Damodaran Valuation
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Equity Instruments & Markets: Part II B40.3331 Relative Valuation and Private Company Valuation Aswath Damodaran
Aswath Damodaran
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The Essence of relative valuation?
In relative valuation, the value of an asset is compared to the values assessed by the market for similar or comparable assets. To do relative valuation then, • • •
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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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Relative valuation is pervasive…
Most valuations on Wall Street are relative valuations. • • •
Almost 85% of equity research reports are based upon a multiple and comparables. More than 50% of all acquisition valuations are based upon multiples Rules of thumb based on multiples are not only common but are often the basis for final valuation judgments.
While there are more discounted cashflow valuations in consulting and corporate finance, they are often relative valuations masquerading as discounted cash flow valuations. • •
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The objective in many discounted cashflow valuations is to back into a number that has been obtained by using a multiple. The terminal value in a significant number of discounted cashflow valuations is estimated using a multiple.
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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
“ If you are going to screw up, make sure that you have lots of company” Ex-portfolio manager Aswath Damodaran
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So, you believe only in intrinsic value? Here’s why you should still care about relative value
Even if you are a true believer in discounted cashflow valuation, presenting your findings on a relative valuation basis will make it more likely that your findings/recommendations will reach a receptive audience. In some cases, relative valuation can help find weak spots in discounted cash flow valuations and fix them. The problem with multiples is not in their use but in their abuse. If we can find ways to frame multiples right, we should be able to use them better.
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Multiples are just standardized estimates of price…
You can standardize either the equity value of an asset or the value of the asset itself, which goes in the numerator. You can standardize by dividing by the •
Earnings of the asset – – – –
•
Price/Earnings Ratio (PE) and variants (PEG and Relative PE) Value/EBIT Value/EBITDA Value/Cash Flow
Book value of the asset – Price/Book Value(of Equity) (PBV) – Value/ Book Value of Assets – Value/Replacement Cost (Tobin’s Q)
•
Revenues generated by the asset – Price/Sales per Share (PS) – Value/Sales
•
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Asset or Industry Specific Variable (Price/kwh, Price per ton of steel ....)
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The Four Steps to Understanding Multiples
Define the multiple •
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 •
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
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 •
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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
Is the multiple consistently defined? •
Proposition 1: Both the value (the numerator) and the standardizing variable ( the denominator) should be to the same claimholders in the firm. In other words, the value of equity should be divided by equity earnings or equity book value, and firm value should be divided by firm earnings or book value.
Is the multiple uniformly estimated? • •
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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 bookvalue based multiples.
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Descriptive Tests
What is the average and standard deviation for this multiple, across the universe (market)? What is the median for this multiple? •
How large are the outliers to the distribution, and how do we deal with the outliers? •
The median for this multiple is often a more reliable comparison point.
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?
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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? •
•
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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
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? •
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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
There are a number of variants on the basic PE ratio in use. They are based upon how the price and the earnings are defined. Price: •
is usually the current price (though some like to use average price over last 6 months or year)
EPS: •
• • •
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Time variants: EPS in most recent financial year (current), EPS in most recent four quarters (trailing), EPS expected in next fiscal year or next four quartes (both called forward) or EPS in some future year Primary, diluted or partially diluted Before or after extraordinary items Measured using different accounting rules (options expensed or not, pension fund income counted or not…)
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PE Ratio: Distribution for the US: January 2004
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PE: Deciphering the Distribution
Mean Standard Error Median Kurtosis Skewness Minimum Maximum Count 500th largest 500th smallest
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Current PE 41.41 2.42 20.76 1062.81 27.78 0.40 6841.25 4032 54.50 11.31
Trailing PE Forward PE 41.53 30.90 3.64 1.10 19.39 19.21 700.63 252.62 24.21 12.48 1.22 2.57 7184.00 1430.00 3492 2281 43.98 31.13 11.13 14.29
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Comparing PE Ratios: US, Europe, Japan and Emerging Markets Median PE Japan = 24.74 US = 20.76 Em. Mkts = 18.87 Europe = 15.99
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PE Ratio: Understanding the Fundamentals
To understand the fundamentals, start with a basic equity discounted cash flow model. With the dividend discount model, P0 =
DPS1 r ! gn
Dividing both sides by the current earnings per share, P0 Payout Ratio * (1 + g n ) = PE = EPS0 r-gn
If this had been a FCFE Model,
P0 =
FCFE1 r ! gn
P0 (FCFE/Earnings) * (1+ g n ) = PE = EPS0 r-g n Aswath Damodaran
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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.
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Using the Fundamental Model to Estimate PE For a High Growth Firm
The price-earnings ratio for a high growth firm can also be related to fundamentals. In the special case of the two-stage dividend discount model, this relationship can be made explicit fairly simply: P0 =
•
" (1+ g)n % EPS0 * Payout Ratio *(1+ g)* $1 ! # (1+ r) n & r-g
+
EPS0 * Payout Ratio n *(1+ g)n *(1+ g n ) (r -g n )(1+ r)n
For a firm that does not pay what it can afford to in dividends, substitute FCFE/Earnings for the payout ratio.
Dividing both sides by the earnings per share: " (1 + g)n % ' Payout Ratio * (1 + g) * $ 1 ! # (1+ r) n & P0 Payout Ratio n *(1+ g) n * (1 + gn ) = + EPS0 r -g (r - g n )(1+ r) n
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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.
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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 Number of years 5 years Forever after year 5 Riskfree rate = T.Bond Rate = 6% Required rate of return = 6% + 1(5.5%)= 11.5%
# (1.25) 5 & 0.2 * (1.25) * %1" 5( 5 $ (1.115) ' 0.5 * (1.25) * (1.08) PE = + = 28.75 (.115 - .25) (.115 - .08) (1.115) 5
!
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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
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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
g=25% g=20% g=15% g=8%
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PE
Ratio
30
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
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I. Assessing Emerging Market PE Ratios - Early 2000 PE: Emerging Markets 35
30
25
20
15
10
5
0 Mexico
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Malaysia
Singapore
Taiwan
Hong Kong
Venezuela
Brazil
Argentina
Chile
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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?
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II. 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
Correlations • •
Correlation between PE ratio and long term interest rates = -0.733 Correlation between PE ratio and yield spread = 0.706
Regression Results PE Ratio = 42.62 - 3.61 (10’yr rate) + 8.47 (10-yr - 2 yr rate) R2 = 59% Input the interest rates as percent. For instance, the predicted PE ratio for Japan with this regression would be: PE: Japan = 42.62 - 3.61 (1.85) + 8.47 (1.27) = 46.70 At an actual PE ratio of 52.25, Japanese stocks are slightly overvalued.
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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% Aswath Damodaran
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III. 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
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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IV. Comparisons of PE across time: PE Ratio for the S&P 500
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Is low (high) PE cheap (expensive)?
A market strategist argues that stocks are over priced because the PE ratio today is too high relative to the average PE ratio across time. Do you agree? Yes No
If you do not agree, what factors might explain the higher PE ratio today?
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E/P Ratios , T.Bond Rates and Term Structure
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Regression Results
There is a strong positive relationship between E/P ratios and T.Bond rates, as evidenced by the correlation of 0.69 between the two variables., In addition, there is evidence that the term structure also affects the PE ratio. In the following regression, using 1960-2003 data, we regress E/P ratios against the level of T.Bond rates and a term structure variable (T.Bond T.Bill rate) E/P = 2.03% + 0.753 T.Bond Rate - 0.355 (T.Bond Rate-T.Bill Rate) (2.19) (6.38) (-1.38) R squared = 50.85%
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Estimate the E/P Ratio Today
T. Bond Rate = T.Bond Rate - T.Bill Rate = Expected E/P Ratio = Expected PE Ratio =
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V. Comparing PE ratios across firms
Company Name Coca-Cola Bottling Molson Inc. Ltd. 'A' Anheuser -Busch Cor by Distiller ies Ltd. Chalone Wine Gr oup Ltd. Andr es Wines Ltd. 'A' Todhunter Int'l Br own-For man 'B' Coor s (Adolph) 'B' PepsiCo, Inc. Coca-Cola Boston Beer 'A' Whitman Cor p. Mondavi (Rober t) 'A' Coca-Cola Enter pr ises
Tr ailing 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 Gr owth 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%
Standar d 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 Natur al Cor p
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? Yes No Why or why not?
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VI. 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 Constant 13.1151 3.471 Growth rate 1.21223 19.27 Emerging Market -13.8531 3.606 Emerging Market is a dummy: 1 if emerging market 0 if not
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t-ratio 3.78 6.29 -3.84
prob 0.0010 ≤ 0.0001 0.0009
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Is Telebras under valued?
Predicted PE = 13.12 + 1.2122 (7.5) - 13.85 (1) = 8.35 At an actual price to earnings ratio of 8.9, Telebras is slightly overvalued.
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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. • •
• •
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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
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 Current PE vs Expected Growth in EPS January 2004: US Companies 1 20
1 00
80
60
Current PE
40
20 0 -20
0
20
40
60
80
Expected Growth in E PS: next 5 y ears
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PE Ratio: Standard Regression for US stocks - January 2004 Mod el Summary Mode l 1
R .467 a
R Square .21 8
Adjusted R Square .217
Std. Er ror of the Estimate 1049.7506205 340
a. Predictor s: ( Constant), PAYOUT, Regre ssion Be ta , Expected Gr owth in EPS: next 5 years
Co effici entsa,b Unstandardized Coefficients Mode l 1
B (Constant) Expected G rowth in EPS: next 5 years Regr ession B eta PAYOUT
Std. Error
9.475
.96 1
.814
.04 6
6.283 6.E-02
Standar dized Coefficients Beta
t
Sig.
9.862
.000
.375
17.55 8
.000
.43 7
.298
14.37 5
.000
.01 4
.092
4.161
.000
a. Dependent Va riable: Current PE b. Weighted Least Square s Regression - We ighted by Mar ket Cap
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Problems with the regression methodology
The basic regression assumes a linear relationship between PE ratios and the financial proxies, and that might not be appropriate. The basic relationship between PE ratios and financial variables itself might not be stable, and if it shifts from year to year, the predictions from the model may not be reliable. The independent variables are correlated with each other. For example, high growth firms tend to have high risk. This multi-collinearity makes the coefficients of the regressions unreliable and may explain the large changes in these coefficients from period to period.
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The Multicollinearity Problem Correlatio ns
Expected G rowth in Reven ues: next 5 year s
Pear son Correlation
PAYOUT
Regr ession Beta .031
.
.228
.000 1185
Sig. (2 -tailed) N
Regression Bet a
Expected Growth in Revenues: next 5 ye ars 1
PAYOUT -.325**
147 2
1472
Pear son Correlation
.03 1
1
-.183**
Sig. (2 -tailed)
.22 8
.
.000
N
147 2
6933
4187
Pear son Correlation
-.325**
-.183**
1
.00 0
.000
.
118 5
4187
4187
Sig. (2 -tailed) N
**. Correlation is significa nt at the 0.01 level (2-tailed).
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Using the PE ratio regression
Assume that you were given the following information for Dell. The firm has an expected growth rate of 10%, a beta of 1.20 and pays no dividends. Based upon the regression, estimate the predicted PE ratio for Dell. Predicted PE =
Dell is actually trading at 22 times earnings. What does the predicted PE tell you?
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The value of growth Time Period Value of extra 1% of growth January 2004 0.812 July 2003 1.228 January 2003 2.621 July 2002 0.859 January 2002 1.003 July 2001 1.251 January 2001 1.457 July 2000 1.761 January 2000 2.105 The value of growth is in terms of additional PE…
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Equity Risk Premium 3.69% 3.88% 4.10% 4.35% 3.62% 3.05% 2.75% 2.20% 2.05%
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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. • •
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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
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
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PE Ratios Less Than The Expected Growth Rate
In January 2004, • •
33% of firms had PE ratios lower than the expected 5-year growth rate 67% of firms had PE ratios higher than the expected 5-year growth rate
In comparison, • •
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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
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)
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PEG Ratio: Distribution
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PEG Ratios: The Beverage Sector Company Name Coca-Cola Bottling Molson Inc. Ltd. 'A' Anheuser -Busch Cor by Distiller ies Ltd. Chalone Wine Gr oup Ltd. Andr es Wines Ltd. 'A' Todhunter Int'l Br own-For man 'B' Coor s (Adolph) 'B' PepsiCo, Inc. Coca-Cola Boston Beer 'A' Whitman Cor p. Mondavi (Rober t) 'A' Coca-Cola Enter pr ises Hansen Natur al Cor p Aver age
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Tr ailing PE 29.18 43.65 24.31 16.24 21.76 14.00% 8.96 8.94 10.07 23.02 33.00 44.33 10.59 25.19 16.47 37.14 9.70 22.66
Gr owth 9.50% 15.50% 11.00% 7.50% 24.08% 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% 1.55 24.70% 25.74% 29.43% 29.52% 31.35% 35.51% 39.58% 44.26% 45.84% 51.34% 62.45%
P EG 3.07 2.82 2.21 2.16
0.13
0.33
2.00
2.56 2.98 0.88 2.30 3.14 2.33 0.62 2.19 1.18 1.38 0.57
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PEG Ratio: Reading the Numbers
The average PEG ratio for the beverage sector is 2.00. The lowest PEG ratio in the group belongs to Hansen Natural, which has a PEG ratio of 0.57. Using this measure of value, Hansen Natural is the most under valued stock in the group the most over valued stock in the group What other explanation could there be for Hansen’s low PEG ratio?
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PEG Ratio: Analysis
To understand the fundamentals that determine PEG ratios, let us return again to a 2-stage equity discounted cash flow model P0 =
" (1+ g)n % EPS0 * Payout Ratio *(1+ g)* $1 ! # (1+ r) n & r-g
+
EPS0 * 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’ " (1+ g)n % Payout Ratio *(1 + g) * $ 1 ! # (1 + r) n & Payout Ratio n * (1+ g)n * (1+ g n ) PEG = + g(r - g) g(r - gn )(1 + r)n
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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)
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A Simple Example
Assume that you have been asked to estimate the PEG ratio for a firm which has the following characteristics: Variable High Growth Phase Stable Growth Phase Expected Growth Rate 25% 8% Payout Ratio 20% 50% Beta 1.00 1.00 Riskfree rate = T.Bond Rate = 6% Required rate of return = 6% + 1(5.5%)= 11.5% The PEG ratio for this firm can be estimated as follows:
# (1.25) 5 & 0.2 * (1.25) * %1" 5( 0.5 * (1.25) 5 * (1.08) $ (1.115) ' PEG = + = 115 or 1.15 .25(.115 - .25) .25(.115 - .08) (1.115) 5
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PEG Ratios and Risk
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PEG Ratios and Quality of Growth
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PE Ratios and Expected Growth
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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. •
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 1: The company that looks most under valued on a PEG ratio basis in a sector may be the riskiest firm in the sector
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. •
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Corollary 3: PEG ratios do not neutralize the growth effect.
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PE, PEG Ratios and Risk 45
2.5
40 2
35 30
1.5 25
PE PEG Ratio
20 1 15 10
0.5
5 0
0 Lowest
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2
3
4
Highest
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PEG Ratio: Returning to the Beverage Sector Company Name Coca-Cola Bottling Molson Inc. Ltd. 'A' Anheuser -Busch Cor by Distiller ies Ltd. Chalone Wine Gr oup Ltd. Andr es Wines Ltd. 'A' Todhunter Int'l Br own-For man 'B' Coor s (Adolph) 'B' PepsiCo, Inc. Coca-Cola Boston Beer 'A' Whitman Cor p. Mondavi (Rober t) 'A' Coca-Cola Enter pr ises Hansen Natur al Cor p
Tr ailing 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
Gr owth 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%
P EG 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
Aver age
22.66
0.13
0.33
2.00
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Analyzing PE/Growth
Given that the PEG ratio is still determined by the expected growth rates, risk and cash flow patterns, it is necessary that we control for differences in these variables. Regressing PEG against risk and a measure of the growth dispersion, we get: PEG = 3.61 -.0286 (Expected Growth) - .0375 (Std Deviation in Prices) R Squared = 44.75% In other words,
• •
PEG ratios will be lower for high growth companies PEG ratios will be lower for high risk companies
We also ran the regression using the deviation of the actual growth rate from the industry-average growth rate as the independent variable, with mixed results.
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Estimating the PEG Ratio for Hansen
Applying this regression to Hansen, the predicted PEG ratio for the firm can be estimated using Hansen’s measures for the independent variables: • •
Expected Growth Rate = 17.00% Standard Deviation in Stock Prices = 62.45%
Plugging in, Expected PEG Ratio for Hansen = 3.61 - .0286 (17) - .0375 (62.45) = 0.78 With its actual PEG ratio of 0.57, Hansen looks undervalued, notwithstanding its high risk.
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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.
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PEG versus Growth PEG Ratio v s Expected Growth in EPS January 2004: US Companies 10
8
6
PEG Ratio
4
2
0 -20
0
20
40
60
80
1 00
Expected Growth in E PS: next 5 y ears
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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.
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PEG versus ln(Expected Growth) PEG vs ln (Expected Growth) January 2004: US Companies 10
8
6
PEG Ratio
4
2
0 0
1
2
3
4
5
ln (Exp ected Gro wth R ate)
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PEG Ratio Regression - US stocks in January 2004 Model Summary Mode l 1
R R Square a .492 .242
Adjusted R Squar e .241
Std. Er ror of the Estimate 91. 242648963259
a. Predictors: ( Constant), LNGROWTH, Re gression B eta, PAYOUT
Co ef fici entsa,b Unstandard ized Coefficients Mode l 1
B 4.308
Std. Er ror .15 5
.539
.03 8
PAYOUT
6.E-03
LNGROWTH
-1.042
(Constant) Regr ession B eta
Standar dized Coefficients Beta
t 27. 774
Sig. .000
.293
14. 249
.000
.00 1
.116
5.262
.000
.05 5
-.404
-18.86
.000
a. Dependent Va riable: PE G Ratio b. Weighted Least Square s Regression - We ighte d by Mar ket Cap
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Applying the PEG ratio regression
Consider Dell again. The stock has an expected growth rate of 10%, a beta of 1.20 and pays out no dividends. What should its PEG ratio be?
If the stock’s actual PE ratio is 23, what does this analysis tell you about the stock?
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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%. • •
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PEG = 16/ 5 = 3.2 PEGY = 16/(5+4.5) = 1.7
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Relative PE: Definition
The relative PE ratio of a firm is the ratio of the PE of the firm to the PE of the market. Relative PE = PE of Firm / PE of Market While the PE can be defined in terms of current earnings, trailing earnings or forward earnings, consistency requires that it be estimated using the same measure of earnings for both the firm and the market. Relative PE ratios are usually compared over time. Thus, a firm or sector which has historically traded at half the market PE (Relative PE = 0.5) is considered over valued if it is trading at a relative PE of 0.7. Relative PE ratios are also used when comparing companies across markets with different PE ratios (Japanese versus US stocks, for example).
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Relative PE: Determinants
To analyze the determinants of the relative PE ratios, let us revisit the discounted cash flow model we developed for the PE ratio. Using the 2-stage DDM model as our basis (replacing the payout ratio with the FCFE/Earnings Ratio, if necessary), we get
" (1+ g j )n % ' Payout Ratio j *(1 + g j ) * $ 1 ! (1+ rj )n & # Payout Ratio j,n *(1 + g j )n *(1 + g j,n ) + rj - g j (rj - g j,n )(1 + rj )n Relative PE j = "$ (1+ g m ) n %' Payout Ratio m * (1+ g m )* 1 ! # (1+ rm )n & Payout Ratio m,n * (1+ g m )n *(1 + gm, n ) + n r g (r g )(1+ r ) m m m m,n m where Payout , g , r = Payout, growth and risk of the firm j
j
j
Payoutm, gm, rm = Payout, growth and risk of the market
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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%
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Estimating Relative PE
The relative PE ratio for this firm can be estimated in two steps. First, we compute the PE ratio for the firm and the market separately: PE firm
PE market
5 " (1.20) % 0.3 * (1.20) * $ 1! # (1.115) 5 & 0.5 * (1.20)5 * (1.06) = + = 15.79 (.115 - .20) (.115 -.06) (1.115)5
" (1.10)5 % 0.3 * (1.10) * $ 1! # (1.115)5 & 0.5 * (1.10) 5 *(1.06) = + = 10.45 5 (.115 - .10) (.115-.06) (1.115)
Relative PE Ratio = 15.79/10.45 = 1.51
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Relative PE and Relative Growth
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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%
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Estimating Relative PE
The relative PE ratio for this firm can be estimated in two steps. First, we compute the PE ratio for the firm and the market separately: PE firm
PE market
" (1.10) 5 % 0.3 * (1.10) * $ 1 ! 5 # (1.17) 5 & 0.5 * (1.10) * (1.06) = + = 8.33 (.17 - .10) (.115- .06) (1.17)5
" (1.10)5 % 0.3 * (1.10) * $ 1! # (1.115)5 & 0.5 * (1.10) 5 *(1.06) = + = 10.45 5 (.115 - .10) (.115-.06) (1.115)
Relative PE Ratio = 8.33/10.45 = 0.80
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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
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0.5
0.75
1
1.25
1.5
1.75
2
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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.
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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
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Using Relative PE ratios
On a relative PE basis, all of the automobile stocks looked cheap in 2000 because they were trading at their lowest relative PE ratios than 1993. Why might the relative PE ratio be lower in 2000 than in 1993?
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Relative PE Ratios: US stocks Model Su mmar y Mode l 1
R .467 a
R Square .21 8
Adjusted R Square .217
Std. Er ror of the Estimate 41.97324
a. Predictors: ( Constant), Regr ession Bet a, RELGR, RELPA YO U
Co ef fici entsa,b Unstandard ized Coefficients Mode l 1
(Constant)
B .379
Std. Er ror .03 8
RELPAYO U
4.E-02
.00 9
RELG R
.506
Regr ession B eta
.251
Standar dized Coefficients Beta
t 9.862
Sig. .000
.092
4.161
.000
.02 9
.375
17. 558
.000
.01 7
.298
14. 375
.000
a. Dependent Va riable: RELPE b. Weighted Least Square s Regression - We ighte d by Mar ket Cap
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Value/Earnings and Value/Cashflow Ratios
While Price earnings ratios look at the market value of equity relative to earnings to equity investors, Value earnings ratios look at the market value of the operating assets of the firm (Enterprise value or EV) relative to operating earnings or cash flows. The form of value to cash flow ratios that has the closest parallels in DCF valuation is the value to Free Cash Flow to the Firm, which is defined as: EV/FCFF = (Market Value of Equity + Market Value of Debt-Cash) EBIT (1-t) - (Cap Ex - Deprecn) - Chg in Working Cap
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Value of Firm/FCFF: Determinants
Reverting back to a two-stage FCFF DCF model, we get: ! (1 + g)n $ FCFF (1 + g) # 1& 0 n FCFF (1+ g)n (1+ g ) " (1+ WACC) % 0 n V0 = + WACC - g (WACC - g )(1 + WACC)n n
• • • • •
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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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Value Multiples
Dividing both sides by the FCFF yields, !# (1 + g)n $ (1 + g) 1" (1 + WACC)n % V0 (1+ g)n (1+ gn ) = + n FCFF0 WACC - g (WACC - gn )(1 + WACC)
The value/FCFF multiples is a function of • •
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the cost of capital the expected growth
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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: • • • •
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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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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?
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Illustration: Using Value/FCFF Approaches to value a firm: MCI Communications
MCI Communications had earnings before interest and taxes of $3356 million in 1994 (Its net income after taxes was $855 million). It had capital expenditures of $2500 million in 1994 and depreciation of $1100 million; Working capital increased by $250 million. It expects free cashflows to the firm to grow 15% a year for the next five years and 5% a year after that. The cost of capital is 10.50% for the next five years and 10% after that. The company faces a tax rate of 36%.
V0 = FCFF0 Aswath Damodaran
(1.15)5 (1.15) 1(1.105)5 .105 -.15
5
(1.15) (1.05) = 31.28 + 5 (.10 - .05)(1.105) 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) + 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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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.
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Enterprise Value/EBITDA Multiple
The Classic Definition Value Market Value of Equity + Market Value of Debt = EBITDA Earnings before Interest, Taxes and Depreciation
The No-Cash Version
Enterprise Value Market Value of Equity + Market Value of Debt - Cash = EBITDA Earnings before Interest, Taxes and Depreciation
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Enterprise Value/EBITDA Distribution - US in January 2004
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Value/EBITDA Multiple: Europe, Japan and Emerging Markets in January 2004
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The Determinants of Value/EBITDA Multiples: Linkage to DCF Valuation
The value of the operating assets of a firm can be written as:
FCFF1 V0 = WACC - g
The numerator can be written as follows: FCFF
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= EBIT (1-t) - (Cex - Depr) - Δ Working Capital = (EBITDA - Depr) (1-t) - (Cex - Depr) - Δ Working Capital = EBITDA (1-t) + Depr (t) - Cex - Δ Working Capital
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From Firm Value to EBITDA Multiples
Now the Value of the firm can be rewritten as, EBITDA (1- t) + Depr (t) - Cex - ! Working Capital Value = WACC - g
Dividing both sides of the equation by EBITDA,
Value (1- t) Depr (t)/EBITDA CEx/EBITDA ! Working Capital/EBITDA = + EBITDA WACC- g WACC -g WACC - g WACC - g
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A Simple Example
Consider a firm with the following characteristics: • • • • • •
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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.
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Calculating Value/EBITDA Multiple
Value = EBITDA
In this case, the Value/EBITDA multiple for this firm can be estimated as follows: (1- .36) .10 -.05
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+
(0.2)(.36) 0.3 0 = 8.24 .10 -.05 .10 - .05 .10 - .05
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Value/EBITDA Multiples and Taxes
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Value/EBITDA and Net Cap Ex
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Value/EBITDA Multiples and Return on Capital
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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
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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
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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?
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Analyzing the Value/EBITDA Multiple
While low value/EBITDA multiples may be a symptom of undervaluation, a few questions need to be answered: • • • •
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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?
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Value/EBITDA Multiples: Market
The multiple of value to EBITDA varies widely across firms in the market, depending upon: •
• •
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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)
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US Market: Cross Sectional Regression January 2004 Model Summary Mode l 1
R .583
R Square a
Adjusted R Square
.34 0
.33 8
Std. Er ror of the Estimate 653 .801855 07239
a. Predictor s: ( Constant), Reinvestment Rate, Expected Gr owth in Revenues: next 5 years, Eff Tax Rat e
Co ef fici entsa,b Unstandardized Coefficie nts Mode l 1
B (Constant)
Std. Er ror
10. 073
.768
-.152
.022
.907 -.015
Eff T ax Rate Expected G rowth in Revenues: next 5 year s Reinvestment Rate
Standardized Coefficie nts Be ta
t
Sig.
13.121
.00 0
-.174
-6.878
.00 0
.039
.563
23.464
.00 0
.006
-.062
-2.420
.01 6
a. Dependent Va riable: EV /EBITDA b. Weighted Least Square s Regression - We ighte d by Mar ket Cap
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Europe: Cross Sectional Regression January 2004 Model Summary Mode l 1
R .542 a
Adjusted R Square .292
R Square .293
Std. Er ror of the Estimate 1581.333005721082 000
a. Predictors: ( Constant), Tax Rate , Reinv Rate , Market Debt to Ca pital
Coefficientsa,b Unstandardized Coefficie nts Mode l 1
(Constant)
B 8.419
Std. Er ror 1.2 79
Mar ket Debt t o Capital
Standardized Coefficie nts Be ta
t 6.580
Sig. .00 0
.58 9
.021
.511
28. 035
.00 0
Reinv Ra te
-.051
.009
-.099
-5.472
.00 0
Tax Rat e
-.152
.029
-.095
-5.236
.00 0
a. Dependent Va riable: EV/EBITDA b. Weighted Least Square s Regression - Weig hted by Marke t Capitalization
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Price-Book Value Ratio: Definition
The price/book value ratio is the ratio of the market value of equity to the book value of equity, i.e., the measure of shareholders’ equity in the balance sheet. Price/Book Value = Market Value of Equity Book Value of Equity Consistency Tests: • •
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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.
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Price to Book Value: US stocks
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Price to Book: Europe, Japan and Emerging Markets
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Price Book Value Ratio: Stable Growth Firm
DPS1 model, Going back to a simple dividend P 0 =discount 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
P0 ROE * Payout Ratio * (1 + g n ) = PBV = BV 0 r-g n
If the return on equity is based upon expected earnings in the next time period, this can be simplified to,
P0 ROE * Payout Ratio = PBV = BV 0 r-g n
Aswath Damodaran
116
Price Book Value Ratio: Stable Growth Firm Another Presentation
This formulation can be simplified even further by relating growth to the return on equity: g = (1 - Payout ratio) * ROE Substituting back into the P/BV equation, P0 ROE - g n = PBV = BV0 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.
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117
Price Book Value Ratio for High Growth Firm
The Price-book ratio for a high-growth firm can be estimated beginning with a 2-stage discounted cash" flow model: (1+ g)n % ' EPS0 * Payout Ratio * (1 + g) * $ 1 ! # (1+ r) n & EPS0 * Payout Ratio n * (1+ g)n *(1+ g n ) P0 = + r -g (r - g n )(1+ r) n
Dividing both sides of the equation by the book value of equity: ' "$ (1+ g)n % * ROE* Payout Ratio *(1+ g)* 1 ! ) # (1+ r) n & P0 ROE n * Payout Ratio n *(1+ g)n *(1+ g n ) , =) + , BV0 r-g (r - gn )(1+ r)n ) , ( +
where
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ROE = Return on Equity in high-growth period ROEn = Return on Equity in stable growth period
118
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%.
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119
Estimating Price/Book Value Ratio
The price/book value ratio for this firm is:
' 0.25 * 0.2 * (1.20) * ) PBV = ) (.12875 ) (
Aswath Damodaran
"$ * (1.20) 5 % 1! # (1.12875) 5 & 0.15 * 0.6 * (1.20)5 * (1.06) , + = 2.66 .20) (.115 - .06) (1.12875) 5 , , +
120
PBV and ROE: The Key
PBV and ROE: Risk Scenarios 4
3.5
Ratios
2
Price/Book
2.5
Value
3
Beta=0.5 Beta=1 Beta=1.5
1.5
1
0.5
0 10%
15%
20%
25%
30%
ROE
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121
PBV/ROE: European Banks Bank Banca di Roma SpA Commerzbank AG Bayerische Hypo und Vereinsbank AG Intesa Bci SpA Natexis Banques Populaires Almanij NV Algemene Mij voor Nijver Credit Industriel et Commercial Credit Lyonnais SA BNL Banca Nazionale del Lavoro SpA Banca Monte dei Paschi di Siena SpA Deutsche Bank AG Skandinaviska Enskilda Banken Nordea Bank AB DNB Holding ASA ForeningsSparbanken AB Danske Bank AS Credit Suisse Group KBC Bankverzekeringsholding Societe Generale Santander Central Hispano SA National Bank of Greece SA San Paolo IMI SpA BNP Paribas Svenska Handelsbanken AB UBS AG Banco Bilbao Vizcaya Argentaria SA ABN Amro Holding NV UniCredito Italiano SpA Rolo Banca 1473 SpA Dexia Average
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Symbol BAHQE COHSO BAXWW BAEWF NABQE ALPK CIECM CREV BAEXC MOGG DEMX SKHS NORDEA DNHLD FOLG DANKAS CRGAL KBCBA SODI BAZAB NAGT SAOEL BNPRB SVKE UBQH BBFUG ABTS UNCZA ROGMBA DECCT
PBV 0.60 0.74 0.82 1.12 1.12 1.17 1.20 1.20 1.22 1.34 1.36 1.39 1.40 1.42 1.61 1.66 1.68 1.69 1.73 1.83 1.87 1.88 2.00 2.12 2.15 2.18 2.21 2.25 2.37 2.76 1.60
ROE 4.15% 5.49% 5.39% 7.81% 7.38% 8.78% 9.46% 6.86% 12.43% 10.86% 17.33% 16.33% 13.69% 16.78% 18.69% 19.09% 14.34% 30.85% 17.55% 11.01% 26.19% 16.57% 18.68% 21.82% 16.64% 22.94% 24.21% 15.90% 16.67% 14.99% 14.96%
122
PBV versus ROE regression
Regressing PBV ratios against ROE for banks yields the following regression: PBV = 0.81 + 5.32 (ROE) R2 = 46% For every 1% increase in ROE, the PBV ratio should increase by 0.0532.
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123
Under and Over Valued Banks?
Bank Banca di Roma SpA Commerzbank AG Bayerische Hypo und Vereinsbank AG Intesa Bci SpA Natexis Banques Populaires Almanij NV Algemene Mij voor Nijver Credit Industriel et Commercial Credit Lyonnais SA BNL Banca Nazionale del Lavoro SpA Banca Monte dei Paschi di Siena SpA Deutsche Bank AG Skandinaviska Enskilda Banken Nordea Bank AB DNB Holding ASA ForeningsSparbanken AB Danske Bank AS Credit Suisse Group KBC Bankverzekeringsholding Societe Generale Santander Central Hispano SA National Bank of Greece SA San Paolo IMI SpA BNP Paribas Svenska Handelsbanken AB UBS AG Banco Bilbao Vizcaya Argentaria SA ABN Amro Holding NV UniCredito Italiano SpA Rolo Banca 1473 SpA Dexia
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Actual 0.60 0.74 0.82 1.12 1.12 1.17 1.20 1.20 1.22 1.34 1.36 1.39 1.40 1.42 1.61 1.66 1.68 1.69 1.73 1.83 1.87 1.88 2.00 2.12 2.15 2.18 2.21 2.25 2.37 2.76
Predicted 1.03 1.10 1.09 1.22 1.20 1.27 1.31 1.17 1.47 1.39 1.73 1.68 1.54 1.70 1.80 1.82 1.57 2.45 1.74 1.39 2.20 1.69 1.80 1.97 1.69 2.03 2.10 1.65 1.69 1.61
Under or Over -41.33% -32.86% -24.92% -8.51% -6.30% -7.82% -8.30% 2.61% -16.71% -3.38% -21.40% -17.32% -9.02% -16.72% -10.66% -9.01% 7.20% -30.89% -0.42% 31.37% -15.06% 11.15% 11.07% 7.70% 27.17% 7.66% 5.23% 36.23% 39.74% 72.04%
124
Looking for undervalued securities - PBV Ratios and ROE
Given the relationship between price-book value ratios and returns on equity, it is not surprising to see firms which have high returns on equity selling for well above book value and firms which have low returns on equity selling at or below book value. The firms which should draw attention from investors are those which provide mismatches of price-book value ratios and returns on equity - low P/BV ratios and high ROE or high P/BV ratios and low ROE.
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125
The Valuation Matrix
MV/BV
Overvalued Low ROE High MV/BV
High ROE High MV/BV
ROE-r
Low ROE Low MV/BV
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Undervalued High ROE Low MV/BV
126
Price to Book vs ROE: Largest Market Cap Firms in the United States: September 2003 20 DE LL
SAP
G
BUD
PFE EBAY
10
GS K
BSX
O RCL MMM PG
MDT
DAZN
WMT BMY
Q COM
MRK
K MB
AMAT
PBV Ratio
JNJ
UL MO FNM
ABN SC 0 0
10
20
30
40
50
60
70
ROE
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127
PBV Matrix: Telecom Companies
12 TelAzteca
10 TelNZ
8
Vimple
Carlton
Cable&W
Teleglobe FranceTel
6
DeutscheTel BritTel TelItalia BCE
4
Portugal Royal Hellenic
AsiaSat HongKong
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
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128
PBV, ROE and Risk: Large Cap US firms
16 14
BUD G PFE
12
O RCL MMM
10
PBV R atio
PG
8 UL
6
MRK
MDT WMT
D QCOM
FNMK MB
4
FRE
2
SC 70 60
50 40
30 20
ROE
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EBAY
10 0
T SM AMAT
AOL V IA/B
0
1
2
3
4
Regressio n Beta
129
IBM: The Rise and Fall and Rise Again
10.00
50.00%
9.00
40.00%
8.00 30.00%
7.00 20.00%
10.00% 5.00 0.00%
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
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ROE
130
PBV Ratio Regression: US January 2004 Mod el Su mmar y Mode l 1
R R Square .943 b .889
a
Adjusted R Square .889
Std. Er ror of the Estimate 117.0574933200291
a. For r egression through the origin (the no-intercept model) , R Square measures the proportion of the variability in the dependent varia ble about the origin explained by regre ssion. This CANNOT b e compared to R Squar e for models which include an intercept. b. Predictors: ROE, R egr ession B eta, PAYOU T, Expected Growth in EPS: next 5 year s
Co effici entsa,b,c Unstandardized Coefficients Mode l 1
B Expected G rowth in EPS: next 5 years PAYOUT
Std. Error
Standar dized Coefficients Beta
t
Sig.
8.E-02
.00 4
.256
21.93 5
.000
2.E-03
.00 1
.017
1.551
.121
Regr ession B eta
.599
.04 2
.151
14.24 9
.000
ROE
.140
.00 3
.628
50.73 1
.000
a. Dependent Va riable: PBV Ratio b. Linear Regr ession through the Origin c. Weighted Least Squares R egre ssion - Weig hted by Marke t Cap
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131
PBV Ratio Regression- Europe January 2004 Mod el Summary Mode l 1
R R Square .830 b .689
a
Adjusted R Squar e .689
Std. Error of the Estimate 154.4404 7748882220
a. For r egression through the origin (the no-intercept model) , R Squar e mea sur es the prop or tion of the va riability in the depende nt variable about the origin explained by regression. This CA NNOT be compare d to R Square for models which include an inter cept. b. Predictors: ROE, Payout Ra tio, B ETA
Coefficientsa ,b,c Unstandardized Coefficie nts Mode l 1
Payout Ratio BE TA ROE
Standardized Coefficie nts
B 8.E-03
Std. Er ror .002
Be ta .074
t 3.667
Sig. .00 0
1.399
.114
.291
12. 279
.00 0
.10 4
.004
.537
28. 148
.00 0
a. Dependent Va riable: PB V b. Linear Regr ession through the Origin c. Weighted Least Squares R egre ssion - Weighted by Marke t Capitalization
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132
PBV Regression: Emerging Markets January 2004 Mod el Summary Mode l 1
a
R R Square .795 b .63 1
Adjusted R Square .631
Std. Er ror of the Estimate 2.0708694 612 34543
a. For r egression through the origin (the no-intercept m odel) , R Square mea sur es the proportion of the va riability in the d ependent va riable about the origin explained b y regression. This CANNOT be compared to R Square f or models which include an inter cept. b. Predictors: ROE, Payout Ratio, BETA
Coefficientsa ,b Unstandardized Coefficie nts Mode l 1
Payout Ratio BE TA ROE
Standardized Coefficie nts
B 5.E-03
Std. Er ror .001
Be ta .076
t 4.148
Sig. .00 0
.80 5
.088
.213
9.164
.00 0
9.E-02
.003
.579
29. 414
.00 0
a. Dependent Va riable: PB V b. Linear Regr ession through the Origin
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133
PBV Ratio: Japan in January 2004 Model Su mmar y
Mode l 1
R Net Income > 0 (Selected)
Adjusted R Squar e
R Sq uare a
.815
b
.664
Std. Er ror of the Estimate
.664
848.8652 371625490 00
a. For r egression through the origin (the no-intercept model) , R Square mea sur es the prop or tion of the va riability in the depende nt va riable about the origin explained b y regression. This CANNOT be compare d to R Square for models which include an intercept. Co ef fici entsa,b,c,d b. Predictors: B ETA, ROE Unstandardized Coefficie nts Mode l 1
B
Standardized Coefficie nts
Std. Er ror
Be ta
t
Sig.
ROE
.189
.007
.597
28.912
.00 0
BE TA
.973
.073
.276
13.359
.00 0
a. Dependent Va riable: PBV b. Linear Regr ession through the Origin c. Weighted Least Square s R egression - Weighted by Mar ket Capitalization d. Selecting only cases for which Net Income > 0
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134
Value/Book Value Ratio: Definition
While the price to book ratio is a equity multiple, both the market value and the book value can be stated in terms of the firm. Value/Book Value = Market Value of Equity + Market Value of Debt Book Value of Equity + Book Value of Debt
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135
Determinants of Value/Book Ratios
To see the determinants of the value/book ratio, consider the simple free cash flow to the firm model:
FCFF1 V0 = WACC - g
Dividing both sides by the book value, we get:
V0 FCFF1 /BV = BV WACC - g
If we replace, FCFF = EBIT(1-t) - (g/ROC) EBIT(1-t),we get
V0 ROC - g = BV WACC - g Aswath Damodaran
136
Value/Book Ratio: An Example
Consider a stable growth firm with the following characteristics: • • •
Return on Capital = 12% Cost of Capital = 10% Expected Growth = 5%
The value/BV ratio for this firm can be estimated as follows: Value/BV = (.12 - .05)/(.10 - .05) = 1.40 The effects of ROC on growth will increase if the firm has a high growth phase, but the basic determinants will remain unchanged.
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137
Value/Book and the Return Spread
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138
Value/Book Capital Regression - US Model Su mmar y Mode l 1
R .758
R Square a
Adjusted R Square
.575
Std. Er ror of the Estimate
.574
135.06239892 7610600
a. Predictors: ( Constant), Market Debt to Cap ital, Expected Growth in Revenues: next 5 years, ROC
Co ef fici entsa,b Unstandardized Coefficie nts Mode l 1
B (Constant)
Std. Er ror
3.041
.133
Expected G rowth in Revenues: next 5 year s
1.E-02
.008
ROC
9.E-02 -.066
Marke t Debt to Capital
Standardized Coefficie nts Be ta
t
Sig.
22.838
.00 0
.026
1.3 30
.18 4
.004
.446
22.992
.00 0
.003
-.473
-23.04
.00 0
a. Dependent Va riable: Value/BV of Capital b. Weighted Least Square s Regression - We ighte d by Mar ket Cap
Aswath Damodaran
139
Price Sales Ratio: Definition
The price/sales ratio is the ratio of the market value of equity to the sales. Price/ Sales= Market Value of Equity Total Revenues Consistency Tests •
Aswath Damodaran
The price/sales ratio is internally inconsistent, since the market value of equity is divided by the total revenues of the firm.
140
Price/Sales Ratio: US stocks
Revenue Multiples: US Companies in January 2004 600
500
400
300
Price to Sales EV/Sales
200
100
0 10
141
Price to Sales: Europe, Japan and Emerging Markets
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142
Price/Sales Ratio: Determinants
The price/sales ratio of a stable growth firm can be estimated beginning with a 2-stage equity valuation model: P0 =
DPS1 r ! gn
Dividing both sides by the sales per share:
P0 Net Profit Margin* Payout Ratio *(1+ g n ) = PS = Sales 0 r-g n
Aswath Damodaran
143
Price/Sales Ratio for High Growth Firm
When the growth rate is assumed to be high for a future period, the dividend discount model can be written as follows: n
" (1+ g) %' EPS0 * Payout Ratio * (1 + g) * $ 1 ! # (1+ r) n & EPS0 * Payout Ratio n * (1+ g)n *(1+ g n ) P0 = + r -g (r - g n )(1+ r) n
Dividing both sides by the sales per share:
' "$ * (1+ g) n % Net Margin * Payout Ratio * (1+ g)* 1 ! ) # P0 (1+ r)n & Net Marginn * Payout Ratio n * (1+ g) n *(1 + gn ) , = + , Sales 0 ) r -g (r - gn )(1 + r)n ) , ( +
where Net Marginn = Net Margin in stable growth phase
Aswath Damodaran
144
Price Sales Ratios and Profit Margins
The key determinant of price-sales ratios is the profit margin. A decline in profit margins has a two-fold effect. • •
First, the reduction in profit margins reduces the price-sales ratio directly. Second, the lower profit margin can lead to lower growth and hence lower pricesales 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
145
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
' "$ * (1.20)5 % 0.10 * 0.2 * (1.20) * 1 ! ) # (1.12875)5 & 0.06 * 0.60 * (1.20) 5 * (1.06) , PS = ) + , = 1.06 (.12875 - .20) (.115 -.06) (1.12875) 5 ) , ( +
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146
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% Net
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10%
12%
14%
16%
Margin
147
PS/Margins: European Retailers - September 2003
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148
Regression Results: PS Ratios and Margins
Regressing PS ratios against net margins, PS = -.39 + 0.6548 (Net Margin) R2 = 43.5% Thus, a 1% increase in the margin results in an increase of 0.6548 in the price sales ratios. The regression also allows us to get predicted PS ratios for these firms
Aswath Damodaran
149
Current versus Predicted Margins
One of the limitations of the analysis we did in these last few pages is the focus on current margins. Stocks are priced based upon expected margins rather than current margins. For most firms, current margins and predicted margins are highly correlated, making the analysis still relevant. For firms where current margins have little or no correlation with expected margins, regressions of price to sales ratios against current margins (or price to book against current return on equity) will not provide much explanatory power. In these cases, it makes more sense to run the regression using either predicted margins or some proxy for predicted margins.
Aswath Damodaran
150
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
Aswath Damodaran
151
PS Ratios and Margins are not highly correlated
Regressing PS ratios against current margins yields the following PS = 81.36
- 7.54(Net Margin) (0.49)
R2 = 0.04
This is not surprising. These firms are priced based upon expected margins, rather than current margins.
Aswath Damodaran
152
Solution 1: Use proxies for survival and growth: Amazon in early 2000
Hypothesizing that firms with higher revenue growth and higher cash balances should have a greater chance of surviving and becoming profitable, we ran the following regression: (The level of revenues was used to control for size)
PS = 30.61 - 2.77 ln(Rev) + 6.42 (Rev Growth) + 5.11 (Cash/Rev) (0.66) (2.63) (3.49)
R squared = 31.8% Predicted PS = 30.61 - 2.77(7.1039) + 6.42(1.9946) + 5.11 (.3069) = 30.42 Actual PS = 25.63 Stock is undervalued, relative to other internet stocks.
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153
Solution 2: Use forward multiples
You can always estimate price (or value) as a multiple of revenues, earnings or book value in a future year. These multiples are called forward multiples. For young and evolving firms, the values of fundamentals in future years may provide a much better picture of the true value potential of the firm. There are two ways in which you can use forward multiples: •
•
Aswath Damodaran
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.
154
An Example of Forward Multiples: Global Crossing
Global Crossing lost $1.9 billion in 2001 and is expected to continue to lose money for the next 3 years. In a discounted cashflow valuation (see notes on DCF valuation) of Global Crossing, we estimated an expected EBITDA for Global Crossing in five years of $ 1,371 million. The average enterprise value/ EBITDA multiple for healthy telecomm firms is 7.2 currently. Applying this multiple to Global Crossing’s EBITDA in year 5, yields a value in year 5 of • Enterprise Value in year 5 = 1371 * 7.2 = $9,871 million • Enterprise Value today = $ 9,871 million/ 1.1385 = $5,172 million (The cost of capital for Global Crossing is 13.80%) • The probability that Global Crossing will not make it as a going concern is 77% and the distress sale value is only a $ 1 billion (1/2 of book value of assets). • Adjusted Enterprise value = 5172 * .23 + 1000 (.77) = 1,960 million
Aswath Damodaran
155
PS Regression: United States - January 2004 Mod el Summary Mode l 1
R R Square .932 b .869
Adjusted R Square .868
a
Std. Error of the Estimate 114.3056698264723 0
a. For r egression through the origin (the no-intercept model) , R Square measures the proport ion of the variability in the dependent varia ble about the origin explained by regre ssion. This CANNOT be compared to R Squar e for models which include an intercept. b. Predictors: Net Mar gin, Regression Beta, PAYOUT, Expe cted Growth in EPS: Co next 5 years effici entsa,b,c
Unstandardized Coefficients Mode l 1
B Expected G rowth in EPS: next 5 years PAYOUT
Std. Error
Standar dized Coefficients Beta
t
Sig.
4.E-02
.00 4
.136
10.19 5
.000
-.011
.00 1
-.110
-9.425
.000
Regr ession B eta
.549
.04 3
.156
12.65 8
.000
Net Margin
.234
.00 4
.799
59.92 6
.000
a. Dependent Va riable: PS_RATIO b. Linear Regr ession through the Origin c. Weighted Least Squares R egre ssion - Weig hted by Marke t Cap
Aswath Damodaran
156
PS Regression: Europe in January 2004 Model Summary Mode l 1
a
R R Square .757 b .57 4
Adjusted R Square .573
Std. Er ror of the Estimate 134.938678072015
a. For r egression through the origin (the no-intercept m odel) , R Sq uare measures the proportion of the variab ility in the dependent varia ble about the origin explained by regression. This CANNO T be compar ed to R Square for models which include an intercept. b. Predictors: Net Mar gin, Payout Ra tio, BETA Coefficientsa ,b,c Unstandardized Coefficie nts Mode l 1
Standardized Coefficie nts
B 5.E-03
Std. Er ror .002
Be ta .065
t 2.777
Sig. .00 6
BE TA
.93 7
.095
.261
9.909
.00 0
Net Margin
.11 0
.004
.516
26. 153
.00 0
Payout Ratio
a. Dependent Va riable: PS b. Linear Regr ession through the Origin c. Weighted Least Squares R egre ssion - Weighted by Marke t Capitalization
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157
PS Regression in Emerging Markets - January 2004 Model Summary
Mode l 1
R Net Income > .00 (Selected)
R Sq uare a
.834
b
Adjusted R Squar e
.696
.695
Std. Er ror of the Estimate 2.308859441838714
a. For r egression through the origin (the no-intercept model) , R Square measures the proport ion of the variability in the depen dent variable abou t the origin explaine d by re gression. This CANNOT be compared to R Squar e for models which include an intercept. b. Predictors: Net Mar gin, Payout Ra tio, BETA Coefficientsa ,b,c Unstandardized Coefficie nts Mode l 1
Standardized Coefficie nts
B 7.E-03
Std. Er ror .001
Be ta .083
t 4.962
Sig. .00 0
BE TA
.14 2
.087
.030
1.631
.10 3
Net Margin
.14 3
.003
.766
47. 061
.00 0
Payout Ratio
a. Dependent Va riable: PS b. Linear Regr ession through the Origin c. Selecting only cases for which Ne t Income > .00
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158
PS Regression in Japan: January 2004 Model Summary
Mode l 1
R Net Income > 0 (Selected) .721
R Sq uare a
Adjusted R Squar e
.519
.518
Std. Er ror of the Estimate 549.1390 58787986000
a. Predictors: ( Constant), Payout Ratio, Net Mar gin
Coefficientsa ,b,c Unstandardized Coefficie nts Mode l 1
(Constant)
B 2.E-02
Std. Er ror .081
Net Margin
.24 3
.007
8.E-03
.002
Payout Ratio
Standardized Coefficie nts Be ta
t .242
Sig. .80 8
.737
34. 627
.00 0
.079
3.719
.00 0
a. Dependent Va riable: PS b. Weighted Least Square s Regression - We ighted by Mar ket Capitalization c. Selecting only cases for which Ne t Income > 0
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Value/Sales Ratio: Definition
The value/sales ratio is the ratio of the market value of the firm to the sales. Value/ Sales= Market Value of Equity + Market Value of Debt-Cash Total Revenues
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Value/Sales Ratios: Analysis of Determinants
If pre-tax operating margins are used, the appropriate value estimate is that of the firm. In particular, if one makes the assumption that •
Free Cash Flow to the Firm = EBIT (1 - tax rate) (1 - Reinvestment Rate)
Then the Value of the Firm can be written as a function of the after-tax operating margin= (EBIT (1-t)/Sales
n ( + " % (1 + g) *(1 - 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 (WACC - g n )(1 + WACC) n * ) ,
g = Growth rate in after-tax operating income for the first n years gn = Growth rate in after-tax operating income after n years forever (Stable growth rate) RIRGrowth, Stable = Reinvestment rate in high growth and stable periods WACC = Weighted average cost of capital
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Value/Sales Ratio: An Example
Consider, for example, the Value/Sales ratio of Coca Cola. The company had the following characteristics: After-tax Operating Margin =18.56% Sales/BV of Capital = 1.67 Return on Capital = 1.67* 18.56% = 31.02% Reinvestment Rate= 65.00% in high growth; 20% in stable growth; Expected Growth = 31.02% * 0.65 =20.16% (Stable Growth Rate=6%) Length of High Growth Period = 10 years Cost of Equity =12.33% E/(D+E) = 97.65% After-tax Cost of Debt = 4.16% D/(D+E) 2.35% Cost of Capital= 12.33% (.9765)+4.16% (.0235) =12.13%
( + " (1.2016)1 0 % * (1- .65)(1.2016)* $1! 10' 1 0 Value of Firm 0 (1- .20)(1.2016) * (1.06) # (1.1213) & * = .1856* + = 6.10 * Sales 0 .1213- .2016 (.1213- .06)(1.1213)1 0 * ) ,
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Value Sales Ratios and Operating Margins
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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 LIN SCHS
LE
GBIZ
VOXX JILL SAH
FLWS
ROSI MHCO
-0.0
MSEL
-0.000
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PBY CHRS
Z CLWY RUSH LVC
PSRC GDYS RET.TO
MNRO CAO
ITN PGDA
CC
0.5 MTMC ANIC CELL
ORLY ZLC LTD AZO IPAR ANN ZQK PIR RAYS MDLK MENS
GADZ
SPGLA
FINL
CLE FOSL
GLBE HLYW RUS
DAP
BEBE ROST
HMY FNLY
PLCE
PSUN
URBN BKE
PSS DBRN
AEOS
WLSN
IBI MDA
TWMC
ZANY MLG
0.075
0.150 Operating Margin
0.225
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Brand Name Premiums in Valuation
You have been hired to value Coca Cola for an analyst reports and you have valued the firm at 6.10 times revenues, using the model described in the last few pages. Another analyst is arguing that there should be a premium added on to reflect the value of the brand name. Do you agree? Yes No Explain.
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The value of a brand name
One of the critiques of traditional valuation is that is fails to consider the value of brand names and other intangibles. The approaches used by analysts to value brand names are often ad-hoc and may significantly overstate or understate their value. One of the benefits of having a well-known and respected brand name is that firms can charge higher prices for the same products, leading to higher profit margins and hence to higher price-sales ratios and firm value. The larger the price premium that a firm can charge, the greater is the value of the brand name. In general, the value of a brand name can be written as: Value of brand name ={(V/S)b-(V/S)g }* Sales (V/S)b = Value of Firm/Sales ratio with the benefit of the brand name (V/S)g = Value of Firm/Sales ratio of the firm with the generic product
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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
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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
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Value of Coca Cola’s Brand Name
Value of Coke’s Brand Name= ( 6.10 - 0.69) ($18,868 million) = $102 billion Value of Coke as a company = 6.10 ($18,868 million) = $ 115 Billion Approximately 88.69% of the value of the company can be traced to brand name value
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Value/Sales Ratio Regression: US in January 2004 Model Summary Mode l 1
R .726 a
R Square .527
Adjusted R Square .526
Std. Error of the Estimate 150 .9882839615558
a. Predictors: ( Constant), Expected G rowth in Revenue s: next 5 year s, After-tax Oper ating Ma rgin, Mar ket Debt t o Capital
Co ef fici entsa,b Unstandardized Coefficie nts Mode l 1
(Constant) After-tax Oper ating Margin Marke t Debt to Capital Expected G rowth in Revenues: next 5 year s
B 1.252
Std. Er ror .118
.135
.004
-.043 8.E-02
Standardized Coefficie nts Be ta
t 10.576
Sig. .00 0
.605
32.945
.00 0
.003
-.300
-14.99
.00 0
.009
.175
8.7 56
.00 0
a. Dependent Va riable: EV /Sales b. Weighted Least Square s Regression - We ighte d by Mar ket Cap
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Choosing Between the Multiples
As presented in this section, there are dozens of multiples that can be potentially used to value an individual firm. In addition, relative valuation can be relative to a sector (or comparable firms) or to the entire market (using the regressions, for instance) Since there can be only one final estimate of value, there are three choices at this stage: • • •
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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
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
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
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: • •
•
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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
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: • •
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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
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
Managers in every sector tend to focus on specific variables when analyzing strategy and performance. The multiple used will generally reflect this focus. Consider three examples. • •
•
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In retailing: The focus is usually on same store sales (turnover) and profit margins. Not surprisingly, the revenue multiple is most common in this sector. In financial services: The emphasis is usually on return on equity. Book Equity is often viewed as a scarce resource, since capital ratios are based upon it. Price to book ratios dominate. In technology: Growth is usually the dominant theme. PEG ratios were invented in this sector.
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Conventional Usage: A Summary
As a general rule of thumb, the following table provides a way of picking a multiple for a sector
Sector Cyclical Manufacturing High Tech, High Growth High Growth/No Earnings Heavy Infrastructure
REITa Financial Services Retailing
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Multiple Used PE, Relative PE PEG
Rationale Often with normalized earnings Big differences in growth across firms PS, VS Assume future margins will be good VEBITDA Firms in sector have losses in early years and reported earnings can vary depending on depreciation method P/CF Generally no cap ex investments from equity earnings PBV Book value often marked to market PS If leverage is similar across firms VS If leverage is different
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Sector or Market Multiples
The conventional approach to using multiples is to look at the sector or comparable firms. Whether sector or market based multiples make the most sense depends upon how you think the market makes mistakes in valuation •
•
If you think that markets make mistakes on individual firm valuations but that valuations tend to be right, on average, at the sector level, you will use sectorbased valuation only, If you think that markets make mistakes on entire sectors, but is generally right on the overall market level, you will use only market-based valuation
It is usually a good idea to approach the valuation at two levels: • •
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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? One of the two valuations must be wrong. A stock cannot be under and over valued at the same time. It is possible that both valuations are right. What has to be true about valuations in the sector for the second statement to be true?
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Reviewing: The Four Steps to Understanding Multiples
Define the multiple • •
Describe the multiple • •
Multiples have skewed distributions: The averages are seldom good indicators of typical multiples Check for bias, if the multiple cannot be estimated
Analyze the multiple • •
Check for consistency Make sure that they are estimated uniformly
Identify the companion variable that drives the multiple Examine the nature of the relationship
Apply the multiple
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Private Company Valuation Aswath Damodaran
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Process of Valuing Private Companies
Choosing the right model • •
Valuing the Firm versus Valuing Equity Steady State, Two-Stage or Three-Stage
Estimating a Discount Rate •
Cost of Equity – Estimating Betas
•
Cost of Debt – Estimating Default Risk – Estimating an after-tax cost of debt
•
Cost of Capital – Estimating a Debt Ratio
Estimating Cash Flows Completing the Valuation: Depends upon why and for whom the valuation is being done.
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Private Company Valuation: Motive matters
You can value a private company for • • • • •
Legal purposes: Estate tax and divorce court Sale or prospective sale to another individual or private entity. Sale of one partner’s interest to another Sale to a publicly traded firm As prelude to setting offering price in an initial public offering
You can value a division or divisions of a publicly traded firm • • •
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As prelude to a spin off For sale to another entity To do a sum-of-the-parts valuation to determine whether a firm will be worth more broken up or if it is being efficiently run.
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Estimating Cost of Equity for a Private Firm
Most models of risk and return (including the CAPM and the APM) use past prices of an asset to estimate its risk parameters (beta(s)). Private firms and divisions of firms are not traded, and thus do not have past prices. Thus, risk estimation has to be based upon an approach that does not require past prices
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I. Comparable Firm Betas
Collect a group of publicly traded comparable firms, preferably in the same line of business, but more generally, affected by the same economic forces that affect the firm being valued. •
A Simple Test: To see if the group of comparable firms is truly comparable, estimate a correlation between the revenues or operating income of the comparable firms and the firm being valued. If it is high (and positive), of course, your have comparable firms.
If the private firm operates in more than one business line collect comparable firms for each business line
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Estimating comparable firm betas
Estimate the average beta for the publicly traded comparable firms. Estimate the average market value debt-equity ratio of these comparable firms, and calculate the unlevered beta for the business. βunlevered = βlevered / (1 + (1 - tax rate) (Debt/Equity)) Estimate a debt-equity ratio for the private firm, using one of two assumptions: •
Assume that the private firm will move to the industry average debt ratio. The beta for the private firm will converge on the industry average beta.
β private firm = βunlevered (1 + (1 - tax rate) (Industry Average Debt/Equity)) •
Estimate the optimal debt ratio for the private firm, based upon its operating income and cost of capital.
β private firm = βunlevered (1 + (1 - tax rate) (Optimal Debt/Equity)) Estimate a cost of equity based upon this beta.
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Accounting Betas
Step 1: Collect accounting earnings for the private company for as long as there is a history. Step 2: Collect accounting earnings for the S&P 500 for the same time period. Step 3: Regress changes in earnings for the private company against changes in the S&P 500. Step 4: The slope of the regression is the accounting beta There are two serious limitations (a) The number of observations in the regression is small (b) Accountants smooth earnings.
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Estimating a Beta for the NY Yankees
You have three choices for comparable firms: • • •
Firms that derive a significant portion of their revenues from baseball (Traded baseball teams, baseball cards & memorabilia…) Firms that derive a significant portion of their revenues from sports Firms that derive a significant portion of their revenues from entertainment.
Comparable firms Levered Beta Unlevered Beta Baseball firms (2) 0.70 0.64 Sports firms (22) 0.98 0.90 Entertainment firms (91) 0.87 0.79 Management target Levered Beta for Yankees = 0.90 ( 1 + (1-.4) (.25)) = 1.04 Cost of Equity = 6.00% + 1.04 (4%) = 10.16%
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Estimating a beta for InfoSoft: A private software firm Comparable firms include all software firms, with market capitalization of less than $ 500 million. The average beta for these firms is 1.29 and the average debt to equity ratio for these firms is 7.09%. With a 35% tax rate, this yields an unlevered beta of Unlevered Beta = 1.29/ (1 + (1-.35) (.0709)) = 1.24 We will assume that InfoSoft will have a debt to equity ratio comparable to the average for the comparable firms and a similar tax rate, which results in a levered beta of 1.29. Cost of Equity = 6.00% + 1.29 (4%) = 11.16%
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Is beta a good measure of risk for a private firm?
The beta of a firm measures only market risk, and is based upon the assumption that the investor in the business is well diversified. Given that private firm owners often have all or the bulk of their wealth invested in the private business, would you expect their perceived costs of equity to be higher or lower than the costs of equity from using betas? Higher Lower
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Total Risk versus Market Risk
Adjust the beta to reflect total risk rather than market risk. This adjustment is a relatively simple one, since the correlation with the market measures the proportion of the risk that is market risk. Total Beta = Market Beta / Correlation with market
In the New York Yankees example, where the market beta is 0.85 and the Rsquared for comparable firms is 25% (correlation is therefore 0.5), • • •
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Total Unlevered Beta = 0.90/0. 5= 1.80 Total Levered Beta = 1.80 (1 + (1-0.4)(0.25)) =2.07 Total Cost of Equity = 6% + 2.07 (4%)= 14.28%
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When would you use this total risk measure?
Under which of the following scenarios are you most likely to use the total risk measure: when valuing a private firm for an initial public offering when valuing a private firm for sale to a publicly traded firm when valuing a private firm for sale to another private investor Assume that you own a private business. What does this tell you about the best potential buyer for your business?
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Estimating the Cost of Debt for a Private Firm
Basic Problem: Private firms generally do not access public debt markets, and are therefore not rated. Most debt on the books is bank debt, and the interest expense on this debt might not reflect the rate at which they can borrow (especially if the bank debt is old.)
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Estimation Options for Cost of Debt
Solution 1: Assume that the private firm can borrow at the same rate as similar firms (in terms of size) in the industry. Cost of Debt for Private firm = Cost of Debt for similar firms in the industry
Solution 2: Estimate an appropriate bond rating for the company, based upon financial ratios, and use the interest rate estimated bond rating. Cost of Debt for Private firm = Interest Rate based upon estimated bond rating (If using optimal debt ratio, use corresponding rating)
Solution 3: If the debt on the books of the company is long term and recent, the cost of debt can be calculated using the interest expense and the debt outstanding. Cost of Debt for Private firm = Interest Expense / Outstanding Debt If the firm borrowed the money towards the end of the financial year, the interest expenses for the year will not reflect the interest rate on the debt.
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Estimating a Cost of Debt for Yankees and InfoSoft
For the Yankee’s, we will use the interest rate from the most recent loans that the firm has taken on: • •
Interest rate on debt = 7.00% After-tax cost of debt = 7% (1-.4) = 4.2%
For InfoSoft, we will use the interest coverage ratio estimated using the operating income and interest expenses from the most recent year: • • • •
Aswath Damodaran
Interest coverage ratio = EBIT/ Interest expenses = 2000/315 = 6.35 Rating based upon interest coverage ratio = A+ Interest rate on debt = 6% + 0.80% = 6.80% After-tax cost of debt = 6.80% (1-.35) = 4.42%
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Estimating the Cost of Capital
Basic problem: The debt ratios for private firms are stated in book value terms, rather than market value. Furthermore, the debt ratio for a private firm that plans to go public might change as a consequence of that action. Solution 1: Assume that the private firm will move towards the industry average debt ratio. Debt Ratio for Private firm = Industry Average Debt Ratio
Solution 2: Assume that the private firm will move towards its optimal debt ratio. Debt Ratio for Private firm = Optimal Debt Ratio
Consistency in assumptions: The debt ratio assumptions used to calculate the beta, the debt rating and the cost of capital weights should be consistent.
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Estimating Costs of Capital
Cost of Equity E/ (D+E) Cost of Debt AT Cost of Debt D/(D+E) Cost of Capital
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New York Yankees 14.28%(total beta) 80.00% 7.00% 4.20% 20.00% 12.26%
InfoSoft Corporation 11.16%(market beta) 93.38% 6.80% 4.42% 6.62% 10.71%
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Estimating Cash Flows for a Private Firm
Shorter history: Private firms often have been around for much shorter time periods than most publicly traded firms. There is therefore less historical information available on them. Different Accounting Standards: The accounting statements for private firms are often based upon different accounting standards than public firms, which operate under much tighter constraints on what to report and when to report. Intermingling of personal and business expenses: In the case of private firms, some personal expenses may be reported as business expenses. Separating “Salaries” from “Dividends”: It is difficult to tell where salaries end and dividends begin in a private firm, since they both end up with the owner.
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Estimating Private Firm Cash Flows
Restate earnings, if necessary, using consistent accounting standards. •
To get a measure of what is reasonable, look at profit margins of comparable publicly traded firms in the same business
If any of the expenses are personal, estimate the income without these expenses. Estimate a “reasonable” salary based upon the services the owner provides the firm.
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The Yankee’s Revenues
Net Home Game Receipts Road Receipts Concessions & Parking National TV Revenues Local TV Revenues National Licensing Stadium Advertising Other Revenues
Pittsburg Pirates $ 22,674,597 $ 1,613,172 $ 3,755,965 $ 15,000,000 $ 11,000,000 $ 4,162,747 $ 100,000 $ 1,000,000
Baltimore Orioles $ 47,353,792 $ 7,746,030 $ 22,725,449 $ 15,000,000 $ 18,183,000 $ 3,050,949 $ 4,391,383 $ 9,200,000
New York Yankees $ 52,000,000 $ 9,000,000 $ 25,500,000 $ 15,000,000 $ 90,000,000 $ 6,000,000 $ 5,500,000 $ 6,000,000
Total Revenues
$ 59,306,481
$ 127,650,602
$ 209,000,000
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The Yankee’s Expenses
Player Salaries Team Operating Expenses Player Development Stadium & Game Operations$ Other Player Costs G & A Costs Broadcasting Rent & Amortization Total Operating Expenses
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Pittsburg Pirates $ 33,155,366 $ 6,239,025 $ 8,136,551 5,270,986 $ 2,551,000 $ 6,167,617 $ 1,250,000 $ $ 62,770,545
Baltimore Orioles $ 62,771,482 $ 6,803,907 $ 12,768,399 $ 4,869,790 $ 6,895,751 $ 9,321,151 $ $ 6,252,151 $ 109,682,631
New York Yankees $ 91,000,000 $ 7,853,000 $ 15,000,000 $ 7,800,000 $ 7,500,000 $ 11,000,000 $ $ $ 140,153,000
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Adjustments to Operating Income
Total Revenues Total Operating Expenses EBIT Adjustments Adjusted EBIT Taxes (at 40%) EBIT (1-tax rate)
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Pittsburg Pirates $59,306,481 $62,770,545 -$3,464,064 $1,500,000 -$1,964,064 -$785,626 -$1,178,439
Baltimore Orioles $127,650,602 $109,682,631 $17,967,971 $2,200,000 $20,167,971 $8,067,189 $12,100,783
New York Yankees $209,000,000 $140,153,000 $68,847,000 $4,500,000 $73,347,000 $29,338,800 $44,008,200
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InfoSoft’s Operating Income Stated Operating Income Sales & Other Operating Revenues - Operating Costs & Expenses - Depreciation - Research and Development Expenses Operating Income
$20,000.00 $13,000.00 $1,000.00 $4,000.00 $2,000.00
Adjusted Operating Income Operating Income
$ 2000.00
+ R& D Expenses - Amortization of Research Asset
$ 4000.00 $ 2311.00
Adjusted Operating Income
$ 3689.00
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Estimating Cash Flows for Yankees
We will assume a 3% growth rate in perpetuity for operating income. To generate this growth, we will assume that the Yankee’s will earn 20% on their new investments. This yields a reinvestment rate of Reinvestment rate = g/ ROC = 3%/20% = 15% Estimated Free Cash Flow to Firm
EBIT (1- tax rate) = - Reinvestment = $ FCFF
Aswath Damodaran
$ 44,008,200 6,601,230 $ 37,406,970
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From Cash Flows to Value
Once you have estimated the cash flows and the cost of capital, you can value a private firm using conventional methods. If you are valuing a firm for sale to a private business, • •
Use the total beta and the cost of equity emerging from that to estimate the cost of capital. Discount the cash flows using this cost of capital
If you are valuing a firm for an initial public offering, stay with the market beta and cost of capital.
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Valuing the Yankees FCFF = $ 37,406,970 Cost of capital = 12.26% Expected Growth rate= 3.00% Value of Yankees = $ 37,406,970 (1.03)/(.1226-.03) = $ 415,902,192
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What if?
We are assuming that the Yankees have to reinvest to generate growth. If they can get the city to pick up the tab, the value of the Yankees can be estimated as follows: • •
FCFF = EBIT (1-t) - Reinvestment = $44.008 mil - 0 = $ 44.008 million Value of Yankees = 44.008*1.03/(.1226 - .03) = $ 489 million
If on top of this, we assume that the buyer is a publicly traded firm and we use the market beta instead of the total beta • • •
Aswath Damodaran
FCFF = $ 44.008 million Cost of capital = 8.95% Value of Yankees = 44.008 (1.03) / (.0895 - .03) = $ 761.6 million
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InfoSoft: A Valuation Current Cashflow to Firm Reinvestment Rate EBIT(1-t) : 2,933 106.82% - Nt CpX 2,633 - Chg WC 500 = FCFF Reinvestment Rate = 106.82%
Return on Capital 23.67%
Expected Growth in EBIT (1-t) 1.1217*.2367 = .2528 25.28%
Stable Growth g = 5%; Beta = 1.20; D/(D+E) = 6.62%;ROC=17.2% Reinvestment Rate=29.07% Terminal Value10 = 6743/(.1038-.05) = 125,391
Firm Value: + Cash: - Debt: =Equity
73,909 500 4,583 69,826
EBIT(1t) - Reinv FCFF
3675 3926 -251
4604 4918 -314
5768 6161 -393
7227 7720 -493
9054 9671 -617
9507 2764 6743
Discount at Cost of Capital (WACC) = 11.16% (0.9338) + 4.42% (0.0662) = 10.71%
Cost of Equity 11.16%
Cost of Debt (6+0.80%)(1-.35) = 4.42%
Riskfree Rate: Government Bond Rate = 6%
+
Beta 1.29
Unlevered Beta for Sectors: 1.24
Aswath Damodaran
Weights E = 93.38% D = 6.62%
X
Risk Premium 4%
Firm’s D/E Ratio: 7.09%
Historical US Premium 4%
Country Risk Premium 0%
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Play investment banker: Price this IPO
The value of equity that we have arrived at for Infosoft is $69.5 million. If you plan to have 10 million shares outstanding, estimate the value per share?
Would this also be your offering price? If not, why not?
Would you answer be different, if the initial offering were for only 1 million shares - the owners will retain the remaining 9 million for subsequent offerings?
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Valuation Motives and the Next Step in Private Company Valuation: Control and Illiquidity
If valuing a private business for sale (in whole or part) to another individual (to stay private), it is necessary that we estimate • •
If valuing a business for taking public, it is necessary to estimate • •
a illiquidity discount associated with the fact that private businesses cannot be easily bought and sold a control premium (if more than 50% of the business is being sold) the effects of creating different classes of shares in the initial public offer the effects of options or warrants on the issuance price per share
If valuing a business for sale (in whole or part) to a publicly traded firm, there should be no illiquidity discount, because stock in the parent firm will trade but there may, however, be a premium associated with the publicly traded firm being able to take better advantage of the private firm’s strengths
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Conventional Practice on Illiquidity
In private company valuation, illiquidity is a constant theme that analysts talk about. All the talk, though, seems to lead to a rule of thumb. The illiquidity discount for a private firm is between 20-30% and does not vary across private firms.
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Determinants of the Illiquidity Discount
Type of Assets owned by the Firm: The more liquid the assets owned by the firm, the lower should be the illiquidity discount for the firm Size of the Firm: The larger the firm, the smaller should be the percentage illiquidity discount. Health of the Firm: Healthier firms should sell for a smaller discount than troubled firms. Cash Flow Generating Capacity: Firms which are generating large amounts of cash from operations should sell for a smaller discounts than firms which do not generate large cash flows. Size of the Block: The liquidity discount should increase with the size of the portion of the firm being sold.
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Illiquidity Discounts and Type of Business
Rank the following assets (or private businesses) in terms of the liquidity discount you would apply to your valuation (from biggest discount to smallest) A New York City Cab Medallion A small privately owned five-and-dime store in your town A large privately owned conglomerate, with significant cash balances and real estate holdings. A large privately owned ski resort that is losing money
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Empirical Evidence on Illiquidity Discounts: Restricted Stock
Restricted securities are securities issued by a company, but not registered with the SEC, that can be sold through private placements to investors, but cannot be resold in the open market for a two-year holding period, and limited amounts can be sold after that. Restricted securities trade at significant discounts on publicly traded shares in the same company. •
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Maher examined restricted stock purchases made by four mutual funds in the period 1969-73 and concluded that they traded an average discount of 35.43% on publicly traded stock in the same companies. Moroney reported a mean discount of 35% for acquisitions of 146 restricted stock issues by 10 investment companies, using data from 1970. In a recent study of this phenomenon, Silber finds that the median discount for restricted stock is 33.75%.
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Cross Sectional Differences : Restricted Stock
Silber (1991) develops the following relationship between the size of the discount and the characteristics of the firm issuing the registered stock – LN(RPRS) = 4.33 +0.036 LN(REV) - 0.142 LN(RBRT) + 0.174 DERN + 0.332 DCUST where, RPRS = Relative price of restricted stock (to publicly traded stock) REV = Revenues of the private firm (in millions of dollars) RBRT = Restricted Block relative to Total Common Stock in % DERN = 1 if earnings are positive; 0 if earnings are negative; DCUST = 1 if there is a customer relationship with the investor; 0 otherwise;
Interestingly, Silber finds no effect of introducing a control dummy - set equal to one if there is board representation for the investor and zero otherwise.
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Adjusting the average illiquidity discount for firm characteristics - Silber Regression
The Silber regression does provide us with a sense of how different the discount will be for a firm with small revenues versus one with large revenues. Consider, for example, two profitable firms that are equal in every respect except for revenues. Assume that the first firm has revenues of 10 million and the second firm has revenues of 100 million. The Silber regression predicts illiquidity discounts of the following: • • •
For firm with 100 million in revenues: 44.5% For firm with 10 million in revenues: 48.9% Difference in illiquidity discounts: 4.4%
If your base discount for a firm with 10 million in revenues is 25%, the illiquidity discount for a firm with 100 million in revenues would be 20.6%.
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Liquidity Discount and Revenues Figure 24.1: Illiquidity Discounts: Base Discount of 25% for profitable firm with $ 10 million in revenues 40.00%
35.00%
Discount as % of Value
30.00%
25.00%
20.00%
15.00%
10.00%
5.00%
0.00% 5
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Revenues Profitable firm
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Unprofitable firm
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Application to the Yankees
To estimate the illiquidity discount for the Yankees, we assume that the base discount for a firm with $10 million in revenues would be 25%. The Yankee’s revenues of $209 million should result in a lower discount on their value. We estimate the difference in the illiquidity discount between a firm with $10 million in revenue and $209 million in revenue to be 5.90%. To do this, we first estimated the illiquidity discount in the Silber equation for a firm with $10 million in revenues. Expected illiquidity discount = 48.94% We then re-estimated the illiquidity discount with revenues of $ 209 million: Expected illiquidity discount = 43.04% Difference in discount = 48.94% - 43.04% = 5.90% The estimated illiquidity discount for the Yankees would therefore be 19.10%, which is the base discount of 25% adjusted for the illiquidty difference.
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An Alternate Approach to the Illiquidity Discount: Bid Ask Spread
The bid ask spread is the difference between the price at which you can buy a security and the price at which you can sell it, at the same point. In other words, it is the illiqudity discount on a publicly traded stock. Studies have tied the bid-ask spread to • • •
the size of the firm the trading volume on the stock the degree
Regressing the bid-ask spread against variables that can be measured for a private firm (such as revenues, cash flow generating capacity, type of assets, variance in operating income) and are also available for publicly traded firms offers promise.
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A Bid-Ask Spread Regression Using data from the end of 2000, for instance, we regressed the bid-ask spread against annual revenues, a dummy variable for positive earnings (DERN: 0 if negative and 1 if positive), cash as a percent of firm value and trading volume. Spread = 0.145 – 0.0022 ln (Annual Revenues) -0.015 (DERN) – 0.016 (Cash/Firm Value) – 0.11 ($ Monthly trading volume/ Firm Value) You could plug in the values for a private firm into this regression (with zero trading volume) and estimate the spread for the firm. We could substitute in the revenues of the Yankees ($209 million), the fact that it has positive earnings and the cash as a percent of revenues held by the firm (3%): Spread = 0.145 – 0.0022 ln (Annual Revenues) -0.015 (DERN) – 0.016 (Cash/Firm Value) – 0.11 ($ Monthly trading volume/ Firm Value) = 0.145 – 0.0022 ln (209) -0.015 (1) – 0.016 (.03) – 0.11 (0) = .1178 or 11.78% Based on this approach, we would estimate an illiquidity discount of 11.78% for the Yankees.
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What is control worth?
The Value of Control X
Probability that you can change the management of the firm
Takeover Restrictions
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Voting Rules & Rights
Access to Funds
Size of company
Change in firm value from changing management
Value of the firm run optimally
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Value of the firm run status quo
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Where control matters…
In publicly traded firms, control is a factor • • •
In the pricing of every publicly traded firm, since a portion of every stock can be attributed to the market’s views about control. In acquisitions, it will determine how much you pay as a premium for a firm to control the way it is run. When shares have voting and non-voting shares, the value of control will determine the price difference.
In private firms, control usually becomes an issue when you consider how much to pay for a private firm. • • •
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You may pay a premium for a badly managed private firm because you think you could run it better. The value of control is directly related to the discount you would attach to a minority holding (51%, but could be less…), you would be willing to pay the appropriate proportion of the optimal value of the firm. When you buy a minority interest in a firm, you will be willing to pay the appropriate fraction of the status quo value of the firm. For badly managed firms, there can be a significant difference in value between 51% of a firm and 49% of the same firm. This is the minority discount. If you own a private firm and you are trying to get a private equity or venture capital investor to invest in your firm, it may be in your best interests to offer them a share of control in the firm even though they may have well below 51%.
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