Equity Instruments & Markets: Part II B Relative Valuation

Transcription

1 Equity Instruments & Markets: Part II B Relative Valuation Aswath Damodaran Aswath Damodaran 1

2 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 2

3 What is relative valuation? In relative valuation, the value of an asset is compared to the values assessed by the market for similar or comparable assets. To do relative valuation then, we need to identify comparable assets and obtain market values for these assets convert these market values into standardized values, since the absolute prices cannot be compared This process of standardizing creates price multiples. compare the standardized value or multiple for the asset being analyzed to the standardized values for comparable asset, controlling for any differences between the firms that might affect the multiple, to judge whether the asset is under or over valued Aswath Damodaran 3

4 Standardizing Value Prices can be standardized using a common variable such as earnings, cashflows, book value or revenues. Earnings Multiples Price/Earnings Ratio (PE) and variants (PEG and Relative PE) Value/EBIT Value/EBITDA Value/Cash Flow Book Value Multiples Price/Book Value(of Equity) (PBV) Value/ Book Value of Assets Value/Replacement Cost (Tobin s Q) Revenues Price/Sales per Share (PS) Value/Sales Industry Specific Variable (Price/kwh, Price per ton of steel...) Aswath Damodaran 4

5 The Four Steps to Understanding Multiples Define the multiple In use, the same multiple can be defined in different ways by different users. When comparing and using multiples, estimated by someone else, it is critical that we understand how the multiples have been estimated Describe the multiple Too many people who use a multiple have no idea what its cross sectional distribution is. If you do not know what the cross sectional distribution of a multiple is, it is difficult to look at a number and pass judgment on whether it is too high or low. Analyze the multiple It is critical that we understand the fundamentals that drive each multiple, and the nature of the relationship between the multiple and each variable. Apply the multiple Defining the comparable universe and controlling for differences is far more difficult in practice than it is in theory. Aswath Damodaran 5

6 Definitional Tests Is the multiple consistently defined? Proposition 1: Both the value (the numerator) and the standardizing variable ( the denominator) should be to the same claimholders in the firm. In other words, the value of equity should be divided by equity earnings or equity book value, and firm value should be divided by firm earnings or book value. Is the multiple 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. Aswath Damodaran 6

7 Descriptive Tests What is the average and standard deviation for this multiple, across the universe (market)? What is the median for this multiple? The median for this multiple is often a more reliable comparison point. How large are the outliers to the distribution, and how do we deal with the outliers? Throwing out the outliers may seem like an obvious solution, but if the outliers all lie on one side of the distribution (they usually are large positive numbers), this can lead to a biased estimate. Are there cases where the multiple cannot be estimated? Will ignoring these cases lead to a biased estimate of the multiple? How has this multiple changed over time? Aswath Damodaran 7

8 Analytical Tests What are the fundamentals that determine and drive these multiples? Proposition 2: Embedded in every multiple are all of the variables that drive every discounted cash flow valuation - growth, risk and cash flow patterns. In fact, using a simple discounted cash flow model and basic algebra should yield the fundamentals that drive a multiple How do changes in these fundamentals change the multiple? The relationship between a fundamental (like growth) and a multiple (such as PE) is seldom linear. For example, if firm A has twice the growth rate of firm B, it will generally not trade at twice its PE ratio Proposition 3: It is impossible to properly compare firms on a multiple, if we do not know the nature of the relationship between fundamentals and the multiple. Aswath Damodaran 8

9 Application Tests Given the firm that we are valuing, what is a comparable firm? While traditional analysis is built on the premise that firms in the same sector are comparable firms, valuation theory would suggest that a comparable firm is one which is similar to the one being analyzed in terms of fundamentals. Proposition 4: There is no reason why a firm cannot be compared with another firm in a very different business, if the two firms have the same risk, growth and cash flow characteristics. Given the comparable firms, how do we adjust for differences across firms on the fundamentals? Proposition 5: It is impossible to find an exactly identical firm to the one you are valuing. Aswath Damodaran 9

10 Price Earnings Ratio: Definition PE = Market Price per Share / Earnings per Share There are a number of variants on the basic PE ratio in use. They are based upon how the price and the earnings are defined. Price: is usually the current price is sometimes the average price for the year EPS: earnings per share in most recent financial year earnings per share in trailing 12 months (Trailing PE) forecasted earnings per share next year (Forward PE) forecasted earnings per share in future year Aswath Damodaran 10

11 PE Ratio: Descriptive Statistics PE Ratios: January Number of firms Current PE Trailing PE Forward PE < > 100 PE Ratio Aswath Damodaran 11

12 PE: Deciphering the Distribution Current PE Trailing PE Forward PE Mean Standard Erro Median Mode Standard Devia Minimum Maximum Count Largest(10) Smallest(10) Aswath Damodaran 12

13 PE Ratio: Understanding the Fundamentals To understand the fundamentals, start with a basic equity discounted cash flow model. With the dividend discount model, P 0 = DPS 1 r g n Dividing both sides by the earnings per share, P 0 EPS 0 = PE = Payout Ratio *(1 + g n ) r-g n If this had been a FCFE Model, P 0 = FCFE 1 r g n P 0 EPS 0 = PE = (FCFE/Earnings)*(1 + g n ) r-g n Aswath Damodaran 13

14 PE Ratio and Fundamentals Proposition: Other things held equal, higher growth firms will have higher PE ratios than lower growth firms. Proposition: Other things held equal, higher risk firms will have lower PE ratios than lower risk firms Proposition: Other things held equal, firms with lower reinvestment needs will have higher PE ratios than firms with higher reinvestment rates. Of course, other things are difficult to hold equal since high growth firms, tend to have risk and high reinvestment rats. Aswath Damodaran 14

15 Using the Fundamental Model to Estimate PE For a High Growth Firm The price-earnings ratio for a high growth firm can also be related to fundamentals. In the special case of the two-stage dividend discount model, this relationship can be made explicit fairly simply: P 0 = EPS 0 *Payout Ratio*(1+ g)* 1 (1+g)n (1+r) n r - g + EPS 0 *Payout Ratio n *(1+g)n *(1+g n ) (r -g n )(1+r) n For a firm that does not pay what it can afford to in dividends, substitute FCFE/Earnings for the payout ratio. Dividing both sides by the earnings per share: P 0 EPS 0 = Payout Ratio *(1 +g)* 1 (1+g)n (1+ r) n r - g + Payout Ratio n *(1+g) n *(1 +g n ) (r - g n )(1+ r) n Aswath Damodaran 15

16 Expanding the Model In this model, the PE ratio for a high growth firm is a function of growth, risk and payout, exactly the same variables that it was a function of for the stable growth firm. The only difference is that these inputs have to be estimated for two phases - the high growth phase and the stable growth phase. Expanding to more than two phases, say the three stage model, will mean that risk, growth and cash flow patterns in each stage. Aswath Damodaran 16

17 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 Riskfree rate = T.Bond Rate = 6% Required rate of return = 6% + 1(5.5%)= 11.5% 0.2 * (1.25) * 1 (1.25)5 (1.115) 5 PE = ( ) * (1.25)5 *(1.08) ( ) (1.115) 5 = Aswath Damodaran 17

18 PE and Growth: Firm grows at x% for 5 years, 8% thereafter PE Ratios and Expected Growth: Interest Rate Scenarios PE Ratio r=4% r=6% r=8% r=10% % 10% 15% 20% 25% 30% 35% 40% 45% 50% Expected Growth Rate Aswath Damodaran 18

19 PE Ratios and Length of High Growth: 25% growth for n years; 8% thereafter PE Ratios and Length of High Growth Period PE Ratio 30 g=25% g=20% g=15% g=10% Length of High Growth Period Aswath Damodaran 19

20 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 PE Ratio g=25% g=20% g=15% g=8% Beta Aswath Damodaran 20

21 PE and Payout PE Ratios and Payour Ratios: Growth Scenarios PE g=25% g=20% g=15% g=10% % 20% 40% 60% 80% 100% Payout Ratio Aswath Damodaran 21

22 PE: Emerging Markets Mexico Malaysia Singapore Taiwan Hong Kong Venezuela Brazil Argentina Chile Aswath Damodaran 22

23 Comparisons across countries In July 2000, a market strategist is making the argument that Brazil and Venezuela are cheap relative to Chile, because they have much lower PE ratios. Would you agree? Yes No What are some of the factors that may cause one market s PE ratios to be lower than another market s PE? Aswath Damodaran 23

24 A Comparison across countries Country PE Dividend Yield 2-yr rate 10-yr rate 10yr - 2yr UK % 5.93% 5.85% -0.08% Germany % 5.06% 5.32% 0.26% France % 5.11% 5.48% 0.37% Switzerland % 3.62% 3.83% 0.21% Belgium % 5.15% 5.70% 0.55% Italy % 5.27% 5.70% 0.43% Sweden % 4.67% 5.26% 0.59% Netherlands % 5.10% 5.47% 0.37% Australia % 6.29% 6.25% -0.04% Japan % 0.58% 1.85% 1.27% US % 6.05% 5.85% -0.20% Canada % 5.70% 5.77% 0.07% Aswath Damodaran 24

25 Correlations and Regression of PE Ratios Correlations Correlation between PE ratio and long term interest rates = Correlation between PE ratio and yield spread = Regression Results PE Ratio = (10 yr rate) (10-yr - 2 yr rate) R 2 = 59% Input the interest rates as percent. For instance, the predicted PE ratio for Japan with this regression would be: PE: Japan = (1.85) (1.27) = At an actual PE ratio of 52.25, Japanese stocks are slightly overvalued. Aswath Damodaran 25

26 Predicted PE Ratios Country Actual PE Predicted PE Over/Undervalued by Australia Britain Canada France Germany Japan Netherlands Switzerland U.S Aswath Damodaran 26

27 An Example with Emerging Markets: 1994 Country Risk PE Ratio Interest Rates GDP Nom Growth Country Peru % 22.00% 20 South Korea % 17.70% 20 Malaysia % 12.10% 30 Phillipines % 14.10% 55 India % 16.20% 45 Pakistan % 16.50% 50 Turkey % 79.00% 55 Thailand % 13.20% 30 Chile % 12.40% 25 Brazil % 75.20% 60 Argentina % 11.00% 55 Indonesia % 15.20% 40 Venezuela % 15.70% 75 Mexico % 44.00% 70 Hong Kong % 10.60% 15 Singapore % 13.60% 5 Aswath Damodaran 27

28 Regression Results The regression of PE ratios on these variables provides the following PE = Interest Rates Nominal Growth in GNP Country Risk Aswath Damodaran 28

29 Predicted PE Ratios Country PE Ratio Predicted PE Over or Under Peru % South Korea % Malaysia % Phillipines % India % Pakistan % Turkey % Thailand % Chile % Brazil % Argentina % Indonesia % Venezuela % Mexico % Hong Kong % Singapore % Aswath Damodaran 29

30 Comparisons of PE across time PE Ratio: Aswath Damodaran 30

31 Is low (high) PE cheap (expensive)? A market strategist argues that stocks are over priced because the PE ratio today is too high relative to the average PE ratio across time. Do you agree? Yes No If you do not agree, what factors might explain the higer PE ratio today? Aswath Damodaran 31

32 E/P Ratios, T.Bond Rates and Term Structure 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% Earnings Yield T.Bond Rate Bond-Bill 4.00% 2.00% 0.00% % Aswath Damodaran 32

33 Regression Results There is a strong positive relationship between E/P ratios and T.Bond rates, as evidenced by the correlation of between the two variables., In addition, there is evidence that the term structure also affects the PE ratio. In the following regression, using 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% T.Bond Rate (T.Bond Rate-T.Bill Rate) (2.84) (6.08) (-2.37) R squared = 50% Aswath Damodaran 33

34 Estimate the E/P Ratio Today T. Bond Rate = T.Bond Rate - T.Bill Rate = Expected E/P Ratio = Expected PE Ratio = Aswath Damodaran 34

35 Comparing PE ratios across firms Company Name Trailing PE Expected Growth Standard Dev Coca-Cola Bottling % 20.58% Molson Inc. Ltd. 'A' % 21.88% Anheuser-Busch % 22.92% Corby Distilleries Ltd % 23.66% Chalone Wine Group Ltd % 24.08% Andres Wines Ltd. 'A' % 24.70% Todhunter Int'l % 25.74% Brown-Forman 'B' % 29.43% Coors (Adolph) 'B' % 29.52% PepsiCo, Inc % 31.35% Coca-Cola % 35.51% Boston Beer 'A' % 39.58% Whitman Corp % 44.26% Mondavi (Robert) 'A' % 45.84% Coca-Cola Enterprises % 51.34% Hansen Natural Corp % 62.45% Aswath Damodaran 35

36 A Question You are reading an equity research report on this sector, and the analyst claims that Andres Wine and Hansen Natural are under valued because they have low PE ratios. Would you agree? Yes No Why or why not? Aswath Damodaran 36

37 Using comparable firms- Pros and Cons The most common approach to estimating the PE ratio for a firm is to choose a group of comparable firms, to calculate the average PE ratio for this group and to subjectively adjust this average for differences between the firm being valued and the comparable firms. Problems with this approach. The definition of a 'comparable' firm is essentially a subjective one. The use of other firms in the industry as the control group is often not a solution because firms within the same industry can have very different business mixes and risk and growth profiles. There is also plenty of potential for bias. Even when a legitimate group of comparable firms can be constructed, differences will continue to persist in fundamentals between the firm being valued and this group. Aswath Damodaran 37

38 Using the entire crosssection: A regression approach In contrast to the 'comparable firm' approach, the information in the entire cross-section of firms can be used to predict PE ratios. The simplest way of summarizing this information is with a multiple regression, with the PE ratio as the dependent variable, and proxies for risk, growth and payout forming the independent variables. Aswath Damodaran 38

39 PE versus Growth Expected Growth in EPS: next 5 years Aswath Damodaran 39

40 PE Ratio: Standard Regression Model 1 a. Model Summary Adjusted R Std. Error of R R Square Square the Estimate.461 a ********** Predictors: (Constant), Payout Ratio, Expected Growth in EPS: next 5 years, BETA Model 1 a. (Constant) Expected Growth in EPS: next 5 years BETA Payout Ratio Dependent Variable: Trailing PE Coefficients a Unstandardized Coefficients Standar dized Coefficients B Std. Error Beta t Sig Aswath Damodaran 40

41 Second Thoughts? Based on this regression, estimate the PE ratio for a firm with no growth, no payout and no risk. Is there a problem with your prediction? Aswath Damodaran 41

42 PE Regression- No Intercept Model 1 a. b. Model Summary R R Square a Square the Estimate Adjusted R Std. Error of.795 b ********** 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. Predictors: Payout Ratio, Expected Growth in EPS: next 5 years, BETA Model 1 a. Expected Growth in EPS: next 5 years BETA Payout Ratio Dependent Variable: Trailing PE b. Linear Regression through the Origin Coefficients a,b Unstandardized Coefficients B Std. Error Standar dized Coefficients Beta t Sig. Aswath Damodaran 42

43 Problems with the regression methodology The basis 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. Aswath Damodaran 43

44 The Multicollinearity Problem Trailing PE Expected Growth in EPS: next 5 years BETA Payout Ratio Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) Correlations Expected Growth in EPS: Trailing PE next 5 years BETA Payout Ratio **.212** ** ** -.083** **.356** ** ** -.075** N **. Correlation is significant at the 0.01 level (2-tailed). Aswath Damodaran 44

45 Using the PE ratio regression Assume that you were given the following information for Dell. The firm has an expected growth rate of 15%, a beta of 1.20 and pays no dividends. Based upon the regression, estimate the predicted PE ratio for Dell. Dell is actually trading at 23 times earnings. What does the predicted PE tell you? Aswath Damodaran 45

46 Investment Strategies that compare PE to the expected growth rate If we assume that all firms within a sector have similar growth rates and risk, a strategy of picking the lowest PE ratio stock in each sector will yield undervalued stocks. Portfolio managers and analysts sometimes compare PE ratios to the expected growth rate to identify under and overvalued stocks. In the simplest form of this approach, firms with PE ratios less than their expected growth rate are viewed as undervalued. In its more general form, the ratio of PE ratio to growth is used as a measure of relative value. Aswath Damodaran 46

47 Problems with comparing PE ratios to expected growth In its simple form, there is no basis for believing that a firm is undervalued just because it has a PE ratio less than expected growth. This relationship may be consistent with a fairly valued or even an overvalued firm, if interest rates are high, or if a firm is high risk. As interest rate decrease (increase), fewer (more) stocks will emerge as undervalued using this approach. Aswath Damodaran 47

48 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 % 6% 7% 8% 9% 10% T.Bond Rate Aswath Damodaran 48

49 PE Ratios Less Than The Expected Growth Rate In January 2001, 23.55% of firms had PE ratios lower than the expected 5-year growth rate 76.45% of firms had PE ratios higher than the expected 5-year growth rate In comparison, 25.6% of firms had PE ratios lower than the expected 5-year growth rate in September % of firms had PE ratios less than the expected 5-year growth rate in September % of firm had PE ratios less than the expected 5-year growth rate in Aswath Damodaran 49

50 PEG Ratio: Definition The PEG ratio is the ratio of price earnings to expected growth in earnings per share. Definitional tests: PEG = PE / Expected Growth Rate in Earnings 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 50

51 PEG Ratio: Distribution Std. Dev = 1.89 Mean = 1.81 N = PEG Ratio Aswath Damodaran 51

52 PEG Ratios: The Beverage Sector Company Name Trailing PE Growth Std Dev PEG Coca-Cola Bottling % 20.58% 3.07 Molson Inc. Ltd. 'A' % 21.88% 2.82 Anheuser-Busch % 22.92% 2.21 Corby Distilleries Ltd % 23.66% 2.16 Chalone Wine Group Ltd % 24.08% 1.55 Andres Wines Ltd. 'A' % 24.70% 2.56 Todhunter Int'l % 25.74% 2.98 Brown-Forman 'B' % 29.43% 0.88 Coors (Adolph) 'B' % 29.52% 2.30 PepsiCo, Inc % 31.35% 3.14 Coca-Cola % 35.51% 2.33 Boston Beer 'A' % 39.58% 0.62 Whitman Corp % 44.26% 2.19 Mondavi (Robert) 'A' % 45.84% 1.18 Coca-Cola Enterprises % 51.34% 1.38 Hansen Natural Corp % 62.45% 0.57 Aswath Damodaran Average

53 PEG Ratio: Reading the Numbers The average PEG ratio for the beverage sector is The lowest PEG ratio in the group belongs to Hansen Natural, which has a PEG ratio of 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 53

54 PEG Ratio: Analysis To understand the fundamentals that determine PEG ratios, let us return again to a 2-stage equity discounted cash flow model P 0 = EPS 0 *Payout Ratio*(1+ g)* 1 (1+g)n (1+r) n r - g + EPS 0 *Payout Ratio n *(1+g)n *(1+g n ) (r -g n )(1+r) n Dividing both sides of the equation by the earnings gives us the equation for the PE ratio. Dividing it again by the expected growth g PEG = Payout Ratio*(1+ g) * 1 (1+g)n (1 + r) n g(r - g) + Payout Ratio n * (1+g)n *(1+g n ) g(r - g n )(1 + r) n Aswath Damodaran 54

55 PEG Ratios and Fundamentals Risk and payout, which affect PE ratios, continue to affect PEG ratios as well. Implication: When comparing PEG ratios across companies, we are making implicit or explicit assumptions about these variables. Dividing PE by expected growth does not neutralize the effects of expected growth, since the relationship between growth and value is not linear and fairly complex (even in a 2-stage model) Aswath Damodaran 55

56 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 Riskfree rate = T.Bond Rate = 6% Required rate of return = 6% + 1(5.5%)= 11.5% The PEG ratio for this firm can be estimated as follows: PEG = 0.2 * (1.25) * 1 (1.25) 5 (1.115) 5.25( ) * (1.25) 5 *(1.08) =.115 or ( ) (1.115) Aswath Damodaran 56

57 PEG Ratios and Risk PEG Ratios and Beta: Different Growth Rates PEG Ratio 1.5 g =25% g=20% g=15% g=8% Beta Aswath Damodaran 57

58 PEG Ratios and Quality of Growth PEG Ratios and Retention Ratios PEG Ratio PEG Retention Ratio Aswath Damodaran 58

59 PE Ratios and Expected Growth PEG Ratios, Expected Growth and Interest Rates PEG Ratio r=6% r=8% r=10% % 10% 15% 20% 25% 30% 35% 40% 45% 50% Expected Growth Rate Aswath Damodaran 59

60 PEG Ratios and Fundamentals: Propositions Proposition 1: High risk companies will trade at much lower PEG ratios than low risk companies with the same expected growth rate. Corollary 1: The company that looks most under valued on a PEG ratio basis in a sector may be the riskiest firm in the sector Proposition 2: Companies that can attain growth more efficiently by investing less in better return projects will have higher PEG ratios than companies that grow at the same rate less efficiently. Corollary 2: Companies that look cheap on a PEG ratio basis may be companies with high reinvestment rates and poor project returns. Proposition 3: Companies with very low or very high growth rates will tend to have higher PEG ratios than firms with average growth rates. This bias is worse for low growth stocks. Corollary 3: PEG ratios do not neutralize the growth effect. Aswath Damodaran 60

61 PE, PEG Ratios and Risk PE PEG Ratio Lowest Highest 0 Aswath Damodaran 61

62 PEG Ratio: Returning to the Beverage Sector Company Name Trailing PE Growth Std Dev PEG Coca-Cola Bottling % 20.58% 3.07 Molson Inc. Ltd. 'A' % 21.88% 2.82 Anheuser-Busch % 22.92% 2.21 Corby Distilleries Ltd % 23.66% 2.16 Chalone Wine Group Ltd % 24.08% 1.55 Andres Wines Ltd. 'A' % 24.70% 2.56 Todhunter Int'l % 25.74% 2.98 Brown-Forman 'B' % 29.43% 0.88 Coors (Adolph) 'B' % 29.52% 2.30 PepsiCo, Inc % 31.35% 3.14 Coca-Cola % 35.51% 2.33 Boston Beer 'A' % 39.58% 0.62 Whitman Corp % 44.26% 2.19 Mondavi (Robert) 'A' % 45.84% 1.18 Coca-Cola Enterprises % 51.34% 1.38 Hansen Natural Corp % 62.45% 0.57 Aswath Damodaran Average

63 Analyzing PE/Growth Given that the PEG ratio is still determined by the expected growth rates, risk and cash flow patterns, it is necessary that we control for differences in these variables. Regressing PEG against risk and a measure of the growth dispersion, we get: PEG = (Expected Growth) (Std Deviation in Prices) In other words, PEG ratios will be lower for high growth companies PEG ratios will be lower for high risk companies R Squared = 44.75% 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. Aswath Damodaran 63

64 Estimating the PEG Ratio for Pepsico Applying this regression to Pepsico, the predicted PEG ratio for the firm can be estimated using Pepsi s measures for the independent variables: Expected Growth Rate = 10.50% Standard Deviation in Stock Prices = 31.35% Plugging in, Expected PEG Ratio for Pepsi = (.105) (.3135) = 2.13 With its actual PEG ratio of 3.14, Pepsi looks significantly over valued. Aswath Damodaran 64

65 Extending the Comparables This analysis, which is restricted to firms in the software sector, can be expanded to include all firms in the firm, as long as we control for differences in risk, growth and payout. To look at the cross sectional relationship, we first plotted PEG ratios against expected growth rates. Aswath Damodaran 65

66 PEG versus Growth Expected Growth in EPS: next 5 years Aswath Damodaran 66

67 Analyzing the Relationship The relationship in not linear. In fact, the smallest firms seem to have the highest PEG ratios and PEG ratios become relatively stable at higher growth rates. To make the relationship more linear, we converted the expected growth rates in ln(expected growth rate). The relationship between PEG ratios and ln(expected growth rate) was then plotted. Aswath Damodaran 67

68 PEG versus ln(expected Growth) LNGROWTH Aswath Damodaran 68

69 Market PEG Ratio Regression Model 1 a. b. Model Summary R R Square a Square the Estimate Adjusted R Std. Error of.859 b ********** 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. Predictors: LNGROWTH, Payout Ratio, BETA Model 1 a. BETA Payout Ratio LNGROWTH Dependent Variable: PEG Ratio Unstandardized Coefficients b. Linear Regression through the Origin Coefficients a,b Standar dized Coefficients B Std. Error Beta t Sig Aswath Damodaran 69

70 Applying the PEG ratio regression Consider Dell again. The stock has an expected growth rate of 15%, a beta of 1.20 and pays out no dividends. What should its PEG ratio be? If the stock s actual PE ratio is 23, what does this analysis tell you about the stock? Aswath Damodaran 70

71 A Variant on PEG Ratio: The PEGY ratio The PEG ratio is biased against low growth firms because the relationship between value and growth is non-linear. One variant that has been devised to consolidate the growth rate and the expected dividend yield: PEGY = PE / (Expected Growth Rate + Dividend Yield) As an example, Con Ed has a PE ratio of 16, an expected growth rate of 5% in earnings and a dividend yield of 4.5%. PEG = 16/ 5 = 3.2 PEGY = 16/(5+4.5) = 1.7 Aswath Damodaran 71

72 Relative PE: Definition The relative PE ratio of a firm is the ratio of the PE of the firm to the PE of the market. Relative PE = PE of Firm / PE of Market While the PE can be defined in terms of current earnings, trailing earnings or forward earnings, consistency requires that it be estimated using the same measure of earnings for both the firm and the market. Relative PE ratios are usually compared over time. Thus, a firm or sector which has historically traded at half the market PE (Relative PE = 0.5) is considered over valued if it is trading at a relative PE of 0.7. Aswath Damodaran 72

73 Relative PE: Cross Sectional Distribution Std. Dev = 1.03 Mean = 1.00 N = RELPE Aswath Damodaran 73

74 Relative PE: Distributional Statistics 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. Aswath Damodaran 74

75 Relative PE: Determinants To analyze the determinants of the relative PE ratios, let us revisit the discounted cash flow model we developed for the PE ratio. Using the 2-stage DDM model as our basis (replacing the payout ratio with the FCFE/Earnings Ratio, if necessary), we get Relative PE j = Payout Ratio j *(1+g j )* 1 (1+g j )n (1+r j ) n + Payout Ratio j,n *(1+g j ) n *(1+g j,n ) r j - g j (r j - g j,n )(1 + r j ) n Payout Ratio m * (1+g m )* 1 (1+g m) n (1+r m ) n + Payout Ratio m,n * (1+g m ) n *(1+g m,n) r m - g m (r m - g m,n )(1+r m ) n where Payout j, g j, r j = Payout, growth and risk of the firm Payout m, g m, r m = Payout, growth and risk of the market Aswath Damodaran 75

76 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 Riskfree Rate = 6% Aswath Damodaran 76

77 Estimating Relative PE The relative PE ratio for this firm can be estimated in two steps. First, we compute the PE ratio for the firm and the market separately: 0.3 *(1.20) * 1 (1.20)5 (1.115) 5 PE firm = ( ) * (1.20)5 * (1.06) ( ) (1.115) 5 = *(1.10) * 1 (1.10)5 (1.115) 5 PE market = ( ) * (1.10)5 *(1.06) ( ) (1.115) 5 = Relative PE Ratio = 15.79/10.45 = 1.51 Aswath Damodaran 77

78 Relative PE and Relative Growth Relative PE and Relative Growth Rates: Market Growth Scenarios Relative PE Market g=5% Market g=10% Market g=15% % 50% 100% 150% 200% 250% 300% Firm's Growth Rate/Market Growth Rate Aswath Damodaran 78

79 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 Beta after year Riskfree Rate = 6% Aswath Damodaran 79

80 Estimating Relative PE The relative PE ratio for this firm can be estimated in two steps. First, we compute the PE ratio for the firm and the market separately: 0.3 * (1.10)* 1 (1.10) 5 (1.17) 5 PE firm = ( ) * (1.10)5 * (1.06) ( ) (1.17) 5 = *(1.10) * 1 (1.10)5 (1.115) 5 PE market = ( ) * (1.10)5 *(1.06) ( ) (1.115) 5 = Relative PE Ratio = 8.33/10.45 = 0.80 Aswath Damodaran 80

81 Relative PE and Relative Risk Relative PE and Relative Risk: Stable Beta Scenarios Beta stays at current level Beta drops to 1 in stable phase Aswath Damodaran 81

82 Relative PE: Summary of Determinants The relative PE ratio of a firm is determined by two variables. In particular, it will increase as the firm s growth rate relative to the market increases. The rate of change in the relative PE will itself be a function of the market growth rate, with much greater changes when the market growth rate is higher. In other words, a firm or sector with a growth rate twice that of the market will have a much higher relative PE when the market growth rate is 10% than when it is 5%. decrease as the firm s risk relative to the market increases. The extent of the decrease depends upon how long the firm is expected to stay at this level of relative risk. If the different is permanent, the effect is much greater. Relative PE ratios seem to be unaffected by the level of rates, which might give them a decided advantage over PE ratios. Aswath Damodaran 82

83 Relative PE Ratios: The Auto Sector Relative PE Ratios: Auto Stocks Ford Chrysler GM Aswath Damodaran 83

84 Using Relative PE ratios 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 84

85 Relative PEs: Why do they change? 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 85

86 Relative PE Ratios: Market Analysis Model 1 a. Model Summary Adjusted R Std. Error of R R Square Square the Estimate.461 a Predictors: (Constant), RELPYT, RELGR, BETA Model 1 (Constant) BETA RELGR Unstandardized Coefficients Coefficients a Standar dized Coefficients B Std. Error Beta t Sig RELPYT 1.702E a. Dependent Variable: RELPE Aswath Damodaran 86

87 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. 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) Consistency Tests: EBIT (1-t) - (Cap Ex - Deprecn) - Chg in WC 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. Aswath Damodaran 87

88 Value/FCFF Distribution Std. Dev = Mean = 21.0 N = VALFCFF Aswath Damodaran 88

89 Value of Firm/FCFF: Determinants Reverting back to a two-stage FCFF DCF model, we get: (1 + g) n FCFF (1 + g) 1-0 (1+WACC) n FCFF V 0 = + 0 (1+g) n (1+g n ) WACC - g (WACC - g )(1 + WACC) n n V 0 = Value of the firm (today) FCFF 0 = 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 g n = Expected growth rate in FCFF in stable growth period (after n years) Aswath Damodaran 89

90 Value Multiples Dividing both sides by the FCFF yields, V 0 FCFF 0 = (1 + g) n (1 + g) 1- (1 + WACC) n WACC - g + (1+g) n (1+g n ) (WACC - g n )(1 + WACC) n The value/fcff multiples is a function of the cost of capital the expected growth Aswath Damodaran 90

91 Alternatives to FCFF - EBIT and EBITDA Most analysts find FCFF to complex or messy to use in multiples (partly because capital expenditures and working capital have to be estimated). They use modified versions of the multiple with the following alternative denominator: after-tax operating income or EBIT(1-t) pre-tax operating income or EBIT net operating income (NOI), a slightly modified version of operating income, where any non-operating expenses and income is removed from the EBIT EBITDA, which is earnings before interest, taxes, depreciation and amortization. Aswath Damodaran 91

92 Value/FCFF Multiples and the Alternatives Assume that you have computed the value of a firm, using discounted cash flow models. Rank the following multiples in the order of magnitude from lowest to highest? Value/EBIT Value/EBIT(1-t) Value/FCFF Value/EBITDA What assumption(s) would you need to make for the Value/EBIT(1-t) ratio to be equal to the Value/FCFF multiple? Aswath Damodaran 92

93 Illustration: Using Value/FCFF Approaches to value a firm: MCI Communications MCI Communications had earnings before interest and taxes of $3356 million in 1994 (Its net income after taxes was $855 million). It had capital expenditures of $2500 million in 1994 and depreciation of $1100 million; Working capital increased by $250 million. It expects free cashflows to the firm to grow 15% a year for the next five years and 5% a year after that. The cost of capital is 10.50% for the next five years and 10% after that. The company faces a tax rate of 36%. V 0 FCFF 0 = (1.15) 1- (1.15)5 (1.105) (1.15) 5 (1.05) ( )(1.105) 5 = Aswath Damodaran 93

94 Multiple Magic In this case of MCI there is a big difference between the FCFF and short cut measures. For instance the following table illustrates the appropriate multiple using short cut measures, and the amount you would overpay by if you used the FCFF multiple. Free Cash Flow to the Firm = EBIT (1-t) - Net Cap Ex - Change in Working Capital = 3356 (1-0.36) = $ 498 million $ Value Correct Multiple FCFF $ EBIT (1-t) $2, EBIT $ 3, EBITDA $4, Aswath Damodaran 94

95 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 95

96 Value/EBITDA Multiple The Classic Definition Value EBITDA = Market Value of Equity + Market Value of Debt Earnings before Interest, Taxes and Depreciation The No-Cash Version Value EBITDA = Market Value of Equity + Market Value of Debt - Cash Earnings before Interest, Taxes and Depreciation When cash and marketable securities are netted out of value, none of the income from the cash and securities should be reflected in the denominator. Aswath Damodaran 96

97 Value/EBITDA Distribution Std. Dev = Mean = 11.7 N = EV/EBITDA Aswath Damodaran 97

98 The Determinants of Value/EBITDA Multiples: Linkage to DCF Valuation Firm value can be written as: V 0 = FCFF 1 WACC - g The numerator can be written as follows: FCFF = EBIT (1-t) - (Cex - Depr) - Working Capital = (EBITDA - Depr) (1-t) - (Cex - Depr) - Working Capital = EBITDA (1-t) + Depr (t) - Cex - Working Capital Aswath Damodaran 98

99 From Firm Value to EBITDA Multiples Now the Value of the firm can be rewritten as, Value = EBITDA (1-t) + Depr (t) - Cex - Working Capital WACC - g Dividing both sides of the equation by EBITDA, Value EBITDA = (1- t) WACC-g + Depr (t)/ebitda WACC -g - CEx/EBITDA WACC - g - Working Capital/EBITDA WACC - g Aswath Damodaran 99

100 A Simple Example Consider a firm with the following characteristics: Tax Rate = 36% Capital Expenditures/EBITDA = 30% Depreciation/EBITDA = 20% Cost of Capital = 10% The firm has no working capital requirements The firm is in stable growth and is expected to grow 5% a year forever. Note that the return on capital implied in this growth rate can be calculated as follows: g = ROC * Reinvestment Rate.05 = ROC * Net Cap Ex/EBIT (1-t) = ROC * ( )/[(1-.2)(1-.36)] Solving for ROC, ROC = 25.60% Aswath Damodaran 100

101 Calculating Value/EBITDA Multiple In this case, the Value/EBITDA multiple for this firm can be estimated as follows: Value EBITDA = (1-.36) (0.2)(.36) = 8.24 Aswath Damodaran 101

102 Value/EBITDA Multiples and Taxes VEBITDA Multiples and Tax Rates Value/EBITDA % 10% 20% 30% 40% 50% Tax Rate Aswath Damodaran 102

103 Value/EBITDA and Net Cap Ex Value/EBITDA and Net Cap Ex Ratios Value/EBITDA % 5% 10% 15% 20% 25% 30% Net Cap Ex/EBITDA Aswath Damodaran 103

104 Value/EBITDA Multiples and Return on Capital Value/EBITDA and Return on Capital Value/EBITDA 6 WACC=10% WACC=9% WACC=8% % 7% 8% 9% 10% 11% 12% 13% 14% 15% Return on Capital Aswath Damodaran 104

105 Value/EBITDA Multiple: Trucking Companies Company Name Value EBITDA Value/EBITDA KLLM Trans. Svcs. $ $ Ryder System $ 5, $ 1, Rollins Truck Leasing $ 1, $ 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. $ 1, $ Covenant Transport Inc $ $ Builders Transport $ $ Werner Enterprises $ $ Landstar Sys. $ $ AMERCO $ 1, $ 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. $ 1, $ Intrenet Inc. $ $ Swift Transportation $ $ Landair Services $ $ CNF Transportation $ 2, $ Budget Group Inc $ 1, $ Caliber System $ 2, $ Knight Transportation Inc $ $ Heartland Express $ $ Greyhound CDA Transn Corp $ $ Mark VII $ $ Coach USA Inc $ $ US 1 Inds Inc. $ 5.60 $ (0.17) NA Average 5.61 Aswath Damodaran 105

106 A Test on EBITDA Ryder System looks very cheap on a Value/EBITDA multiple basis, relative to the rest of the sector. What explanation (other than misvaluation) might there be for this difference? Aswath Damodaran 106

107 Analyzing the Value/EBITDA Multiple While low value/ebitda multiples may be a symptom of undervaluation, a few questions need to be answered: Is the operating income next year expected to be significantly lower than the EBITDA for the most recent period? (Price may have dropped) Does the firm have significant capital expenditures coming up? (In the trucking business, the life of the trucking fleet would be a good indicator) Does the firm have a much higher cost of capital than other firms in the sector? Does the firm face a much higher tax rate than other firms in the sector? Aswath Damodaran 107

108 Value/EBITDA Multiples: Market The multiple of value to EBITDA varies widely across firms in the market, depending upon: how capital intensive the firm is (high capital intensity firms will tend to have lower value/ebitda ratios), and how much reinvestment is needed to keep the business going and create growth how high or low the cost of capital is (higher costs of capital will lead to lower Value/EBITDA multiples) how high or low expected growth is in the sector (high growth sectors will tend to have higher Value/EBITDA multiples) Aswath Damodaran 108

109 US Market: Cross Sectional Regression Model 1 a. Model Summary Adjusted R Std. Error of R R Square Square the Estimate.479 a ********** Predictors: (Constant), Eff Tax Rate, Reinvestment Rate, Expected Growth in EPS: next 5 years, Standard Deviation Coefficients a Model 1 a. (Constant) Standard Deviation Eff Tax Rate Expected Growth in EPS: next 5 years CPEXVAL Dependent Variable: EVEBITD1 Unstandardized Coefficients Standar dized Coefficients B Std. Error Beta t Sig Aswath Damodaran 109

110 Price-Book Value Ratio: Definition The price/book value ratio is the ratio of the market value of equity to the book value of equity, i.e., the measure of shareholders equity in the balance sheet. Price/Book Value = Market Value of Equity Consistency Tests: Book Value of Equity 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 110

111 Price to Book Value: Distribution Std. Dev = 2.85 Mean = 2.79 N = PBV Ratio Aswath Damodaran 111

112 Price Book Value Ratio: Stable Growth Firm Going back to a simple dividend discount model, P 0 = DPS 1 r g n Defining the return on equity (ROE) = EPS 0 / Book Value of Equity, the value of equity can be written as: P 0 = BV 0 *ROE*Payout Ratio*(1 + g n ) r-g n P 0 = PBV = ROE*Payout Ratio*(1 + g n ) BV 0 r-g n If the return on equity is based upon expected earnings in the next time period, this can be simplified to, P 0 BV 0 = PBV = ROE *Payout Ratio r-g n Aswath Damodaran 112

113 Price Book Value Ratio: Stable Growth Firm Another Presentation This formulation can be simplified even further by relating growth to the return on equity: g = (1 - Payout ratio) * ROE Substituting back into the P/BV equation, P 0 BV 0 = PBV = ROE - g n r-g 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 113