Relative Valuation PDF

RELATIVE VALUATION © All Slides | Aswath Damodaran  THE ESSENCE OF RELATIVE VALUATION (PRICING) 2 q In relative valuation, the price of an asset is compared to the prices assessed by the market for similar or comparable assets. q To do relative valuation then, q...

RELATIVE VALUATION © All Slides | Aswath Damodaran  THE ESSENCE OF RELATIVE VALUATION (PRICING) 2 q In relative valuation, the price of an asset is compared to the prices assessed by the market for similar or comparable assets. q To do relative valuation then, q we need to identify comparable assets and obtain market pricing for these assets q convert these market prices into standardized prices, since the absolute prices cannot be compared This process of standardizing creates price multiples. q compare the standardized price or multiple for the asset being analyzed to the standardized prices for comparable assets, controlling for any differences between the firms that might affect the multiple, to judge whether the asset is under or over priced. © All Slides | Aswath Damodaran  RELATIVE VALUATION IS PERVASIVE… 3 q Most asset valuations are relative. q Most equity valuations on Wall Street are relative valuations. q Almost 85% of equity research reports are based upon a multiple and comparables. q More than 50% of all acquisition valuations are based upon multiples q Rules of thumb based on multiples are not only common but are often the basis for final valuation judgments. q While there are more discounted cashflow valuations in consulting and corporate finance, they are often relative valuations masquerading as discounted cash flow valuations. q The objective in many discounted cashflow valuations is to back into a number that has been obtained by using a multiple. q The terminal value in a significant number of discounted cashflow valuations is estimated using a multiple. © All Slides | Aswath Damodaran  THE MARKET IMPERATIVE…. 4 q Relative valuation is much more likely to reflect market perceptions and moods than discounted cash flow valuation. This can be an advantage when it is important that the price reflect these perceptions as is the case when q the objective is to sell a security at that price today (as in the case of an IPO) q investing on “momentum” based strategies q With relative valuation, there will always be a significant proportion of securities that are under valued and over valued. q Since portfolio managers are judged based upon how they perform on a relative basis (to the market and other money managers), relative valuation is more tailored to their needs q Relative valuation generally requires less information than discounted cash flow valuation (especially when multiples are used as screens) © All Slides | Aswath Damodaran  MULTIPLES ARE JUST STANDARDIZED ESTIMATES OF PRICE… 5 Market value of equity Market value for the firm Market value of operating assets of firm Firm value = Market value of equity Enterprise value (EV) = Market value of equity + Market value of debt + Market value of debt - Cash Numerator = What you are paying for the asset Multiple = Denominator = What you are getting in return Revenues Earnings Cash flow Book Value a. Accounting a. To Equity investors a. To Equity a. Equity revenues - Net Income - Net Income + Depreciation = BV of equity b. Drivers - Earnings per share - Free CF to Equity b. Firm - # Customers b. To Firm b. To Firm = BV of debt + BV of equity - # Subscribers - Operating income (EBIT) - EBIT + DA (EBITDA) c. Invested Capital = # units - Free CF to Firm = BV of equity + BV of debt - Cash © All Slides | Aswath Damodaran  THE FOUR STEPS TO DECONSTRUCTING MULTIPLES 6 q Define the multiple q 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 q Describe the multiple q 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. q Analyze the multiple q It is critical that we understand the fundamentals that drive each multiple, and the nature of the relationship between the multiple and each variable. q Apply the multiple q Defining the comparable universe and controlling for differences is far more difficult in practice than it is in theory. © All Slides | Aswath Damodaran  DEFINITIONAL TESTS 7 q Is the multiple consistently defined? q 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. q Is the multiple uniformly estimated? q The variables used in defining the multiple should be estimated uniformly across assets in the “comparable firm” list. q If earnings-based multiples are used, the accounting rules to measure earnings should be applied consistently across assets. The same rule applies with book-value based multiples. © All Slides | Aswath Damodaran  EXAMPLE 1: PRICE EARNINGS RATIO: DEFINITION 8 PE = Market Price per Share / Earnings per Share q There are many variants on the basic PE ratio in use. They are based upon how the price and the earnings are defined. Price: is usually the current price is sometimes the average price for the year EPS: EPS in most recent financial year EPS in trailing 12 months Forecasted earnings per share next year Forecasted earnings per share in future year © All Slides | Aswath Damodaran  EXAMPLE 2: STAYING ON PE RATIOS 9 q Assuming that you are comparing the PE ratios across technology companies, many of which have options outstanding. What measure of PE ratio would yield the most consistent comparisons? a) Price/ Primary EPS (actual shares, no options) b) Price/ Fully Diluted EPS (actual shares + all options) c) Price/ Partially Diluted EPS (counting only in-the-money options) d) Other © All Slides | Aswath Damodaran  EXAMPLE 3: ENTERPRISE VALUE /EBITDA MULTIPLE 10 q The enterprise value to EBITDA multiple is obtained by netting cash out against debt to arrive at enterprise value and dividing by EBITDA. Enterprise Value Market Value of Equity + Market Value of Debt - Cash = EBITDA Earnings before Interest, Taxes and Depreciation q Why do we net out cash from firm value? q What happens if a firm has cross holdings which are categorized as: q Minority interests? q Majority active interests? © All Slides | Aswath Damodaran  EXAMPLE 4: A HOUSING PRICE MULTIPLE 11 q The bubbles and busts in housing prices has led investors to search for a multiple that they can use to determine when housing prices are getting out of line. q One measure that has acquired adherents is the ratio of housing price to annual net rental income (for renting out the same house). q Assume that you decide to compute this ratio and compare it to the multiple at which stocks are trading. q Which valuation ratio would be the one that corresponds to the house price/rent ratio? a) Price Earnings Ratio b) EV to Sales c) EV to EBITDA d) EV to EBIT © All Slides | Aswath Damodaran  DESCRIPTIVE TESTS 12 q What is the average and standard deviation for this multiple, across the universe (market)? q What is the median for this multiple? q The median for this multiple is often a more reliable comparison point. q How large are the outliers to the distribution, and how do we deal with the outliers? q 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. q Are there cases where the multiple cannot be estimated? Will ignoring these cases lead to a biased estimate of the multiple? q How has this multiple changed over time? © All Slides | Aswath Damodaran  1. MULTIPLES HAVE SKEWED DISTRIBUTIONS… US COMPANY PE RATIOS 13 © All Slides | Aswath Damodaran  2. MAKING STATISTICS “DICEY” 14 US firms in January 2024 © All Slides | Aswath Damodaran  3. MARKETS HAVE A LOT IN COMMON : COMPARING GLOBAL PES 15 © All Slides | Aswath Damodaran  3A. AND THE DIFFERENCES ARE SOMETIMES REVEALING… 16 © All Slides | Aswath Damodaran  4. SIMPLISTIC RULES ALMOST ALWAYS BREAK DOWN…6 TIMES EBITDA WAS NOT CHEAP IN 2010… 17 © All Slides | Aswath Damodaran  BUT IT MAY WORK IN 2024, UNLESS YOU ARE IN JAPAN OR RUSSIA.. 18 © All Slides | Aswath Damodaran  ANALYTICAL TESTS 19 q What are the fundamentals that determine and drive these multiples? q Proposition 2: Embedded in every multiple are all of the variables that drive every discounted cash flow valuation - growth, risk and cash flow patterns. q How do changes in these fundamentals change the multiple? q The relationship between a fundamental (like growth) and a multiple (such as PE) is almost never linear. q Proposition 3: It is impossible to properly compare firms on a multiple, if we do not know how fundamentals and the multiple move. © All Slides | Aswath Damodaran  A SIMPLE ANALYTICAL DEVICE 20 © All Slides | Aswath Damodaran  I. PE RATIOS 21 q To understand the fundamentals, start with a basic equity discounted cash flow model. q With the dividend discount model, q Dividing both sides by the current earnings per share, DPS1 P0 = r − gn q If this had been a FCFE Model, P0 Payout Ratio*(1+ g n ) = PE= EPS0 r-gn FCFE1 P0 = r − gn P0 (FCFE/Earnings)*(1+ g n ) = PE= EPS0 r-gn © All Slides | Aswath Damodaran  USING THE FUNDAMENTAL MODEL TO ESTIMATE PE FOR A HIGH GROWTH FIRM 22 q 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: " (1+g)n % EPS0 *Payout Ratio*(1+g)*$1− n ' n # (1+r) & EPS0 *Payout Ratio n *(1+g) *(1+g n ) P0 = + r-g (r-g n )(1+r)n q For a firm that does not pay what it can afford to in dividends, substitute FCFE/Earnings for the payout ratio. q Dividing both sides by the earnings per share: " (1 + g)n %' Payout Ratio * (1 + g) * $ 1 − P0 # (1+ r) n & Payout Ratio n *(1+ g) n * (1 + gn ) = + EPS0 r -g (r - g n )(1+ r) n © All Slides | Aswath Damodaran  A SIMPLE EXAMPLE 23 q Assume that you have been asked to estimate the PE ratio for a firm which has the following characteristics: Variable High Growth Stable Growth Expected Growth Rate 15% 1.5% Payout Ratio 25% 92.5% (based on ROE = 20%) Beta 1.00 1.00 Number of years 5 years Forever after year 5 q Riskfree rate = Treasury Bond Rate = 1.5%, ERP = 5% q Required rate of return = 1.5% + 1(5%)= 6.5% 1.15!.25 ∗ 1.15 ∗ 1 −.925 ∗ 1.15! ∗ 1.015 1.065! 𝑃𝐸 = + = 29.15.065 −.15.065 −.015 1.065 ! © All Slides | Aswath Damodaran  A. PE, GROWTH AND INTEREST RATES 24 © All Slides | Aswath Damodaran  B. PE AND RISK: A FOLLOW UP EXAMPLE 25 © All Slides | Aswath Damodaran  C. PE AND GROWTH QUALITY: VALUE ADDITION AND DESTRUCTION 26 © All Slides | Aswath Damodaran  EXAMPLE 1: THE CHEAPEST MARKETS AT THE START OF 2024 27 Country # firms median(EV/EBITDA) median(Trailing PE) Zambia 15 3.75 4.31 Kenya 50 3.70 4.43 Ghana 23 2.74 5.34 Cyprus 64 8.14 6.08 Pakistan 424 5.14 6.24 Serbia 17 5.64 6.69 Kazakhstan 21 5.78 6.82 Isle of Man 16 5.34 7.32 Sri Lanka 262 7.09 7.49 Mauritius 75 8.72 7.51 Tanzania 15 6.27 7.52 Nigeria 126 5.40 7.90 Macau 16 4.87 8.30 Ivory Coast 34 4.39 8.41 Tunisia 76 7.73 8.68 Bermuda 62 7.46 8.69 Malawi 14 5.02 8.71 Colombia 28 5.36 8.71 Chile 122 6.80 8.84 Lithuania 29 7.47 8.87 © All Slides | Aswath Damodaran  EXAMPLE 2: CONTROLLING FOR DIFFERENCES - AN OLD EXAMPLE WITH EMERGING MARKETS: JUNE 2000 28 Country PE Ratio Interest GDP Real Country Rates Growth Risk Argentina 14 18.00% 2.50% 45 Brazil 21 14.00% 4.80% 35 Chile 25 9.50% 5.50% 15 Hong Kong 20 8.00% 6.00% 15 India 17 11.48% 4.20% 25 Indonesia 15 21.00% 4.00% 50 Malaysia 14 5.67% 3.00% 40 Mexico 19 11.50% 5.50% 30 Pakistan 14 19.00% 3.00% 45 Peru 15 18.00% 4.90% 50 Phillipines 15 17.00% 3.80% 45 Singapore 24 6.50% 5.20% 5 South Korea 21 10.00% 4.80% 25 Thailand 21 12.75% 5.50% 25 Turkey 12 25.00% 2.00% 35 Venezuela 20 15.00% 3.50% 45 © All Slides | Aswath Damodaran  REGRESSION RESULTS 29 q 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% q What do the coefficients tell you about how each of these variables play into PE ratio differences across countries? © All Slides | Aswath Damodaran  PREDICTED PE RATIOS 30 Country PE Ratio Interest GDP Real Country Predicted PE Rates Growth Risk Argentina 14 18.00% 2.50% 45 13.57 Brazil 21 14.00% 4.80% 35 18.55 Chile 25 9.50% 5.50% 15 22.22 Hong Kong 20 8.00% 6.00% 15 23.11 India 17 11.48% 4.20% 25 18.94 Indonesia 15 21.00% 4.00% 50 15.09 Malaysia 14 5.67% 3.00% 40 15.87 Mexico 19 11.50% 5.50% 30 20.39 Pakistan 14 19.00% 3.00% 45 14.26 Peru 15 18.00% 4.90% 50 16.71 Phillipines 15 17.00% 3.80% 45 15.65 Singapore 24 6.50% 5.20% 5 23.11 South Korea 21 10.00% 4.80% 25 19.98 Thailand 21 12.75% 5.50% 25 20.85 Turkey 12 25.00% 2.00% 35 13.35 Venezuela 20 15.00% 3.50% 45 15.35 © All Slides | Aswath Damodaran  EXAMPLE 3: US STOCKS ARE EXPENSIVE, JUST LOOK AT THE PE RATIO 31 © All Slides | Aswath Damodaran  A COUNTER: NO, THEY ARE CHEAP, RELATIVE TO THE ALTERNATIVES.. 32 © All Slides | Aswath Damodaran  THE TIE BREAKER: E/P RATIOS , T.BOND RATES AND TERM STRUCTURE 33 © All Slides | Aswath Damodaran  REGRESSION RESULTS 34 Correlation between E/P and interest rates q In the following regression, using 1960-2023 data, we regress E/P ratios against the level of T.Bond rates and a term structure variable (T.Bond - T.Bill rate) EP Ratio = 0.0350 + 0.5576 T.Bond Rate - 0.1161 (T.Bond Rate - T.Bill Rate) (6.57) (7.40) (-0.12) R squared = 45.78% q In 2008, this is what the regression looked like: E/P = 2.56% + 0.7044 T.Bond Rate – 0.3289 (T.Bond Rate-T.Bill Rate) (4.71) (7.10) (1.46) R squared = 50.71% The R-squared has dropped and the differential with the T.Bill rate has lost significance. How would you read this result? © All Slides | Aswath Damodaran  II. PEG RATIO 35 q PEG Ratio = PE ratio/ Expected Growth Rate in EPS q For consistency, you should make sure that your earnings growth reflects the EPS that you use in your PE ratio computation. q The growth rates should preferably be over the same time period. q To understand the fundamentals that determine PEG ratios, let us return again to a 2-stage equity discounted cash flow model: " (1+g)n % EPS0 *Payout Ratio*(1+g)*$1− n ' n # (1+r) & EPS0 *Payout Ratio n *(1+g) *(1+g n ) P0 = + r-g (r-g n )(1+r)n q 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− n ' n # (1+r) & Payout Ratio n *(1+g) *(1+g n ) PEG= + g(r-g) g(r-g n )(1+r)n © All Slides | Aswath Damodaran  PEG RATIOS AND FUNDAMENTALS 36 q Risk and payout, which affect PE ratios, continue to affect PEG ratios as well. q Implication: When comparing PEG ratios across companies, we are making implicit or explicit assumptions about these variables. q 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) © All Slides | Aswath Damodaran  A SIMPLE EXAMPLE 37 q 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 15% 1.5% Payout Ratio 25% 92.5% Beta 1.00 1.00 q Riskfree rate = Treasury Bond Rate = 1.5%, ERP = 5% q Required rate of return = 1.5% + 1(5%)= 6.5% q The PEG ratio for this firm can be estimated as follows 1.15!.25 ∗ 1.15 ∗ 1 −.925 ∗ 1.15! ∗ 1.015 1.065! 𝑃𝐸𝐺 = + ! = 1.94.15 ∗.065 −.15.15.065 −.015 1.065 © All Slides | Aswath Damodaran  A. PEG RATIOS ARE RISK-SENSITIVE 38 © All Slides | Aswath Damodaran  B. PEG RATIOS ARE AFFECTED BY THE QUALITY OF GROWTH 39 © All Slides | Aswath Damodaran  C. PEG RATIOS ARE NOT GROWTH NEUTRAL… 40 © All Slides | Aswath Damodaran  PEG RATIOS AND FUNDAMENTALS: PROPOSITIONS 41 q Proposition 1: High risk companies will trade at much lower PEG ratios than low risk companies with the same expected growth rate. q 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 q 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. q Corollary 2: Companies that look cheap on a PEG ratio basis may be companies with high reinvestment rates and poor project returns. q 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. q Corollary 3: PEG ratios do not neutralize the growth effect. © All Slides | Aswath Damodaran  III. BOOK VALUE MULTIPLES 42 q With book value multiples, you scale the market value (which is what the market values your company at) to its book value (which is the accounting estimate of value. It can take two forms: q Price to Book = Market Capitalization/ Book Value of Equity q EV to Invested Capital = Enterprise Value/ (Book Value of Equity + Book Value of Debt – Cash) q To the extent that you believe that accountants have a better (or a more conservative) estimate of value, or that book value is a proxy for liquidation value, a company that trades at below its book value is cheap. © All Slides | Aswath Damodaran  PRICE TO BOOK RATIO: DETERMINANTS 43 ¨ Going back to a simple dividend discount model, DPS1 P0 = r − gn ¨ Defining the return on equity (ROE) = EPS0 / Book Value of Equity, the value of equity can be written as: BV0 *ROE*Payout Ratio*(1+ g n ) P0 = r-gn P0 ROE*Payout Ratio*(1+ g n ) = PBV= BV0 r-gn ¨ 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= BV0 r-gn © All Slides | Aswath Damodaran  PRICE BOOK VALUE RATIO: STABLE GROWTH FIRM ANOTHER PRESENTATION 44 q This formulation can be simplified even further by relating growth to the return on equity: g = (1 - Payout ratio) * ROE q Substituting back into the P/BV equation, P0 ROE - g n = PBV= BV0 r-gn q 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. q Building on this equation, a company that is expected to generate a ROE higher (lower than, equal to) its cost of equity should trade at a price to book ratio higher (less than, equal to) one. © All Slides | Aswath Damodaran  NOW CHANGING TO AN ENTERPRISE VALUE MULTIPLE EV/ BOOK CAPITAL 45 ¨ 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 © All Slides | Aswath Damodaran  IV. EV TO EBITDA MULTIPLES 46 q With EV to EBITDA multiples, you scale enterprise value to earnings before interest, taxes, depreciation and amortization: q EV to EBITDA = Enterprise Value/ EBITDA q There are variants where even more gets added back, including stock- based compensation and R&D q EV to EBITDA multiples have become far more widely used in the last four decades than they used to be for both good and bad reasons: q The good reasons include less sampling bias (since fewer companies have negative EBITDA) and that it is based on cash flows. q The bad reason is that it will give you lower absolute numbers than PE ratios, and for those without perspective, that may signify cheapness. © All Slides | Aswath Damodaran  EV TO EBITDA - DETERMINANTS 47 q The value of the operating assets of a firm can be written as: FCFF1 EV0 = WACC - g q Now the value of the firm can be rewritten as EBITDA € (1- t) + Depr (t) - Cex - Δ Working Capital EV = WACC - g q Dividing both sides of the equation by EBITDA, EV (1- t) Depr (t)/EBITDA CEx/EBITDA Δ Working Capital/EBITDA = + - - €EBITDA WACC - g WACC - g WACC - g WACC - g q The determinants of EV/EBITDA are: € q The cost of capital q Expected growth rate q Tax rate q Reinvestment rate (or ROC) © All Slides | Aswath Damodaran  A SIMPLE EXAMPLE 48 q Consider a firm with the following characteristics: q Tax Rate = 36% q Capital Expenditures/EBITDA = 30% q Depreciation/EBITDA = 20% q Cost of Capital = 10% q The firm has no working capital requirements q The firm is in stable growth and is expected to grow 5% a year forever. q In this case, the Value/EBITDA multiple for this firm can be estimated as follows: Value (1-.36) (0.2)(.36) 0.3 0 = + - - = 8.24 EBITDA.10 -.05.10 -.05.10 -.05.10 -.05 © All Slides | Aswath Damodaran  THE DETERMINANTS OF EV/EBITDA 49 q Tax Reinvestment Rates Needs Excess Returns © All Slides | Aswath Damodaran  V. REVENUE MULTIPLES 50 q With revenue multiples, you scale market value to the revenues generated by a firm. There are two variants in use: q Price to Sales = Market Capitalization / Sales q EV to Sales = Enterprise Value / Sales q The former, while widely used, is internally inconsistent and can be misleading for firms with significant debt loads and/or cash holdings. q The biggest selling point for revenue multiples is that you lose far fewer firms when computing the multiple, since revenues cannot be negative. © All Slides | Aswath Damodaran  EV/SALES RATIO: DETERMINANTS 51 q If pre-tax operating margins are used, the appropriate value estimate is that of the firm. In particular, if one makes the replaces the FCFF with the expanded version: Free Cash Flow to the Firm = EBIT (1 - tax rate) (1 - Reinvestment Rate) q Then the Value of the Firm can be written as a function of the after- tax operating margin= (EBIT (1-t)/Sales ( " (1+g)n % + * (1-RIR growth )(1+g)* $1− ' - Value * # (1+WACC)n & (1-RIR stable )(1+g)n *(1+g n ) - =After-tax Oper. Margin* + Sales0 * 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) RIR Growth, Stable = Reinvestment rate in high growth and stable periods WACC = Weighted average cost of capital © All Slides | Aswath Damodaran  THE VALUE OF A BRAND NAME 52 q One of the critiques of traditional valuation is that is fails to consider the value of brand names and other intangibles. q The approaches used by analysts to value brand names are often ad- hoc and may significantly overstate or understate their value. q 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. q In general, the value of a brand name can be written as: q Value of brand name ={(V/S)b-(V/S)g }* Sales q (V/S)b = Value of Firm/Sales ratio with the benefit of the brand name q (V/S)g = Value of Firm/Sales ratio of the firm with the generic product © All Slides | Aswath Damodaran  VALUING BRAND NAME 53 Coca Cola With Cott Margins Current Revenues = $21,962.00 $21,962.00 Length of high-growth period 10 10 Reinvestment Rate = 50% 50% Operating Margin (after-tax) 15.57% 5.28% Sales/Capital (Turnover ratio) 1.34 1.34 Return on capital (after-tax) 20.84% 7.06% Growth rate during period (g) = 10.42% 3.53% Cost of Capital during period = 7.65% 7.65% Stable Growth Period Growth rate in steady state = 4.00% 4.00% Return on capital = 7.65% 7.65% Reinvestment Rate = 52.28% 52.28% Cost of Capital = 7.65% 7.65% Value of Firm = $79,611.25 $15,371.24 Value of brand name = $79,611 -$15,371 = $64,240 million © All Slides | Aswath Damodaran  THE DETERMINANTS OF MULTIPLES… 54 © All Slides | Aswath Damodaran  APPLICATION TESTS 55 q Given the firm that we are valuing, what is a “comparable” firm? q 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. q 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. q Given the comparable firms, how do we adjust for differences across firms on the fundamentals? q It is impossible to find an exactly identical firm to the one you are valuing. q You need to control for differences across firms. © All Slides | Aswath Damodaran  THE SAMPLING CHOICE 56 q Ideally, you would like to find lots of publicly traded firms that look just like your firm, in terms of fundamentals, and compare the pricing of your firm to the pricing of these other publicly traded firms. Since, they are all just like your firm, there will be no need to control for differences. q In practice, it is very difficult (and perhaps impossible) to find firms that share the same risk, growth and cash flow characteristics of your firm. Even if you are able to find such firms, they will very few in number. The trade off then becomes: Small sample of Large sample firms that are of firms that are “just like” your similar in some firm dimensions but different on others © All Slides | Aswath Damodaran  THE ”CONTROL FOR DIFFERENCES” CHOICES 57 1. Direct comparisons: If the comparable firms are “just like” your firm, you can compare multiples directly across the firms and conclude that your firm is expensive (cheap) if it trades at a multiple higher (lower) than the other firms. 2. Story telling: If there is a key dimension on which the firms vary, you can tell a story based upon your understanding of how value varies on that dimension. An example: This company trades at 12 times earnings, whereas the rest of the sector trades at 10 times earnings, but I think it is cheap because it has a much higher growth rate than the rest of the sector. 3. Modified multiple: You can modify the multiple to incorporate the dimension on which there are differences across firms. 4. Statistical techniques: If your firms vary on more than one dimension, you can try using multiple regressions (or variants thereof) to arrive at a “controlled” estimate for your firm. © All Slides | Aswath Damodaran  1. JUST STORY TELLING TRAILING PE ACROSS BEVERAGE COMPANIES 58 Company Name Trailing PE Expected Growth Standard Deviation Coca-Cola Bottling 29.18 9.50% 20.58% Molson Inc. Ltd. 'A' 43.65 15.50% 21.88% Anheuser-Busch 24.31 11.00% 22.92% Corby Distilleries Ltd. 16.24 7.50% 23.66% Chalone Wine Group 21.76 14.00% 24.08% Andres Wines Ltd. 'A' 8.96 3.50% 24.70% Todhunter Int'l 8.94 3.00% 25.74% Brown-Forman 'B' 10.07 11.50% 29.43% Coors (Adolph) 'B' 23.02 10.00% 29.52% PepsiCo, Inc. 33.00 10.50% 31.35% Coca-Cola 44.33 19.00% 35.51% Boston Beer 'A' 10.59 17.13% 39.58% Whitman Corp. 25.19 11.50% 44.26% Mondavi (Robert) 'A' 16.47 14.00% 45.84% Coca-Cola Enterprises 37.14 27.00% 51.34% Hansen Natural Corp 9.70 17.00% 62.45% © All Slides | Aswath Damodaran  A QUESTION 59 q 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? a. Yes b. No q Why or why not? © All Slides | Aswath Damodaran  2: STATISTICAL CONTROLS COMPARING PE RATIOS ACROSS TELECOM COMPANIES 60 Company Name PE Growth PT Indosat ADR 7.8 0.06 Telebras ADR 8.9 0.075 Telecom Corporation of New Zealand ADR 11.2 0.11 Telecom Argentina Stet - France Telecom SA ADR B 12.5 0.08 Hellenic Telecommunication Organization SA ADR 12.8 0.12 Telecomunicaciones de Chile ADR 16.6 0.08 Swisscom AG ADR 18.3 0.11 Asia Satellite Telecom Holdings ADR 19.6 0.16 Portugal Telecom SA ADR 20.8 0.13 Telefonos de Mexico ADR L 21.1 0.14 Matav RT ADR 21.5 0.22 Telstra ADR 21.7 0.12 Gilat Communications 22.7 0.31 Deutsche Telekom AG ADR 24.6 0.11 British Telecommunications PLC ADR 25.7 0.07 Tele Danmark AS ADR 27 0.09 Telekomunikasi Indonesia ADR 28.4 0.32 Cable & Wireless PLC ADR 29.8 0.14 APT Satellite Holdings ADR 31 0.33 Telefonica SA ADR 32.5 0.18 Royal KPN NV ADR 35.7 0.13 Telecom Italia SPA ADR 42.2 0.14 Nippon Telegraph & Telephone ADR 44.3 0.2 France Telecom SA ADR 45.2 0.19 Korea Telecom ADR 71.3 0.44 © All Slides | Aswath Damodaran  PE, GROWTH AND RISK 61 Dependent variable is: PE R squared = 66.2% R squared (adjusted) = 63.1% Variable Coefficient SE t-ratio Probability Constant 13.1151 3.471 3.78 0.0010 Growth rate 121.223 19.27 6.29 ≤ 0.0001 Emerging Market -13.8531 3.606 -3.84 0.0009 Emerging Market is a dummy: 1 if emerging market 0 if not © All Slides | Aswath Damodaran  IS TELEBRAS UNDER VALUED? 62 q Plugging in Telebras’s expected growth rate and the fact that it is an emerging market company into the regression: q Predicted PE = 13.12 + 121.22 (.075) - 13.85 (1) = 8.35 q At an actual price to earnings ratio of 8.9, Telebras is slightly overvalued. q Bottom line: Just because a company trades at a low PE ratio does not make it cheap. © All Slides | Aswath Damodaran  3: AN EYEBALLING EXERCISE PBV RATIOS ACROSS EUROPEAN BANKS IN 2010 63 Name PBV Ratio Return on Equity Standard Deviation BAYERISCHE HYPO-UND VEREINSB 0.80 -1.66% 49.06% COMMERZBANK AG 1.09 -6.72% 36.21% DEUTSCHE BANK AG -REG 1.23 1.32% 35.79% BANCA INTESA SPA 1.66 1.56% 34.14% BNP PARIBAS 1.72 12.46% 31.03% BANCO SANTANDER CENTRAL HISP 1.86 11.06% 28.36% SANPAOLO IMI SPA 1.96 8.55% 26.64% BANCO BILBAO VIZCAYA ARGENTA 1.98 11.17% 18.62% SOCIETE GENERALE 2.04 9.71% 22.55% ROYAL BANK OF SCOTLAND GROUP 2.09 20.22% 18.35% HBOS PLC 2.15 22.45% 21.95% BARCLAYS PLC 2.23 21.16% 20.73% UNICREDITO ITALIANO SPA 2.30 14.86% 13.79% KREDIETBANK SA LUXEMBOURGEOI 2.46 17.74% 12.38% ERSTE BANK DER OESTER SPARK 2.53 10.28% 21.91% STANDARD CHARTERED PLC 2.59 20.18% 19.93% HSBC HOLDINGS PLC 2.94 18.50% 19.66% LLOYDS TSB GROUP PLC 3.33 32.84% 18.66% Average 2.05 12.54% 24.99% Median 2.07 11.82% 21.93% © All Slides | Aswath Damodaran  THE MEDIAN TEST… 64 q We are looking for stocks that trade at low price to book ratios, while generating high returns on equity, with low risk. But what is a low price to book ratio? Or a high return on equity? Or a low risk q One simple measure of what is par for the sector are the median values for each of the variables. A simplistic decision rule on under and over valued stocks would therefore be: q Undervalued stocks: Trade at price to book ratios below the median for the sector,(2.07), generate returns on equity higher than the sector median (11.82%) and have standard deviations lower than the median (21.93%). q Overvalued stocks: Trade at price to book ratios above the median for the sector and generate returns on equity lower than the sector median. © All Slides | Aswath Damodaran  THE STATISTICAL ALTERNATIVE 65 q We are looking for stocks that trade at low price to book ratios, while generating high returns on equity. But what is a low price to book ratio? Or a high return on equity? q Taking the sample of 18 banks, we ran a regression of PBV against ROE and standard deviation in stock prices (as a proxy for risk). PBV = 2.27 + 3.63 ROE - 2.68 Std dev (5.56) (3.32) (2.33) R squared of regression = 79% q Reading the regression tea leaves: q Every 1% increase in the return on equity at a European bank increases its price to book ratio by 0.0363. q Every 1% increase in the standard deviation in equity reduces the price to book ratio by 0.0268. q The regression predictions will have a standard error, which is inversely proportionate to the R squared. © All Slides | Aswath Damodaran  AND THESE PREDICTIONS? 66 © All Slides | Aswath Damodaran  EXAMPLE 4: MORE STATISTICS AND A LARGER SAMPLE PRICE TO BOOK VERSUS ROE 67 © All Slides | Aswath Damodaran  MISSING GROWTH? 68 © All Slides | Aswath Damodaran  PBV, ROE AND RISK: LARGE CAP US FIRMS 69 Most overval ued Cheapest Most underval ued © All Slides | Aswath Damodaran  BRINGING IT ALL TOGETHER… LARGEST US STOCKS IN JANUARY 2010 70 © All Slides | Aswath Damodaran  UPDATED PBV RATIOS – LARGEST MARKET CAP US COMPANIES -UPDATED TO JANUARY 2024 71 © All Slides | Aswath Damodaran  EXAMPLE 5: OVERLOOKED FUNDAMENTALS? EV/EBITDA MULTIPLE FOR TRUCKING COMPANIES Company Name Value EBITDA Value/EBITDA 72 KLLM Trans. Svcs. $ 114.32 $ 48.81 2.34 Ryder System $ 5,158.04 $ 1,838.26 2.81 Rollins Truck Leasing $ 1,368.35 $ 447.67 3.06 Cannon Express Inc. $ 83.57 $ 27.05 3.09 Hunt (J.B.) $ 982.67 $ 310.22 3.17 Yellow Corp. $ 931.47 $ 292.82 3.18 Roadway Express $ 554.96 $ 169.38 3.28 Marten Transport Ltd. $ 116.93 $ 35.62 3.28 Kenan Transport Co. $ 67.66 $ 19.44 3.48 M.S. Carriers $ 344.93 $ 97.85 3.53 Old Dominion Freight $ 170.42 $ 45.13 3.78 Trimac Ltd $ 661.18 $ 174.28 3.79 Matlack Systems $ 112.42 $ 28.94 3.88 XTRA Corp. $ 1,708.57 $ 427.30 4.00 Covenant Transport Inc $ 259.16 $ 64.35 4.03 Builders Transport $ 221.09 $ 51.44 4.30 Werner Enterprises $ 844.39 $ 196.15 4.30 Landstar Sys. $ 422.79 $ 95.20 4.44 AMERCO $ 1,632.30 $ 345.78 4.72 USA Truck $ 141.77 $ 29.93 4.74 Frozen Food Express $ 164.17 $ 34.10 4.81 Arnold Inds. $ 472.27 $ 96.88 4.87 Greyhound Lines Inc. $ 437.71 $ 89.61 4.88 USFreightways $ 983.86 $ 198.91 4.95 Golden Eagle Group Inc. $ 12.50 $ 2.33 5.37 Arkansas Best $ 578.78 $ 107.15 5.40 Airlease Ltd. $ 73.64 $ 13.48 5.46 Celadon Group $ 182.30 $ 32.72 5.57 Amer. Freightways $ 716.15 $ 120.94 5.92 Transfinancial Holdings $ 56.92 $ 8.79 6.47 Vitran Corp. 'A' $ 140.68 $ 21.51 6.54 Interpool Inc. $ 1,002.20 $ 151.18 6.63 Intrenet Inc. $ 70.23 $ 10.38 6.77 Swift Transportation $ 835.58 $ 121.34 6.89 Landair Services $ 212.95 $ 30.38 7.01 CNF Transportation $ 2,700.69 $ 366.99 7.36 Budget Group Inc $ 1,247.30 $ 166.71 7.48 Caliber System $ 2,514.99 $ 333.13 7.55 Knight Transportation Inc $ 269.01 $ 28.20 9.54 Heartland Express $ 727.50 $ 64.62 11.26 Greyhound CDA Transn Corp $ 83.25 $ 6.99 11.91 Mark VII $ 160.45 $ 12.96 12.38 Coach USA Inc $ 678.38 $ 51.76 13.11 US 1 Inds Inc. $ 5.60 $ (0.17) NA Average 5.61 © All Slides | Aswath Damodaran  A TEST ON EBITDA 73 q 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? q What general lessons would you draw from this on the EV/EBITDA multiples for infrastructure companies as their infrastructure ages? © All Slides | Aswath Damodaran  EXAMPLE 6: PRICING ACROSS TIME - PS RATIOS GROCERY STORES - US IN JANUARY 2007 74 1.6 WF MI 1.4 1.2 1.0 ARD.8.6 WMK R DK O ATS SWY.4 AHO.2 PTMK PS_RATIO MARSA 0.0 -.2 R sq = 0.5947 -3 -2 -1 0 1 2 3 4 5 Net Margin Whole Foods: In 2007: Net Margin was 3.41% and Price/ Sales ratio was 1.41 Predicted Price to Sales = 0.07 + 10.49 (0.0341) = 0.43 © All Slides | Aswath Damodaran  THE DIFFERENCE TWO YEARS CAN MAKE: GROCERY STORES - US IN JANUARY 2009 75 Whole Foods: In 2009, Net Margin had dropped to 2.77% and Price to Sales ratio was down to 0.31. Predicted Price to Sales = 0.07 + 10.49 (.0277) = 0.36 © All Slides | Aswath Damodaran  IS THIS STEADY STATE? IN 2010.. 76 Whole Foods: In 2010, Net Margin had dropped to 1.44% and Price to Sales ratio increased to 0.50. Predicted Price to Sales = 0.06 + 11.43 (.0144) = 0.22 © All Slides | Aswath Damodaran  THERE IS A NEW KID IN TOWN: JANUARY 2015 77 There is a new star in town (Sprouts) PS = 0.557 + 0.085 Net Margin Whole Foods = 0.557 + 8.50 (0.0408) = 0.90 At 1.35 times sales, Whole Foods is overvalued (again) © All Slides | Aswath Damodaran  EXAMPLE 7: NOTHING’S WORKING! INTERNET STOCKS IN EARLY 2000.. 78 30 PKSI LCOS SPYG 20 INTM MMXI SCNT MQST FFIV ATHM A CNET d DCLK j INTW RAMP P 10 CSGP CBIS NTPA S NETO SONEPCLN APNT CLKS EDGRPSIX ATHY AMZN SPLN BIDS ALOY ACOM EGRP BIZZ IIXL ITRA ANET ONEM ABTL INFO FATB RMII TMNT GEEK -0 TURF PPOD BUYX ELTX GSVI ROWE -0.8 -0.6 -0.4 -0.2 AdjMargin © All Slides | Aswath Damodaran  PS RATIOS AND MARGINS ARE NOT HIGHLY CORRELATED 79 q Regressing PS ratios against current margins yields the following PS = 81.36 - 7.54(Net Margin) R2 = 0.04 (0.49) q This is not surprising. These firms are priced based upon expected margins, rather than current margins. © All Slides | Aswath Damodaran  SOLUTION 1: USE PROXIES FOR SURVIVAL AND GROWTH: AMAZON IN EARLY 2000 80 q 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% q Predicted PS = 30.61 - 2.77(7.1039) + 6.42(1.9946) + 5.11 (.3069) = 30.42 q Actual PS = 25.63 Stock is undervalued, relative to other internet stocks. © All Slides | Aswath Damodaran  SOLUTION 2: USE FORWARD MULTIPLES WATCH OUT FOR BUMPS IN THE ROAD (TESLA IN 2013) 81 © All Slides | Aswath Damodaran  THE MARKET SETS THE RULES… 82 q While we can compute multiples based upon accounting numbers (revenues, earnings, EBITDA or book value), you can also compute the multiple that market are paying on any quantifiable variable. q You can compute market cap or EV per employee, per subscriber, per customer etc. q The question of whether you should do so is not a theoretical one. It is set by the market. q Ultimately, your job in pricing is to figure what the market cares about when pricing companies and replicate it. © All Slides | Aswath Damodaran  AN EXAMPLE: LET THE MARKET TELL YOU WHAT MATTERS.. SOCIAL MEDIA IN OCTOBER 2013 83 Number of Enterprise users Company Market Cap value Revenues EBITDA Net Income (millions) EV/User EV/Revenue EV/EBITDA PE Facebook $173,540.00 $160,090.00 $7,870.00 $3,930.00 $1,490.00 1230.00 $130.15 20.34 40.74 116.47 Linkedin $23,530.00 $19,980.00 $1,530.00 $182.00 $27.00 277.00 $72.13 13.06 109.78 871.48 Pandora $7,320.00 $7,150.00 $655.00 -$18.00 -$29.00 73.40 $97.41 10.92 NA NA Groupon $6,690.00 $5,880.00 $2,440.00 $125.00 -$95.00 43.00 $136.74 2.41 47.04 NA Netflix $25,900.00 $25,380.00 $4,370.00 $277.00 $112.00 44.00 $576.82 5.81 91.62 231.25 Yelp $6,200.00 $5,790.00 $233.00 $2.40 -$10.00 120.00 $48.25 24.85 2412.50 NA Open Table $1,720.00 $1,500.00 $190.00 $63.00 $33.00 14.00 $107.14 7.89 23.81 52.12 Zynga $4,200.00 $2,930.00 $873.00 $74.00 -$37.00 27.00 $108.52 3.36 39.59 NA Zillow $3,070.00 $2,860.00 $197.00 -$13.00 -$12.45 34.50 $82.90 14.52 NA NA Trulia $1,140.00 $1,120.00 $144.00 -$6.00 -$18.00 54.40 $20.59 7.78 NA NA Tripadvisor $13,510.00 $12,860.00 $945.00 $311.00 $205.00 260.00 $49.46 13.61 41.35 65.90 Average $130.01 11.32 350.80 267.44 Median $97.41 10.92 44.20 116.47 © All Slides | Aswath Damodaran  READ THE TEA LEAVES: SEE WHAT THE MARKET CARES ABOUT 84 Market Enterprise Net Number of Cap value Revenues EBITDA Income users (millions) Market Cap 1. Enterprise value 0.9998 1. Revenues 0.8933 0.8966 1. EBITDA 0.9709 0.9701 0.8869 1. Net Income 0.8978 0.8971 0.8466 0.9716 1. Number of users (millions) 0.9812 0.9789 0.8053 0.9354 0.8453 1. Twitter had 240 million users at the time of its IPO. What price would you attach to the company? © All Slides | Aswath Damodaran  PRICING ACROSS THE ENTIRE MARKET: WHY NOT? 85 q In contrast to the 'comparable firm' approach, the information in the entire cross-section of firms can be used to predict PE ratios. q 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. © All Slides | Aswath Damodaran  PE RATIO VERSUS THE MARKET PE VERSUS EXPECTED EPS GROWTH: JANUARY 2024 86 © All Slides | Aswath Damodaran  PE RATIO: STANDARD REGRESSION FOR US STOCKS - JANUARY 2024 87 The regression is run with growth and payout entered as decimals, i.e., 25% is entered as 0.25) © All Slides | Aswath Damodaran  PROBLEMS WITH THE REGRESSION METHODOLOGY 88 q Non-linearity: The basic regression assumes a linear relationship between PE ratios and the financial proxies, and that might not be appropriate. q Non-stationarity: 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. For instance, the 2022 regression has a markedly lower R-squared than the regressions in prior years, as the COVID effect on earnings plays out. q Multi-collinearity: 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. © All Slides | Aswath Damodaran  STATISTICALLY INSIGNIFICANT? 89 q If a coefficient in a regression is statistically insignificant, all it is doing is adding noise to the regression prediction. q There are simple statistical tests of significance, such as the t statistics (>2 is very good, 1-2 is marginal,