yields a value in year 5of

• 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


PS Regression: United States - January 2004Model Summary

.932b .869 .868 114.30566982647230

Model

1

R R Squarea

Adjusted RSquare

Std. Error of theEstimate

For regression through the origin (the no-intercept model) , RSquare measures the proport ion of the variability in thedependent variable about the origin explained by regression.This CANNOT be compared to R Square for models whichinclude an intercept.

a.

Predictors: Net Margin, Regression Beta, PAYOUT, Expected

Growth in EPS: next 5 years

b.

Coeffici entsa,b,c

4.E-02 .004 .136 10.195 .000

-.011 .001 -.110 -9.425 .000

.549 .043 .156 12.658 .000

.234 .004 .799 59.926 .000


PAYOUT

Regression Beta

Net Margin

Model

1

B Std. Error


Beta


t Sig.

Dependent Variable: PS_RATIOa.


Weighted Least Squares Regression - Weighted by Market Capc.


PS Regression: Europe in January 2004

Model Summary

.757b .574 .573 134.938678072015

Model

1

R R Squarea

Adjusted RSquare

Std. Error of theEstimate

For regression through the origin (the no-intercept model) ,R Square measures the proportion of the variab ility in thedependent variable about the origin explained byregression. This CANNOT be compar ed to R Square for

models which include an intercept.

a.

Predictors: Net Mar gin, Payout Ratio, BETAb.

Coefficientsa ,b,c

5.E-03 .002 .065 2.777 .006

.937 .095 .261 9.909 .000

.110 .004 .516 26.153 .000

Payout Ratio

BETA

Net Margin

Model

1

B Std. Er ror


Beta


t Sig.

Dependent Variable: PSa.


Weighted Least Squares Regression - Weighted by Market Capitalizationc.


PS Regression in Emerging Markets - January 2004Model Summary

.834b

.696 .695 2.308859441838714

Model

1

Net Income> .00

(Selected)

R

R SquareaAdjusted R


Estimate

For regression through the origin (the no-intercept model) , RSquare measures the proport ion of the variability in the dependentvariable about the origin explained by regression. This CANNOT becompared to R Squar e for models which include an intercept.

a.

Predictors: Net Margin, Payout Ratio, BETAb. Coefficientsa ,b,c

7.E-03 .001 .083 4.962 .000

.142 .087 .030 1.631 .103

.143 .003 .766 47.061 .000

Payout Ratio

BETA

Net Margin

Model

1

B Std. Er ror


Beta


t Sig.



Selecting only cases for which Net Income > .00c.


PS Regression in Japan: January 2004

Model Summary

.721a

.519 .518 549.139058787986000

Model

1

Net Income> 0

(Selected)

R

R SquareAdjusted R

Square Std. Error of the Estimate

Predictors: (Constant), Payout Ratio, Net Margina.

Coefficientsa ,b,c

2.E-02 .081 .242 .808

.243 .007 .737 34.627 .000

8.E-03 .002 .079 3.719 .000

(Constant)

Net Margin

Payout Ratio

Model

1

B Std. Er ror


Beta


t Sig.


Weighted Least Squares Regression - We ighted by Market Capitalizationb.

Selecting only cases for which Net Income > 0c.


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


Value/Sales Ratios: Analysis of Determinants

If pre-tax operating margins are used, the appropriate value estimate is that ofthe 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

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

rate)RIRGrowth, Stable = Reinvestment rate in high growth and stable periodsWACC = Weighted average cost of capital

Value

Sales0

= After - tax Oper. Margin *

(1 - RIRgrowth)(1 + g)* 1!(1 + g)

n

(1+ WACC)n

"

# $

%

& '

WACC - g+

(1- RIRstable)(1 + g)n *(1+ gn )

(WACC - gn )(1+ WACC)n

(

)

* * * *

+

,

- - - -


Value/Sales Ratio: An Example

Consider, for example, the Value/Sales ratio of Coca Cola. The company hadthe following characteristics:

After-tax Operating Margin =18.56% Sales/BV of Capital = 1.67Return 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 yearsCost 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 Firm0

Sales0

= .1856*

(1- .65)(1.2016)* 1!(1.2016)

1 0

(1.1213)1 0

"

# $

%

& '

.1213- .2016+

(1- .20)(1.2016)1 0* (1.06)

(.1213- .06)(1.1213)1 0

(

)

* * * *

+

,

- - - -

= 6.10


Value Sales Ratios and Operating Margins


MSELGDYS RET.TO MLG

MHCOZANYPSRC

FINLROSIFLWS LVC TWMCSPGLASAH RUSH MDADBRNGADZ WLSNCELL FNLYJILL

IBICLWYANIC VOXX CHRS PSS BKEZMTMC HMYPBYURBN

ROST AEOSPGDACC BEBEITN

CAOGBIZ DAP RUSMNROSCHS HLYWMENSLE LIN MDLK

RAYS PIR GLBEZQKMIKECWTR IPAR ANNAZONSITBBY

LTDZLCORLY

FOSLPSUN CLEPLCEJWLSATH

PCCC WSM

TLB

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TWTR

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BIDDABRISEE

CHCSCDWC LUX

-0.0

0.5

1.0

1.5

2.0

-0.000 0.075 0.150 0.225

Operating Margin

V/Sales

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


Brand Name Premiums in Valuation

You have been hired to value Coca Cola for an analyst reports and you havevalued the firm at 6.10 times revenues, using the model described in the lastfew pages. Another analyst is arguing that there should be a premium addedon to reflect the value of the brand name. Do you agree?

Yes No Explain.


The value of a brand name

One of the critiques of traditional valuation is that is fails to consider thevalue of brand names and other intangibles.

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

One of the benefits of having a well-known and respected brand name is thatfirms can charge higher prices for the same products, leading to higher profitmargins and hence to higher price-sales ratios and firm value. The larger theprice premium that a firm can charge, the greater is the value of the brandname.

In general, the value of a brand name can be written as:Value of brand name ={(V/S)b-(V/S)g }* Sales(V/S)b = Value of Firm/Sales ratio with the benefit of the brand name(V/S)g = Value of Firm/Sales ratio of the firm with the generic product


Illustration: Valuing a brand name: Coca Cola

Coca Cola Generic Cola CompanyAT Operating Margin 18.56% 7.50%Sales/BV of Capital 1.67 1.67ROC 31.02% 12.53%Reinvestment Rate 65.00% (19.35%) 65.00% (47.90%)Expected Growth 20.16% 8.15%Length 10 years 10 yeaCost of Equity 12.33% 12.33%E/(D+E) 97.65% 97.65%AT Cost of Debt 4.16% 4.16%D/(D+E) 2.35% 2.35%Cost of Capital 12.13% 12.13%Value/Sales Ratio 6.10 0.69


Value of Coca Cola’s Brand Name

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


Value/Sales Ratio Regression: US in January 2004Model Summary

.726a .527 .526 150 .9882839615558

Model

1



Estimate

Predictors: (Constant), Expected G rowth in Revenues: next 5years, After-tax Oper ating Ma rgin, Market Debt to Capital

a.

Coef fici entsa,b

1.252 .118 10.576 .000

.135 .004 .605 32.945 .000

-.043 .003 -.300 -14.99 .000

8.E-02 .009 .175 8.756 .000

(Constant)

After-tax OperatingMargin



Model

1

B Std. Er ror


Be ta


t Sig.

Dependent Variable: EV/Salesa.



Choosing Between the Multiples

As presented in this section, there are dozens of multiples that can bepotentially 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 atthis stage:

• Use a simple average of the valuations obtained using a number of differentmultiples

• Use a weighted average of the valuations obtained using a nmber of differentmultiples

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


Averaging Across Multiples

This procedure involves valuing a firm using five or six or more multiples andthen taking an average of the valuations across these multiples.

This is completely inappropriate since it averages good estimates with poorones equally.

If some of the multiples are “sector based” and some are “market based”, thiswill also average across two different ways of thinking about relativevaluation.


Weighted Averaging Across Multiples

In this approach, the estimates obtained from using different multiples areaveraged, with weights on each based upon the precision of each estimate.The more precise estimates are weighted more and the less precise onesweighted less.

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

Precision of Estimate = 1 / Standard Error of Estimatewhere the standard error of the predicted value is used in the denominator.

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


Picking one Multiple

This is usually the best way to approach this issue. While a range of valuescan be obtained from a number of multiples, the “best estimate” value isobtained 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 runregressions of these multiples against fundamentals, use the multiple that worksbest at explaining differences across firms in that sector.

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


Self Serving Multiple Choice

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

If there is a significant bias in the valuation towards high or low values, it istempting to pick the multiple that best reflects this bias. Once the multiple thatworks best is picked, the other multiples can be abandoned and never broughtup.

This approach, while yielding very biased and often absurd valuations, mayserve other purposes very well.

As a user of valuations, it is always important to look at the biases of theentity 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.)


The Statistical Approach

One of the advantages of running regressions of multiples againstfundamentals across firms in a sector is that you get R-squared values on theregression (that provide information on how well fundamentals explaindifferences across multiples in that sector).

As a rule, it is dangerous to use multiples where valuation fundamentals (cashflows, risk and growth) do not explain a significant portion of the differencesacross firms in the sector.

As a caveat, however, it is not necessarily true that the multiple that has thehighest R-squared provides the best estimate of value for firms in a sector.


A More Intuitive Approach

Managers in every sector tend to focus on specific variables when analyzingstrategy 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 isoften viewed as a scarce resource, since capital ratios are based upon it. Price tobook ratios dominate.

• In technology: Growth is usually the dominant theme. PEG ratios were invented inthis sector.


Conventional Usage: A Summary

As a general rule of thumb, the following table provides a way of picking amultiple for a sector

Sector Multiple Used RationaleCyclical Manufacturing PE, Relative PE Often with normalized earningsHigh Tech, High Growth PEG Big differences in growth across

firmsHigh Growth/No Earnings PS, VS Assume future margins will be goodHeavy Infrastructure VEBITDA Firms in sector have losses in early

years and reported earnings can varydepending on depreciation method

REITa P/CF Generally no cap ex investments from equity earnings

Financial Services PBV Book value often marked to marketRetailing PS If leverage is similar across firms

VS If leverage is different


Sector or Market Multiples

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

Whether sector or market based multiples make the most sense depends uponhow you think the market makes mistakes in valuation

• If you think that markets make mistakes on individual firm valuations but thatvaluations 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 onthe 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.


A Test

You have valued Earthlink Networks, an internet service provider, relative toother internet companies using Price/Sales ratios and find it to be undervalued almost 50% .When you value it relative to the market, using themarket regression, you find it to be overvalued by almost 50%. How wouldyou reconcile the two findings?

One of the two valuations must be wrong. A stock cannot be under and overvalued 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?


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


Private Company Valuation

Aswath Damodaran


Process of Valuing Private Companies

Choosing the right model• Valuing the Firm versus Valuing Equity• Steady State, Two-Stage or Three-Stage

Estimating a Discount Rate• Cost of Equity

– Estimating Betas• Cost of Debt

– Estimating Default Risk– Estimating an after-tax cost of debt

• Cost of Capital– Estimating a Debt Ratio

Estimating Cash Flows Completing the Valuation: Depends upon why and for whom the valuation is

being done.


Private Company Valuation: Motive matters

You can value a private company for• Legal purposes: Estate tax and divorce court• Sale or prospective sale to another individual or private entity.• Sale of one partner’s interest to another• Sale to a publicly traded firm• As prelude to setting offering price in an initial public offering

You can value a division or divisions of a publicly traded firm• As prelude to a spin off• For sale to another entity• To do a sum-of-the-parts valuation to determine whether a firm will be worth more

broken up or if it is being efficiently run.


Estimating Cost of Equity for a Private Firm

Most models of risk and return (including the CAPM and the APM) use pastprices of an asset to estimate its risk parameters (beta(s)).

Private firms and divisions of firms are not traded, and thus do not have pastprices.

Thus, risk estimation has to be based upon an approach that does not requirepast prices


I. Comparable Firm Betas

Collect a group of publicly traded comparable firms, preferably in the sameline of business, but more generally, affected by the same economic forcesthat affect the firm being valued.

• A Simple Test: To see if the group of comparable firms is truly comparable,estimate a correlation between the revenues or operating income of the comparablefirms and the firm being valued. If it is high (and positive), of course, your havecomparable firms.

If the private firm operates in more than one business line collect comparablefirms for each business line


Estimating comparable firm betas

Estimate the average beta for the publicly traded comparable firms. Estimate the average market value debt-equity ratio of these comparable

firms, and calculate the unlevered beta for the business. βunlevered = βlevered / (1 + (1 - tax rate) (Debt/Equity))

Estimate a debt-equity ratio for the private firm, using one of two assumptions:• Assume that the private firm will move to the industry average debt ratio. The beta

for the private firm will converge on the industry average beta. β private firm = βunlevered (1 + (1 - tax rate) (Industry Average Debt/Equity))• Estimate the optimal debt ratio for the private firm, based upon its operating

income and cost of capital.β private firm = βunlevered (1 + (1 - tax rate) (Optimal Debt/Equity))

Estimate a cost of equity based upon this beta.


Accounting Betas

Step 1: Collect accounting earnings for the private company for as long asthere is a history.

Step 2: Collect accounting earnings for the S&P 500 for the same time period. Step 3: Regress changes in earnings for the private company against changes

in the S&P 500. Step 4: The slope of the regression is the accounting beta There are two serious limitations -

(a) The number of observations in the regression is small(b) Accountants smooth earnings.


Estimating a Beta for the NY Yankees

You have three choices for comparable firms:• Firms that derive a significant portion of their revenues from baseball (Traded

baseball teams, baseball cards & memorabilia…)• Firms that derive a significant portion of their revenues from sports• Firms that derive a significant portion of their revenues from entertainment.

Comparable firms Levered Beta Unlevered BetaBaseball firms (2) 0.70 0.64Sports firms (22) 0.98 0.90Entertainment firms (91) 0.87 0.79 Management target Levered Beta for Yankees = 0.90 ( 1 + (1-.4) (.25)) = 1.04 Cost of Equity = 6.00% + 1.04 (4%) = 10.16%


Estimating a beta for InfoSoft: A private software firm

Comparable firms include all software firms, with market capitalization ofless than $ 500 million.

The average beta for these firms is 1.29 and the average debt to equity ratiofor these firms is 7.09%. With a 35% tax rate, this yields an unlevered beta of

Unlevered Beta = 1.29/ (1 + (1-.35) (.0709)) = 1.24 We will assume that InfoSoft will have a debt to equity ratio comparable to

the average for the comparable firms and a similar tax rate, which results in alevered beta of 1.29.

Cost of Equity = 6.00% + 1.29 (4%) = 11.16%


Is beta a good measure of risk for a private firm?

The beta of a firm measures only market risk, and is based upon theassumption that the investor in the business is well diversified. Given thatprivate firm owners often have all or the bulk of their wealth invested in theprivate business, would you expect their perceived costs of equity to be higheror lower than the costs of equity from using betas?

Higher Lower


Total Risk versus Market Risk

Adjust the beta to reflect total risk rather than market risk. This adjustment isa relatively simple one, since the correlation with the market measures theproportion of the risk that is market risk.

Total Beta = Market Beta / Correlation with market In the New York Yankees example, where the market beta is 0.85 and the R-

squared for comparable firms is 25% (correlation is therefore 0.5),• Total Unlevered Beta = 0.90/0. 5= 1.80• Total Levered Beta = 1.80 (1 + (1-0.4)(0.25)) =2.07• Total Cost of Equity = 6% + 2.07 (4%)= 14.28%


When would you use this total risk measure?

Under which of the following scenarios are you most likely to use the totalrisk measure:

when valuing a private firm for an initial public offering when valuing a private firm for sale to a publicly traded firm when valuing a private firm for sale to another private investor Assume that you own a private business. What does this tell you about the

best potential buyer for your business?


Estimating the Cost of Debt for a Private Firm

Basic Problem: Private firms generally do not access public debt markets, andare therefore not rated.

Most debt on the books is bank debt, and the interest expense on this debtmight not reflect the rate at which they can borrow (especially if the bank debtis old.)


Estimation Options for Cost of Debt

Solution 1: Assume that the private firm can borrow at the same rate assimilar firms (in terms of size) in the industry.

Cost of Debt for Private firm = Cost of Debt for similar firms in the industry Solution 2: Estimate an appropriate bond rating for the company, based upon

financial ratios, and use the interest rate estimated bond rating.Cost of Debt for Private firm = Interest Rate based upon estimated bond rating (If

using optimal debt ratio, use corresponding rating) Solution 3: If the debt on the books of the company is long term and recent,

the cost of debt can be calculated using the interest expense and the debtoutstanding.

Cost of Debt for Private firm = Interest Expense / Outstanding DebtIf the firm borrowed the money towards the end of the financial year, the interest

expenses for the year will not reflect the interest rate on the debt.


Estimating a Cost of Debt for Yankees and InfoSoft

For the Yankee’s, we will use the interest rate from the most recent loans thatthe firm has taken on:

• Interest rate on debt = 7.00%• After-tax cost of debt = 7% (1-.4) = 4.2%

For InfoSoft, we will use the interest coverage ratio estimated using theoperating income and interest expenses from the most recent year:

• Interest coverage ratio = EBIT/ Interest expenses = 2000/315 = 6.35• Rating based upon interest coverage ratio = A+• Interest rate on debt = 6% + 0.80% = 6.80%• After-tax cost of debt = 6.80% (1-.35) = 4.42%


Estimating the Cost of Capital

Basic problem: The debt ratios for private firms are stated in book valueterms, rather than market value. Furthermore, the debt ratio for a private firmthat plans to go public might change as a consequence of that action.

Solution 1: Assume that the private firm will move towards the industryaverage debt ratio.

Debt Ratio for Private firm = Industry Average Debt Ratio Solution 2: Assume that the private firm will move towards its optimal debt

ratio.Debt Ratio for Private firm = Optimal Debt Ratio

Consistency in assumptions: The debt ratio assumptions used to calculatethe beta, the debt rating and the cost of capital weights should beconsistent.


Estimating Costs of Capital

New York InfoSoftYankees Corporation

Cost of Equity 14.28%(total beta) 11.16%(market beta)E/ (D+E) 80.00% 93.38%Cost of Debt 7.00% 6.80%AT Cost of Debt 4.20% 4.42%D/(D+E) 20.00% 6.62%Cost of Capital 12.26% 10.71%


Estimating Cash Flows for a Private Firm

Shorter history: Private firms often have been around for much shorter timeperiods than most publicly traded firms. There is therefore less historicalinformation available on them.

Different Accounting Standards: The accounting statements for privatefirms are often based upon different accounting standards than public firms,which operate under much tighter constraints on what to report and when toreport.

Intermingling of personal and business expenses: In the case of privatefirms, some personal expenses may be reported as business expenses.

Separating “Salaries” from “Dividends”: It is difficult to tell where salariesend and dividends begin in a private firm, since they both end up with theowner.


Estimating Private Firm Cash Flows

Restate earnings, if necessary, using consistent accounting standards.• To get a measure of what is reasonable, look at profit margins of comparable

publicly traded firms in the same business If any of the expenses are personal, estimate the income without these

expenses. Estimate a “reasonable” salary based upon the services the owner provides the

firm.


The Yankee’s Revenues

Pittsburg Pirates Baltimore Orioles New York YankeesNet Home Game Receipts $ 22,674,597 $ 47,353,792 $ 52,000,000 Road Receipts $ 1,613,172 $ 7,746,030 $ 9,000,000 Concessions & Parking $ 3,755,965 $ 22,725,449 $ 25,500,000 National TV Revenues $ 15,000,000 $ 15,000,000 $ 15,000,000 Local TV Revenues $ 11,000,000 $ 18,183,000 $ 90,000,000 National Licensing $ 4,162,747 $ 3,050,949 $ 6,000,000 Stadium Advertising $ 100,000 $ 4,391,383 $ 5,500,000 Other Revenues $ 1,000,000 $ 9,200,000 $ 6,000,000

Total Revenues $ 59,306,481 $ 127,650,602 $ 209,000,000


The Yankee’s Expenses

Pittsburg Pirates Baltimore Orioles New York YankeesPlayer Salaries $ 33,155,366 $ 62,771,482 $ 91,000,000 Team Operating Expenses $ 6,239,025 $ 6,803,907 $ 7,853,000 Player Development $ 8,136,551 $ 12,768,399 $ 15,000,000 Stadium & Game Operations$ 5,270,986 $ 4,869,790 $ 7,800,000 Other Player Costs $ 2,551,000 $ 6,895,751 $ 7,500,000 G & A Costs $ 6,167,617 $ 9,321,151 $ 11,000,000 Broadcasting $ 1,250,000 $ - $ - Rent & Amortization $ - $ 6,252,151 $ - Total Operating Expenses $ 62,770,545 $ 109,682,631 $ 140,153,000


Adjustments to Operating Income

Pittsburg Pirates Baltimore Orioles New York YankeesTotal Revenues $59,306,481 $127,650,602 $209,000,000Total Operating Expenses $62,770,545 $109,682,631 $140,153,000EBIT -$3,464,064 $17,967,971 $68,847,000Adjustments $1,500,000 $2,200,000 $4,500,000Adjusted EBIT -$1,964,064 $20,167,971 $73,347,000Taxes (at 40%) -$785,626 $8,067,189 $29,338,800EBIT (1-tax rate) -$1,178,439 $12,100,783 $44,008,200


InfoSoft’s Operating Income

Stated Operating IncomeSales & Other Operating Revenues $20,000.00 - Operating Costs & Expenses $13,000.00 - Depreciation $1,000.00 - Research and Development Expenses $4,000.00 Operating Income $2,000.00Adjusted Operating Income Operating Income $ 2000.00+ R& D Expenses $ 4000.00- Amortization of Research Asset $ 2311.00Adjusted Operating Income $ 3689.00


Estimating Cash Flows for Yankees

We will assume a 3% growth rate in perpetuity for operating income. Togenerate this growth, we will assume that the Yankee’s will earn 20% on theirnew investments. This yields a reinvestment rate of

Reinvestment rate = g/ ROC = 3%/20% = 15% Estimated Free Cash Flow to FirmEBIT (1- tax rate) = $ 44,008,200 - Reinvestment = $ 6,601,230 FCFF $ 37,406,970


From Cash Flows to Value

Once you have estimated the cash flows and the cost of capital, you can valuea private firm using conventional methods.

If you are valuing a firm for sale to a private business,• Use the total beta and the cost of equity emerging from that to estimate the cost of

capital.• Discount the cash flows using this cost of capital

If you are valuing a firm for an initial public offering, stay with the marketbeta and cost of capital.


Valuing the Yankees

FCFF = $ 37,406,970Cost of capital = 12.26%Expected Growth rate= 3.00%

Value of Yankees = $ 37,406,970 (1.03)/(.1226-.03)= $ 415,902,192


What if?

We are assuming that the Yankees have to reinvest to generate growth. If theycan get the city to pick up the tab, the value of the Yankees can be estimatedas follows:

• FCFF = EBIT (1-t) - Reinvestment = $44.008 mil - 0 = $ 44.008 million• Value of Yankees = 44.008*1.03/(.1226 - .03) = $ 489 million

If on top of this, we assume that the buyer is a publicly traded firm and we usethe market beta instead of the total beta

• FCFF = $ 44.008 million• Cost of capital = 8.95%• Value of Yankees = 44.008 (1.03) / (.0895 - .03) = $ 761.6 million


Current Cashflow to FirmEBIT(1-t) : 2,933- Nt CpX 2,633- Chg WC 500= FCFF <200>Reinvestment Rate = 106.82%

Expected Growth in EBIT (1-t)1.1217*.2367 = .252825.28%

Stable Growthg = 5%; Beta = 1.20; D/(D+E) = 6.62%;ROC=17.2%Reinvestment Rate=29.07%

Terminal Value10= 6743/(.1038-.05) = 125,391

Cost of Equity11.16%

Cost of Debt(6+0.80%)(1-.35)= 4.42%

WeightsE = 93.38% D = 6.62%

Discount at Cost of Capital (WACC) = 11.16% (0.9338) + 4.42% (0.0662) = 10.71%

Firm Value: 73,909+ Cash: 500- Debt: 4,583=Equity 69,826

Riskfree Rate:Government Bond Rate = 6%

+Beta 1.29 X

Risk Premium4%

Unlevered Beta for Sectors: 1.24

Firm’s D/ERatio: 7.09%

Historical US Premium4%

Country RiskPremium0%

InfoSoft: A Valuation

Reinvestment Rate106.82%

Return on Capital23.67%

EBIT(1-t)- ReinvFCFF

36753926 -251

46044918 -314

57686161 -393

72277720 -493

9054 9671 -617

950727646743


Play investment banker: Price this IPO

The value of equity that we have arrived at for Infosoft is $69.5 million. Ifyou plan to have 10 million shares outstanding, estimate the value per share?

Would this also be your offering price? If not, why not?

Would you answer be different, if the initial offering were for only 1 millionshares - the owners will retain the remaining 9 million for subsequentofferings?


Valuation Motives and the Next Step in Private CompanyValuation: Control and Illiquidity

If valuing a private business for sale (in whole or part) to another individual(to stay private), it is necessary that we estimate

• a illiquidity discount associated with the fact that private businesses cannot beeasily bought and sold

• a control premium (if more than 50% of the business is being sold) If valuing a business for taking public, it is necessary to estimate

• the effects of creating different classes of shares in the initial public offer• the effects of options or warrants on the issuance price per share

If valuing a business for sale (in whole or part) to a publicly traded firm, thereshould be no illiquidity discount, because stock in the parent firm will tradebut there may, however, be a premium associated with the publicly tradedfirm being able to take better advantage of the private firm’s strengths


Conventional Practice on Illiquidity

In private company valuation, illiquidity is a constant theme that analysts talkabout.

All the talk, though, seems to lead to a rule of thumb. The illiquidity discountfor a private firm is between 20-30% and does not vary across private firms.


Determinants of the Illiquidity Discount

Type of Assets owned by the Firm: The more liquid the assets owned by thefirm, the lower should be the illiquidity discount for the firm

Size of the Firm: The larger the firm, the smaller should be the percentageilliquidity discount.

Health of the Firm: Healthier firms should sell for a smaller discount thantroubled firms.

Cash Flow Generating Capacity: Firms which are generating large amountsof cash from operations should sell for a smaller discounts than firms whichdo not generate large cash flows.

Size of the Block: The liquidity discount should increase with the size of theportion of the firm being sold.


Illiquidity Discounts and Type of Business

Rank the following assets (or private businesses) in terms of the liquiditydiscount you would apply to your valuation (from biggest discount tosmallest)

A New York City Cab Medallion A small privately owned five-and-dime store in your town A large privately owned conglomerate, with significant cash balances and real

estate holdings. A large privately owned ski resort that is losing money


Empirical Evidence on Illiquidity Discounts: RestrictedStock

Restricted securities are securities issued by a company, but not registeredwith the SEC, that can be sold through private placements to investors, butcannot be resold in the open market for a two-year holding period, and limitedamounts can be sold after that. Restricted securities trade at significantdiscounts on publicly traded shares in the same company.

• Maher examined restricted stock purchases made by four mutual funds in theperiod 1969-73 and concluded that they traded an average discount of 35.43% onpublicly traded stock in the same companies.

• Moroney reported a mean discount of 35% for acquisitions of 146 restricted stockissues by 10 investment companies, using data from 1970.

• In a recent study of this phenomenon, Silber finds that the median discount forrestricted stock is 33.75%.


Cross Sectional Differences : Restricted Stock

Silber (1991) develops the following relationship between the size of thediscount and the characteristics of the firm issuing the registered stock –

LN(RPRS) = 4.33 +0.036 LN(REV) - 0.142 LN(RBRT) + 0.174 DERN + 0.332DCUST

where,RPRS = Relative price of restricted stock (to publicly traded stock)REV = Revenues of the private firm (in millions of dollars)RBRT = Restricted Block relative to Total Common Stock in %DERN = 1 if earnings are positive; 0 if earnings are negative;DCUST = 1 if there is a customer relationship with the investor; 0 otherwise;

Interestingly, Silber finds no effect of introducing a control dummy - set equalto one if there is board representation for the investor and zero otherwise.


Adjusting the average illiquidity discount for firmcharacteristics - Silber Regression

The Silber regression does provide us with a sense of how different thediscount will be for a firm with small revenues versus one with large revenues.

Consider, for example, two profitable firms that are equal in every respectexcept for revenues. Assume that the first firm has revenues of 10 million andthe second firm has revenues of 100 million. The Silber regression predictsilliquidity discounts of the following:

• For firm with 100 million in revenues: 44.5%• For firm with 10 million in revenues: 48.9%• Difference in illiquidity discounts: 4.4%

If your base discount for a firm with 10 million in revenues is 25%, theilliquidity discount for a firm with 100 million in revenues would be 20.6%.


Liquidity Discount and Revenues

Figure 24.1: Illiquidity Discounts: Base Discount of 25% for profitable firm with $ 10 million in revenues

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

5 10 15 20 25 30 35 40 45 50 100 200 300 400 500 1000

Revenues

Dis

count

as %

of

Val

ue

Profitable firm Unprofitable firm


Application to the Yankees

To estimate the illiquidity discount for the Yankees, we assume that the base discount for a firmwith $10 million in revenues would be 25%. The Yankee’s revenues of $209 million should result ina lower discount on their value. We estimate the difference in the illiquidity discount between a firmwith $10 million in revenue and $209 million in revenue to be 5.90%. To do this, we first estimatedthe illiquidity discount in the Silber equation for a firm with $10 million in revenues.

Expected illiquidity discount = 48.94% We then re-estimated the illiquidity discount with revenues of $ 209 million:

Expected illiquidity discount = 43.04% Difference in discount = 48.94% - 43.04% = 5.90% The estimated illiquidity discount for the Yankees would therefore be 19.10%, which is the base

discount of 25% adjusted for the illiquidty difference.


An Alternate Approach to the Illiquidity Discount: Bid AskSpread

The bid ask spread is the difference between the price at which you can buy asecurity and the price at which you can sell it, at the same point.

In other words, it is the illiqudity discount on a publicly traded stock. Studies have tied the bid-ask spread to

• the size of the firm• the trading volume on the stock• the degree

Regressing the bid-ask spread against variables that can be measured for aprivate firm (such as revenues, cash flow generating capacity, type of assets,variance in operating income) and are also available for publicly traded firmsoffers promise.


A Bid-Ask Spread Regression

Using data from the end of 2000, for instance, we regressed the bid-ask spread againstannual revenues, a dummy variable for positive earnings (DERN: 0 if negative and 1 ifpositive), cash as a percent of firm value and trading volume.

Spread = 0.145 – 0.0022 ln (Annual Revenues) -0.015 (DERN) – 0.016 (Cash/Firm Value)– 0.11 ($ Monthly trading volume/ Firm Value)

You could plug in the values for a private firm into this regression (with zero tradingvolume) and estimate the spread for the firm.

We could substitute in the revenues of the Yankees ($209 million), the fact that it haspositive earnings and the cash as a percent of revenues held by the firm (3%):

Spread = 0.145 – 0.0022 ln (Annual Revenues) -0.015 (DERN) – 0.016 (Cash/Firm Value)– 0.11 ($ Monthly trading volume/ Firm Value)

= 0.145 – 0.0022 ln (209) -0.015 (1) – 0.016 (.03) – 0.11 (0) = .1178 or 11.78% Based on this approach, we would estimate an illiquidity discount of 11.78% for the

Yankees.


What is control worth?

The Value of Control

Probability that you can change the management of the firm

Change in firm value from changingmanagementX

Takeover Restrictions

Voting Rules & Rights

Access to Funds

Size of company

Value of the firm run optimally

Value of the firm run status quo-


Where control matters…

In publicly traded firms, control is a factor• In the pricing of every publicly traded firm, since a portion of every stock can be

attributed to the market’s views about control.• In acquisitions, it will determine how much you pay as a premium for a firm to

control the way it is run.• When shares have voting and non-voting shares, the value of control will

determine the price difference. In private firms, control usually becomes an issue when you consider how

much to pay for a private firm.• You may pay a premium for a badly managed private firm because you think you

could run it better.• The value of control is directly related to the discount you would attach to a

minority holding (<50%) as opposed to a majority holding.• The value of control also becomes a factor in how much of an ownership stake you

will demand in exchange for a private equity investment.


Status Quo and Optimal Value

Eisner Enterprises is a poorly-managed firm that is expected to generate $ 10million in after-tax cashflows in perpetuity (if run by existing management)and is all-equity funded with a cost of equity of 10%. Estimate the status quovalue:

If you believe that you can improve the after-tax cashflows to $ 12 million ayear in perpetuity and that you could lower the cost of capital to 8% bymoving to a higher debt ratio. Estimate the optimal value for EisnerEnterprises.


Scenario 1: Valuing shares in a publicly traded firm

Assume that, based upon your assessment of takeover defenses in the firm,you estimate that there is a 40% probability that management in EisnerEnterprises will change. If there are 10 million shares outstanding in the firm,estimate the value per share?

What do you think will happen to the value per share if another firm in thesame industry is the target of a hostile acquisition?


Scenario 2: Publicly traded firm with voting and non-votingshares

Assume that Eisner Enterprises has 5 million voting shares and 5 million non-voting shares. If the probability of control changing remains 40% and non-voting shares are completely unprotected, estimate the value per voting andnon-voting share:

• Value per non-voting share =• Value per voting share =

If the incumbent managers own 35% of the voting shares, will yourassessment of the value per voting share change? If so, why? If not, why not?


Value of stock in a publicly traded firm

When a firm is badly managed, the market still assesses the probability that itwill be run better in the future and attaches a value of control to the stockprice today:

With voting shares and non-voting shares, a disproportionate share of thevalue of control will go to the voting shares. In the extreme scenario wherenon-voting shares are completely unprotected:

!

Value per share =Status Quo Value + Probability of control change (Optimal - Status Quo Value)

Number of shares outstanding

!

Value per non - voting share =Status Quo Value

# Voting Shares + # Non - voting shares

!

Value per voting share = Value of non - voting share + Probability of control change (Optimal - Status Quo Value)

# Voting Shares


Empirical Studies on Voting versus Non-Voting Shares

Studies that compare the prices of traded voting shares against the prices oftraded non-voting shares, to examine the value of the voting rightsconcludethat while the voting shares generally trade at a premium over the non-voting shares, the premium is small.

• Lease, McConnell and Mikkelson (1983) find an average premium of only 5.44%for the voting shares. (There are similar findings in DeAngelo and DeAngelo(1985) and Megginson (1990))

• These studies have been critiqued for underestimating the value of control, becausethe probability of gaining control by acquiring these voting shares is consideredlow for two reasons - first, a substantial block of the voting shares is often still heldby one or two individuals in many of these cases, and second, the prices used inthese studies are based upon small block trades, which are unlikely to give thebuyer majority control.


Scenario 3: Control Value in a Private firm

Assume now that Eisner Enterprises is a private firm. If you were bidding for100% of Eisner Enterprises, what is the maximum you would be willing tobid?

What about 51% of Eisner Enterprises?

What about 49% of Eisner Enterprises?


Minority and Majority interests

When you get a controlling interest in a private firm (generally >51%, butcould be less…), you would be willing to pay the appropriate proportion ofthe optimal value of the firm.

When you buy a minority interest in a firm, you will be willing to pay theappropriate fraction of the status quo value of the firm.

For badly managed firms, there can be a significant difference in valuebetween 51% of a firm and 49% of the same firm. This is the minoritydiscount.

If you own a private firm and you are trying to get a private equity or venturecapital investor to invest in your firm, it may be in your best interests to offerthem a share of control in the firm even though they may have well below51%.

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