Equity Instruments & Markets: Part II B Relative Valuation

Transcription

1 Equity Istrumets & Markets: Part II B Relative Valuatio Aswath Damodara Aswath Damodara 1

2 Why relative valuatio? If you thik I m crazy, you should see the guy who lives across the hall Jerry Seifeld talkig about Kramer i a Seifeld episode A little iaccuracy sometimes saves tos of explaatio H.H. Muro Aswath Damodara 2

3 What is relative valuatio? I relative valuatio, the value of a asset is compared to the values assessed by the market for similar or comparable assets. To do relative valuatio the, we eed to idetify comparable assets ad obtai market values for these assets covert these market values ito stadardized values, sice the absolute prices caot be compared This process of stadardizig creates price multiples. compare the stadardized value or multiple for the asset beig aalyzed to the stadardized values for comparable asset, cotrollig for ay differeces betwee the firms that might affect the multiple, to judge whether the asset is uder or over valued Aswath Damodara 3

4 Stadardizig Value Prices ca be stadardized usig a commo variable such as earigs, cashflows, book value or reveues. Earigs Multiples Price/Earigs Ratio (PE) ad variats (PEG ad Relative PE) Value/EBIT Value/EBITDA Value/Cash Flow Book Value Multiples Price/Book Value(of Equity) (PBV) Value/ Book Value of Assets Value/Replacemet Cost (Tobi s Q) Reveues Price/Sales per Share (PS) Value/Sales Idustry Specific Variable (Price/kwh, Price per to of steel...) Aswath Damodara 4

5 The Four Steps to Uderstadig Multiples Defie the multiple I use, the same multiple ca be defied i differet ways by differet users. Whe comparig ad usig multiples, estimated by someoe else, it is critical that we uderstad how the multiples have bee estimated Describe the multiple Too may people who use a multiple have o idea what its cross sectioal distributio is. If you do ot kow what the cross sectioal distributio of a multiple is, it is difficult to look at a umber ad pass judgmet o whether it is too high or low. Aalyze the multiple It is critical that we uderstad the fudametals that drive each multiple, ad the ature of the relatioship betwee the multiple ad each variable. Apply the multiple Defiig the comparable uiverse ad cotrollig for differeces is far more difficult i practice tha it is i theory. Aswath Damodara 5

6 Defiitioal Tests Is the multiple cosistetly defied? Propositio 1: Both the value (the umerator) ad the stadardizig variable ( the deomiator) should be to the same claimholders i the firm. I other words, the value of equity should be divided by equity earigs or equity book value, ad firm value should be divided by firm earigs or book value. Is the multiple uiformly estimated? The variables used i defiig the multiple should be estimated uiformly across assets i the comparable firm list. If earigs-based multiples are used, the accoutig rules to measure earigs should be applied cosistetly across assets. The same rule applies with book-value based multiples. Aswath Damodara 6

7 Descriptive Tests What is the average ad stadard deviatio for this multiple, across the uiverse (market)? What is the media for this multiple? The media for this multiple is ofte a more reliable compariso poit. How large are the outliers to the distributio, ad how do we deal with the outliers? Throwig out the outliers may seem like a obvious solutio, but if the outliers all lie o oe side of the distributio (they usually are large positive umbers), this ca lead to a biased estimate. Are there cases where the multiple caot be estimated? Will igorig these cases lead to a biased estimate of the multiple? How has this multiple chaged over time? Aswath Damodara 7

8 Aalytical Tests What are the fudametals that determie ad drive these multiples? Propositio 2: Embedded i every multiple are all of the variables that drive every discouted cash flow valuatio - growth, risk ad cash flow patters. I fact, usig a simple discouted cash flow model ad basic algebra should yield the fudametals that drive a multiple How do chages i these fudametals chage the multiple? The relatioship betwee a fudametal (like growth) ad a multiple (such as PE) is seldom liear. For example, if firm A has twice the growth rate of firm B, it will geerally ot trade at twice its PE ratio Propositio 3: It is impossible to properly compare firms o a multiple, if we do ot kow the ature of the relatioship betwee fudametals ad the multiple. Aswath Damodara 8

9 Applicatio Tests Give the firm that we are valuig, what is a comparable firm? While traditioal aalysis is built o the premise that firms i the same sector are comparable firms, valuatio theory would suggest that a comparable firm is oe which is similar to the oe beig aalyzed i terms of fudametals. Propositio 4: There is o reaso why a firm caot be compared with aother firm i a very differet busiess, if the two firms have the same risk, growth ad cash flow characteristics. Give the comparable firms, how do we adjust for differeces across firms o the fudametals? Propositio 5: It is impossible to fid a exactly idetical firm to the oe you are valuig. Aswath Damodara 9

10 Price Earigs Ratio: Defiitio PE = Market Price per Share / Earigs per Share There are a umber of variats o the basic PE ratio i use. They are based upo how the price ad the earigs are defied. Price: is usually the curret price is sometimes the average price for the year EPS: earigs per share i most recet fiacial year earigs per share i trailig 12 moths (Trailig PE) forecasted earigs per share ext year (Forward PE) forecasted earigs per share i future year Aswath Damodara 10

11 PE Ratio: Descriptive Statistics for the US PE Ratio Distributio: US Stocks i September Number of firms Curret PE Trailig PE Forward PE >100 PE Ratio Aswath Damodara 11

12 PE: Decipherig the Distributio Curret PE Trailig PE Forward PE Mea Stadard Error Media Stadard Deviatio Skewess Miimum Maximum Cout Largest(500) Smallest(500) Aswath Damodara 12

13 PE Distributio: Europe ad Emergig Markets i September 2003 PE Ratios: Europe ad Emergig Market Compaies Number of firms Europe Emergig Markets < >100 PE Ratio Aswath Damodara 13

14 Comparig PE Ratios: US, Europe ad Emergig Markets 25.00% Distributio of PE Ratios: July 2003 Media PE US = Europe = Em Mkts = % % of firms fallig i class 15.00% 10.00% US Europe Emergig Markets 5.00% 0.00% < >100 PE ratio class Aswath Damodara 14

15 PE Ratio: Uderstadig the Fudametals To uderstad the fudametals, start with a basic equity discouted cash flow model. With the divided discout model, P 0 = DPS 1 r - g Dividig both sides by the earigs per share, P 0 = PE = Payout Ratio * (1 + g ) EPS 0 r-g If this had bee a FCFE Model, P 0 = FCFE 1 r - g P 0 = PE = (FCFE/Earigs)* (1 + g ) EPS 0 r-g Aswath Damodara 15

16 PE Ratio ad Fudametals Propositio: Other thigs held equal, higher growth firms will have higher PE ratios tha lower growth firms. Propositio: Other thigs held equal, higher risk firms will have lower PE ratios tha lower risk firms Propositio: Other thigs held equal, firms with lower reivestmet eeds will have higher PE ratios tha firms with higher reivestmet rates. Of course, other thigs are difficult to hold equal sice high growth firms, ted to have risk ad high reivestmet rats. Aswath Damodara 16

17 Usig the Fudametal Model to Estimate PE For a High Growth Firm The price-earigs ratio for a high growth firm ca also be related to fudametals. I the special case of the two-stage divided discout model, this relatioship ca be made explicit fairly simply: Ê (1+ g) EPS 0 * Payout Ratio *(1+ g)* Á ˆ 1 - Ë (1+ r) P 0 = r - g + EPS 0 * Payout Ratio *(1+ g) *(1+ g ) (r -g )(1+ r) For a firm that does ot pay what it ca afford to i divideds, substitute FCFE/Earigs for the payout ratio. Dividig both sides by the earigs per share: P 0 EPS 0 = Ê (1 + g) Payout Ratio * (1 + g) * Á ˆ 1 - Ë (1+ r) r - g + Payout Ratio *(1+ g) * (1 + g ) (r - g )(1+ r) Aswath Damodara 17

18 Expadig the Model I this model, the PE ratio for a high growth firm is a fuctio of growth, risk ad payout, exactly the same variables that it was a fuctio of for the stable growth firm. The oly differece is that these iputs have to be estimated for two phases - the high growth phase ad the stable growth phase. Expadig to more tha two phases, say the three stage model, will mea that risk, growth ad cash flow patters i each stage. Aswath Damodara 18

19 A Simple Example Assume that you have bee asked to estimate the PE ratio for a firm which has the followig characteristics: Variable High Growth Phase Stable Growth Phase Expected Growth Rate 25% 8% Payout Ratio 20% 50% Beta Number of years 5 years Forever after year 5 Riskfree rate = T.Bod Rate = 6% Required rate of retur = 6% + 1(5.5%)= 11.5% Ê ˆ 0.2 * (1.25) * Á 1- (1.25)5 Ë (1.115) 5 PE = ( ) * (1.25)5 * (1.08) ( ) (1.115) 5 = Aswath Damodara 19

20 PE ad Growth: Firm grows at x% for 5 years, 8% thereafter PE Ratios ad Expected Growth: Iterest Rate Scearios PE Ratio r=4% r=6% r=8% r=10% % 10% 15% 20% 25% 30% 35% 40% 45% 50% Expected Growth Rate Aswath Damodara 20

21 PE Ratios ad Legth of High Growth: 25% growth for years; 8% thereafter PE Ratios ad Legth of High Growth Period PE Ratio 30 g=25% g=20% g=15% g=10% Legth of High Growth Period Aswath Damodara 21

22 PE ad Risk: Effects of Chagig Betas o PE Ratio: Firm with x% growth for 5 years; 8% thereafter PE Ratios ad Beta: Growth Scearios PE Ratio g=25% g=20% g=15% g=8% Beta Aswath Damodara 22

23 PE ad Payout PE Ratios ad Payour Ratios: Growth Scearios PE g=25% g=20% g=15% g=10% % 20% 40% 60% 80% 100% Payout Ratio Aswath Damodara 23

24 I. Assessig Emergig Market PE Ratios - Early 2000 PE: Emergig Markets Mexico Malaysia Sigapore Taiwa Hog Kog Veezuela Brazil Argetia Chile Aswath Damodara 24

25 Comparisos across coutries o o I July 2000, a market strategist is makig the argumet that Brazil ad Veezuela 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 oe market s PE ratios to be lower tha aother market s PE? Aswath Damodara 25

26 II. A Compariso across coutries: Jue 2000 Coutry PE Divided Yield 2-yr rate 10-yr rate 10yr - 2yr UK % 5.93% 5.85% -0.08% Germay % 5.06% 5.32% 0.26% Frace % 5.11% 5.48% 0.37% Switzerlad % 3.62% 3.83% 0.21% Belgium % 5.15% 5.70% 0.55% Italy % 5.27% 5.70% 0.43% Swede % 4.67% 5.26% 0.59% Netherlads % 5.10% 5.47% 0.37% Australia % 6.29% 6.25% -0.04% Japa % 0.58% 1.85% 1.27% US % 6.05% 5.85% -0.20% Caada % 5.70% 5.77% 0.07% Aswath Damodara 26

27 Correlatios ad Regressio of PE Ratios Correlatios Correlatio betwee PE ratio ad log term iterest rates = Correlatio betwee PE ratio ad yield spread = Regressio Results PE Ratio = (10 yr rate) (10-yr - 2 yr rate) R 2 = 59% Iput the iterest rates as percet. For istace, the predicted PE ratio for Japa with this regressio would be: PE: Japa = (1.85) (1.27) = At a actual PE ratio of 52.25, Japaese stocks are slightly overvalued. Aswath Damodara 27

28 Predicted PE Ratios Coutry Actual PE Predicted PE Uder or Over UK % Germay % Frace % Switzerlad % Belgium % Italy % Swede % Netherlads % Australia % Japa % Uited States % Caada % Aswath Damodara 28

29 III. A Example with Emergig Markets: Jue 2000 Coutry PE Ratio Iterest Rates GDP Real Growth Coutry Risk Argetia % 2.50% 45 Brazil % 4.80% 35 Chile % 5.50% 15 Hog Kog % 6.00% 15 Idia % 4.20% 25 Idoesia % 4.00% 50 Malaysia % 3.00% 40 Mexico % 5.50% 30 Pakista % 3.00% 45 Peru % 4.90% 50 Phillipies % 3.80% 45 Sigapore % 5.20% 5 South Korea % 4.80% 25 Thailad % 5.50% 25 Turkey % 2.00% 35 Veezuela % 3.50% 45 Aswath Damodara 29

30 Regressio Results The regressio of PE ratios o these variables provides the followig PE = Iterest Rates Growth i GDP Coutry Risk R Squared = 73% Aswath Damodara 30

31 Predicted PE Ratios Coutry PE Ratio Iterest GDP Real Coutry Rates Growth Risk Predicted PE Argetia % 2.50% Brazil % 4.80% Chile % 5.50% Hog Kog % 6.00% Idia % 4.20% Idoesia % 4.00% Malaysia % 3.00% Mexico % 5.50% Pakista % 3.00% Peru % 4.90% Phillipies % 3.80% Sigapore % 5.20% South Korea % 4.80% Thailad % 5.50% Turkey % 2.00% Veezuela % 3.50% Aswath Damodara 31

32 IV. Comparisos of PE across time: PE Ratio for the S&P 500 PE Ratio: Aswath Damodara 32

33 Is low (high) PE cheap (expesive)? A market strategist argues that stocks are over priced because the PE ratio today is too high relative to the average PE ratio across time. Do you agree? q Yes q No If you do ot agree, what factors might explai the higher PE ratio today? Aswath Damodara 33

34 E/P Ratios, T.Bod Rates ad Term Structure EP Ratios ad Iterest Rates: % 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% % Year Earigs Yield T.Bod Rate Bod-Bill Aswath Damodara 34

35 Regressio Results There is a strog positive relatioship betwee E/P ratios ad T.Bod rates, as evideced by the correlatio of 0.70 betwee the two variables., I additio, there is evidece that the term structure also affects the PE ratio. I the followig regressio, usig data, we regress E/P ratios agaist the level of T.Bod rates ad a term structure variable (T.Bod - T.Bill rate) E/P = 1.98% T.Bod Rate (T.Bod Rate-T.Bill Rate) (1.94) (6.29) (-1.42) R squared = 50.5% Aswath Damodara 35

36 Estimate the E/P Ratio Today T. Bod Rate = T.Bod Rate - T.Bill Rate = Expected E/P Ratio = Expected PE Ratio = Aswath Damodara 36

37 V. Comparig PE ratios across firms Compay Name Trailig PE Expected Growth Stadard Dev Coca-Cola Bottlig % 20.58% Molso Ic. Ltd. 'A' % 21.88% Aheuser-Busch % 22.92% Corby Distilleries Ltd % 23.66% Chaloe Wie Group Ltd % 24.08% Adres Wies Ltd. 'A' % 24.70% Todhuter It'l % 25.74% Brow-Forma 'B' % 29.43% Coors (Adolph) 'B' % 29.52% PepsiCo, Ic % 31.35% Coca-Cola % 35.51% Bosto Beer 'A' % 39.58% Whitma Corp % 44.26% Modavi (Robert) 'A' % 45.84% Coca-Cola Eterprises % 51.34% Hase Natural Corp % 62.45% Aswath Damodara 37

38 A Questio You are readig a equity research report o this sector, ad the aalyst claims that Adres Wie ad Hase Natural are uder valued because they have low PE ratios. Would you agree? o o Yes No Why or why ot? Aswath Damodara 38

39 VI. Comparig PE Ratios across a Sector Compay Name PE Growth PT Idosat ADR Telebras ADR Telecom Corporatio of New Zealad ADR Telecom Argetia Stet - Frace Telecom SA ADR B Helleic Telecommuicatio Orgaizatio SA ADR Telecomuicacioes de Chile ADR Swisscom AG ADR Asia Satellite Telecom Holdigs ADR Portugal Telecom SA ADR Telefoos de Mexico ADR L Matav RT ADR Telstra ADR Gilat Commuicatios Deutsche Telekom AG ADR British Telecommuicatios PLC ADR Tele Damark AS ADR Telekomuikasi Idoesia ADR Cable & Wireless PLC ADR APT Satellite Holdigs ADR Telefoica SA ADR Royal KPN NV ADR Telecom Italia SPA ADR Nippo Telegraph & Telephoe ADR Frace Telecom SA ADR Korea Telecom ADR Aswath Damodara 39

40 PE, Growth ad Risk Depedet variable is: PE R squared = 66.2% R squared (adjusted) = 63.1% Variable Coefficiet SE t-ratio prob Costat Growth rate Emergig Market Emergig Market is a dummy: 1 if emergig market 0 if ot Aswath Damodara 40

41 Is Telebras uder valued? Predicted PE = (7.5) (1) = 8.35 At a actual price to earigs ratio of 8.9, Telebras is slightly overvalued. Aswath Damodara 41

42 Usig comparable firms- Pros ad Cos The most commo approach to estimatig the PE ratio for a firm is to choose a group of comparable firms, to calculate the average PE ratio for this group ad to subjectively adjust this average for differeces betwee the firm beig valued ad the comparable firms. Problems with this approach. The defiitio of a 'comparable' firm is essetially a subjective oe. The use of other firms i the idustry as the cotrol group is ofte ot a solutio because firms withi the same idustry ca have very differet busiess mixes ad risk ad growth profiles. There is also plety of potetial for bias. Eve whe a legitimate group of comparable firms ca be costructed, differeces will cotiue to persist i fudametals betwee the firm beig valued ad this group. Aswath Damodara 42

43 Usig the etire crosssectio: A regressio approach I cotrast to the 'comparable firm' approach, the iformatio i the etire cross-sectio of firms ca be used to predict PE ratios. The simplest way of summarizig this iformatio is with a multiple regressio, with the PE ratio as the depedet variable, ad proxies for risk, growth ad payout formig the idepedet variables. Aswath Damodara 43

44 PE versus Growth Curret PE versus Expected Growth Rate 500 US Stocks - September Curret PE Expected Growth i E PS: ext 5 y ears Aswath Damodara 44

45 PE Ratio: Stadard Regressio for US stocks - September 2003 Model 1 R R Square Model Summary Adjusted R Square Std. Er ror of the Estimate.505 a a. Pr edictors: (Costat), Value Lie Beta, Expected G rowth i EPS: ext 5 years, Payout Ratio Model 1 (Costat) Expected Growth i EPS: ext 5 year s Payout Ratio Value Lie Beta a. Depedet Var iable: Cur ret PE Ustadard ized Coefficiets Coefficiets a,b Stadar dized Coefficiets 95% Cofidece Iterval for B B Std. Error Beta t Sig. Lower Boud Upper Boud E b. Weighted Least Squares Regre ssio - Weighted by Mar ket Cap Aswath Damodara 45

46 Problems with the regressio methodology The basic regressio assumes a liear relatioship betwee PE ratios ad the fiacial proxies, ad that might ot be appropriate. The basic relatioship betwee PE ratios ad fiacial variables itself might ot be stable, ad if it shifts from year to year, the predictios from the model may ot be reliable. The idepedet variables are correlated with each other. For example, high growth firms ted to have high risk. This multi-colliearity makes the coefficiets of the regressios ureliable ad may explai the large chages i these coefficiets from period to period. Aswath Damodara 46

47 The Multicolliearity Problem Correlatios Expected G rowth i EPS: ext 5 years Value Lie Bet a Payout Ratio Pea rso Correla tio Sig. (2-tailed) N Pea rso Correla tio Sig. (2-tailed) N Pea rso Correla tio Sig. (2-tailed) N Expected Growth i EPS: ext 5 Value years Lie Beta Payout Ratio ** ** ** ** ** ** **. Correlatio is sig ificat at the 0.01 level (2-tailed). Aswath Damodara 47

48 PE Ratio without a costat - US Stocks Model 1 Model 1 Expected Growth i EPS: ext 5 year s Payout Ratio Value Lie Beta a. Depedet Var iable: Cur ret PE b. Liear Regr essio through the Origi Model Summary R R Square a Square Adjusted R Std. Er ror of the Estimate.856 b a. For regre ssio through the origi (the o-itercept model), R Squar e measur es the proportio of the variability i the depedet variable about the origi explaied by regressio. T his CANNOT be compar ed to R Square for models which iclude a itercept. b. Predictor s: V alue Lie B eta, P ayout Ratio, Expected Gr owth i EPS: ext 5 years Coefficiets a,b,c Ustadardized Coefficiets B Std. Error Stadar dized Coefficiets Beta 95% Cofidece Iterval for B t Sig. Lower Boud Upper Boud E c. Weighted Least Squares Regre ssio - Weighted by Market Cap Aswath Damodara 48

49 Usig the PE ratio regressio Assume that you were give the followig iformatio for Dell. The firm has a expected growth rate of 10%, a beta of 1.20 ad pays o divideds. Based upo the regressio, estimate the predicted PE ratio for Dell. Predicted PE = Dell is actually tradig at 22 times earigs. What does the predicted PE tell you? Aswath Damodara 49

50 The value of growth Time Period Value of extra 1% of growth Equity Risk Premium July % Jauary % July % Jauary % July % Jauary % July % Jauary % The value of growth is i terms of additioal PE Aswath Damodara 50

51 Ivestmet Strategies that compare PE to the expected growth rate If we assume that all firms withi a sector have similar growth rates ad risk, a strategy of pickig the lowest PE ratio stock i each sector will yield udervalued stocks. Portfolio maagers ad aalysts sometimes compare PE ratios to the expected growth rate to idetify uder ad overvalued stocks. I the simplest form of this approach, firms with PE ratios less tha their expected growth rate are viewed as udervalued. I its more geeral form, the ratio of PE ratio to growth is used as a measure of relative value. Aswath Damodara 51

52 Problems with comparig PE ratios to expected growth I its simple form, there is o basis for believig that a firm is udervalued just because it has a PE ratio less tha expected growth. This relatioship may be cosistet with a fairly valued or eve a overvalued firm, if iterest rates are high, or if a firm is high risk. As iterest rate decrease (icrease), fewer (more) stocks will emerge as udervalued usig this approach. Aswath Damodara 52

53 PE Ratio versus Growth - The Effect of Iterest rates: Average Risk firm with 25% growth for 5 years; 8% thereafter Figure 14.2: PE Ratios ad T.Bod Rates P/E Ratio T.Bod Rate Aswath Damodara 53

54 PE Ratios Less Tha The Expected Growth Rate I Jauary 2003, 32% of firms had PE ratios lower tha the expected 5-year growth rate 68% of firms had PE ratios higher tha the expected 5-year growth rate I compariso, 38.1% of firms had PE ratios less tha the expected 5-year growth rate i September % of firm had PE ratios less tha the expected 5-year growth rate i Aswath Damodara 54

55 PEG Ratio: Defiitio The PEG ratio is the ratio of price earigs to expected growth i earigs per share. PEG = PE / Expected Growth Rate i Earigs Defiitioal tests: Is the growth rate used to compute the PEG ratio o the same base? (base year EPS) over the same period?(2 years, 5 years) from the same source? (aalyst projectios, cosesus estimates..) Is the earigs used to compute the PE ratio cosistet with the growth rate estimate? No double coutig: If the estimate of growth i earigs per share is from the curret year, it would be a mistake to use forward EPS i computig PE If lookig at foreig stocks or ADRs, is the earigs used for the PE ratio cosistet with the growth rate estimate? (US aalysts use the ADR EPS) Aswath Damodara 55

56 PEG Ratio: Distributio PEG Ratio: US Stocks i September < >10 Curret PE/ Expected growth i EPS ext 5 years Aswath Damodara 56

57 PEG Ratios: The Beverage Sector Compay Name Trailig PE Growth Std Dev PEG Coca-Cola Bottlig % 20.58% 3.07 Molso Ic. Ltd. 'A' % 21.88% 2.82 Aheuser-Busch % 22.92% 2.21 Corby Distilleries Ltd % 23.66% 2.16 Chaloe Wie Group Ltd % 24.08% 1.55 Adres Wies Ltd. 'A' % 24.70% 2.56 Todhuter It'l % 25.74% 2.98 Brow-Forma 'B' % 29.43% 0.88 Coors (Adolph) 'B' % 29.52% 2.30 PepsiCo, Ic % 31.35% 3.14 Coca-Cola % 35.51% 2.33 Bosto Beer 'A' % 39.58% 0.62 Whitma Corp % 44.26% 2.19 Modavi (Robert) 'A' % 45.84% 1.18 Coca-Cola Eterprises % 51.34% 1.38 Hase Natural Corp % 62.45% 0.57 Average Aswath Damodara 57

58 PEG Ratio: Readig the Numbers o o The average PEG ratio for the beverage sector is The lowest PEG ratio i the group belogs to Hase Natural, which has a PEG ratio of Usig this measure of value, Hase Natural is the most uder valued stock i the group the most over valued stock i the group What other explaatio could there be for Hase s low PEG ratio? Aswath Damodara 58

59 PEG Ratio: Aalysis To uderstad the fudametals that determie PEG ratios, let us retur agai to a 2-stage equity discouted cash flow model Ê (1+ g) EPS 0 * Payout Ratio *(1+ g)* Á ˆ 1 - Ë (1+ r) P 0 = r - g + EPS 0 * Payout Ratio *(1+ g) *(1+ g ) (r -g )(1+ r) Dividig both sides of the equatio by the earigs gives us the equatio for the PE ratio. Dividig it agai by the expected growth g PEG = Ê (1+ g) Payout Ratio *(1 + g) * Á ˆ 1 - Ë (1 + r) g(r - g) + Payout Ratio * (1+ g) * (1+ g ) g(r - g )(1 + r) Aswath Damodara 59

60 PEG Ratios ad Fudametals Risk ad payout, which affect PE ratios, cotiue to affect PEG ratios as well. Implicatio: Whe comparig PEG ratios across compaies, we are makig implicit or explicit assumptios about these variables. Dividig PE by expected growth does ot eutralize the effects of expected growth, sice the relatioship betwee growth ad value is ot liear ad fairly complex (eve i a 2-stage model) Aswath Damodara 60

61 A Simple Example Assume that you have bee asked to estimate the PEG ratio for a firm which has the followig characteristics: Variable High Growth Phase Stable Growth Phase Expected Growth Rate 25% 8% Payout Ratio 20% 50% Beta Riskfree rate = T.Bod Rate = 6% Required rate of retur = 6% + 1(5.5%)= 11.5% The PEG ratio for this firm ca be estimated as follows: PEG = Ê 0.2 * (1.25) * Á 1 - (1.25) 5 ˆ Ë (1.115) 5.25( ) * (1.25) 5 *(1.08) =.115 or ( ) (1.115) Aswath Damodara 61

62 PEG Ratios ad Risk PEG Ratios ad Beta: Differet Growth Rates PEG Ratio g =25% g=20% g=15% g=8% Beta Aswath Damodara 62

63 PEG Ratios ad Quality of Growth PEG Ratios ad Retetio Ratios PEG Ratio Retetio Ratio Aswath Damodara 63

64 PEG Ratios ad Expected Growth PEG Ratios, Expected Growth ad Iterest Rates PEG Ratio 1.50 r=6% r=8% r=10% % 10% 15% 20% 25% 30% 35% 40% 45% 50% Expected Growth Rate Aswath Damodara 64

65 PEG Ratios ad Fudametals: Propositios Propositio 1: High risk compaies will trade at much lower PEG ratios tha low risk compaies with the same expected growth rate. Corollary 1: The compay that looks most uder valued o a PEG ratio basis i a sector may be the riskiest firm i the sector Propositio 2: Compaies that ca attai growth more efficietly by ivestig less i better retur projects will have higher PEG ratios tha compaies that grow at the same rate less efficietly. Corollary 2: Compaies that look cheap o a PEG ratio basis may be compaies with high reivestmet rates ad poor project returs. Propositio 3: Compaies with very low or very high growth rates will ted to have higher PEG ratios tha firms with average growth rates. This bias is worse for low growth stocks. Corollary 3: PEG ratios do ot eutralize the growth effect. Aswath Damodara 65

66 PE, PEG Ratios ad Risk PE PEG Ratio Lowest Highest 0 Aswath Damodara 66

67 PEG Ratio: Returig to the Beverage Sector Compay Name Trailig PE Growth Std Dev PEG Coca-Cola Bottlig % 20.58% 3.07 Molso Ic. Ltd. 'A' % 21.88% 2.82 Aheuser-Busch % 22.92% 2.21 Corby Distilleries Ltd % 23.66% 2.16 Chaloe Wie Group Ltd % 24.08% 1.55 Adres Wies Ltd. 'A' % 24.70% 2.56 Todhuter It'l % 25.74% 2.98 Brow-Forma 'B' % 29.43% 0.88 Coors (Adolph) 'B' % 29.52% 2.30 PepsiCo, Ic % 31.35% 3.14 Coca-Cola % 35.51% 2.33 Bosto Beer 'A' % 39.58% 0.62 Whitma Corp % 44.26% 2.19 Modavi (Robert) 'A' % 45.84% 1.18 Coca-Cola Eterprises % 51.34% 1.38 Hase Natural Corp % 62.45% 0.57 Average Aswath Damodara 67

68 Aalyzig PE/Growth Give that the PEG ratio is still determied by the expected growth rates, risk ad cash flow patters, it is ecessary that we cotrol for differeces i these variables. Regressig PEG agaist risk ad a measure of the growth dispersio, we get: PEG = (Expected Growth) (Std Deviatio i Prices) R Squared = 44.75% I other words, PEG ratios will be lower for high growth compaies PEG ratios will be lower for high risk compaies We also ra the regressio usig the deviatio of the actual growth rate from the idustry-average growth rate as the idepedet variable, with mixed results. Aswath Damodara 68

69 Estimatig the PEG Ratio for Hase Applyig this regressio to Hase, the predicted PEG ratio for the firm ca be estimated usig Hase s measures for the idepedet variables: Expected Growth Rate = 17.00% Stadard Deviatio i Stock Prices = 62.45% Pluggig i, Expected PEG Ratio for Hase = (17) (62.45) = 0.78 With its actual PEG ratio of 0.57, Hase looks udervalued, otwithstadig its high risk. Aswath Damodara 69

70 Extedig the Comparables This aalysis, which is restricted to firms i the software sector, ca be expaded to iclude all firms i the firm, as log as we cotrol for differeces i risk, growth ad payout. To look at the cross sectioal relatioship, we first plotted PEG ratios agaist expected growth rates. Aswath Damodara 70

71 PEG versus Growth PEG Ratio v ersus Expected Growth Rate US Stocks - September 2003 PEG=Curret P E/Expected Growth Rate Expected Growth i E PS: ext 5 y ears Aswath Damodara 71

72 Aalyzig the Relatioship The relatioship i ot liear. I fact, the smallest firms seem to have the highest PEG ratios ad PEG ratios become relatively stable at higher growth rates. To make the relatioship more liear, we coverted the expected growth rates i l(expected growth rate). The relatioship betwee PEG ratios ad l(expected growth rate) was the plotted. Aswath Damodara 72

73 PEG versus l(expected Growth) PEG versus l(growth) 50 US Stocks - September 2003 PEG=Curret PE/Exp Grow th Rate l(growth Rate) Aswath Damodara 73

74 PEG Ratio Regressio - US stocks i September 2003 Model Summary Model 1 Adjusted R Std. Er ror of R R Sq uare Square the Estimate.646 a a. Predictors: (Costat), LNGROWTH, V alue Lie B eta, Payout Ratio Model 1 (Costat) Payout Ratio Value Lie Beta LNGROWTH a. Depedet Var iable: PEGRATIO Ustadardized Coefficiets Co ef fici ets a,b Stadar dized Coefficiets 95% Cofidece Iterval for B B Std. Er ror Beta t Sig. Lower Boud Upper Boud E b. Weighted Least Squares Regre ssio - Weighted by Mar ket Cap Aswath Damodara 74

75 Applyig the PEG ratio regressio Cosider Dell agai. The stock has a expected growth rate of 10%, a beta of 1.20 ad pays out o divideds. What should its PEG ratio be? If the stock s actual PE ratio is 23, what does this aalysis tell you about the stock? Aswath Damodara 75

76 A Variat o PEG Ratio: The PEGY ratio The PEG ratio is biased agaist low growth firms because the relatioship betwee value ad growth is o-liear. Oe variat that has bee devised to cosolidate the growth rate ad the expected divided yield: PEGY = PE / (Expected Growth Rate + Divided Yield) As a example, Co Ed has a PE ratio of 16, a expected growth rate of 5% i earigs ad a divided yield of 4.5%. PEG = 16/ 5 = 3.2 PEGY = 16/(5+4.5) = 1.7 Aswath Damodara 76

77 Relative PE: Defiitio 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 ca be defied i terms of curret earigs, trailig earigs or forward earigs, cosistecy requires that it be estimated usig the same measure of earigs for both the firm ad 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 cosidered over valued if it is tradig at a relative PE of 0.7. Relative PE ratios are also used whe comparig compaies across markets with differet PE ratios (Japaese versus US stocks, for example) Aswath Damodara 77

78 Relative PE: Cross Sectioal Distributio Relative PE: US Stocks i September Number of firms 600 Frequecy >5 Relative PE Aswath Damodara 78

79 Relative PE: Distributioal Statistics The average relative PE is always oe. The media relative PE is much lower, sice PE ratios are skewed towards higher values. Thus, more compaies trade at PE ratios less tha the market PE ad have relative PE ratios less tha oe. Aswath Damodara 79

80 Relative PE: Determiats Relative PE j = To aalyze the determiats of the relative PE ratios, let us revisit the discouted cash flow model we developed for the PE ratio. Usig the 2-stage DDM model as our basis (replacig the payout ratio with the FCFE/Earigs Ratio, if ecessary), we get Ê Payout Ratio j *(1 + g j ) * 1 - (1+ g j ) ˆ Á Ë (1+ r j ) + Payout Ratio *(1 + g ) j, j *(1 + g j, ) r j - g j (r j - g j, )(1 + r j ) Ê Payout Ratio m * (1+ g m )* Á 1 - (1+ g ) m ˆ Ë (1+ r m ) + Payout Ratio * (1+ g m, m ) *(1 + g ) m, r m - g m (r m - g m, )(1+ r m ) where Payout j, g j, r j = Payout, growth ad risk of the firm Payout m, g m, r m = Payout, growth ad risk of the market Aswath Damodara 80

81 Relative PE: A Simple Example Cosider the followig example of a firm growig at twice the rate as the market, while havig the same growth ad risk characteristics of the market: Firm Market Expected growth rate 20% 10% Legth of Growth Period 5 years 5 years Payout Ratio: first 5 yrs 30% 30% Growth Rate after yr 5 6% 6% Payout Ratio after yr 5 50% 50% Beta Riskfree Rate = 6% Aswath Damodara 81

82 Estimatig Relative PE The relative PE ratio for this firm ca be estimated i two steps. First, we compute the PE ratio for the firm ad the market separately: Ê 0.3 * (1.20) * Á 1- (1.20) 5 ˆ Ë (1.115) 5 PE firm = ( ) * (1.20)5 * (1.06) ( ) (1.115) 5 = Ê 0.3 * (1.10) * Á 1- (1.10)5 ˆ Ë (1.115) 5 PE market = ( ) * (1.10) 5 *(1.06) ( ) (1.115) 5 = Relative PE Ratio = 15.79/10.45 = 1.51 Aswath Damodara 82

83 Relative PE ad Relative Growth Relative PE ad Relative Growth Rates: Market Growth Scearios Relative PE Market g=5% Market g=10% Market g=15% % 50% 100% 150% 200% 250% 300% Firm's Growth Rate/Market Growth Rate Aswath Damodara 83

84 Relative PE: Aother Example I this example, cosider a firm with twice the risk as the market, while havig the same growth ad payout characteristics as the firm: Firm Market Expected growth rate 10% 10% Legth 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 i first 5 years Beta after year Riskfree Rate = 6% Aswath Damodara 84

85 Estimatig Relative PE The relative PE ratio for this firm ca be estimated i two steps. First, we compute the PE ratio for the firm ad the market separately: Ê 0.3 * (1.10) * Á 1 - (1.10) 5 ˆ Ë (1.17) 5 PE firm = ( ) * (1.10)5 * (1.06) ( ) (1.17) 5 = 8.33 Ê 0.3 * (1.10) * Á 1- (1.10)5 ˆ Ë (1.115) 5 PE market = ( ) * (1.10) 5 *(1.06) ( ) (1.115) 5 = Relative PE Ratio = 8.33/10.45 = 0.80 Aswath Damodara 85

86 Relative PE ad Relative Risk Relative PE ad Relative Risk: Stable Beta Scearios Beta stays at curret level Beta drops to 1 i stable phase Aswath Damodara 86

87 Relative PE: Summary of Determiats The relative PE ratio of a firm is determied by two variables. I particular, it will icrease as the firm s growth rate relative to the market icreases. The rate of chage i the relative PE will itself be a fuctio of the market growth rate, with much greater chages whe the market growth rate is higher. I other words, a firm or sector with a growth rate twice that of the market will have a much higher relative PE whe the market growth rate is 10% tha whe it is 5%. decrease as the firm s risk relative to the market icreases. The extet of the decrease depeds upo how log the firm is expected to stay at this level of relative risk. If the differet is permaet, the effect is much greater. Relative PE ratios seem to be uaffected by the level of rates, which might give them a decided advatage over PE ratios. Aswath Damodara 87

88 Relative PE Ratios: The Auto Sector Relative PE Ratios: Auto Stocks Ford Chrysler GM Aswath Damodara 88

89 Usig Relative PE ratios O a relative PE basis, all of the automobile stocks look cheap because they are tradig at their lowest relative PE ratios i five years. Why might the relative PE ratio be lower today tha it was 5 years ago? Aswath Damodara 89

90 Relative PEs: Why do they chage? Historically, GM has traded at the highest relative PE ratio of the three auto compaies, ad Chrysler has traded at the lowest. I the last two or three years, this historical relatioship has bee upeded with Ford ad Chrysler ow tradig at the higher ratios tha GM. Aalyst projectios for earigs growth at the three compaies are about the same. How would you explai the shift? Aswath Damodara 90

91 Relative PE Ratios: US stocks Model 1 Model Summary R R Square a Square Adjusted R Std. Error of the Estimate.856 b a. For regre ssio through the origi (the o-itercept model), R Squar e measur es the proportio of the variability i the depedet variable about the origi explaied by regressio. T his CANNOT be compar ed to R Square f or models which iclude a iter cept. b. Predictors: R elative Payout, Relative Growth, Value Lie B eta Model 1 Model Summary R R Square a Square Adjusted R Std. Error of the Estimate.856 b a. For regre ssio through the origi (the o-itercept model), R Squar e measur es the proportio of the variability i the depedet variable about the origi explaied by regressio. T his CANNOT be compar ed to R Square f or models which iclude a iter cept. b. Predictors: R elative Payout, Relative Growth, Value Lie B eta Aswath Damodara 91

92 Value/Earigs ad Value/Cashflow Ratios While Price earigs ratios look at the market value of equity relative to earigs to equity ivestors, Value earigs ratios look at the market value of the firm relative to operatig earigs. Value to cash flow ratios modify the earigs umber to make it a cash flow umber. The form of value to cash flow ratios that has the closest parallels i DCF valuatio is the value to Free Cash Flow to the Firm, which is defied as: Value/FCFF = (Market Value of Equity + Market Value of Debt-Cash) Cosistecy Tests: EBIT (1-t) - (Cap Ex - Deprec) - Chg i WC If the umerator is et of cash (or if et debt is used, the the iterest icome from the cash should ot be i deomiator The iterest expeses added back to get to EBIT should correspod to the debt i the umerator. If oly log term debt is cosidered, oly log term iterest should be added back. Aswath Damodara 92

93 Value of Firm/FCFF: Determiats V 0 = Revertig back to a two-stage FCFF DCF model, we get: Ê (1 + g) ˆ FCFF (1 + g) Á 1-0 Ë (1+ WACC) FCFF + 0 (1+ g) (1+ g ) WACC - g (WACC - g )(1 + WACC) V 0 = Value of the firm (today) FCFF 0 = Free Cashflow to the firm i curret year g = Expected growth rate i FCFF i extraordiary growth period (first years) WACC = Weighted average cost of capital g = Expected growth rate i FCFF i stable growth period (after years) Aswath Damodara 93

94 Value Multiples Dividig both sides by the FCFF yields, V 0 FCFF 0 = Ê (1 + g) Á 1- Ë (1 + g) (1 + WACC) WACC - g ˆ + (1+ g) (1+ g ) (WACC - g )(1 + WACC) The value/fcff multiples is a fuctio of the cost of capital the expected growth Aswath Damodara 94

95 Alteratives to FCFF - EBIT ad EBITDA Most aalysts fid FCFF to complex or messy to use i multiples (partly because capital expeditures ad workig capital have to be estimated). They use modified versios of the multiple with the followig alterative deomiator: after-tax operatig icome or EBIT(1-t) pre-tax operatig icome or EBIT et operatig icome (NOI), a slightly modified versio of operatig icome, where ay o-operatig expeses ad icome is removed from the EBIT EBITDA, which is earigs before iterest, taxes, depreciatio ad amortizatio. Aswath Damodara 95

96 Value/FCFF Multiples ad the Alteratives o o o o Assume that you have computed the value of a firm, usig discouted cash flow models. Rak the followig multiples i the order of magitude from lowest to highest? Value/EBIT Value/EBIT(1-t) Value/FCFF Value/EBITDA What assumptio(s) would you eed to make for the Value/EBIT(1-t) ratio to be equal to the Value/FCFF multiple? Aswath Damodara 96

97 Illustratio: Usig Value/FCFF Approaches to value a firm: MCI Commuicatios MCI Commuicatios had earigs before iterest ad taxes of $3356 millio i 1994 (Its et icome after taxes was $855 millio). It had capital expeditures of $2500 millio i 1994 ad depreciatio of $1100 millio; Workig capital icreased by $250 millio. It expects free cashflows to the firm to grow 15% a year for the ext five years ad 5% a year after that. The cost of capital is 10.50% for the ext five years ad 10% after that. The compay faces a tax rate of 36%. V 0 FCFF 0 = Ê Á ˆ (1.15) 1- (1.15)5 Ë (1.105) (1.15) 5 (1.05) ( )(1.105) 5 = Aswath Damodara 97

98 Multiple Magic I this case of MCI there is a big differece betwee the FCFF ad short cut measures. For istace the followig table illustrates the appropriate multiple usig short cut measures, ad the amout you would overpay by if you used the FCFF multiple. Free Cash Flow to the Firm = EBIT (1-t) - Net Cap Ex - Chage i Workig Capital = 3356 (1-0.36) = $ 498 millio $ Value Correct Multiple FCFF $ EBIT (1-t) $2, EBIT $ 3, EBITDA $4, Aswath Damodara 98

99 Reasos for Icreased Use of Value/EBITDA 1. The multiple ca be computed eve for firms that are reportig et losses, sice earigs before iterest, taxes ad depreciatio are usually positive. 2. For firms i certai idustries, such as cellular, which require a substatial ivestmet i ifrastructure ad log gestatio periods, this multiple seems to be more appropriate tha the price/earigs ratio. 3. I leveraged buyouts, where the key factor is cash geerated by the firm prior to all discretioary expeditures, the EBITDA is the measure of cash flows from operatios that ca be used to support debt paymet at least i the short term. 4. By lookig at cashflows prior to capital expeditures, it may provide a better estimate of optimal value, especially if the capital expeditures are uwise or ear substadard returs. 5. By lookig at the value of the firm ad cashflows to the firm it allows for comparisos across firms with differet fiacial leverage. Aswath Damodara 99

100 Eterprise Value/EBITDA Multiple The Classic Defiitio Value EBITDA = Market Value of Equity + Market Value of Debt Earigs before Iterest, Taxes ad Depreciatio The No-Cash Versio Eterprise Value EBITDA = Market Value of Equity + Market Value of Debt - Cash Earigs before Iterest, Taxes ad Depreciatio Aswath Damodara 100

101 Value/EBITDA Distributio - US i September 2003 EV/EBITDA Multiples: US Stocks i September Number of firms EV/EBITDA < >50 Multiple of EBIT/EBITDA Aswath Damodara 101

102 Value/EBITDA Multiple: Europe ad Emergig Markets i September 2003 EV/EBITDA: Europe ad Emergig Markets Number of firms 300 Europe Emergig Markets < >50 EV/EBITDA Aswath Damodara 102

103 The Determiats of Value/EBITDA Multiples: Likage to DCF Valuatio Firm value ca be writte as: V 0 = FCFF 1 WACC - g The umerator ca be writte as follows: FCFF = EBIT (1-t) - (Cex - Depr) - D Workig Capital = (EBITDA - Depr) (1-t) - (Cex - Depr) - D Workig Capital = EBITDA (1-t) + Depr (t) - Cex - D Workig Capital Aswath Damodara 103

104 From Firm Value to EBITDA Multiples Now the Value of the firm ca be rewritte as, Value = EBITDA (1- t) + Depr (t) - Cex - D Workig Capital WACC - g Dividig both sides of the equatio by EBITDA, Value EBITDA = (1- t) WACC- g + Depr (t)/ebitda WACC -g - CEx/EBITDA WACC - g - D Workig Capital/EBITDA WACC - g Aswath Damodara 104

105 A Simple Example Cosider a firm with the followig characteristics: Tax Rate = 36% Capital Expeditures/EBITDA = 30% Depreciatio/EBITDA = 20% Cost of Capital = 10% The firm has o workig capital requiremets The firm is i stable growth ad is expected to grow 5% a year forever. Aswath Damodara 105

106 Calculatig Value/EBITDA Multiple Value EBITDA = (1-.36) I this case, the Value/EBITDA multiple for this firm ca be estimated as follows: + (0.2)(.36) = 8.24 Aswath Damodara 106

107 Value/EBITDA Multiples ad Taxes VEBITDA Multiples ad Tax Rates Value/EBITDA % 10% 20% 30% 40% 50% Tax Rate Aswath Damodara 107

108 Value/EBITDA ad Net Cap Ex Value/EBITDA ad Net Cap Ex Ratios Value/EBITDA % 5% 10% 15% 20% 25% 30% Net Cap Ex/EBITDA Aswath Damodara 108

109 Value/EBITDA Multiples ad Retur o Capital Value/EBITDA ad Retur o Capital Value/EBITDA 6 WACC=10% WACC=9% WACC=8% % 7% 8% 9% 10% 11% 12% 13% 14% 15% Retur o Capital Aswath Damodara 109

110 Value/EBITDA Multiple: Truckig Compaies Compay Name Value EBITDA Value/EBITDA KLLM Tras. Svcs. $ $ Ryder System $ 5, $ 1, Rollis Truck Leasig $ 1, $ Cao Express Ic. $ $ Hut (J.B.) $ $ Yellow Corp. $ $ Roadway Express $ $ Marte Trasport Ltd. $ $ Kea Trasport Co. $ $ M.S. Carriers $ $ Old Domiio Freight $ $ Trimac Ltd $ $ Matlack Systems $ $ XTRA Corp. $ 1, $ Coveat Trasport Ic $ $ Builders Trasport $ $ Werer Eterprises $ $ Ladstar Sys. $ $ AMERCO $ 1, $ USA Truck $ $ Froze Food Express $ $ Arold Ids. $ $ Greyhoud Lies Ic. $ $ USFreightways $ $ Golde Eagle Group Ic. $ $ Arkasas Best $ $ Airlease Ltd. $ $ Celado Group $ $ Amer. Freightways $ $ Trasfiacial Holdigs $ $ Vitra Corp. 'A' $ $ Iterpool Ic. $ 1, $ Itreet Ic. $ $ Swift Trasportatio $ $ Ladair Services $ $ CNF Trasportatio $ 2, $ Budget Group Ic $ 1, $ Caliber System $ 2, $ Kight Trasportatio Ic $ $ Heartlad Express $ $ Greyhoud CDA Tras Corp $ $ Mark VII $ $ Coach USA Ic $ $ US 1 Ids Ic. $ 5.60 $ (0.17) NA Average 5.61 Aswath Damodara 110

111 A Test o EBITDA Ryder System looks very cheap o a Value/EBITDA multiple basis, relative to the rest of the sector. What explaatio (other tha misvaluatio) might there be for this differece? Aswath Damodara 111

112 Aalyzig the Value/EBITDA Multiple While low value/ebitda multiples may be a symptom of udervaluatio, a few questios eed to be aswered: Is the operatig icome ext year expected to be sigificatly lower tha the EBITDA for the most recet period? (Price may have dropped) Does the firm have sigificat capital expeditures comig up? (I the truckig busiess, the life of the truckig fleet would be a good idicator) Does the firm have a much higher cost of capital tha other firms i the sector? Does the firm face a much higher tax rate tha other firms i the sector? Aswath Damodara 112

113 Value/EBITDA Multiples: Market The multiple of value to EBITDA varies widely across firms i the market, depedig upo: how capital itesive the firm is (high capital itesity firms will ted to have lower value/ebitda ratios), ad how much reivestmet is eeded to keep the busiess goig ad 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 i the sector (high growth sectors will ted to have higher Value/EBITDA multiples) Aswath Damodara 113

114 US Market: Cross Sectioal Regressio September 2003 Model 1 R R Square Model Summary Adjusted R Squar e Std. Er ror of the Estimate.649 a a. Pr edictors: (Costat), Reivestmet Rate, Expected Growth i Reveues: ext 5 year s, Eff Tax Rate Model 1 (Costat) Eff T ax Rate Expected G rowth i Reveues: ext 5 year s Reivestmet Rate a. Depedet Var iable: EV/EBITDA Co ef fici ets a,b Ustadardized Coefficiets Stadardized Coefficiets B Std. Er ror Be ta t Sig E b. Weighted Least Squares Regre ssio - Weighted by Market Cap Aswath Damodara 114

115 Europe: Cross Sectioal Regressio September 2003 Model 1 R R Square Model Summary Adjusted R Square Std. Error of the Estimate.458 a a. Pr edictors: (Costat), Market Debt to Capital, R eivestmet Rate, ROC, Tax Rate Model 1 (Costat) Reivestmet Ra te Tax Rate ROC Market Debt to Capital a. Depedet Var iable: EV/EBITDA Ustadard ized Coefficiets B Co ef fici ets a,b Std. Error Stadar dized Coefficiets Beta E E b. Weighted Least Squares Regre ssio - Weighted by Market Capitalizatio t Sig. Aswath Damodara 115

116 Price-Book Value Ratio: Defiitio 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 i the balace sheet. Price/Book Value = Market Value of Equity Cosistecy Tests: Book Value of Equity If the market value of equity refers to the market value of equity of commo stock outstadig, the book value of commo equity should be used i the deomiator. If there is more that oe class of commo stock outstadig, the market values of all classes (eve the o-traded classes) eeds to be factored i. Aswath Damodara 116

117 Price to Book Value: US stocks BV Multiples: US Stocks i September Number of firms PBV VBV < >10 BV Ratio Aswath Damodara 117

118 Price to Book: Europe ad Emergig Markets PBV Ratios: Europe ad Emergig Markets - Sept Number of firms Europe Emergig Markets < >5 P/BV Ratio Aswath Damodara 118

119 Price Book Value Ratio: Stable Growth Firm Goig back to a simple divided discout model, P 0 = DPS 1 r - g Defiig the retur o equity (ROE) = EPS 0 / Book Value of Equity, the value of equity ca be writte as: P 0 = BV 0 * ROE * Payout Ratio * (1 + g ) r-g P 0 = PBV = ROE * Payout Ratio * (1 + g ) BV 0 r-g If the retur o equity is based upo expected earigs i the ext time period, this ca be simplified to, P 0 BV 0 = PBV = ROE * Payout Ratio r-g Aswath Damodara 119

120 Price Book Value Ratio: Stable Growth Firm Aother Presetatio This formulatio ca be simplified eve further by relatig growth to the retur o equity: g = (1 - Payout ratio) * ROE Substitutig back ito the P/BV equatio, P 0 BV 0 = PBV = ROE - g r-g The price-book value ratio of a stable firm is determied by the differetial betwee the retur o equity ad the required rate of retur o its projects. Aswath Damodara 120

121 Price Book Value Ratio for a Stable Growth Firm: Example Jeapharm was the most respected pharmaceutical maufacturer i East Germay. Jeapharm was expected to have reveues of 230 millio DM ad earigs before iterest ad taxes of 30 millio DM i The firm had a book value of assets of 110 millio DM, ad a book value of equity of 58 millio DM. The iterest expeses i 1991 is expected to be 15 millio DM. The corporate tax rate is 40%. The firm was expected to maitai sales i its iche product, a cotraceptive pill, ad grow at 5% a year i the log term, primarily by expadig ito the geeric drug market. The average beta of pharmaceutical firms traded o the Frakfurt Stock exchage was The te-year bod rate i Germay at the time of this valuatio was 7%; the risk premium for stocks over bods is assumed to be 5.5%. Aswath Damodara 121

122 Estimatig a Price/Book Ratio for Jeapharm Expected Net Icome = (EBIT - Iterest Expese)*(1-t)* 1+g) = (30-15) *(1-0.4)* (1.05) = 9.45 mil DM Retur o Equity = Expected Net Icome / Book Value of Equity = 9.45 / 58 = 16.29% Cost o Equity = 7% (5.5%) = % Price/Book Value Ratio = (ROE - g) / (r - g) = ( ) / ( ) = 1.46 Estimated MV of equity = BV of Equity * Price/BV ratio = 58 * 1.46 = $ mil DM Aswath Damodara 122

123 Price Book Value Ratio for High Growth Firm The Price-book ratio for a high-growth firm ca be estimated begiig with a 2-stage discouted cash flow model: Ê (1+ g) EPS 0 * Payout Ratio * (1 + g) * Á ˆ 1 - (1+ r) Ë P 0 = r - g + EPS 0 * Payout Ratio * (1+ g) *(1+ g ) (r - g )(1+ r) Dividig both sides of the equatio by the book value of equity: È Ê ROE* Payout Ratio *(1+ g)* Á 1 - P 0 Í Ë = BV Í 0 r - g Í Î (1+ g) ˆ (1+ r) + ROE * Payout Ratio *(1+ g) *(1+ g ) (r - g )(1+ r) where ROE = Retur o Equity i high-growth period ROE = Retur o Equity i stable growth period Aswath Damodara 123

124 PBV Ratio for High Growth Firm: Example Assume that you have bee asked to estimate the PBV ratio for a firm which has the followig characteristics: High Growth Phase Stable Growth Phase Legth of Period 5 years Forever after year 5 Retur o Equity 25% 15% Payout Ratio 20% 60% Growth Rate.80*.25=.20.4*.15=.06 Beta Cost of Equity % 11.50% The riskfree rate is 6% ad the risk premium used is 5.5%. Aswath Damodara 124

125 Estimatig Price/Book Value Ratio The price/book value ratio for this firm is: È Ê 0.25 * 0.2 * (1.20) * Á 1 - (1.20) 5 ˆ Í Ë ( ) 5 PBV = Í ( ) Í Î * 0.6 * (1.20)5 * (1.06) ( ) ( ) 5 = 2.66 Aswath Damodara 125

126 PBV ad ROE: The Key PBV ad ROE: Risk Scearios Price/Book Value Ratios Beta=0.5 Beta=1 Beta= % 15% 20% 25% 30% ROE Aswath Damodara 126

127 PBV/ROE: Europea Baks Bak Symbol PBV ROE Baca di Roma SpA BAHQE % Commerzbak AG COHSO % Bayerische Hypo ud Vereisbak AG BAXWW % Itesa Bci SpA BAEWF % Natexis Baques Populaires NABQE % Almaij NV Algemee Mij voor Nijver ALPK % Credit Idustriel et Commercial CIECM % Credit Lyoais SA CREV % BNL Baca Nazioale del Lavoro SpA BAEXC % Baca Mote dei Paschi di Siea SpA MOGG % Deutsche Bak AG DEMX % Skadiaviska Eskilda Bake SKHS % Nordea Bak AB NORDEA % DNB Holdig ASA DNHLD % ForeigsSparbake AB FOLG % Daske Bak AS DANKAS % Credit Suisse Group CRGAL % KBC Bakverzekerigsholdig KBCBA % Societe Geerale SODI % Satader Cetral Hispao SA BAZAB % Natioal Bak of Greece SA NAGT % Sa Paolo IMI SpA SAOEL % BNP Paribas BNPRB % Sveska Hadelsbake AB SVKE % UBS AG UBQH % Baco Bilbao Vizcaya Argetaria SA BBFUG % ABN Amro Holdig NV ABTS % UiCredito Italiao SpA UNCZA % Rolo Baca 1473 SpA ROGMBA % Dexia DECCT % Average % Aswath Damodara 127

128 PBV versus ROE regressio Regressig PBV ratios agaist ROE for baks yields the followig regressio: PBV = (ROE) R 2 = 46% For every 1% icrease i ROE, the PBV ratio should icrease by Aswath Damodara 128

129 Uder ad Over Valued Baks? Bak Actual Predicted Uder or Over Baca di Roma SpA % Commerzbak AG % Bayerische Hypo ud Vereisbak AG % Itesa Bci SpA % Natexis Baques Populaires % Almaij NV Algemee Mij voor Nijver % Credit Idustriel et Commercial % Credit Lyoais SA % BNL Baca Nazioale del Lavoro SpA % Baca Mote dei Paschi di Siea SpA % Deutsche Bak AG % Skadiaviska Eskilda Bake % Nordea Bak AB % DNB Holdig ASA % ForeigsSparbake AB % Daske Bak AS % Credit Suisse Group % KBC Bakverzekerigsholdig % Societe Geerale % Satader Cetral Hispao SA % Natioal Bak of Greece SA % Sa Paolo IMI SpA % BNP Paribas % Sveska Hadelsbake AB % UBS AG % Baco Bilbao Vizcaya Argetaria SA % ABN Amro Holdig NV % UiCredito Italiao SpA % Rolo Baca 1473 SpA % Dexia % Aswath Damodara 129

130 Lookig for udervalued securities - PBV Ratios ad ROE Give the relatioship betwee price-book value ratios ad returs o equity, it is ot surprisig to see firms which have high returs o equity sellig for well above book value ad firms which have low returs o equity sellig at or below book value. The firms which should draw attetio from ivestors are those which provide mismatches of price-book value ratios ad returs o equity - low P/BV ratios ad high ROE or high P/BV ratios ad low ROE. Aswath Damodara 130

131 The Valuatio Matrix MV/BV Overvalued Low ROE High MV/BV High ROE High MV/BV ROE-r Low ROE Low MV/BV Udervalued High ROE Low MV/BV Aswath Damodara 131

132 Price to Book vs ROE: Largest Market Cap Firms i the Uited States: September SAP DE LL G BUD 10 BSX EBAY D MDT AZN WMT QCOM BMY ORCL MMM PG JNJ MRK PFE UL GS K PBV Ratio AMAT SC 20 KMB ABN MO FNM ROE Aswath Damodara 132

133 PBV Matrix: Telecom Compaies 12 TelAzteca 10 8 Carlto TelNZ Vimple 6 Teleglobe FraceTel Cable&W 4 2 DeutscheTel BritTel TelItalia BCE Nippo DamarkChiaTel Espaa TelArgFrace PhilTel Telmex TelArgetia Portugal Royal Helleic TelIdo TelPeru Televisas Idast HogKog AsiaSat APT CallNet Aoima GrupoCetro ROE Aswath Damodara 133

134 PBV, ROE ad Risk: Large Cap US firms BV R atio BUD G PFE ORCL PG MMM UL MRK FNMKMB MDT D WMT QCOM EBAY TSM AMAT ROE FRE SC AOL VIA/B Regressio Beta Aswath Damodara 134

135 IBM: The Rise ad Fall ad Rise Agai % % % % Price to Book % 0.00% Retur o Equity % % % Year % PBV ROE Aswath Damodara 135

136 PBV Ratio Regressio: US September 2003 Model 1 Model Summary R R Sq uare a Square Adjusted R Std. Er ror of the Estimate.909 b a. For regre ssio through the origi (the o-itercept model), R Squar e me asur es the proportio of the variability i the depe det variable about the origi explaied by regr essio. T his CANNOT be compared to R Square for models which iclude a itercep t. b. Predictor s: ROE, Expected G rowth i EPS: ext 5 years, Payout Ratio, Value Lie B eta Model 1 Expected Growth i EPS: ext 5 year s Payout Ratio Value Lie Beta ROE a. Depedet Var iable: PBV Ratio b. Liear Regr essio through the Or igi Coefficiets a,b,c Ustadardized Coefficiets B Std. Error Stadardized Coefficiets Be ta E c. Weighted Least Squares R egre ssio - Weig hted by Mar ket Cap t Sig. Aswath Damodara 136

137 PBV Ratio Regressio- Europe September 2003 Model Summary Model 1 R R Square a Square Adjusted R Std. Error of the Estimate.827 b a. For regre ssio through the origi (the o-itercept model), R Square mea sur es the proportio of the variability i the depedet var iable about the origi explaied by r egre ssio. This CANNOT be compare d to R Squar e for models which iclude a itercept. b. Predictors: R OE, Payout Ratio, Beta Model 1 Payout Ratio Beta ROE a. Depedet Var iable: PBV Coefficiets a,b Ustadardized Coefficiets b. Liear Regr essio through the Origi Stadardized Coefficiets B Std. Er ror Beta t Sig E E Aswath Damodara 137

138 PBV Regressio: Emergig Markets July 2003 Model 1 Model Summary Adjusted R R R Square Square Std. Error of the Estimate.561 a a. Pr edictors: (Costat), ROE, Payout R atio, BETA Model 1 (Costat) Payout Ratio BETA ROE a. Depedet Var iable: PBV Ustadardized Coefficiets Coefficiets a,b Stadardized Coefficiets B Std. Er ror Beta t Sig E E b. Weighted Least Squares Regre ssio - Weighted by Market Cap Corr ected Aswath Damodara 138

139 Value/Book Value Ratio: Defiitio While the price to book ratio is a equity multiple, both the market value ad the book value ca be stated i terms of the firm. Value/Book Value = Market Value of Equity + Market Value of Debt Book Value of Equity + Book Value of Debt Aswath Damodara 139

140 Determiats of Value/Book Ratios To see the determiats of the value/book ratio, cosider the simple free cash flow to the firm model: V 0 = FCFF 1 WACC - g Dividig both sides by the book value, we get: V 0 BV = FCFF /BV 1 WACC - g If we replace, FCFF = EBIT(1-t) - (g/roc) EBIT(1-t),we get V 0 BV = ROC - g WACC - g Aswath Damodara 140

141 Value/Book Ratio: A Example Cosider a stable growth firm with the followig characteristics: Retur o Capital = 12% Cost of Capital = 10% Expected Growth = 5% The value/bv ratio for this firm ca be estimated as follows: Value/BV = ( )/( ) = 1.40 The effects of ROC o growth will icrease if the firm has a high growth phase, but the basic determiats will remai uchaged. Aswath Damodara 141

142 Value/Book ad the Retur Spread Value/BV Ratios ad Retur Spreads Value/BV Ratio WACC=8% WACC=10% WACC=12% % -1% 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% ROC - WACC Aswath Damodara 142

143 Value/Book Capital Regressio - US Model Summary Model 1 Adjusted R Std. Er ror of the R R Square Square Estimate.780 a a. Pr edictors: (Costat), Market Debt to Capital, Expected Growth i Reveues: ext 5 years, ROC Model 1 (Costat) ROC Expected Growth i Reveues: ext 5 years Market Debt to Capital a. Depedet Var iable: Value/BV of Capital Co efficiets a,b Ustadardized Coefficiets b. Weighted Least Squares Regre ssio - Weighted by Mar ket Cap Stadar dized Coefficiets B Std. Er ror Beta t Sig E E Aswath Damodara 143

144 Price Sales Ratio: Defiitio The price/sales ratio is the ratio of the market value of equity to the sales. Price/ Sales= Market Value of Equity Cosistecy Tests Total Reveues The price/sales ratio is iterally icosistet, sice the market value of equity is divided by the total reveues of the firm. Aswath Damodara 144

145 Price/Sales Ratio: US stocks Reveue Multiples: US Stocks i September Number of firms PS EV/Sales < >5 Reveue Multiple Aswath Damodara 145

146 Price to Sales: Europe ad Emergig Markets Price to Sales: Europe ad Emergig Markets i Sept Number of firms Europe Emergig Markets < >5 PS ratio Aswath Damodara 146

147 Price/Sales Ratio: Determiats The price/sales ratio of a stable growth firm ca be estimated begiig with a 2-stage equity valuatio model: P 0 = DPS 1 r - g Dividig both sides by the sales per share: P 0 Sales 0 = PS = Net Profit Margi* Payout Ratio *(1+ g ) r-g Aswath Damodara 147

148 Price/Sales Ratio for High Growth Firm P 0 = Whe the growth rate is assumed to be high for a future period, the divided discout model ca be writte as follows: Ê EPS 0 * Payout Ratio * (1 + g) * Á 1 - Ë r - g (1+ g) (1+ r) ˆ + EPS 0 * Payout Ratio * (1+ g) *(1+ g ) (r - g )(1+ r) Dividig both sides by the sales per share: È Ê Net Margi * Payout Ratio * (1+ g)* Á 1 - P 0 Í Ë = Sales Í 0 r - g Í Î (1+ g) (1+ r) ˆ + Net Margi * Payout Ratio * (1+ g) *(1 + g ) (r - g )(1 + r) where Net Margi = Net Margi i stable growth phase Aswath Damodara 148

149 Price Sales Ratios ad Profit Margis The key determiat of price-sales ratios is the profit margi. A declie i profit margis has a two-fold effect. First, the reductio i profit margis reduces the price-sales ratio directly. Secod, the lower profit margi ca lead to lower growth ad hece lower price-sales ratios. Expected growth rate = Retetio ratio * Retur o Equity = Retetio Ratio *(Net Profit / Sales) * ( Sales / BV of Equity) = Retetio Ratio * Profit Margi * Sales/BV of Equity Aswath Damodara 149

150 Price/Sales Ratio: A Example High Growth Phase Stable Growth Legth of Period 5 years Forever after year 5 Net Margi 10% 6% Sales/BV of Equity Beta Payout Ratio 20% 60% Expected Growth (.1)(2.5)(.8)=20% (.06)(2.5)(.4)=.06 Riskless Rate =6% È Ê 0.10 * 0.2 * (1.20) * Á 1 - (1.20)5 ˆ Í Ë ( ) 5 PS = Í ( ) Í Î * 0.60 * (1.20) 5 * (1.06) ( ) ( ) 5 = 1.06 Aswath Damodara 150

151 Effect of Margi Chages Price/Sales Ratios ad Net Margis PS Ratio % 4% 6% 8% 10% 12% 14% 16% Net Margi Aswath Damodara 151

152 PS/Margis: Europea Retailers - September FOLLI 4 HDF ITX ETI HMB 3 CLASB VARDA BUL ULG 2 US E AB M PUB EVER MAB Price to Sales 1 WEVE DC PHO 0 Rsq = Net Margi Aswath Damodara 152

153 Regressio Results: PS Ratios ad Margis Regressig PS ratios agaist et margis, PS = (Net Margi) R 2 = 43.5% Thus, a 1% icrease i the margi results i a icrease of i the price sales ratios. The regressio also allows us to get predicted PS ratios for these firms Aswath Damodara 153

154 Curret versus Predicted Margis Oe of the limitatios of the aalysis we did i these last few pages is the focus o curret margis. Stocks are priced based upo expected margis rather tha curret margis. For most firms, curret margis ad predicted margis are highly correlated, makig the aalysis still relevat. For firms where curret margis have little or o correlatio with expected margis, regressios of price to sales ratios agaist curret margis (or price to book agaist curret retur o equity) will ot provide much explaatory power. I these cases, it makes more sese to ru the regressio usig either predicted margis or some proxy for predicted margis. Aswath Damodara 154

155 Curret versus Predicted Margis Oe of the limitatios of the aalysis we did i these last few pages is the focus o curret margis. Stocks are priced based upo expected margis rather tha curret margis. For most firms, curret margis ad predicted margis are highly correlated, makig the aalysis still relevat. For firms where curret margis have little or o correlatio with expected margis, regressios of price to sales ratios agaist curret margis (or price to book agaist curret retur o equity) will ot provide much explaatory power. I these cases, it makes more sese to ru the regressio usig either predicted margis or some proxy for predicted margis. Aswath Damodara 155

156 A Case Study: The Iteret Stocks 30 PKSI 20 INTM SCNT LCOS MMXI SPYG A d j P S 10-0 INTW RAMP MQST CNET CSGP NETO APNT SONE CLKS PCLN SPLN EDGR PSIX BIDS ATHY AMZN ALOY ACOM BIZZ EGRP IIXL ITRA ONEM FATB ABTL INFO ANET RMII TMNT GEEK TURF PPOD GSVI BUYX ELTX ROWE CBIS FFIV ATHM DCLK NTPA AdjMargi Aswath Damodara 156

157 PS Ratios ad Margis are ot highly correlated Regressig PS ratios agaist curret margis yields the followig PS = (Net Margi) R 2 = 0.04 (0.49) This is ot surprisig. These firms are priced based upo expected margis, rather tha curret margis. Aswath Damodara 157

158 Solutio 1: Use proxies for survival ad growth: Amazo i early 2000 Hypothesizig that firms with higher reveue growth ad higher cash balaces should have a greater chace of survivig ad becomig profitable, we ra the followig regressio: (The level of reveues was used to cotrol for size) PS = l(rev) (Rev Growth) (Cash/Rev) (0.66) (2.63) (3.49) R squared = 31.8% Predicted PS = (7.1039) (1.9946) (.3069) = Actual PS = Stock is udervalued, relative to other iteret stocks. Aswath Damodara 158

159 Solutio 2: Use forward multiples You ca always estimate price (or value) as a multiple of reveues, earigs or book value i a future year. These multiples are called forward multiples. For youg ad evolvig firms, the values of fudametals i future years may provide a much better picture of the true value potetial of the firm. There are two ways i which you ca use forward multiples: Look at value today as a multiple of reveues or earigs i the future (say 5 years from ow) for all firms i the comparable firm list. Use the average of this multiple i cojuctio with your firm s earigs or reveues to estimate the value of your firm today. Estimate value as a multiple of curret reveues or earigs for more mature firms i the group ad apply this multiple to the forward earigs or reveues to the forward earigs for your firm. This will yield the expected value for your firm i the forward year ad will have to be discouted back to the preset to get curret value. Aswath Damodara 159

160 A Example of Forward Multiples: Global Crossig Global Crossig lost $1.9 billio i 2001 ad is expected to cotiue to lose moey for the ext 3 years. I a discouted cashflow valuatio (see otes o DCF valuatio) of Global Crossig, we estimated a expected EBITDA for Global Crossig i five years of $ 1,371 millio. The average eterprise value/ EBITDA multiple for healthy telecomm firms is 7.2 curretly. Applyig this multiple to Global Crossig s EBITDA i year 5, yields a value i year 5 of Eterprise Value i year 5 = 1371 * 7.2 = $9,871 millio Eterprise Value today = $ 9,871 millio/ = $5,172 millio (The cost of capital for Global Crossig is 13.80%) The probability that Global Crossig will ot make it as a goig cocer is 77% ad the distress sale value is oly a $ 1 billio (1/2 of book value of assets). Adjusted Eterprise value = 5172 * (.77) = 1,960 millio Aswath Damodara 160

161 PS Regressio: Uited States - September 2003 Model 1 Net Margi Value Lie Be ta Payout Ratio Model 1 Expected Growth i EPS: ext 5 year s a. Depedet Variable: PS b. Liear Regr essio through the Origi Model Summary R R Square a Square Adjusted R Std. Er ror of the Estimate.854 b a. For regre ssio through the origi (the o-itercept mode l), R Square mea sur es the proportio of the variability i the depedet variable about the origi explaied by r egre ssio. This CANNOT be compare d to R Squar e for models which iclude a itercept. b. Predictors: Expected Gr owth i EPS: ext 5 years, Payout Ratio, Net Margi, Value Lie Beta Co ef fici ets a,b,c Ustadardized Coefficiets c. Weighted Least Squares Regre ssio - Weighted by Market Cap B Stadardized Coefficiets Std. Error Be ta t Sig E Aswath Damodara 161

162 PS Regressio: Europe i September 2003 Model Summary Model 1 R R Square a Squar e Adjusted R Std. Error of the Estimate.826 b a. For regre ssio through the origi (the o-itercept mode l), R Squar e measur es the pr oportio of the variability i the depedet variable about the origi explaied by regressio. This CANNOT be compa red to R Square for mode ls which iclude a itercept. b. Predictors: Net Ma rgi, Payout Ratio, Bet a Model 1 Payout Ratio Beta Net Margi a. Depedet Var iable: PS Ustadardized Coefficiets b. Liear Regr essio through the Origi Co effici ets a,b,c Stadar dized Coefficiets B Std. Er ror Beta t Sig. 2.E c. Weighted Least Squares Regre ssio - Weighted by Market Capitalizatio Aswath Damodara 162

163 PS Regressio i Emergig Markets - July 2003 Model 1 Model Summary Adjusted R R R Square Square Std. Error of the Estimate.507 a a. Pr edictors: (Costat), Net Margi, P ayout Ratio, BETA Model 1 (Costat) Payout Ratio BETA Net Margi a. Depedet Var iable: PS Co effici ets a,b Ustadardized Coefficiets Stadar dized Coefficiets B Std. Er ror Beta t Sig E E b. Weighted Least Squares Regre ssio - Weighted by Mar ket Cap Corrected Aswath Damodara 163

164 Value/Sales Ratio: Defiitio 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 Reveues Aswath Damodara 164

165 Value/Sales Ratios: Aalysis of Determiats If pre-tax operatig margis are used, the appropriate value estimate is that of the firm. I particular, if oe makes the assumptio that Free Cash Flow to the Firm = EBIT (1 - tax rate) (1 - Reivestmet Rate) The the Value of the Firm ca be writte as a fuctio of the after-tax operatig margi= (EBIT (1-t)/Sales È Ê (1 + g) ˆ Í (1 - RIR growth )(1 + g)* Á 1- Value (1+ WACC) Ë = After - tax Oper. Margi * Í Sales 0 Í WACC - g Í Î + (1- RIR stable )(1 + g) *(1+ g ) (WACC - g )(1+ WACC) g = Growth rate i after-tax operatig icome for the first years g = Growth rate i after-tax operatig icome after years forever (Stable growth rate) RIR Growth, Stable = Reivestmet rate i high growth ad stable periods WACC = Weighted average cost of capital Aswath Damodara 165

166 Value/Sales Ratio: A Example Cosider, for example, the Value/Sales ratio of Coca Cola. The compay had the followig characteristics: After-tax Operatig Margi =18.56% Sales/BV of Capital = 1.67 Retur o Capital = 1.67* 18.56% = 31.02% Reivestmet Rate= 65.00% i high growth; 20% i stable growth; Expected Growth = 31.02% * 0.65 =20.16% (Stable Growth Rate=6%) Legth 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% È Ê (1-.65)(1.2016)* 1- (1.2016)10 ˆ Í Á Value of Firm 0 Ë (1.1213) 10 =.1856* Í Sales 0 Í Í Î + (1-.20)(1.2016)10 * (1.06) ( )(1.1213) 10 = 6.10 Aswath Damodara 166

167 Value Sales Ratios ad Operatig Margis Coca Cola: The Operatig Margi Effect Value/Sales Ratio $ Value Value/Sales $ Value % 8% 10% 12% 14% 16% 18% 20% Operatig Margi 0 Aswath Damodara 167

168 U.S. Specialty Retailers: V/S vs Operatig Margi 2.0 ISEE CDWC DABR BID CHCS LUX VVTV MBAY TOO BFCI 1.5 TWTR CPWM HOTT SCC TLB V / S a l e s PCCC BBY NSIT SATH ORLY ZLC LTD AZO IPAR ANN PSUN CWTRMIKE ZQK RAYS PIR GLBE LE LIN MENS MDLK SCHS MNRO GBIZ DAP CAO CC ITN PGDA ROST URBN MTMC PBY HMY Z ANIC VOXX CHRS PSS BKE CLWY CELL JILL FNLY GADZ SAH RUSH DBRN WLSN FLWS ROSI LVC SPGLA TWMC FINL PSRC ZANY MHCO GDYS RET.TO MLG MSEL WSM JWL PLCE AEOS IBI CLE RUS FOSL HLYW BEBE MDA Operatig Margi Aswath Damodara 168

169 Brad Name Premiums i Valuatio o o You have bee hired to value Coca Cola for a aalyst reports ad you have valued the firm at 6.10 times reveues, usig the model described i the last few pages. Aother aalyst is arguig that there should be a premium added o to reflect the value of the brad ame. Do you agree? Yes No Explai. Aswath Damodara 169

170 The value of a brad ame Oe of the critiques of traditioal valuatio is that is fails to cosider the value of brad ames ad other itagibles. The approaches used by aalysts to value brad ames are ofte adhoc ad may sigificatly overstate or uderstate their value. Oe of the beefits of havig a well-kow ad respected brad ame is that firms ca charge higher prices for the same products, leadig to higher profit margis ad hece to higher price-sales ratios ad firm value. The larger the price premium that a firm ca charge, the greater is the value of the brad ame. I geeral, the value of a brad ame ca be writte as: Value of brad ame ={(V/S) b -(V/S) g }* Sales (V/S) b = Value of Firm/Sales ratio with the beefit of the brad ame (V/S)g = Value of Firm/Sales ratio of the firm with the geeric product Aswath Damodara 170

171 Illustratio: Valuig a brad ame: Coca Cola Coca Cola Geeric Cola Compay AT Operatig Margi 18.56% 7.50% Sales/BV of Capital ROC 31.02% 12.53% Reivestmet Rate 65.00% (19.35%) 65.00% (47.90%) Expected Growth 20.16% 8.15% Legth 10 years 10 yea Cost of Equity 12.33% 12.33% E/(D+E) 97.65% 97.65% AT Cost of Debt 4.16% 4.16% D/(D+E) 2.35% 2.35% Cost of Capital 12.13% 12.13% Value/Sales Ratio Aswath Damodara 171

172 Value of Coca Cola s Brad Name Value of Coke s Brad Name= ( ) ($18,868 millio) = $102 billio Value of Coke as a compay = 6.10 ($18,546 millio) = $ 115 Billio Approximately 88.69% of the value of the compay ca be traced to brad ame value Aswath Damodara 172

173 Value/Sales Ratio Regressio: US i September 2003 Model 1 Model 1 Expected Growth i Reveues: ext 5 years Market Debt to Capital After-tax Oper ati g Margi Reivestmet Ra te a. Depedet Var iable: EV/Sales b. Liear Regr essio through the Or igi Model Summary R R Sq uare a Square Adjusted R Std. Error of the Estimate.871 b a. For regre ssio through the origi (the o-itercept model), R Square mea sures the proport io of the variability i the depedet variable about the origi explaied by regre ssio. This CANNOT be compared to R Squar e for models which iclude a itercept. b. Predictor s: After-tax Coefficiets Operatig Mar gi, Reivestmet Rate, Expected Growth i Reveues: ext 5 year s, Stadard Deviatio Ustadardized Stadar dized Coefficiets Coefficiets B Std. Er ror c. Weighted Least Square s R egre ssio - Weig hted by Mar ket Cap Beta E E t Sig. Aswath Damodara 173

174 Choosig Betwee the Multiples As preseted i this sectio, there are dozes of multiples that ca be potetially used to value a idividual firm. I additio, relative valuatio ca be relative to a sector (or comparable firms) or to the etire market (usig the regressios, for istace) Sice there ca be oly oe fial estimate of value, there are three choices at this stage: Use a simple average of the valuatios obtaied usig a umber of differet multiples Use a weighted average of the valuatios obtaied usig a mber of differet multiples Choose oe of the multiples ad base your valuatio o that multiple Aswath Damodara 174

175 Averagig Across Multiples This procedure ivolves valuig a firm usig five or six or more multiples ad the takig a average of the valuatios across these multiples. This is completely iappropriate sice it averages good estimates with poor oes equally. If some of the multiples are sector based ad some are market based, this will also average across two differet ways of thikig about relative valuatio. Aswath Damodara 175

176 Weighted Averagig Across Multiples I this approach, the estimates obtaied from usig differet multiples are averaged, with weights o each based upo the precisio of each estimate. The more precise estimates are weighted more ad the less precise oes weighted less. The precisio of each estimate ca be estimated fairly simply for those estimated based upo regressios as follows: Precisio of Estimate = 1 / Stadard Error of Estimate where the stadard error of the predicted value is used i the deomiator. This approach is more difficult to use whe some of the estimates are subjective ad some are based upo more quatitative techiques. Aswath Damodara 176

177 Pickig oe Multiple This is usually the best way to approach this issue. While a rage of values ca be obtaied from a umber of multiples, the best estimate value is obtaied usig oe multiple. The multiple that is used ca be chose i oe of two ways: Use the multiple that best fits your objective. Thus, if you wat the compay to be udervalued, you pick the multiple that yields the highest value. Use the multiple that has the highest R-squared i the sector whe regressed agaist fudametals. Thus, if you have tried PE, PBV, PS, etc. ad ru regressios of these multiples agaist fudametals, use the multiple that works best at explaiig differeces across firms i that sector. Use the multiple that seems to make the most sese for that sector, give how value is measured ad created. Aswath Damodara 177

178 Self Servig Multiple Choice Whe a firm is valued usig several multiples, some will yield really high values ad some really low oes. If there is a sigificat bias i the valuatio towards high or low values, it is temptig to pick the multiple that best reflects this bias. Oce the multiple that works best is picked, the other multiples ca be abadoed ad ever brought up. This approach, while yieldig very biased ad ofte absurd valuatios, may serve other purposes very well. As a user of valuatios, it is always importat to look at the biases of the etity doig the valuatio, ad askig some questios: Why was this multiple chose? What would the value be if a differet multiple were used? (You pick the specific multiple that you wat to see tried.) Aswath Damodara 178

179 The Statistical Approach Oe of the advatages of ruig regressios of multiples agaist fudametals across firms i a sector is that you get R-squared values o the regressio (that provide iformatio o how well fudametals explai differeces across multiples i that sector). As a rule, it is dagerous to use multiples where valuatio fudametals (cash flows, risk ad growth) do ot explai a sigificat portio of the differeces across firms i the sector. As a caveat, however, it is ot ecessarily true that the multiple that has the highest R-squared provides the best estimate of value for firms i a sector. Aswath Damodara 179

180 A More Ituitive Approach As a geeral rule of thumb, the followig table provides a way of pickig a multiple for a sector Sector Multiple Used Ratioale Cyclical Maufacturig PE, Relative PE Ofte with ormalized earigs High Tech, High Growth PEG Big differeces i growth across firms High Growth/No Earigs PS, VS Assume future margis will be good Heavy Ifrastructure VEBITDA Firms i sector have losses i early years ad reported earigs ca vary depedig o depreciatio method REITa P/CF Geerally o cap ex ivestmets from equity earigs Fiacial Services PBV Book value ofte marked to market Retailig PS If leverage is similar across firms VS If leverage is differet Aswath Damodara 180

181 Sector or Market Multiples The covetioal approach to usig multiples is to look at the sector or comparable firms. Whether sector or market based multiples make the most sese depeds upo how you thik the market makes mistakes i valuatio If you thik that markets make mistakes o idividual firm valuatios but that valuatios ted to be right, o average, at the sector level, you will use sector-based valuatio oly, If you thik that markets make mistakes o etire sectors, but is geerally right o the overall market level, you will use oly market-based valuatio It is usually a good idea to approach the valuatio at two levels: At the sector level, use multiples to see if the firm is uder or over valued at the sector level At the market level, check to see if the uder or over valuatio persists oce you correct for sector uder or over valuatio. Aswath Damodara 181

182 A Test o o You have valued Earthlik Networks, a iteret service provider, relative to other iteret compaies usig Price/Sales ratios ad fid it to be uder valued almost 50%.Whe you value it relative to the market, usig the market regressio, you fid it to be overvalued by almost 50%. How would you recocile the two fidigs? Oe of the two valuatios must be wrog. A stock caot be uder ad over valued at the same time. It is possible that both valuatios are right. What has to be true about valuatios i the sector for the secod statemet to be true? Aswath Damodara 182

183 Reviewig: The Four Steps to Uderstadig Multiples Defie the multiple Check for cosistecy Make sure that they are estimated uiformally Describe the multiple Multiples have skewed distributios: The averages are seldom good idicators of typical multiples Check for bias, if the multiple caot be estimated Aalyze the multiple Idetify the compaio variable that drives the multiple Examie the ature of the relatioship Apply the multiple Aswath Damodara 183

184 Private Compay Valuatio Aswath Damodara Aswath Damodara 184

185 Process of Valuig Private Compaies Choosig the right model Valuig the Firm versus Valuig Equity Steady State, Two-Stage or Three-Stage Estimatig a Discout Rate Cost of Equity Estimatig Betas Cost of Debt Estimatig Default Risk Estimatig a after-tax cost of debt Cost of Capital Estimatig a Debt Ratio Estimatig Cash Flows Completig the Valuatio: Depeds upo why ad for whom the valuatio is beig doe. Aswath Damodara 185

186 Estimatig Cost of Equity for a Private Firm Most models of risk ad retur (icludig the CAPM ad the APM) use past prices of a asset to estimate its risk parameters (beta(s)). Private firms ad divisios of firms are ot traded, ad thus do ot have past prices. Thus, risk estimatio has to be based upo a approach that does ot require past prices Aswath Damodara 186

187 I. Comparable Firm Betas Collect a group of publicly traded comparable firms, preferably i the same lie of busiess, but more geerally, affected by the same ecoomic forces that affect the firm beig valued. A Simple Test: To see if the group of comparable firms is truly comparable, estimate a correlatio betwee the reveues or operatig icome of the comparable firms ad the firm beig valued. If it is high (ad positive), of course, your have comparable firms. If the private firm operates i more tha oe busiess lie collect comparable firms for each busiess lie Aswath Damodara 187

188 Estimatig 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, ad calculate the ulevered beta for the busiess. b ulevered = b levered / (1 + (1 - tax rate) (Debt/Equity)) Estimate a debt-equity ratio for the private firm, usig oe of two assumptios: Assume that the private firm will move to the idustry average debt ratio. The beta for the private firm will coverge o the idustry average beta. b private firm = b ulevered (1 + (1 - tax rate) (Idustry Average Debt/Equity)) Estimate the optimal debt ratio for the private firm, based upo its operatig icome ad cost of capital. b private firm = b ulevered (1 + (1 - tax rate) (Optimal Debt/Equity)) Estimate a cost of equity based upo this beta. Aswath Damodara 188

189 Accoutig Betas Step 1: Collect accoutig earigs for the private compay for as log as there is a history. Step 2: Collect accoutig earigs for the S&P 500 for the same time period. Step 3: Regress chages i earigs for the private compay agaist chages i the S&P 500. Step 4: The slope of the regressio is the accoutig beta There are two serious limitatios - (a) The umber of observatios i the regressio is small (b) Accoutats smooth earigs. Aswath Damodara 189

190 Estimatig a Beta for the NY Yakees You have three choices for comparable firms: Firms that derive a sigificat portio of their reveues from baseball (Traded baseball teams, baseball cards & memorabalia ) Firms that derive a sigificat portio of their reveues from sports Firms that derive a sigificat portio of their reveues from etertaimet. Comparable firms Levered Beta Ulevered Beta Baseball firms (2) Sports firms (22) Etertaimet firms (91) Maagemet target Levered Beta for Yakees = 0.90 ( 1 + (1-.4) (.25)) = 1.04 Cost of Equity = 6.00% (4%) = 10.16% Aswath Damodara 190

191 Estimatig a beta for IfoSoft: A private software firm Comparable firms iclude all software firms, with market capitalizatio of less tha $ 500 millio. The average beta for these firms is 1.29 ad the average debt to equity ratio for these firms is 7.09%. With a 35% tax rate, this yields a ulevered beta of Ulevered Beta = 1.29/ (1 + (1-.35) (.0709)) = 1.24 We will assume that IfoSoft will have a debt to equity ratio comparable to the average for the comparable firms ad a similar tax rate, which results i a levered beta of Cost of Equity = 6.00% (4%) = 11.16% Aswath Damodara 191

192 Is beta a good measure of risk for a private firm? o o The beta of a firm measures oly market risk, ad is based upo the assumptio that the ivestor i the busiess is well diversified. Give that private firm owers ofte have all or the bulk of their wealth ivested i the private busiess, would you expect their perceived costs of equity to be higher or lower tha the costs of equity from usig betas? Higher Lower Aswath Damodara 192

193 Total Risk versus Market Risk Adjust the beta to reflect total risk rather tha market risk. This adjustmet is a relatively simple oe, sice the correlatio with the market measures the proportio of the risk that is market risk. Total Beta = Market Beta / Correlatio with market I the New York Yakees example, where the market beta is 0.85 ad the R-squared for comparable firms is 25% (correlatio is therefore 0.5), Total Ulevered 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% (4%)= 14.28% Aswath Damodara 193

194 Whe would you use this total risk measure? o o o Uder which of the followig scearios are you most likely to use the total risk measure: whe valuig a private firm for a iitial public offerig whe valuig a private firm for sale to a publicly traded firm whe valuig a private firm for sale to aother private ivestor Assume that you ow a private busiess. What does this tell you about the best potetial buyer for your busiess? Aswath Damodara 194

195 Estimatig the Cost of Debt for a Private Firm Basic Problem: Private firms geerally do ot access public debt markets, ad are therefore ot rated. Most debt o the books is bak debt, ad the iterest expese o this debt might ot reflect the rate at which they ca borrow (especially if the bak debt is old.) Aswath Damodara 195

196 Estimatio Optios for Cost of Debt Solutio 1: Assume that the private firm ca borrow at the same rate as similar firms (i terms of size) i the idustry. Cost of Debt for Private firm = Cost of Debt for similar firms i the idustry Solutio 2: Estimate a appropriate bod ratig for the compay, based upo fiacial ratios, ad use the iterest rate estimated bod ratig. Cost of Debt for Private firm = Iterest Rate based upo estimated bod ratig (If usig optimal debt ratio, use correspodig ratig) Solutio 3: If the debt o the books of the compay is log term ad recet, the cost of debt ca be calculated usig the iterest expese ad the debt outstadig. Cost of Debt for Private firm = Iterest Expese / Outstadig Debt If the firm borrowed the moey towards the ed of the fiacial year, the iterest expeses for the year will ot reflect the iterest rate o the debt. Aswath Damodara 196

197 Estimatig a Cost of Debt for Yakees ad IfoSoft For the Yakee s, we will use the iterest rate from the most recet loas that the firm has take o: Iterest rate o debt = 7.00% After-tax cost of debt = 7% (1-.4) = 4.2% For IfoSoft, we will use the iterest coverage ratio estimated usig the operatig icome ad iterest expeses from the most recet year: Iterest coverage ratio = EBIT/ Iterest expeses = 2000/315 = 6.35 Ratig based upo iterest coverage ratio = A+ Iterest rate o debt = 6% % = 6.80% After-tax cost of debt = 6.80% (1-.35) = 4.42% Aswath Damodara 197

198 Estimatig the Cost of Capital Basic problem: The debt ratios for private firms are stated i book value terms, rather tha market value. Furthermore, the debt ratio for a private firm that plas to go public might chage as a cosequece of that actio. Solutio 1: Assume that the private firm will move towards the idustry average debt ratio. Debt Ratio for Private firm = Idustry Average Debt Ratio Solutio 2: Assume that the private firm will move towards its optimal debt ratio. Debt Ratio for Private firm = Optimal Debt Ratio Cosistecy i assumptios: The debt ratio assumptios used to calculate the beta, the debt ratig ad the cost of capital weights should be cosistet. Aswath Damodara 198

199 Estimatig Costs of Capital New York IfoSoft Yakees Corporatio Cost of Equity 14.28%(total beta) 11.16%(market beta) E/ (D+E) 80.00% 93.38% Cost of Debt 7.00% 6.80% AT Cost of Debt 4.20% 4.42% D/(D+E) 20.00% 6.62% Cost of Capital 12.26% 10.71% Aswath Damodara 199

200 Estimatig Cash Flows for a Private Firm Shorter history: Private firms ofte have bee aroud for much shorter time periods tha most publicly traded firms. There is therefore less historical iformatio available o them. Differet Accoutig Stadards: The accoutig statemets for private firms are ofte based upo differet accoutig stadards tha public firms, which operate uder much tighter costraits o what to report ad whe to report. Itermiglig of persoal ad busiess expeses: I the case of private firms, some persoal expeses may be reported as busiess expeses. Separatig Salaries from Divideds : It is difficult to tell where salaries ed ad divideds begi i a private firm, sice they both ed up with the ower. Aswath Damodara 200

201 Estimatig Private Firm Cash Flows Restate earigs, if ecessary, usig cosistet accoutig stadards. To get a measure of what is reasoable, look at profit margis of comparable publicly traded firms i the same busiess If ay of the expeses are persoal, estimate the icome without these expeses. Estimate a reasoable salary based upo the services the ower provides the firm. Aswath Damodara 201

202 The Yakee s Reveues Pittsburg Pirates Baltimore Orioles New York Yakees Net Home Game Receipts $ 22,674,597 $ 47,353,792 $ 52,000,000 Road Receipts $ 1,613,172 $ 7,746,030 $ 9,000,000 Cocessios & Parkig $ 3,755,965 $ 22,725,449 $ 25,500,000 Natioal TV Reveues $ 15,000,000 $ 15,000,000 $ 15,000,000 Local TV Reveues $ 11,000,000 $ 18,183,000 $ 90,000,000 Natioal Licesig $ 4,162,747 $ 3,050,949 $ 6,000,000 Stadium Advertisig $ 100,000 $ 4,391,383 $ 5,500,000 Other Reveues $ 1,000,000 $ 9,200,000 $ 6,000,000 Total Reveues $ 59,306,481 $ 127,650,602 $ 209,000,000 Aswath Damodara 202

203 The Yakee s Expeses Pittsburg Pirates Baltimore Orioles New York Yakees Player Salaries $ 33,155,366 $ 62,771,482 $ 91,000,000 Team Operatig Expeses $ 6,239,025 $ 6,803,907 $ 7,853,000 Player Developmet $ 8,136,551 $ 12,768,399 $ 15,000,000 Stadium & Game Operatios$ 5,270,986 $ 4,869,790 $ 7,800,000 Other Player Costs $ 2,551,000 $ 6,895,751 $ 7,500,000 G & A Costs $ 6,167,617 $ 9,321,151 $ 11,000,000 Broadcastig $ 1,250,000 $ - $ - Ret & Amortizatio $ - $ 6,252,151 $ - Total Operatig Expeses $ 62,770,545 $ 109,682,631 $ 140,153,000 Aswath Damodara 203

204 Adjustmets to Operatig Icome Pittsburg Pirates Baltimore Orioles New York Yakees Total Reveues $59,306,481 $127,650,602 $209,000,000 Total Operatig Expeses $62,770,545 $109,682,631 $140,153,000 EBIT -$3,464,064 $17,967,971 $68,847,000 Adjustmets $1,500,000 $2,200,000 $4,500,000 Adjusted EBIT -$1,964,064 $20,167,971 $73,347,000 Taxes (at 40%) -$785,626 $8,067,189 $29,338,800 EBIT (1-tax rate) -$1,178,439 $12,100,783 $44,008,200 Aswath Damodara 204

205 IfoSoft s Operatig Icome Stated Operatig Icome Sales & Other Operatig Reveues $20, Operatig Costs & Expeses $13, Depreciatio $1, Research ad Developmet Expeses $4, Operatig Icome $2, Adjusted Operatig Icome Operatig Icome $ R& D Expeses $ Amortizatio of Research Asset $ Adjusted Operatig Icome $ Aswath Damodara 205

206 Estimatig Cash Flows for Yakees We will assume a 3% growth rate i perpetuity for operatig icome. To geerate this growth, we will assume that the Yakee s will ear 20% o their ew ivestmets. This yields a reivestmet rate of Reivestmet rate = g/ ROC = 3%/20% = 15% Estimated Free Cash Flow to Firm EBIT (1- tax rate) = $ 44,008,200 - Reivestmet = $ 6,601,230 FCFF $ 37,406,970 Aswath Damodara 206

207 From Cash Flows to Value Oce you have estimated the cash flows ad the cost of capital, you ca value a private firm usig covetioal methods. If you are valuig a firm for sale to a private busiess, Use the total beta ad the cost of equity emergig from that to estimate the cost of capital. Discout the cash flows usig this cost of capital If you are valuig a firm for a iitial public offerig, stay with the market beta ad cost of capital. Aswath Damodara 207

208 Valuig the Yakees FCFF = $ 37,406,970 Cost of capital = 12.26% Expected Growth rate= 3.00% Value of Yakees = $ 37,406,970 (1.03)/( ) = $ 415,902,192 Aswath Damodara 208

209 What if? We are assumig that the Yakees have to reivest to geerate growth. If they ca get the city to pick up the tab, the value of the Yakees ca be estimated as follows: FCFF = EBIT (1-t) - Reivestmet = $ mil - 0 = $ millio Value of Yakees = *1.03/( ) = $ 489 millio If o top of this, we assume that the buyer is a publicly traded firm ad we use the market beta istead of the total beta FCFF = $ millio Cost of capital = 8.95% Value of Yakees = (1.03) / ( ) = $ millio Aswath Damodara 209

210 Curret Cashflow to Firm EBIT(1-t) : 2,933 - Nt CpX 2,633 - Chg WC 500 = FCFF <200> Reivestmet Rate = % IfoSoft: A Valuatio Reivestmet Rate % Expected Growth i EBIT (1-t) *.2367 = % Retur o Capital 23.67% Stable Growth g = 5%; Beta = 1.20; D/(D+E) = 6.62%;ROC=17.2% Reivestmet Rate=29.07% Termial Value10= 6743/( ) = 125,391 Firm Value: 73,909 + Cash: Debt: 4,583 =Equity 69,826 EBIT(1- t) - Reiv FCFF Discout at Cost of Capital (WACC) = 11.16% (0.9338) % (0.0662) = 10.71% Cost of Equity 11.16% Cost of Debt (6+0.80%)(1-.35) = 4.42% Weights E = 93.38% D = 6.62% Riskfree Rate: Govermet Bod Rate = 6% + Beta 1.29 X Risk Premium 4% Ulevered Beta for Sectors: 1.24 Firm s D/E Ratio: 7.09% Historical US Premium 4% Coutry Risk Premium 0% Aswath Damodara 210

211 From Equity Value to Value Per Share.. Oce you have estimated equity value for the firm, to get to equity value per share, you have to decide o the umber of shares i the firm. That choice will be drive primarily by the price rage you wat the stock to trade at. For istace, if you wat IfoSoft stock to trade at about $20 per share, you would create 3.5 millio shares. ($ 69/3.5 is roughly $ 20..) Aswath Damodara 211

212 Valuatio Motives ad the Next Step i Private Compay Valuatio If valuig a private busiess for sale (i whole or part) to aother idividual (to stay private), it is ecessary that we estimate a illiquidity discout associated with the fact that private busiesses caot be easily bought ad sold a cotrol premium (if more tha 50% of the busiess is beig sold) If valuig a busiess for takig public, it is ecessary to estimate the effects of creatig differet classes of shares i the iitial public offer the effects of optios or warrats o the issuace price per share If valuig a busiess for sale (i whole or part) to a publicly traded firm, there should be o illiquidity discout, because stock i the paret firm will trade but there may, however, be a premium associated with the publicly traded firm beig able to take better advatage of the private firm s stregths Aswath Damodara 212

213 Aalyzig the Effect of Illiquidity o Value Ivestmets which are less liquid should trade for less tha otherwise similar ivestmets which are more liquid. The size of the illiquidity discout should deped upo Type of Assets owed by the Firm: The more liquid the assets owed by the firm, the lower should be the liquidity discout for the firm Size of the Firm: The larger the firm, the smaller should be size of the liquidity discout. Health of the Firm: Stock i healthier firms should sell for a smaller discout tha stock i troubled firms. Cash Flow Geeratig Capacity: Securities i firms which are geeratig large amouts of cash from operatios should sell for a smaller discouts tha securities i firms which do ot geerate large cash flows. Size of the Block: The liquidity discout should icrease with the size of the portio of the firm beig sold. Aswath Damodara 213

214 Illiquidity Discouts ad Type of Busiess o o o o Rak the followig assets (or private busiesses) i terms of the liquidity discout you would apply to your valuatio (from biggest discout to smallest) A New York City Cab Medallio A small privately owed five-ad-dime store i your tow A large privately owed coglomerate, with sigificat cash balaces ad real estate holdigs. A large privately owed ski resort that is losig moey Aswath Damodara 214

215 Empirical Evidece o Illiquidity Discouts: Restricted Stock Restricted securities are securities issued by a compay, but ot registered with the SEC, that ca be sold through private placemets to ivestors, but caot be resold i the ope market for a two-year holdig period, ad limited amouts ca be sold after that. Restricted securities trade at sigificat discouts o publicly traded shares i the same compay. Maher examied restricted stock purchases made by four mutual fuds i the period ad cocluded that they traded a average discout of 35.43% o publicly traded stock i the same compaies. Moroey reported a mea discout of 35% for acquisitios of 146 restricted stock issues by 10 ivestmet compaies, usig data from I a recet study of this pheomeo, Silber fids that the media discout for restricted stock is 33.75%. Aswath Damodara 215

216 Cross Sectioal Differeces : Restricted Stock Silber (1991) develops the followig relatioship betwee the size of the discout ad the characteristics of the firm issuig the registered stock LN(RPRS) = LN(REV) LN(RBRT) DERN DCUST where, RPRS = Relative price of restricted stock (to publicly traded stock) REV = Reveues of the private firm (i millios of dollars) RBRT = Restricted Block relative to Total Commo Stock i % DERN = 1 if earigs are positive; 0 if earigs are egative; DCUST = 1 if there is a customer relatioship with the ivestor; 0 otherwise; Iterestigly, Silber fids o effect of itroducig a cotrol dummy - set equal to oe if there is board represetatio for the ivestor ad zero otherwise. Aswath Damodara 216

217 Usig the Study Results to Estimate Illiquidity Discouts Approach 1: Use the average liquidity discout, based upo past studies, of 20% for private firms. Adjust subjectively for size - make the discout smaller for larger firms. Approach 2: Estimate the discout as a fuctio of the determiats - the size of the firm, the stability of cash flows, the type of assets ad cash flow geeratig capacity. Plug i the values for your compay ito the regressio to estimate the liquidity discout. Aswath Damodara 217

218 Liquidity Discout ad Reveues Figure 24.1: Illiquidity Discouts: Base Discout of 25% for profitable firm with $ 10 millio i reveues 40.00% 35.00% 30.00% Discout as % of Value 25.00% 20.00% 15.00% 10.00% 5.00% 0.00% Reveues Profitable firm Uprofitable firm Aswath Damodara 218

219 Applicatio to the Yakees To estimate the illiquidity discout for the Yakees, we assume that the base discout for a firm with $10 millio i reveues would be 25%. The Yakee s reveues of $209 millio should result i a lower discout o their value. We estimate the differece i the illiquidity discout betwee a firm with $10 millio i reveue ad $209 millio i reveue to be 19.10%. To do this, we first estimated the illiquidity discout i the Silber equatio for a firm with $10 millio i reveues. Expected illiquidity discout = 48.94% We the reestimated the illiquidity discout with reveues of $ 209 millio: Expected illiquidity discout = 43.04% Differece i discout = 48.94% % = 5.90% The estimated illiquidity discout for the Yakees would therefore be 19.10%, which is the base discout of 25% adjusted for the reveue differece. Aswath Damodara 219

220 A Alterate Approach to the Illiquidity Discout: Bid Ask Spread The bid ask spread is the differece betwee the price at which you ca buy a security ad the price at which you ca sell it, at the same poit. I other words, it is the illiqudity discout o a publicly traded stock. Studies have tied the bid-ask spread to the size of the firm the tradig volume o the stock the degree Regressig the bid-ask spread agaist variables that ca be measured for a private firm (such as reveues, cash flow geeratig capacity, type of assets, variace i operatig icome) ad are also available for publicly traded firms offers promise. Aswath Damodara 220

221 A Bid-Ask Spread Regressio Usig data from the ed of 2000, for istace, we regressed the bid-ask spread agaist aual reveues, a dummy variable for positive earigs (DERN: 0 if egative ad 1 if positive), cash as a percet of firm value ad tradig volume. Spread = l (Aual Reveues) (DERN) (Cash/Firm Value) 0.11 ($ Mothly tradig volume/ Firm Value) You could plug i the values for a private firm ito this regressio (with zero tradig volume) ad estimate the spread for the firm. We could substitute i the reveues of the Yakees ($209 millio), the fact that it has positive earigs ad the cash as a percet of reveues held by the firm (3%): Spread = l (Aual Reveues) (DERN) (Cash/Firm Value) 0.11 ($ Mothly tradig volume/ Firm Value) = l (209) (1) (.03) 0.11 (0) =.1178 or 11.78% Based o this approach, we would estimate a illiquidity discout of 11.78% for the Yakees. Aswath Damodara 221

222 The Effects of Cotrol o o o o This aalysis assumes that the etire orgaizatio is up for sale. Assume ow that you are buyig out oe of the limited parters i the Yakees, who ows 10% of the orgaizatio. Would you be willig to pay to pay 10% of the estimated value? Yes No If ot, would you pay less or more tha this amout? Less More Why? Aswath Damodara 222

223 Valuig Iitial Public Offerigs Discouted Cash Flow Approach Value the firm ad the equity i the firm usig traditioal discouted cash flow models. From the value of the equity, subtract out the value of ay o-commo stock equity claims o the firm (such as warrats ad optios) Divide the value of the equity by the total umber of shares outstadig, icludig the shares that are retaied by the existig owers of the firm Relative Valuatio Approach Choose a group of comparable firms Choose a multiple (preferably oe that is widely used i the sector( Estimate a multiple for this firm based upo its characteristics, relative to the comparable firms Aswath Damodara 223

224 Votig ad No-Votig Shares If oe class of shares have o votig rights while the other class of shares do, the differece i votig rights, other thigs beig equal, should make the latter more valuable. The differece i value should be a fuctio of the value of cotrollig the firm. Aswath Damodara 224

225 A Geeral Framework for Valuig Cotrol The value of the cotrol premium that will be paid to acquire a block of equity will deped upo two factors - Probability that cotrol of firm will chage: This refers to the probability that icumbet maagemet will be replaced. this ca be either through acquisitio or through existig stockholders exercisig their muscle. Value of Gaiig Cotrol of the Compay: The value of gaiig cotrol of a compay arises from two sources - the icrease i value that ca be wrought by chages i the way the compay is maaged ad ru, ad the side beefits ad perquisites of beig i cotrol Value of Gaiig Cotrol = Preset Value (Value of Compay with chage i cotrol - Value of compay without chage i cotrol) + Side Beefits of Cotrol Aswath Damodara 225

226 A Simple Example Assume that a private firm has a value of $ 100 millio ru by icumbet maagers ad $ 150 millio rue optimally. The firm creates 10 millio votig shares ad offers 70% to the public. Sice the potetial for chagig maagemet is created by this offerig, the value per share will fall betwee $10 ad $15, depedig upo the probability that is attached to the maagemet chage. Thus, if the probability of the maagemet chage is 60%, the value per share will be $ Value/Shr = (150*.6+100*.4)/10 = $13 Aswath Damodara 226

227 The Effect of Votig ad No-votig shares Now assume that this firm had issued 9 millio o-votig shares, with maagemet retaiig 1 millio votig shares with complete cotrol. I this case, the o-votig shares will get little or oe of the estimated value chage from optimal maagemet. I fact, the values of the two classes ca be estimated. Value: o-votig share = Status Quo Value/ Total umber of shares = 100/10 = $ 10 per share Value: votig share = Status Quo Value/ Total umber of shares + (Optimal Value- Status Quo Value) * Prob of chage)/ Votig shares = 100/10 + (( )*.6)/1 = $ 40 per share Aswath Damodara 227

228 Determiats of Probability of Cotrol Chagig Legal Restrictios o Takeovers: The greater the legal restrictios o takeovers the smaller the probability of cotrol chagig. Ati-takeover ad Pro-icumbet restrictios i corporate charter: The greater the restrictios o takeovers ad o chages i icumbet maagemet the lower the probability of cotrol chagig. Market Attitudes towards Cotrol Chages: The probability of cotrol chagig will be much greater is markets accept ad welcome challeges to icumbet maagemet s authority. Size of stock holdig cotrolled by icumbet maagemet: The greater the proportio, the lower the probability of cotrol chagig. Diffusio of Holdigs: Oe might be able to exert cotrol with less tha 51%, if shares are widely held. Relative umbers of votig ad o-votig shares: The greater the umber of votig shares, relative to o-votig shares, the smaller is the cotrol premium per share. Aswath Damodara 228

229 Determiats of Value of Cotrol Chagig Quality of Icumbet Maagemet: To the degree that the compay is well maaged ad well ru uder the icumbet maagemet, there is o icrease i value that flows from gaiig cotrol of the compay. A badly maaged compay might provide much more opportuity for value creatio from chages i maagemet ad fiacial policy. Ease with which chages i maagemet ca be made: Acquirig cotrol is ot the same thig as exercisig cotrol. The easier it is to exercise cotrol, the greater will be the value to the cotrol. The difficulty of exercisig cotrol will geerally icrease with the size of the firm ad with the umber of lies of busiess it is i. It is much easier to go ito a small firm with oe lie of busiess ad chage the way it is ru, tha it is to do the same with a larger ad more diversified orgaizatio. While cotrol may still be exercised evetually, the preset value of the icreased cotrol will be much smaller. Aswath Damodara 229

230 Empirical Studies o Votig versus No-Votig Shares Studies that compare the prices of traded votig shares agaist the prices of traded o-votig shares, to examie the value of the votig rightscoclude that while the votig shares geerally trade at a premium over the o-votig shares, the premium is small. Lease, McCoell ad Mikkelso (1983) fid a average premium of oly 5.44% for the votig shares. (There are similar fidigs i DeAgelo ad DeAgelo (1985) ad Meggiso (1990)) These studies have bee critiqued for uderestimatig the value of cotrol, because the probability of gaiig cotrol by acquirig these votig shares is cosidered low for two reasos - first, a substatial block of the votig shares is ofte still held by oe or two idividuals i may of these cases, ad secod, the prices used i these studies are based upo small block trades, which are ulikely to give the buyer majority cotrol. Aswath Damodara 230

231 A Test: Reader s Digest o o Reader s Digest has two classes of shares outstadig - votig ad o-votig. These are the additioal facts: The compay has see its stock price drop substatially over the last 3 years, ad aalysts believe that the compay s valuable brad ame is ot beig used well by icumbet maagemet Of the outstadig votig shares, 71% is held by two charitable istitutios, which are cotrolled by the curret CEO of the firm. Would you expect the votig shares to trade at a sigificat premium over the o-votig shares? Yes No Aswath Damodara 231

232 A Example of a IPO Valuatio: Estee Lauder Aswath Damodara 232