Damodaran On Relval

Equity Instruments & Markets: Part II B40.3331 Relative Valuation Aswath Damodaran

Aswath Damodaran

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Why relative valuation?

“If you think I’m crazy, you should see the guy who lives across the hall” Jerry Seinfeld talking about Kramer in a Seinfeld episode “ A little inaccuracy sometimes saves tons of explanation” H.H. Munro

Aswath Damodaran

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What is relative valuation?

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In relative valuation, the value of an asset is compared to the values assessed by the market for similar or comparable assets. To do relative valuation then, • we need to identify comparable assets and obtain market values for these assets • convert these market values into standardized values, since the absolute prices cannot be compared This process of standardizing creates price multiples. • compare the standardized value or multiple for the asset being analyzed to the standardized values for comparable asset, controlling for any differences between the firms that might affect the multiple, to judge whether the asset is under or over valued

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Standardizing Value

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

Price/Earnings Ratio (PE) and variants (PEG and Relative PE) Value/EBIT Value/EBITDA Value/Cash Flow

• Book Value Multiples – Price/Book Value(of Equity) (PBV) – Value/ Book Value of Assets – Value/Replacement Cost (Tobin’s Q)

• Revenues – Price/Sales per Share (PS) – Value/Sales

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

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The Four Steps to Understanding Multiples

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Define the multiple • In use, the same multiple can be defined in different ways by different users. When comparing and using multiples, estimated by someone else, it is critical that we understand how the multiples have been estimated

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Describe the multiple • Too many people who use a multiple have no idea what its cross sectional distribution is. If you do not know what the cross sectional distribution of a multiple is, it is difficult to look at a number and pass judgment on whether it is too high or low.

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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.

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Apply the multiple • Defining the comparable universe and controlling for differences is far more difficult in practice than it is in theory.

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Definitional Tests

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Is the multiple consistently defined? • Proposition 1: Both the value (the numerator) and the standardizing variable ( the denominator) should be to the same claimholders in the firm. In other words, the value of equity should be divided by equity earnings or equity book value, and firm value should be divided by firm earnings or book value.

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Is the multiple uniformally estimated? • The variables used in defining the multiple should be estimated uniformly across assets in the “comparable firm” list. • If earnings-based multiples are used, the accounting rules to measure earnings should be applied consistently across assets. The same rule applies with book-value based multiples.

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Descriptive Tests

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What is the average and standard deviation for this multiple, across the universe (market)? What is the median for this multiple? • The median for this multiple is often a more reliable comparison point.

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How large are the outliers to the distribution, and how do we deal with the outliers? • Throwing out the outliers may seem like an obvious solution, but if the outliers all lie on one side of the distribution (they usually are large positive numbers), this can lead to a biased estimate.

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Are there cases where the multiple cannot be estimated? Will ignoring these cases lead to a biased estimate of the multiple? How has this multiple changed over time?

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Analytical Tests

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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

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How do changes in these fundamentals change the multiple? • The relationship between a fundamental (like growth) and a multiple (such as PE) is seldom linear. For example, if firm A has twice the growth rate of firm B, it will generally not trade at twice its PE ratio • Proposition 3: It is impossible to properly compare firms on a multiple, if we do not know the nature of the relationship between fundamentals and the multiple.

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Application Tests

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Given the firm that we are valuing, what is a “comparable” firm? • While traditional analysis is built on the premise that firms in the same sector are comparable firms, valuation theory would suggest that a comparable firm is one which is similar to the one being analyzed in terms of fundamentals. • Proposition 4: There is no reason why a firm cannot be compared with another firm in a very different business, if the two firms have the same risk, growth and cash flow characteristics.

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Given the comparable firms, how do we adjust for differences across firms on the fundamentals? • Proposition 5: It is impossible to find an exactly identical firm to the one you are valuing.

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Price Earnings Ratio: Definition

PE = Market Price per Share / Earnings per Share n

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There are a number of variants on the basic PE ratio in use. They are based upon how the price and the earnings are defined. Price: is usually the current price is sometimes the average price for the year EPS: earnings per share in most recent financial year earnings per share in trailing 12 months (Trailing PE) forecasted earnings per share next year (Forward PE) forecasted earnings per share in future year

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

1200

1000

Number of firms

800

Current PE 600

Trailing PE Forward PE

400

200

0 0-4

4-6

6-8

8 - 10

10 - 15

15-20

20-25

25-30

30-35

35-40

40 - 45

45- 50

50 -75

75 100

> 100

PE ratio

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

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PE Ratio: Understanding the Fundamentals

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To understand the fundamentals, start with a basic equity discounted cash flow model. With the dividend discount model, P0 =

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DPS1 r − gn

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

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If this had been a FCFE Model, P0 =

FCFE 1 r − gn

(FCFE/Earnings)*(1 + g n ) P0 = PE = EPS0 r-g n Aswath Damodaran

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PE Ratio and Fundamentals

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

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Using the Fundamental Model to Estimate PE For a High Growth Firm n

The price-earnings ratio for a high growth firm can also be related to fundamentals. In the special case of the two-stage dividend discount model, this relationship can be made explicit fairly simply: P0 =

 ( 1 +g)n  EPS0 * P a y o u t R a t i o * ( 1g + ) *1 −  ( 1 +r) n  r-g

+

EPS 0 *Payout Ration * ( 1 +g)n * ( 1 +g n ) (r - gn )(1+r)n

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

Dividing both sides by the earnings per share:  (1+ g )n   Payout Ratio *(1 + g )*  1 − (1+ r) n   Payout Ratio n * ( 1 + g )n *(1 + gn ) P0 = + (r - g n )(1+ r) n EPS 0 r -g

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Expanding the Model

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In this model, the PE ratio for a high growth firm is a function of growth, risk and payout, exactly the same variables that it was a function of for the stable growth firm. The only difference is that these inputs have to be estimated for two phases - the high growth phase and the stable growth phase. Expanding to more than two phases, say the three stage model, will mean that risk, growth and cash flow patterns in each stage.

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A Simple Example

Assume that you have been asked to estimate the PE ratio for a firm which has the following characteristics: Variable High Growth Phase Stable Growth Phase Expected Growth Rate 25% 8% Payout Ratio 20% 50% Beta 1.00 1.00 n Riskfree rate = T.Bond Rate = 6% n Required rate of return = 6% + 1(5.5%)= 11.5% n

 (1.25)5   0 . 2 * (1.25) *  1− 5 5  (1.115)  0.5 * (1.25) *(1.08) PE = + = 28.75 (.115-.08) (1.115) 5 (.115 - .25)

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PE and Growth: Firm grows at x% for 5 years, 8% thereafter PE Ratios and Expected Growth: Interest Rate Scenarios 180

160

140

PE Ratio

120

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

100

80

60

40

20

0 5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

Expected Growth Rate

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PE Ratios and Length of High Growth: 25% growth for n years; 8% thereafter PE Ratios and Length of High Growth Period 60

50

PE Ratio

40

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

30

20

10

0 0

1

2

3

4

5

6

7

8

9

10

Length of High Growth Period

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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 50 45 40 35

PE Ratio

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

25 20 15 10 5 0 0.75

1.00

1.25

1.50

1.75

2.00

Beta

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PE and Payout

PE Ratios and Payour Ratios: Growth Scenarios 35

30

25

20

PE

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

15

10

5

0 0%

20%

40%

60%

80%

100%

Payout Ratio

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PE: Emerging Markets 35

30

25

20

15

10

5

0 Mexico

Malaysia

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Singapore

Taiwan

Hong Kong

Venezuela

Brazil

Argentina

Chile

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Comparisons across countries

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In July 2000, a market strategist is making the argument that Brazil and Venezuela are cheap relative to Chile, because they have much lower PE ratios. Would you agree? Yes No What are some of the factors that may cause one market’s PE ratios to be lower than another market’s PE?

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A Comparison across countries: June 2000 Country UK Germany France Switzerland Belgium Italy Sweden Netherlands Australia Japan US Canada

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PE 22.02 26.33 29.04 19.6 14.74 28.23 32.39 21.1 21.69 52.25 25.14 26.14

Dividend Yield 2-yr rate 2.59% 5.93% 1.88% 5.06% 1.34% 5.11% 1.42% 3.62% 2.66% 5.15% 1.76% 5.27% 1.11% 4.67% 2.07% 5.10% 3.12% 6.29% 0.71% 0.58% 1.10% 6.05% 0.99% 5.70%

10-yr rate 5.85% 5.32% 5.48% 3.83% 5.70% 5.70% 5.26% 5.47% 6.25% 1.85% 5.85% 5.77%

10yr - 2yr -0.08% 0.26% 0.37% 0.21% 0.55% 0.43% 0.59% 0.37% -0.04% 1.27% -0.20% 0.07%

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Correlations and Regression of PE Ratios

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Correlations • Correlation between PE ratio and long term interest rates = -0.733 • Correlation between PE ratio and yield spread = 0.706

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Regression Results PE Ratio = 42.62 - 3.61 (10’yr rate) + 8.47 (10-yr - 2 yr rate) R2 = 59% Input the interest rates as percent. For instance, the predicted PE ratio for Japan with this regression would be: PE: Japan = 42.62 - 3.61 (1.85) + 8.47 (1.27) = 46.70 At an actual PE ratio of 52.25, Japanese stocks are slightly overvalued.

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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%

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An Example with Emerging Markets: June 2000

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Country

PE Ratio

Argentina Brazil Chile Hong Kong India Indonesia Malaysia Mexico Pakistan Peru Phillipines Singapore South Korea Thailand Turkey Venezuela

14 21 25 20 17 15 14 19 14 15 15 24 21 21 12 20

Interest Rates 18.00% 14.00% 9.50% 8.00% 11.48% 21.00% 5.67% 11.50% 19.00% 18.00% 17.00% 6.50% 10.00% 12.75% 25.00% 15.00%

GDP Real Growth 2.50% 4.80% 5.50% 6.00% 4.20% 4.00% 3.00% 5.50% 3.00% 4.90% 3.80% 5.20% 4.80% 5.50% 2.00% 3.50%

Country Risk 45 35 15 15 25 50 40 30 45 50 45 5 25 25 35 45

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Regression Results

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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%

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Predicted PE Ratios

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Country

PE Ratio

Argentina Brazil Chile Hong Kong India Indonesia Malaysia Mexico Pakistan Peru Phillipines Singapore South Korea Thailand Turkey Venezuela

14 21 25 20 17 15 14 19 14 15 15 24 21 21 12 20

Interest Rates 18.00% 14.00% 9.50% 8.00% 11.48% 21.00% 5.67% 11.50% 19.00% 18.00% 17.00% 6.50% 10.00% 12.75% 25.00% 15.00%

GDP Real Growth 2.50% 4.80% 5.50% 6.00% 4.20% 4.00% 3.00% 5.50% 3.00% 4.90% 3.80% 5.20% 4.80% 5.50% 2.00% 3.50%

Country Risk 45 35 15 15 25 50 40 30 45 50 45 5 25 25 35 45

Predicted PE 13.57 18.55 22.22 23.11 18.94 15.09 15.87 20.39 14.26 16.71 15.65 23.11 19.98 20.85 13.35 15.35

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Comparisons of PE across time: PE Ratio for the S&P 500 PE Ratio: 1960-2000 35.00

30.00

25.00

20.00

15.00

10.00

5.00

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00

98

20

19

96 19

94 19

92 19

90 19

88 19

86 19

84 19

82 19

80 19

78 19

76 19

74 19

72 19

70 19

68 19

66

64

19

19

62 19

19

60

0.00

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Is low (high) PE cheap (expensive)?

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A market strategist argues that stocks are over priced because the PE ratio today is too high relative to the average PE ratio across time. Do you agree? q Yes q No

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If you do not agree, what factors might explain the higer PE ratio today?

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

16.00%

14.00%

12.00%

10.00%

8.00%

Earnings Yield T.Bond Rate Bond-Bill

6.00%

4.00%

2.00%

20 00

19 98

19 96

19 94

19 92

19 90

19 88

19 86

19 84

19 82

19 80

19 78

19 76

19 74

19 72

19 70

19 68

19 66

19 64

19 62

19 60

0.00%

-2.00%

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Regression Results

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There is a strong positive relationship between E/P ratios and T.Bond rates, as evidenced by the correlation of 0.685 between the two variables., In addition, there is evidence that the term structure also affects the PE ratio. In the following regression, using 1960-2000 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 = 1 .88% + 0.776 T.Bond Rate - 0.407 (T.Bond Rate-T.Bill Rate) (2.84) (6.08) (-2.37) R squared = 50%

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Estimate the E/P Ratio Today

n n n n

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

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Comparing PE ratios across firms Company Name Coca-Cola Bottling Molson Inc. Ltd. 'A' Anheuser-Busch Corby Distilleries Ltd. Chalone Wine Group Ltd. Andres Wines Ltd. 'A' Todhunter Int'l Brown-Forman 'B' Coors (Adolph) 'B' PepsiCo, Inc. Coca-Cola Boston Beer 'A' Whitman Corp. Mondavi (Robert) 'A' Coca-Cola Enterprises

Trailing PE 29.18 43.65 24.31 16.24 21.76 8.96 8.94 10.07 23.02 33.00 44.33 10.59 25.19 16.47 37.14

Expected Growth 9.50% 15.50% 11.00% 7.50% 14.00% 3.50% 3.00% 11.50% 10.00% 10.50% 19.00% 17.13% 11.50% 14.00% 27.00%

Standard Dev 20.58% 21.88% 22.92% 23.66% 24.08% 24.70% 25.74% 29.43% 29.52% 31.35% 35.51% 39.58% 44.26% 45.84% 51.34%

Hansen Natural Corp

9.70

17.00%

62.45%

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A Question

You are reading an equity research report on this sector, and the analyst claims that Andres Wine and Hansen Natural are under valued because they have low PE ratios. Would you agree? o Yes o No n Why or why not?

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Comparing PE Ratios across a Sector Company Name PT Indosat ADR Telebras ADR Telecom Corporation of New Zealand ADR Telecom Argentina Stet - France Telecom SA ADR B Hellenic Telecommunication Organization SA ADR Telecomunicaciones de Chile ADR Swisscom AG ADR Asia Satellite Telecom Holdings ADR Portugal Telecom SA ADR Telefonos de Mexico ADR L Matav RT ADR Telstra ADR Gilat Communications Deutsche Telekom AG ADR British Telecommunications PLC ADR Tele Danmark AS ADR Telekomunikasi Indonesia ADR Cable & Wireless PLC ADR APT Satellite Holdings ADR Telefonica SA ADR Royal KPN NV ADR Telecom Italia SPA ADR Nippon Telegraph & Telephone ADR France Telecom SA ADR Korea Telecom ADR

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PE 7.8 8.9 11.2 12.5 12.8 16.6 18.3 19.6 20.8 21.1 21.5 21.7 22.7 24.6 25.7 27 28.4 29.8 31 32.5 35.7 42.2 44.3 45.2 71.3

Growth 0.06 0.075 0.11 0.08 0.12 0.08 0.11 0.16 0.13 0.14 0.22 0.12 0.31 0.11 0.07 0.09 0.32 0.14 0.33 0.18 0.13 0.14 0.2 0.19 0.44

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PE, Growth and Risk Dependent variable is: R squared = 66.2%

PE

R squared (adjusted) = 63.1%

Variable Coefficient SE t-ratio Constant 13.1151 3.471 3.78 Growth rate 121.223 19.27 6.29 Emerging Market -13.8531 3.606 -3.84 Emerging Market is a dummy: 1 if emerging market 0 if not

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prob 0.0010 ≤ 0.0001 0.0009

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Is Telebras under valued? n n

Predicted PE = 13.12 + 121.22 (.075) - 13.85 (1) = 8.35 At an actual price to earnings ratio of 8.9, Telebras is slightly overvalued.

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Using comparable firms- Pros and Cons

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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.

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Problems with this approach. • The definition of a 'comparable' firm is essentially a subjective one. • The use of other firms in the industry as the control group is often not a solution because firms within the same industry can have very different business mixes and risk and growth profiles. • There is also plenty of potential for bias. • Even when a legitimate group of comparable firms can be constructed, differences will continue to persist in fundamentals between the firm being valued and this group.

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Using the entire crosssection: A regression approach

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In contrast to the 'comparable firm' approach, the information in the entire cross-section of firms can be used to predict PE ratios. The simplest way of summarizing this information is with a multiple regression, with the PE ratio as the dependent variable, and proxies for risk, growth and payout forming the independent variables.

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PE versus Growth 120

100

80

60

40

20

0 -20 -20

0

20

40

60

80

100

Expected Growth in EPS: next 5 years

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PE Ratio: Standard Regression Model Summary Model 1

R

.478a

Adjusted R Square .227

R Square .229

Std. Error of the Estimate 803.9541

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

Coefficients

Standar dized Coefficients

Unstandardized Coefficients Model 1

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

a,b

B 13.090

Std. Error 1.164

-3.392 4.938

.908 1.190

.880

.040

Beta

t 11.242

Sig. .000

-.089 .098

-3.737 4.150

.000 .000

.527

22.115

.000

a. Dependent Variable: Current PE b. Weighted Least Squares Regression - Weighted by Market Cap

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Second Thoughts? n

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

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Is there a problem with your prediction?

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PE Regression- No Intercept Model Summary Model 1

R

a

R Square .832

.912b

Adjusted R Square .832

Std. Error of the Estimate 833.0224

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

Standar dized Coefficients

Unstandardized Coefficients Model 1

Beta PAYOUT1 Expected Growth in EPS: next 5 y

a,b,c

B 4.389

Std. Error .609

Beta .188

t 7.212

Sig. .000

13.299

.962

.189

13.823

.000

1.014

.039

.608

25.786

.000

a. Dependent Variable: Current PE b. Linear Regression through the Origin c. Weighted Least Squares Regression - Weighted by Market Cap

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Problems with the regression methodology

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

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The Multicollinearity Problem Correlations

Current PE

Pearson Correlation Sig. (2-tailed)

Current PE 1.000 .

Expected Growth in EPS: next 5 y .342** .000

N Pearson Correlation Sig. (2-tailed) N

3303 .342** .000 2085

Beta

Pearson Correlation Sig. (2-tailed) N

.130** .000 3027

.397** .000 2393

1.000 . 4534

-.213** .000 3114

Payout Ratio

Pearson Correlation Sig. (2-tailed) N

.009 .594 3290

-.078** .000 2143

-.213** .000 3114

1.000 . 3388

Expected Growth in EPS: next 5 y

2085 1.000 . 2675

Beta Payout Ratio .130** .009 .000 .594 3027 .397** .000 2393

3290 -.078** .000 2143

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

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Using the PE ratio regression n

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

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

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Investment Strategies that compare PE to the expected growth rate n

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If we assume that all firms within a sector have similar growth rates and risk, a strategy of picking the lowest PE ratio stock in each sector will yield undervalued stocks. Portfolio managers and analysts sometimes compare PE ratios to the expected growth rate to identify under and overvalued stocks. • In the simplest form of this approach, firms with PE ratios less than their expected growth rate are viewed as undervalued. • In its more general form, the ratio of PE ratio to growth is used as a measure of relative value.

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Problems with comparing PE ratios to expected growth n

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

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

Figure 14.2: PE Ratios and T.Bond Rates 45 40 35 30 25 20 15 10 5 0 5%

6%

7%

8%

9%

10%

T.Bond Rate

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PE Ratios Less Than The Expected Growth Rate

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In September 2001, • 33% of firms had PE ratios lower than the expected 5-year growth rate • 67% of firms had PE ratios higher than the expected 5-year growth rate

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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.

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PEG Ratio: Definition

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The PEG ratio is the ratio of price earnings to expected growth in earnings per share. PEG = PE / Expected Growth Rate in Earnings Definitional tests: • Is the growth rate used to compute the PEG ratio – on the same base? (base year EPS) – over the same period?(2 years, 5 years) – from the same source? (analyst projections, consensus estimates..)

• Is the earnings used to compute the PE ratio consistent with the growth rate estimate? – No double counting: If the estimate of growth in earnings per share is from the current year, it would be a mistake to use forward EPS in computing PE – If looking at foreign stocks or ADRs, is the earnings used for the PE ratio consistent with the growth rate estimate? (US analysts use the ADR EPS) Aswath Damodaran

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PEG Ratio: Distribution 400

300

200

100 Std. Dev = 1.05 Mean = 1.55 N = 2084.00

0

Price/ Expected Growth RAte

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PEG Ratios: The Beverage Sector Company Name Coca-Cola Bottling Molson Inc. Ltd. 'A' Anheuser-Busch Corby Distilleries Ltd. Chalone Wine Group Ltd. Andres Wines Ltd. 'A' Todhunter Int'l Brown-Forman 'B' Coors (Adolph) 'B' PepsiCo, Inc. Coca-Cola Boston Beer 'A' Whitman Corp. Mondavi (Robert) 'A' Coca-Cola Enterprises Hansen Natural Corp Average Aswath Damodaran

Trailing PE 29.18 43.65 24.31 16.24 21.76 8.96 8.94 10.07 23.02 33.00 44.33 10.59 25.19 16.47 37.14 9.70

Growth 9.50% 15.50% 11.00% 7.50% 14.00% 3.50% 3.00% 11.50% 10.00% 10.50% 19.00% 17.13% 11.50% 14.00% 27.00% 17.00%

Std Dev 20.58% 21.88% 22.92% 23.66% 24.08% 24.70% 25.74% 29.43% 29.52% 31.35% 35.51% 39.58% 44.26% 45.84% 51.34% 62.45%

PEG 3.07 2.82 2.21 2.16 1.55 2.56 2.98 0.88 2.30 3.14 2.33 0.62 2.19 1.18 1.38 0.57

22.66

0.13

0.33

2.00

55

PEG Ratio: Reading the Numbers

n

o o n

The average PEG ratio for the beverage sector is 2.00. The lowest PEG ratio in the group belongs to Hansen Natural, which has a PEG ratio of 0.57. Using this measure of value, Hansen Natural is the most under valued stock in the group the most over valued stock in the group What other explanation could there be for Hansen’s low PEG ratio?

Aswath Damodaran

56

PEG Ratio: Analysis

n

To understand the fundamentals that determine PEG ratios, let us return again to a 2-stage equity discounted cash flow model P0 =

n

 ( 1 +g)n  EPS0 * P a y o u t R a t i o * ( 1g + ) *1 −  ( 1 +r) n  r-g

+

EPS 0 *Payout Ration * ( 1 +g)n * ( 1 +g n ) (r - gn )(1+r)n

Dividing both sides of the equation by the earnings gives us the equation for the PE ratio. Dividing it again by the expected growth ‘g’  ( 1 +g)n  Payout Ratio*(1+ g) * 1 −  (1 + r) n  Payout Ratio n * ( 1 +g)n * ( 1 +g n ) PEG = + g(r - gn )(1 + r)n g(r - g)

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57

PEG Ratios and Fundamentals

n

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.

n

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

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58

A Simple Example

Assume that you have been asked to estimate the PEG ratio for a firm which has the following characteristics: Variable High Growth Phase Stable Growth Phase Expected Growth Rate 25% 8% Payout Ratio 20% 50% Beta 1.00 1.00 n Riskfree rate = T.Bond Rate = 6% n Required rate of return = 6% + 1(5.5%)= 11.5% n The PEG ratio for this firm can be estimated as follows: n

PEG =

Aswath Damodaran

 (1.25) 5  0.2 * (1.25) * 1 −  (1.115) 5  .25(.115 - .25)

0.5 * (1.25)5 *(1.08) + = .115 or 1.15 .25(.115-.08) (1.115)5

59

PEG Ratios and Risk

PEG Ratios and Beta: Different Growth Rates 3

2.5

PEG Ratio

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

1.5

1

0.5

0 0.75

1.00

1.25

1.50

1.75

2.00

Beta

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60

PEG Ratios and Quality of Growth

PEG Ratios and Retention Ratios 1.4

1.2

PEG Ratio

1

0.8 PEG 0.6

0.4

0.2

0 1

0.8

0.6

0.4

0.2

0

Retention Ratio

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61

PE Ratios and Expected Growth

PEG Ratios, Expected Growth and Interest Rates 2.50

2.00

1.50

PEG Ratio

r=6% r=8% r=10% 1.00

0.50

0.00 5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

Expected Growth Rate

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62

PEG Ratios and Fundamentals: Propositions

n

Proposition 1: High risk companies will trade at much lower PEG ratios than low risk companies with the same expected growth rate. • Corollary 1: The company that looks most under valued on a PEG ratio basis in a sector may be the riskiest firm in the sector

n

Proposition 2: Companies that can attain growth more efficiently by investing less in better return projects will have higher PEG ratios than companies that grow at the same rate less efficiently. • Corollary 2: Companies that look cheap on a PEG ratio basis may be companies with high reinvestment rates and poor project returns.

n

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

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63

PE, PEG Ratios and Risk 2.5

45

40 2

35

30 1.5 25 PE PEG Ratio 20 1 15

10

0.5

5

0

0 Lowest

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2

3

4

Highest

64

PEG Ratio: Returning to the Beverage Sector Company Name Coca-Cola Bottling Molson Inc. Ltd. 'A' Anheuser-Busch Corby Distilleries Ltd. Chalone Wine Group Ltd. Andres Wines Ltd. 'A' Todhunter Int'l Brown-Forman 'B' Coors (Adolph) 'B' PepsiCo, Inc. Coca-Cola Boston Beer 'A' Whitman Corp. Mondavi (Robert) 'A' Coca-Cola Enterprises Hansen Natural Corp Average Aswath Damodaran

Trailing PE 29.18 43.65 24.31 16.24 21.76 8.96 8.94 10.07 23.02 33.00 44.33 10.59 25.19 16.47 37.14 9.70

Growth 9.50% 15.50% 11.00% 7.50% 14.00% 3.50% 3.00% 11.50% 10.00% 10.50% 19.00% 17.13% 11.50% 14.00% 27.00% 17.00%

Std Dev 20.58% 21.88% 22.92% 23.66% 24.08% 24.70% 25.74% 29.43% 29.52% 31.35% 35.51% 39.58% 44.26% 45.84% 51.34% 62.45%

PEG 3.07 2.82 2.21 2.16 1.55 2.56 2.98 0.88 2.30 3.14 2.33 0.62 2.19 1.18 1.38 0.57

22.66

0.13

0.33

2.00

65

Analyzing PE/Growth

Given that the PEG ratio is still determined by the expected growth rates, risk and cash flow patterns, it is necessary that we control for differences in these variables. n Regressing PEG against risk and a measure of the growth dispersion, we get: PEG = 3.61 - 2.86 (Expected Growth) - 3.75 (Std Deviation in Prices) R Squared = 44.75% n In other words, n

• PEG ratios will be lower for high growth companies • PEG ratios will be lower for high risk companies n

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

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66

Estimating the PEG Ratio for Hansen

n

Applying this regression to Hansen, the predicted PEG ratio for the firm can be estimated using Hansen’s measures for the independent variables: • Expected Growth Rate = 17.00% • Standard Deviation in Stock Prices = 62.45%

Plugging in, Expected PEG Ratio for Hansen = 3.61 - 2.86 (.17) - 3.75 (.6245) = 0.78 n With its actual PEG ratio of 0.57, Hansen looks undervalued, notwithstanding its high risk. n

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67

Extending the Comparables

n

n

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

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68

PEG versus Growth 6

5

4

3

2

1

0 -1 -20

0

20

40

60

80

100

Expected Growth in EPS: next 5 years

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69

Analyzing the Relationship n

n

The relationship in not linear. In fact, the smallest firms seem to have the highest PEG ratios and PEG ratios become relatively stable at higher growth rates. To make the relationship more linear, we converted the expected growth rates in ln(expected growth rate). The relationship between PEG ratios and ln(expected growth rate) was then plotted.

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70

PEG versus ln(Expected Growth) 6

5

4

3

2

1

0 -1 -1

0

1

2

3

4

5

Ln(Expected Growth)

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71

Market PEG Ratio Regression Model Summary Model 1

R

.587a

R Square .344

Adjusted R Square .343

Std. Error of the Estimate 56.7746

a. Predictors: (Constant), LNGROWTH, PAYOUT1, Beta

Coefficients

Standar dized Coefficients

Unstandardized Coefficients Model 1

(Constant) Beta PAYOUT1 LNGROWTH

a,b

B 3.935

Std. Error .112

-7.249E-02 .575 -.867

.064 .084 .037

Beta -.025 .149 -.509

t 35.175

Sig. .000

-1.140 6.873 -23.522

.255 .000 .000

a. Dependent Variable: PEG1 b. Weighted Least Squares Regression - Weighted by Market Cap

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72

Applying the PEG ratio regression n

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

n

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

Aswath Damodaran

73

A Variant on PEG Ratio: The PEGY ratio n

n

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

Aswath Damodaran

74

Relative PE: Definition

n

n

n

The relative PE ratio of a firm is the ratio of the PE of the firm to the PE of the market. Relative PE = PE of Firm / PE of Market While the PE can be defined in terms of current earnings, trailing earnings or forward earnings, consistency requires that it be estimated using the same measure of earnings for both the firm and the market. Relative PE ratios are usually compared over time. Thus, a firm or sector which has historically traded at half the market PE (Relative PE = 0.5) is considered over valued if it is trading at a relative PE of 0.7.

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75

Relative PE: Cross Sectional Distribution

1000

800

600

400

200

Std. Dev = .77 Mean = 1.00 N = 3303.00

0

Relative PE

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76

Relative PE: Distributional Statistics

n n

The average relative PE is always one. The median relative PE is much lower, since PE ratios are skewed towards higher values. Thus, more companies trade at PE ratios less than the market PE and have relative PE ratios less than one.

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77

Relative PE: Determinants

n

To analyze the determinants of the relative PE ratios, let us revisit the discounted cash flow model we developed for the PE ratio. Using the 2-stage DDM model as our basis (replacing the payout ratio with the FCFE/Earnings Ratio, if necessary), we get n  ( 1 +g j )   Payout Ratio j * ( 1+ g j ) * 1 − n ( 1 +r )   j

Relative PE j =

rj - g j  ( 1 +g m ) n    Payout Ratio m * ( 1 +g m ) * 1 − n ( 1 +rm )   rm - gm

where Aswath Damodaran

n

+

+

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

n

Payout Ratio m,n * ( 1 +g m )n * ( 1+ gm,n ) (rm - gm,n ) ( 1 +rm )

n

Payoutj, gj, rj = Payout, growth and risk of the firm Payoutm, gm, rm = Payout, growth and risk of the market 78

Relative PE: A Simple Example

Consider the following example of a firm growing at twice the rate as the market, while having the same growth and risk characteristics of the market: Firm Market Expected growth rate 20% 10% Length of Growth Period 5 years 5 years Payout Ratio: first 5 yrs 30% 30% Growth Rate after yr 5 6% 6% Payout Ratio after yr 5 50% 50% Beta 1.00 1.00 Riskfree Rate = 6% n

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79

Estimating Relative PE

n

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

5  (1.20)  0 . 3 * (1.20) * 1−  (1.115) 5 

PE market =

n

(.115 - .20)

5  (1.10)  0 . 3 * (1.10) *  1−  (1.115)5 

(.115 - .10)

0.5 * (1.20)5 * (1.06) = 15.79 5 (.115 -.06) (1.115)

+

+

0.5 * (1.10) 5 *(1.06) = 10.45 5 (.115-.06) (1.115)

Relative PE Ratio = 15.79/10.45 = 1.51

Aswath Damodaran

80

Relative PE and Relative Growth

Relative PE and Relative Growth Rates: Market Growth Scenarios 3.50

3.00

Relative PE

2.50

2.00

Market g=5% Market g=10% Market g=15%

1.50

1.00

0.50

0.00 0%

50%

100%

150%

200%

250%

300%

Firm's Growth Rate/Market Growth Rate

Aswath Damodaran

81

Relative PE: Another Example

In this example, consider a firm with twice the risk as the market, while having the same growth and payout characteristics as the firm: Firm Market Expected growth rate 10% 10% Length of Growth Period 5 years 5 years Payout Ratio: first 5 yrs 30% 30% Growth Rate after yr 5 6% 6% Payout Ratio after yr 5 50% 50% Beta in first 5 years 2.00 1.00 Beta after year 5 1.00 1.00 Riskfree Rate = 6% n

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82

Estimating Relative PE

n

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

 (1.10) 5  0.3 * (1.10)* 1 −  (1.17) 5 

PE market =

n

(.17 - . 1 0 )

0 . 5 * (1.10)5 * (1.06) + = 8.33 (.115-.06) (1.17)5

5  (1.10)  0 . 3 * (1.10) *  1−  (1.115)5 

(.115 - .10)

+

0.5 * (1.10) 5 *(1.06) = 10.45 5 (.115-.06) (1.115)

Relative PE Ratio = 8.33/10.45 = 0.80

Aswath Damodaran

83

Relative PE and Relative Risk

Relative PE and Relative Risk: Stable Beta Scenarios 4.5

4

3.5

3

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

1.5

1

0.5

0 0.25

Aswath Damodaran

0.5

0.75

1

1.25

1.5

1.75

2

84

Relative PE: Summary of Determinants

n

The relative PE ratio of a firm is determined by two variables. In particular, it will • increase as the firm’s growth rate relative to the market increases. The rate of change in the relative PE will itself be a function of the market growth rate, with much greater changes when the market growth rate is higher. In other words, a firm or sector with a growth rate twice that of the market will have a much higher relative PE when the market growth rate is 10% than when it is 5%. • decrease as the firm’s risk relative to the market increases. The extent of the decrease depends upon how long the firm is expected to stay at this level of relative risk. If the different is permanent, the effect is much greater.

n

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

Aswath Damodaran

85

Relative PE Ratios: The Auto Sector

Relative PE Ratios: Auto Stocks 1.20

1.00

0.80

Ford Chrysler GM

0.60

0.40

0.20

0.00 1993

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1994

1995

1996

1997

1998

1999

2000

86

Using Relative PE ratios

n

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

Aswath Damodaran

87

Relative PEs: Why do they change?

n

Historically, GM has traded at the highest relative PE ratio of the three auto companies, and Chrysler has traded at the lowest. In the last two or three years, this historical relationship has been upended with Ford and Chrysler now trading at the higher ratios than GM. Analyst projections for earnings growth at the three companies are about the same. How would you explain the shift?

Aswath Damodaran

88

Relative PE Ratios: Market Analysis Model Summary Model 1

R

.478a

R Square .229

Adjusted R Square .227

Std. Error of the Estimate 41.4196

a. Predictors: (Constant), Beta, RELPYT, RELGR

Coefficients

Standar dized Coefficients

Unstandardized Coefficients Model 1

(Constant) RELGR RELPYT Beta

B

a,b

.674

Std. Error .060

.835 4.431E-02 -.175

.038 .011 .047

Beta .527 .098 -.089

t 11.242

Sig. .000

22.115 4.150 -3.737

.000 .000 .000

a. Dependent Variable: RELPE b. Weighted Least Squares Regression - Weighted by Market Cap

Aswath Damodaran

89

Value/Earnings and Value/Cashflow Ratios

While Price earnings ratios look at the market value of equity relative to earnings to equity investors, Value earnings ratios look at the market value of the firm relative to operating earnings. Value to cash flow ratios modify the earnings number to make it a cash flow number. n The form of value to cash flow ratios that has the closest parallels in DCF valuation is the value to Free Cash Flow to the Firm, which is defined as: Value/FCFF = (Market Value of Equity + Market Value of Debt-Cash) EBIT (1-t) - (Cap Ex - Deprecn) - Chg in WC n Consistency Tests: n

• •

Aswath Damodaran

If the numerator is net of cash (or if net debt is used, then the interest income from the cash should not be in denominator The interest expenses added back to get to EBIT should correspond to the debt in the numerator. If only long term debt is considered, only long term interest should be added back.

90

Value/FCFF Distribution 800

600

400

200 Std. Dev = 21.77 Mean = 20.6 N = 3063.00

0

Enterprise Value/FCFF

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91

Value of Firm/FCFF: Determinants

n

Reverting back to a two-stage FCFF DCF model, we get:  (1 + g)n  FCFF (1 + g) 1  n ( 1 +g ) 0 n FCFF ( 1 +g)  ( 1 +WACC)  0 n V0 = + WACC - g (WACC - g )(1 + WACC)n n • • •

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

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92

Value Multiples

n

Dividing both sides by the FCFF yields,  (1 + g)n  (1 + g) 1  (1 + WACC)n  V0 ( 1 +g)n ( 1 +gn ) = + WACC - g FCFF0 (WACC - gn )(1 + WACC)n

n

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

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93

Alternatives to FCFF - EBIT and EBITDA

n

Most analysts find FCFF to complex or messy to use in multiples (partly because capital expenditures and working capital have to be estimated). They use modified versions of the multiple with the following alternative denominator: • after-tax operating income or EBIT(1-t) • pre-tax operating income or EBIT • net operating income (NOI), a slightly modified version of operating income, where any non-operating expenses and income is removed from the EBIT • EBITDA, which is earnings before interest, taxes, depreciation and amortization.

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94

Value/FCFF Multiples and the Alternatives

n

o o o o n

Assume that you have computed the value of a firm, using discounted cash flow models. Rank the following multiples in the order of magnitude from lowest to highest? Value/EBIT Value/EBIT(1-t) Value/FCFF Value/EBITDA What assumption(s) would you need to make for the Value/EBIT(1-t) ratio to be equal to the Value/FCFF multiple?

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95

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

n

n

n

n

MCI Communications had earnings before interest and taxes of $3356 million in 1994 (Its net income after taxes was $855 million). It had capital expenditures of $2500 million in 1994 and depreciation of $1100 million; Working capital increased by $250 million. It expects free cashflows to the firm to grow 15% a year for the next five years and 5% a year after that. The cost of capital is 10.50% for the next five years and 10% after that. The company faces a tax rate of 36%.

 (1.15)5  (1.15)  1V0 (1.105)5  (1.15) 5 (1.05) = 31.28 = + 5 FCFF0 .105 -.15 (.10 - .05)(1.105) Aswath Damodaran

96

Multiple Magic

n

In this case of MCI there is a big difference between the FCFF and short cut measures. For instance the following table illustrates the appropriate multiple using short cut measures, and the amount you would overpay by if you used the FCFF multiple. Free Cash Flow to the Firm = EBIT (1-t) - Net Cap Ex - Change in Working Capital = 3356 (1 - 0.36) + 1100 - 2500 - 250 = $ 498 million $ Value Correct Multiple FCFF $498 31.28382355 EBIT (1-t) $2,148 7.251163362 EBIT $ 3,356 4.640744552 EBITDA $4,456 3.49513885

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97

Reasons for Increased Use of Value/EBITDA

1. The multiple can be computed even for firms that are reporting net losses, since earnings before interest, taxes and depreciation are usually positive. 2. For firms in certain industries, such as cellular, which require a substantial investment in infrastructure and long gestation periods, this multiple seems to be more appropriate than the price/earnings ratio. 3. In leveraged buyouts, where the key factor is cash generated by the firm prior to all discretionary expenditures, the EBITDA is the measure of cash flows from operations that can be used to support debt payment at least in the short term. 4. By looking at cashflows prior to capital expenditures, it may provide a better estimate of “optimal value”, especially if the capital expenditures are unwise or earn substandard returns. 5. By looking at the value of the firm and cashflows to the firm it allows for comparisons across firms with different financial leverage. Aswath Damodaran 98

Value/EBITDA Multiple

n

The Classic Definition Market Value of Equity + Market Value of Debt Value = EBITDA Earnings before Interest, Taxes and Depreciation

n

The No-Cash Version

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

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

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99

Value/EBITDA Distribution 1200

1000

800

600

400

200

Std. Dev = 8.06 Mean = 8.0 N = 3630.00

0

EV/EBITDA

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100

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

Firm value can be written as:

FCFF1 V0 = WACC - g n

The numerator can be written as follows: FCFF

Aswath Damodaran

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

101

From Firm Value to EBITDA Multiples

n

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

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

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

Aswath Damodaran

102

A Simple Example

n

Consider a firm with the following characteristics: • • • • • •

Aswath Damodaran

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

103

Calculating Value/EBITDA Multiple

n

In this case, the Value/EBITDA multiple for this firm can be estimated as follows: Value = EBITDA

Aswath Damodaran

( 1 -.36) (0.2)(.36) 0.3 0 + = 8.24 .10 - . 0 5 .10 - . 0 5 .10 - .05 .10 - .05

104

Value/EBITDA Multiples and Taxes

VEBITDA Multiples and Tax Rates 16

14

12

Value/EBITDA

10

8

6

4

2

0 0%

10%

20%

30%

40%

50%

Tax Rate

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105

Value/EBITDA and Net Cap Ex

Value/EBITDA and Net Cap Ex Ratios 12

10

Value/EBITDA

8

6

4

2

0 0%

5%

10%

15%

20%

25%

30%

Net Cap Ex/EBITDA

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106

Value/EBITDA Multiples and Return on Capital

Value/EBITDA and Return on Capital 12

10

Value/EBITDA

8

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

6

4

2

0 6%

7%

8%

9%

10%

11%

12%

13%

14%

15%

Return on Capital

Aswath Damodaran

107

Value/EBITDA Multiple: Trucking Companies Company Name KLLM Trans. Svcs. Ryder System Rollins Truck Leasing Cannon Express Inc. Hunt (J.B.) Yellow Corp. Roadway Express Marten Transport Ltd. Kenan Transport Co. M.S. Carriers Old Dominion Freight Trimac Ltd Matlack Systems XTRA Corp. Covenant Transport Inc Builders Transport Werner Enterprises Landstar Sys. AMERCO USA Truck Frozen Food Express Arnold Inds. Greyhound Lines Inc. USFreightways Golden Eagle Group Inc. Arkansas Best Airlease Ltd. Celadon Group Amer. Freightways Transfinancial Holdings Vitran Corp. 'A' Interpool Inc. Intrenet Inc. Swift Transportation Landair Services CNF Transportation Budget Group Inc Caliber System Knight Transportation Inc Heartland Express Greyhound CDA Transn Corp Mark VII Coach USA Inc US 1 Inds Inc. Average

Aswath Damodaran

Value $ 114.32 $ 5,158.04 $ 1,368.35 $ 83.57 $ 982.67 $ 931.47 $ 554.96 $ 116.93 $ 67.66 $ 344.93 $ 170.42 $ 661.18 $ 112.42 $ 1,708.57 $ 259.16 $ 221.09 $ 844.39 $ 422.79 $ 1,632.30 $ 141.77 $ 164.17 $ 472.27 $ 437.71 $ 983.86 $ 12.50 $ 578.78 $ 73.64 $ 182.30 $ 716.15 $ 56.92 $ 140.68 $ 1,002.20 $ 70.23 $ 835.58 $ 212.95 $ 2,700.69 $ 1,247.30 $ 2,514.99 $ 269.01 $ 727.50 $ 83.25 $ 160.45 $ 678.38 $ 5.60

EBITDA Value/EBITDA $ 48.81 2.34 $ 1,838.26 2.81 $ 447.67 3.06 $ 27.05 3.09 $ 310.22 3.17 $ 292.82 3.18 $ 169.38 3.28 $ 35.62 3.28 $ 19.44 3.48 $ 97.85 3.53 $ 45.13 3.78 $ 174.28 3.79 $ 28.94 3.88 $ 427.30 4.00 $ 64.35 4.03 $ 51.44 4.30 $ 196.15 4.30 $ 95.20 4.44 $ 345.78 4.72 $ 29.93 4.74 $ 34.10 4.81 $ 96.88 4.87 $ 89.61 4.88 $ 198.91 4.95 $ 2.33 5.37 $ 107.15 5.40 $ 13.48 5.46 $ 32.72 5.57 $ 120.94 5.92 $ 8.79 6.47 $ 21.51 6.54 $ 151.18 6.63 $ 10.38 6.77 $ 121.34 6.89 $ 30.38 7.01 $ 366.99 7.36 $ 166.71 7.48 $ 333.13 7.55 $ 28.20 9.54 $ 64.62 11.26 $ 6.99 11.91 $ 12.96 12.38 $ 51.76 13.11 $ (0.17) NA 5.61

108

A Test on EBITDA

n

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

Aswath Damodaran

109

Analyzing the Value/EBITDA Multiple

n

While low value/EBITDA multiples may be a symptom of undervaluation, a few questions need to be answered: • Is the operating income next year expected to be significantly lower than the EBITDA for the most recent period? (Price may have dropped) • Does the firm have significant capital expenditures coming up? (In the trucking business, the life of the trucking fleet would be a good indicator) • Does the firm have a much higher cost of capital than other firms in the sector? • Does the firm face a much higher tax rate than other firms in the sector?

Aswath Damodaran

110

Value/EBITDA Multiples: Market

n

The multiple of value to EBITDA varies widely across firms in the market, depending upon: • how capital intensive the firm is (high capital intensity firms will tend to have lower value/EBITDA ratios), and how much reinvestment is needed to keep the business going and create growth • how high or low the cost of capital is (higher costs of capital will lead to lower Value/EBITDA multiples) • how high or low expected growth is in the sector (high growth sectors will tend to have higher Value/EBITDA multiples)

Aswath Damodaran

111

US Market: Cross Sectional Regression Model Summary Model 1

R

.526a

R Square .277

Adjusted R Square .276

Std. Error of the Estimate 426.8390

a. Predictors: (Constant), Eff Tax Rate, ROC1, Expected Growth in EPS: next 5 y

Coefficients

Standar dized Coefficients

Unstandardized Coefficients Model 1

(Constant)

B 7.221

Std. Error .617

.287

.016

11.123 -.110

.670 .014

Expected Growth in EPS: next 5 y ROC1 Eff Tax Rate

a,b

Beta

t 11.707

Sig. .000

.344

17.739

.000

.319 -.155

16.610 -7.917

.000 .000

a. Dependent Variable: EV/EBITDA b. Weighted Least Squares Regression - Weighted by Market Cap

Aswath Damodaran

112

Price-Book Value Ratio: Definition

n

n

n

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

Aswath Damodaran

113

Price to Book Value: Distribution 1000

800

600

400

200

Std. Dev = 2.36 Mean = 2.39 N = 4866.00

0

PBV Ratio

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114

Price Book Value Ratio: Stable Growth Firm

n

Going back to a simple dividend discount model, P0 =

n

DPS1 r − gn

Defining the return on equity (ROE) = EPS0 / Book Value of Equity, the value of equity can be written as: P0 =

BV 0 *ROE*Payout Ratio *(1 + gn ) r - gn

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

n

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

Aswath Damodaran

115

Price Book Value Ratio: Stable Growth Firm Another Presentation n

n

This formulation can be simplified even further by relating growth to the return on equity: g = (1 - Payout ratio) * ROE Substituting back into the P/BV equation, R O E - gn P0 = PBV = BV 0 r - gn

n

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

Aswath Damodaran

116

Price Book Value Ratio for a Stable Growth Firm: Example n

n

n

n

n

n

Jenapharm was the most respected pharmaceutical manufacturer in East Germany. Jenapharm was expected to have revenues of 230 million DM and earnings before interest and taxes of 30 million DM in 1991. The firm had a book value of assets of 110 million DM, and a book value of equity of 58 million DM. The interest expenses in 1991 is expected to be 15 million DM. The corporate tax rate is 40%. The firm was expected to maintain sales in its niche product, a contraceptive pill, and grow at 5% a year in the long term, primarily by expanding into the generic drug market. The average beta of pharmaceutical firms traded on the Frankfurt Stock exchange was 1.05. The ten-year bond rate in Germany at the time of this valuation was 7%; the risk premium for stocks over bonds is assumed to be 5.5%.

Aswath Damodaran

117

Estimating a Price/Book Ratio for Jenapharm

n

n

n n

n

Expected Net Income = (EBIT - Interest Expense)*(1-t)* 1+g) = (30 15) *(1-0.4)* (1.05) = 9.45 mil DM Return on Equity = Expected Net Income / Book Value of Equity = 9.45 / 58 = 16.29% Cost on Equity = 7% + 1.05 (5.5%) = 12.775% Price/Book Value Ratio = (ROE - g) / (r - g) = (.1629 - .05) / (.12775 .05) = 1.46 Estimated MV of equity = BV of Equity * Price/BV ratio = 58 * 1.46 = $ 84.50 mil DM

Aswath Damodaran

118

Price Book Value Ratio for High Growth Firm

n

The Price-book ratio for a high-growth firm can be estimated beginning with a 2-stage discounted cash flow model:  (1+ g)n   EPS 0 *Payout Ratio *(1 + g )*  1 − ( 1 +r) n   EPS 0 * Payout Ration * ( 1 + gn) * ( 1 + gn ) P0 = + ( r- g n )(1+ r) n r -g

n

Dividing both sides of the equation by the book value of equity:   ( 1 +g)n   ROE* Payout Ratio*(1+ g)* 1 − n n   ( 1 +r)  P0 ROE n * Payout Ratio n * ( 1 +g) * ( 1 +g n )  = +  (r - gn )(1+r)n r-g BV0    

where

Aswath Damodaran

ROE = Return on Equity in high-growth period ROEn = Return on Equity in stable growth period 119

PBV Ratio for High Growth Firm: Example

Assume that you have been asked to estimate the PBV ratio for a firm which has the following characteristics: High Growth Phase Stable Growth Phase Length of Period 5 years Forever after year 5 Return on Equity 25% 15% Payout Ratio 20% 60% Growth Rate .80*.25=.20 .4*.15=.06 Beta 1.25 1.00 Cost of Equity 12.875% 11.50% The riskfree rate is 6% and the risk premium used is 5.5%. n

Aswath Damodaran

120

Estimating Price/Book Value Ratio

n

The price/book value ratio for this firm is:

 0.25 * 0.2 * (1.20) *  PBV =  (.12875  

Aswath Damodaran

5  1 − (1.20)   (1.12875) 5 

.20)

 5 0.15 * 0.6 * (1.20) * (1.06)  = 2.66 + (.115 - .06) (1.12875) 5   

121

PBV and ROE: The Key

PBV and ROE: Risk Scenarios 4

3.5

Price/Book Value Ratios

3

2.5 Beta=0.5 Beta=1 Beta=1.5

2

1.5

1

0.5

0 10%

15%

20%

25%

30%

ROE

Aswath Damodaran

122

PBV/ROE: Oil Companies Company Name Crown Cent. Petr.'A' Giant Industries Harken Energy Corp. Getty Petroleum Mktg. Pennzoil-Quaker State Ashland Inc. Shell Transport USX-Marathon Group Lakehead Pipe Line Amerada Hess Tosco Corp. Occidental Petroleum Royal Dutch Petr. Murphy Oil Corp. Texaco Inc. Phillips Petroleum Chevron Corp. Repsol-YPF ADR Unocal Corp. Kerr-McGee Corp. Exxon Mobil Corp. BP Amoco ADR Clayton Williams Energy Average

Aswath Damodaran

Ticker Symbol CNPA GI HEC GPM PZL ASH SC MRO LHP AHC TOS OXY RD MUR TX P CHV REP UCL KMG XOM BPA CWEI

PBV 0.29 0.54 0.64 0.95 0.95 1.13 1.45 1.59 1.72 1.77 1.95 2.15 2.33 2.40 2.44 2.64 3.03 3.24 3.53 3.59 4.22 4.66 5.57 2.30

ROE -14.60% 7.47% -5.83% 6.26% 3.99% 10.27% 13.41% 13.42% 13.28% 16.69% 15.44% 16.68% 13.41% 14.49% 13.77% 17.92% 15.69% 13.43% 10.67% 28.88% 11.20% 14.34% 31.02% 12.23%

123

PBV versus ROE regression

n

n

Regressing PBV ratios against ROE for oil companies yields the following regression: PBV = 1.04 + 10.24 (ROE) R2 = 49% For every 1% increase in ROE, the PBV ratio should increase by 0.1024.

Aswath Damodaran

124

Valuing Pemex

n

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

Aswath Damodaran

125

Looking for undervalued securities - PBV Ratios and ROE n

n

Given the relationship between price-book value ratios and returns on equity, it is not surprising to see firms which have high returns on equity selling for well above book value and firms which have low returns on equity selling at or below book value. The firms which should draw attention from investors are those which provide mismatches of price-book value ratios and returns on equity low P/BV ratios and high ROE or high P/BV ratios and low ROE.

Aswath Damodaran

126

The Valuation Matrix

MV/BV

Overvalued Low ROE High MV/BV

High ROE High MV/BV

ROE-r

Low ROE Low MV/BV

Aswath Damodaran

Undervalued High ROE Low MV/BV

127

Large Market Cap Firms: PBV vs ROE: January 2001

12

QCOM CSCO WAG

10

AES PEP

ADP

8

6

4

2

NTERICY A

VZ BUD

PG HD WMT TXN

ABT JNJ

AMAT

IBM

BAX

KRB MMM MMC INTCKMB DNA SBC PHA CAH BBDB.TO FITB SWY CVS AXP MWD SLR ENE AIG AVE TYC FDC MEL SLB C EDS BLS TOC.TO TGT GS EMR BBV UTX AT FNM BA AA TEF XOM JPM HON LU HI BP DD WFC FRE PNC HCA FSR PHG SNE HWP MU STD BTY AEG USB CHV AHODIS MOT DUK WM TX DOW FBF DT RD ONE UN CPQ HMC FON BNS.TO BCE TMX FTU JDSU BAC REP F ALL MC UL SC GM WCOM DCX T

0 0.0

.1

.2

.3

.4

.5

ROE Aswath Damodaran

128

Company Symbols

Company Name Matsushita Elec. ADR Compaq Computer News Corp. Ltd. ADR AT&T Corp. Schlumberger Ltd. Disney (Walt) Koninklijke Philips NV Time Warner Deutsche Telekom ADR WorldCom Inc. Motorola, Inc. Telefonica SA ADR Banco Santander ADR Sony Corp. ADR Exxon Mobil Corp. Aventis ADR Enron Corp. Pharmacia Corp. Shell Transport Royal Dutch Petr. DaimlerChrysler AG BP Amoco ADR

Aswath Damodaran

Ticker SymbolCompany Name MC British Telecom ADR CPQ Amer. Int'l Group NWS Chevron Corp. T AEGON Ins. Group SLB Sprint Corp. DIS Boeing PHG Hewlett-Packard TWX Banco Bilbao Vis. ADR DT Wells Fargo WCOM Ericsson ADR MOT Texas Instruments TEF Micron Technology STD Bank of America SNE Home Depot XOM McDonald's Corp. AVE SBC Communications ENE Wal-Mart Stores PHA Du Pont SC Citigroup Inc. RD Qualcomm Inc. DCX SmithKline Beecham BPA Chase Manhattan Corp.

Ticker SymbolCompany Name BTY Merrill Lynch & Co. AIG Fannie Mae CHV Tyco Int'l Ltd. AEG Amer. Express FON Corning Inc. BA EMC Corp. HWP Gen'l Electric BBV Intel Corp. WFC Ford Motor ERICY BellSouth Corp. TXN Johnson & Johnson MU Lucent Technologies BAC PepsiCo, Inc. HD Cisco Systems MCD Goldman Sachs SBC Medtronic, Inc. WMT Sun Microsystems DD Applied Materials C Schwab (Charles) QCOM Microsoft Corp. SBH Nokia Corp. ADR CMB Coca-Cola

Ticker Symbol MER FNM TYC AXP GLW EMC GE INTC F BLS JNJ LU PEP CSCO GS MDT SUNW AMAT SCH MSFT NOK KO

Company Name Int'l Business Mach. Abbott Labs. Morgan S. Dean Witter Amgen Dell Computer Amer. Home Products Procter & Gamble Pfizer, Inc. Schering-Plough Merck & Co. Bristol-Myers Squibb Philip Morris Lilly (Eli) Oracle Corp.

Ticker Symbol IBM ABT MWD AMGN DELL AHP PG PFE SGP MRK BMY MO LLY ORCL

129

PBV Matrix: Telecom Companies

12 TelAzteca

10 TelNZ

8

Vimple

Carlton

Cable&W

Teleglobe FranceTel

6

DeutscheTel BritTel TelItalia

Portugal

AsiaSat HongKong

Royal Hellenic

BCE

4

Nippon DanmarkChinaTel Espana

Telmex TelArgFrance PhilTel TelArgentina

2 APT CallNet Anonima

GrupoCentro

0

10

Televisas

TelIndo TelPeru

Indast

0 20

30

40

50

60

ROE

Aswath Damodaran

130

U.S. Banks: Market Cap > $ 1 billion 5.00

MEL

SNV CBH 3.75

WABC WFC

CYN CFR

P B V

2.50 ZION ASO

FVB

CMB

PNC SKYF

FULT

HU

FBF

MRBK OV

1.25

VLY

NBAK

WL

BBT

TRMK

WB

STI

CBC BPOP

FSCO UPC SOTR

CBSS BAC

RGBK

PFGI FTU

KEY UB

BOH

BWE 0.12

0.16

0.20

0.24

ROE

Aswath Damodaran

131

Company Name Westamerica Bancorp Keystone Fin'l Colonial BncGrp. 'A' One Valley Bancorp National BanCorp. of Alaska,In BancWest Corp. Hudson United Bancorp Provident Finl Group Pacific Century Fin'l Centura Banks Trustmark Corp. Sky Finl Group Inc Wilmington Trust Valley Natl Bancp NJ Commerce Bancorp NJ Cullen/Frost Bankers

Aswath Damodaran

Ticker Symbol WABC KSTN CNB OV NBAK BWE HU PFGI BOH CBC TRMK SKYF WL VLY CBH CFR

Company Name Fulton Fin'l First Va. Banks City National Corp. Hibernia Corp. `A' Silicon Valley Bncsh Mercantile Bankshares Compass Bancshares Popular Inc First Security No. Fork Bancorp Natl Commerce Bancrp UnionBancal Corp M&T Bank Corp. Zions Bancorp. Union Planters SouthTrust Corp. Summit Bancorp

Ticker Symbol FULT FVB CYN HIB SIVB MRBK CBSS BPOP FSCO NFB NCBC UB MTB ZION UPC SOTR SUB

Company Name Regions Financial Synovus Financial AmSouth Bancorp. KeyCorp BB&T Corp. Wachovia Corp. PNC Financial Serv. SunTrust Banks State Street Corp. Mellon Financial Corp. Morgan (J.P.) & Co First Union Corp. FleetBoston Fin'l Bank of New York Chase Manhattan Corp. Wells Fargo Bank of America

Ticker Symbol RGBK SNV ASO KEY BBT WB PNC STI STT MEL JPM FTU FBF BK CMB WFC BAC

132

IBM: The Rise and Fall and Rise Again

50.00%

10.00

9.00

40.00%

8.00 30.00%

7.00 20.00%

10.00% 5.00 0.00%

Return on Equity

Price to Book

6.00

4.00

-10.00% 3.00

-20.00% 2.00

-30.00%

1.00

0.00

-40.00% 1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Year PBV

Aswath Damodaran

ROE

133

PBV Ratio Regression Model Summary Model 1

R

.686a

R Square .470

Adjusted R Square .469

Std. Error of the Estimate 167.8482

a. Predictors: (Constant), Beta, ROE1, Expected Growth in EPS: next 5 y

Coefficients

Standar dized Coefficients

Unstandardized Coefficients Model 1

(Constant) Expected Growth in EPS: next 5 y ROE1 Beta

a,b

B 2.719

Std. Error .199

6.325E-02

.008

9.656 -1.438

.253 .183

Beta

t 13.678

Sig. .000

.159

8.302

.000

.667 -.150

38.183 -7.862

.000 .000

a. Dependent Variable: PBV Ratio b. Weighted Least Squares Regression - Weighted by Market Cap

Aswath Damodaran

134

PBV Ratio Regression: Brazil - September 2000 n

n

Regressing PBV against ROE for 177 Brazilian firms (The betas are missing for a lot of firms and meaningless for the rest, and there are no expected growth rate estimates over the long term) PBV = 0.77 + 3.78 (ROE) R squared = 17.3% To run this regression, we used • Only firms with positive returns on equity • Only firms with positive book values of equity

Aswath Damodaran

135

Cross Sectional Regression for Greece: May 2001

R squared = 22% Number of firms in sample = 272 Coefficients Unstandardized Coefficients Model 1

(Constant) ROE

B 2.106

Std. Error .280

11.631

1.535

a

Standar dized Coefficients Beta .418

t 7.531

Sig. .000

7.579

.000

a. Dependent Variable: PBV

Aswath Damodaran

136

Value/Book Value Ratio: Definition

n

n

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

Aswath Damodaran

137

Value/Book Ratio: Description

1400 1200 1000 800 600 400 Std. Dev = 2.63

200

Mean = 2.53 N = 4813.00

0

Value/BV of Capital

Aswath Damodaran

138

Determinants of Value/Book Ratios

n

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

FCFF1 V0 = WACC - g

n

Dividing both sides by the book value, we get:

V0 FCFF1 /BV = WACC - g BV

n

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

V0 ROC - g = WACC - g BV Aswath Damodaran

139

Value/Book Ratio: An Example

n

Consider a stable growth firm with the following characteristics: • Return on Capital = 12% • Cost of Capital = 10% • Expected Growth = 5%

n

n

The value/BV ratio for this firm can be estimated as follows: Value/BV = (.12 - .05)/(.10 - .05) = 1.40 The effects of ROC on growth will increase if the firm has a high growth phase, but the basic determinants will remain unchanged.

Aswath Damodaran

140

Value/Book and the Return Spread

Value/BV Ratios and Return Spreads 4.50 4.00

3.50

Value/BV Ratio

3.00

2.50

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

2.00

1.50 1.00

0.50

10%

9%

8%

7%

6%

5%

4%

3%

2%

1%

0%

-1%

-2%

-

ROC - WACC

Aswath Damodaran

141

Price Sales Ratio: Definition

n

n

n

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

Aswath Damodaran

142

PS Ratios: The Inconsistency Test

n

o o o

Assume that you are comparing price/sales ratios across firms in a sector, and that there are differences in financial leverage across firms. What type of firms will emerge with the lowest price/sales ratios? Low Leverage Firms Average Leverage Firms High Leverage Firms

Aswath Damodaran

143

Price/Sales Ratio: Cross Sectional Distribution

1400 1200 1000 800 600 400 Std. Dev = 2.55

200

Mean = 1.87 N = 4634.00

0

PS RATIO

Aswath Damodaran

144

Price/Sales Ratio: Determinants

n

The price/sales ratio of a stable growth firm can be estimated beginning with a 2-stage equity valuation model: P0 =

n

DPS1 r − gn

Dividing both sides by the sales per share:

Net Profit Margin*Payout Ratio * ( 1+ g n ) P0 = PS = Sales 0 r-gn

Aswath Damodaran

145

Price/Sales Ratio for High Growth Firm

n

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

 (1+ g)n    EPS0 *Payout Ratio*(1 + g )* 1 − ( 1 +r) n   EPS0 * Payout Ration * ( 1 + gn )* ( 1 + gn ) P0 = + ( r- g n )(1+ r) n r -g

n

Dividing both sides by the sales per share:

   ( 1 +g) n  Net Margin * Payout Ratio*( 1 +g ) * 1 −   ( 1 + r)n  Net Margin n * Payout Ratio n * ( 1 +g) n *(1 + gn )  P0 = +  (r - gn )(1 + r)n Sales 0  r -g    

where Net Marginn = Net Margin in stable growth phase Aswath Damodaran

146

Price Sales Ratios and Profit Margins

n n

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

Aswath Damodaran

147

Price/Sales Ratio: An Example

Length of Period Net Margin Sales/BV of Equity Beta Payout Ratio Expected Growth Riskless Rate =6%

High Growth Phase 5 years 10% 2.5 1.25 20% (.1)(2.5)(.8)=20%

Stable Growth Forever after year 5 6% 2.5 1.00 60% (.06)(2.5)(.4)=.06

5    (1.20)  0.10 * 0.2 * (1.20) *  1 − 5  (1.12875)5   0.06 * 0.60 * (1.20) * (1.06)  PS =  +  = 1.06 (.12875 - .20) (.115 -.06) (1.12875)5    

Aswath Damodaran

148

Effect of Margin Changes

Price/Sales Ratios and Net Margins 1.8

1.6

1.4

PS Ratio

1.2

1

0.8

0.6

0.4

0.2

0 2%

4%

6%

8%

10%

12%

14%

16%

Net Margin

Aswath Damodaran

149

PS/Margins: Greek Retailers

Company SPAKIANAKIS SA KOTSOVOLOS SA SANYO HELLAS IMAGE-SOV2VD SA GERMAN0S ELEKTRONIKI JUMBO PHiLIPPOS NAKAS GOODY'S HELLENIC DUTY AS COMPANY FOLLI-FOLLIE

Aswath Damodaran

PS 0.25 0.48 1.12 1.31 1.49 1.61 1.68 1.71 2.24 5.60 7.02 10.82

Net Margin 2.88% 1.91% 5.07% 2.86% 6.94% 6.29% 6.08% 5.04% 6.77% 19.49% 8.23% 29.08%

150

Regression Results: PS Ratios and Margins

n

n

n

Regressing PS ratios against net margins, PS = -.10 + 36.29 (Net Margin) R2 = 78% Thus, a 1% increase in the margin results in an increase of 0.36 in the price sales ratios. The regression also allows us to get predicted PS ratios for these firms

Aswath Damodaran

151

Predicted PS Ratios Symbol SFA KOTSV SANYO IKONA GERM ELATH BABY NAKAS GOODY HDF ASCO FOLLI

Aswath Damodaran

Company PS SPAKIANAKIS SA KOTSOVOLOS SA SANYO HELLAS IMAGE-SOV2VD SA GERMAN0S ELEKTRONIKI JUMBO PHXLXPPOS NAKAS GOODY'S HELLENIC DUTY AS COMPANY FOLLX-FOLLXE

0.25 0.48 1.12 1.31 1.49 1.61 1.68 1.71 2.24 5.60 7.02 10.82

Predicted PS Under or Over Valued 0.94 -73.28% 0.59 -18.47% 1.74 -35.37% 0.94 39.82% 2.42 -38.41% 2.18 -26.47% 2.11 -20.39% 1.73 -1.38% 2.36 -5.01% 6.97 -19.72% 2.89 143.07% 10.45 3.51%

152

Current versus Predicted Margins n

n

n

n

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

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A Case Study: The Internet Stocks 30

PKSI LCOS

20

A d j P S

INTM

SPYG MMXI

SCNT

FFIV

MQST CNET INTW

10 NETO

RAMP

CSGP

APNT SPLN

EDGRPSIX

CLKS

BIDS BIZZ

ONEM -0

CBIS

ABTL

FATB RMII

-0.8

ALOY

IIXL

INFO

TURF

-0.6

ATHY

PPOD GSVI

-0.4

ATHM DCLK NTPA

SONEPCLN AMZN

ITRA

ACOM EGRP ANET TMNT GEEK ELTX BUYX ROWE

-0.2

AdjMargin

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PS Ratios and Margins are not highly correlated n

Regressing PS ratios against current margins yields the following PS = 81.36

n

- 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.

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

Hypothesizing that firms with higher revenue growth and higher cash balances should have a greater chance of surviving and becoming profitable, we ran the following regression: (The level of revenues was used to control for size)

PS = 30.61 - 2.77 ln(Rev) + 6.42 (Rev Growth) + 5.11 (Cash/Rev) (0.66) (2.63) (3.49)

R squared = 31.8% Predicted PS = 30.61 - 2.77(7.1039) + 6.42(1.9946) + 5.11 (.3069) = 30.42 Actual PS = 25.63 Stock is undervalued, relative to other internet stocks.

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Solution 2: Use forward multiples n

n

You can always estimate price (or value) as a multiple of revenues, earnings or book value in a future year. These multiples are called forward multiples. For young and evolving firms, the values of fundamentals in future years may provide a much better picture of the true value potential of the firm. There are two ways in which you can use forward multiples: • Look at value today as a multiple of revenues or earnings in the future (say 5 years from now) for all firms in the comparable firm list. Use the average of this multiple in conjunction with your firm’s earnings or revenues to estimate the value of your firm today. • Estimate value as a multiple of current revenues or earnings for more mature firms in the group and apply this multiple to the forward earnings or revenues to the forward earnings for your firm. This will yield the expected value for your firm in the forward year and will have to be discounted back to the present to get current value.

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An Example of Forward Multiples: Amazon in early 2000 n

n

n

Amazon.com lost $0.63 per share in 2000 but is expected to earn $ 1.50 per share in 2005. At its current price of $ 49 per share, this would translate into a price/future earnings per share of 32.67. In the first approach, this multiple of earnings can be compared to the price/future earnings ratios of comparable firms. If you define comparable firms to be e-tailers, Amazon looks reasonably attractive since the average price/future earnings per share of e-tailers is 65. If, on the other hand, you compared Amazon’s price to future earnings per share to the average price to future earnings per share (in 2004) of specialty retailers, the picture is bleaker. The average price to future earnings for these firms is 12, which would lead to a conclusion that Amazon is over valued. In the second approach, the current price to earnings ratio for specialty retailers, which is estimated to be 20.31 to the earnings per share of Amazon in 2004 (which is estimated to be $1.50). This would yield a target price of $30.46. Discounting this price back to the present using Amazon’s cost of equity of 12.94% results in a value per share: Value per share = Target price in five years/ (1 + Cost of equity)5 = $30.46/1.12945 = $16.58.

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PS Regression Model Summary Model 1

R

.851a

R Square .723

Adjusted R Square .723

Std. Error of the Estimate 88.1869

a. Predictors: (Constant), Beta, MARGIN, PAYOUT, Expected Growth in EPS: next 5 y

Coefficients

Standar dized Coefficients

Unstandardized Coefficients Model 1

Expected Growth in EPS: next 5 y PAYOUT MARGIN Beta

B

a,b,c

Std. Error

Beta

t

Sig.

4.392E-02

.005

.199

9.210

.000

.807

.115

.087

7.007

.000

23.747 -.607

.466 .085

.876 -.187

50.955 -7.110

.000 .000

a. Dependent Variable: PS RATIO b. Linear Regression through the Origin c. Weighted Least Squares Regression - Weighted by Market Cap

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Cross Sectional Regression for Portugal in June 1999 Using data on 74 Portuguese companies from 1999, we regressed PS ratios against profit margins: PS = 0.98 + 6.96 Margin (4.34) (3.07) R2 = 45.29% n

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Value/Sales Ratio: Definition

n

n

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

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Value/Sales Ratio: Cross Sectional Distribution

1400 1200 1000 800 600 400 Std. Dev = 2.48

200

Mean = 2.01 N = 4644.00

0

EV/SALES

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Value/Sales Ratios: Analysis of Determinants

n

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

n

Then the Value of the Firm can be written as a function of the after-tax operating margin= (EBIT (1-t)/Sales n     (1 + g ) (1 - RIRgrowth )(1 + g)* 1−  n n (1+ WACC)  Value (1- RIR stable )(1 + g) * ( 1 +g n )    = After - tax Oper. Margin * +  Sales 0 (WACC - g n ) ( 1 +WACC) n  WACC - g    

g = Growth rate in after-tax operating income for the first n years gn = Growth rate in after-tax operating income after n years forever (Stable growth rate) RIRGrowth, Stable = Reinvestment rate in high growth and stable periods WACC = Weighted average cost of capital Aswath Damodaran

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Value/Sales Ratio: An Example

n

Consider, for example, the Value/Sales ratio of Coca Cola. The company had the following characteristics: After-tax Operating Margin =18.56% Sales/BV of Capital = 1.67 Return on Capital = 1.67* 18.56% = 31.02% Reinvestment Rate= 65.00% in high growth; 20% in stable growth; Expected Growth = 31.02% * 0.65 =20.16% (Stable Growth Rate=6%) Length of High Growth Period = 10 years Cost of Equity =12.33% E/(D+E) = 97.65% After-tax Cost of Debt = 4.16% D/(D+E) 2.35% Cost of Capital= 12.33% (.9765)+4.16% (.0235) = 12.13%

   (1.2016)10   ( 1 -.65)(1.2016)*  1−  10  10 ( 1 -.20)(1.2016) * (1.06)  Value of Firm 0  (1.1213)   = .1856* + = 6.10  (.1213-.06)(1.1213)10  Sales 0 .1213-.2016    

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Value Sales Ratios and Operating Margins

Coca Cola: The Operating Margin Effect 250

12

10

200

150

$ Value

Value/Sales Ratio

8

6

Value/Sales $ Value

100 4

50

2

0

0 6%

8%

10%

12%

14%

16%

18%

20%

Operating Margin

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U.S. Specialty Retailers: V/S vs Operating Margin 2.0

CDWC

LUX

CHCS

ISEE

DABR

MBAY

VVTV

BID

TOO BFCI SCC

1.5 TWTR

CPWM

HOTT

TLB PCCC V / S a l e s

WSM

SATH

JWL

1.0 BBY NSIT

CWTRMIKE LE

LIN SCHS GBIZ

VOXX JILL

CELL

SAH FLWS

ROSI MHCO

-0.0

MSEL

-0.000

Aswath Damodaran

PBY CHRS

Z CLWY RUSH LVC

PSRC

MNRO CAO

ITN PGDA

CC

0.5 MTMC ANIC

ORLY ZLC LTD AZO IPAR ANN ZQK PIR RAYS MDLK MENS

GADZ FINL

SPGLA

CLE FOSL

GLBE HLYW RUS

DAP

BEBE ROST

HMY FNLY

PLCE

PSUN

URBN BKE

PSS DBRN

AEOS

IBI

WLSN

MDA

TWMC

ZANY MLG

GDYS RET.TO

0.075

0.150 Operating Margin

0.225

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Brand Name Premiums in Valuation

n

o o n

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

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The value of a brand name

n

n

n

n

One of the critiques of traditional valuation is that is fails to consider the value of brand names and other intangibles. The approaches used by analysts to value brand names are often adhoc and may significantly overstate or understate their value. One of the benefits of having a well-known and respected brand name is that firms can charge higher prices for the same products, leading to higher profit margins and hence to higher price-sales ratios and firm value. The larger the price premium that a firm can charge, the greater is the value of the brand name. In general, the value of a brand name can be written as: Value of brand name ={(V/S)b-(V/S)g }* Sales (V/S)b = Value of Firm/Sales ratio with the benefit of the brand name (V/S)g = Value of Firm/Sales ratio of the firm with the generic product

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Illustration: Valuing a brand name: Coca Cola

AT Operating Margin Sales/BV of Capital ROC Reinvestment Rate Expected Growth Length Cost of Equity E/(D+E) AT Cost of Debt D/(D+E) Cost of Capital Value/Sales Ratio Aswath Damodaran

Coca Cola 18.56% 1.67 31.02% 65.00% (19.35%) 20.16% 10 years 12.33% 97.65% 4.16% 2.35% 12.13% 6.10

Generic Cola Company 7.50% 1.67 12.53% 65.00% (47.90%) 8.15% 10 yea 12.33% 97.65% 4.16% 2.35% 12.13% 0.69 169

Value of Coca Cola’s Brand Name

n

n n

Value of Coke’s Brand Name = ( 6.10 - 0.69) ($18,868 million) = $102 billion Value of Coke as a company = 6.10 ($18,546 million) = $ 115 Billion Approximately 88.69% of the value of the company can be traced to brand name value

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Value/Sales Ratio Regression: Market Model Summary Model 1

R

R Square .379

.615a

Adjusted R Square .378

Std. Error of the Estimate 110.8277

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

Coefficients

Standar dized Coefficients

Unstandardized Coefficients Model 1

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

B

a,b

.107

Std. Error .090

11.854

.340

6.041E-02

.004

Beta

t 1.196

Sig. .232

.583

34.903

.000

.238

14.274

.000

a. Dependent Variable: EV/SALES b. Weighted Least Squares Regression - Weighted by Market Cap

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Choosing Between the Multiples n

n

n

As presented in this section, there are dozens of multiples that can be potentially used to value an individual firm. In addition, relative valuation can be relative to a sector (or comparable firms) or to the entire market (using the regressions, for instance) Since there can be only one final estimate of value, there are three choices at this stage: • Use a simple average of the valuations obtained using a number of different multiples • Use a weighted average of the valuations obtained using a nmber of different multiples • Choose one of the multiples and base your valuation on that multiple

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Averaging Across Multiples n

n

n

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

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Weighted Averaging Across Multiples n

n

n

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

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Picking one Multiple n

n

This is usually the best way to approach this issue. While a range of values can be obtained from a number of multiples, the “best estimate” value is obtained using one multiple. The multiple that is used can be chosen in one of two ways: • Use the multiple that best fits your objective. Thus, if you want the company to be undervalued, you pick the multiple that yields the highest value. • Use the multiple that has the highest R-squared in the sector when regressed against fundamentals. Thus, if you have tried PE, PBV, PS, etc. and run regressions of these multiples against fundamentals, use the multiple that works best at explaining differences across firms in that sector. • Use the multiple that seems to make the most sense for that sector, given how value is measured and created.

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Self Serving Multiple Choice n

n

n

n

When a firm is valued using several multiples, some will yield really high values and some really low ones. If there is a significant bias in the valuation towards high or low values, it is tempting to pick the multiple that best reflects this bias. Once the multiple that works best is picked, the other multiples can be abandoned and never brought up. This approach, while yielding very biased and often absurd valuations, may serve other purposes very well. As a user of valuations, it is always important to look at the biases of the entity doing the valuation, and asking some questions: • Why was this multiple chosen? • What would the value be if a different multiple were used? (You pick the specific multiple that you want to see tried.)

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The Statistical Approach n

n

n

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

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A More Intuitive Approach n

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

Sector Cyclical Manufacturing High Tech, High Growth

Multiple Used PE, Relative PE PEG

High Growth/No Earnings Heavy Infrastructure

PS, VS VEBITDA

REITa

P/CF

Financial Services Retailing

PBV PS VS

Aswath Damodaran

Rationale Often with normalized earnings Big differences in growth across firms Assume future margins will be good Firms in sector have losses in early years and reported earnings can vary depending on depreciation method Generally no cap ex investments from equity earnings Book value often marked to market If leverage is similar across firms If leverage is different 178

Sector or Market Multiples n

n

The conventional approach to using multiples is to look at the sector or comparable firms. Whether sector or market based multiples make the most sense depends upon how you think the market makes mistakes in valuation • If you think that markets make mistakes on individual firm valuations but that valuations tend to be right, on average, at the sector level, you will use sector-based valuation only, • If you think that markets make mistakes on entire sectors, but is generally right on the overall market level, you will use only market-based valuation

n

It is usually a good idea to approach the valuation at two levels: • At the sector level, use multiples to see if the firm is under or over valued at the sector level • At the market level, check to see if the under or over valuation persists once you correct for sector under or over valuation.

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A Test You have valued Earthlink Networks, an internet service provider, relative to other internet companies using Price/Sales ratios and find it to be under valued almost 50% .When you value it relative to the market, using the market regression, you find it to be overvalued by almost 50%. How would you reconcile the two findings? o One of the two valuations must be wrong. A stock cannot be under and over valued at the same time. o It is possible that both valuations are right. What has to be true about valuations in the sector for the second statement to be true? n

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Reviewing: The Four Steps to Understanding Multiples n

Define the multiple • Check for consistency • Make sure that they are estimated uniformally

n

Describe the multiple • Multiples have skewed distributions: The averages are seldom good indicators of typical multiples • Check for bias, if the multiple cannot be estimated

n

Analyze the multiple • Identify the companion variable that drives the multiple • Examine the nature of the relationship

n

Apply the multiple

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