The relationship between price and book value has always attracted the attention

Transcription

1 ch19_p511_541.qxd 12/5/11 2:22 PM Page 511 CHAPTER 19 Book Value Multiples The relatioship betwee price ad book value has always attracted the attetio of ivestors. Stocks sellig for well below the book value of equity have geerally bee cosidered good cadidates for udervalued portfolios, while those sellig for more tha book value have bee targets for overvalued portfolios. This chapter begis by examiig the price book value ratio i more detail, the determiats of this ratio, ad how best to evaluate or estimate the ratio. I the secod part of the chapter, we tur our attetio to variats of the priceto-book ratio. I particular, we focus o the value-to-book ratio ad Tobi s Q a ratio of market value of assets to their replacemet cost. PRICE-TO-BOOK EQUITY The market value of the equity i a firm reflects the market s expectatio of the firm s earig power ad cash flows. The book value of equity is the differece betwee the book value of assets ad the book value of liabilities, a umber that is largely determied by accoutig covetios. I the Uited States, the book value of assets is the origial price paid for the assets reduced by ay allowable depreciatio o the assets. Cosequetly, the book value of a asset decreases as it ages. The book value of liabilities similarly reflects the at-issue values of the liabilities. Sice the book value of a asset reflects its origial cost, it might deviate sigificatly from market value if the earig power of the asset has icreased or declied sigificatly sice its acquisitio. Why Aalysts Use Book Value ad the Dowside There are several reasos why ivestors fid the price book value ratio useful i ivestmet aalysis. The first is that the book value provides a relatively stable, ituitive measure of value that ca be compared to the market price. For ivestors who istictively mistrust discouted cash flow estimates of value, the book value is a much simpler bechmark for compariso. The secod is that, give reasoably cosistet accoutig stadards across firms, price book value ratios ca be compared across similar firms for sigs of uder- or overvaluatio. Fially, eve firms with egative earigs, which caot be valued usig price-earigs ratios, ca be evaluated usig price book value ratios; there are far fewer firms with egative book value tha there are firms with egative earigs. There are several disadvatages associated with measurig ad usig price book value ratios. First, book values, like earigs, are affected by accoutig 511

2 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES decisios o depreciatio ad other variables. Whe accoutig stadards vary widely across firms, the price book value ratios may ot be comparable. A similar statemet ca be made about comparig price book value ratios across coutries with differet accoutig stadards. Secod, book value may ot carry much meaig for service ad techology firms that do ot have sigificat tagible assets. Third, the book value of equity ca become egative if a firm has a sustaied strig of egative earigs reports, leadig to a egative price book value ratio. Defiitio The price-to-book ratio is computed by dividig the market price per share by the curret book value of equity per share. Price per share Price-to-book ratio = PBV = Book value of equity per share While the multiple is fudametally cosistet the umerator ad deomiator are both equity values there is a potetial for icosistecy if you are ot careful about how you compute book value of equity per share. I particular, If there are multiple classes of shares outstadig, the price per share ca be differet for differet classes of shares, ad it is ot clear how the book equity should be apportioed amog shares. You should ot iclude the portio of the equity that is attributable to preferred stock i computig the book value of equity, sice the market value of equity refers oly to commo equity. Some of the problems ca be alleviated by computig the price-to-book ratio usig the total market value of equity ad book value of equity, rather tha pershare values. Price-to-book ratio = PBV = Market value of equity Book value of equity The safest way to measure this ratio whe there are multiple classes of equity is to use the composite market value of all classes of commo stock i the umerator ad the composite book value of equity i the deomiator you would still igore preferred stock for this computatio. There are two other measuremet issues that you have to cofrot i computig this multiple. The first relates to the book value of equity, which as a accoutig measure gets updated ifrequetly oce every quarter for U.S. compaies ad oce every year for Europea compaies. While most aalysts use the most curret book value of equity, there are some who use the average over the previous year or the book value of equity at the ed of the latest fiacial year. Cosistecy demads that you use the same measure of book equity for all firms i your sample. The secod ad more difficult problem cocers the value of optios outstadig. Techically, you would eed to compute the estimated market value of maagemet

3 ch19_p511_541.qxd 12/5/11 2:22 PM Page 513 Price-to-Book Equity 513 optios ad coversio optios (i bods ad preferred stock) ad add them to the market value of equity before computig the price to book value ratio. 1 If you have a small sample of comparable firms ad optios represet a large portio of equity value, you should do this. With larger samples ad less sigificat optio issues, you ca stay with the covetioal measure of market value of equity. Accoutig stadards ca affect book values of equity ad price to book ratios ad skew comparisos made across firms. For istace, assume that you are comparig the price-to-book ratios of techology firms i two markets, ad that oe of them allows research expeses to be capitalized ad the other does ot. You should expect to see lower price-to-book value ratios i the former, sice the book value of equity will be augmeted by the value of the research asset. ADJUSTING BOOK EQUITY FOR BUYBACKS AND ACQUISITIONS I recet years, firms i the Uited States have icreasigly tured to buyig back stock as a way of returig cash to stockholders. Whe a firm buys back stock, the book equity of the firm declies by the amout of the buyback. Although this is precisely what happes whe firms pay a cash divided as well, buybacks ted to be much larger tha regular divideds ad thus have a bigger impact o book equity. To illustrate, assume that you have a firm that has a market value of equity of $100 millio ad a book value of equity of $50 millio; its price-to-book ratio is If the firm borrows $25 millio ad buys back stock, its book equity will declie to $25 millio ad its market equity will drop to $75 millio. The resultig price-to-book ratio is 3. With acquisitios, the effect o price-to-book ratios ca vary dramatically depedig o how the acquisitio is accouted for. If the acquirig firm uses purchase accoutig, the book equity of the firm will icrease by the market value of the acquired firm. If, however, it uses poolig, the book equity will icrease by the book value of the acquired firm. Give that the book value is less tha the market value for most firms, the price-to-book ratio will be much higher for firms that use poolig o acquisitios tha for those that use purchase accoutig. To compare price-to-book ratios across firms whe some firms i the sample buy back stocks ad some do ot or whe there are wide differeces i both the magitude ad the accoutig for acquisitios ca be problematic. Oe way to adjust for the differeces is to take out the goodwill from acquisitios ad to add back the market value of buybacks to the book equity to come up with a adjusted book value of equity. The price-to-book ratios ca the be computed based o this adjusted book value of equity. 1 If you do ot do this ad compare price to book ratios across firms with widely differet amouts of optios outstadig, you could misidetify firms with more optios outstadig as udervalued the market value of traded commo stock at these firms will be lower because of the optio overhag.

4 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES Descriptio To get a sese of what comprises a high, low, or average price to book value ratio, we computed the ratio for every firm listed i the Uited States, ad Figure 19.1 summarizes the distributio of price-to-book ratios i Jauary Note that this distributio is heavily skewed, as is evideced by the fact that the average price-to book-value ratio of firms is 4.59 while the media price-to-book ratio is much lower at Aother poit worth makig about price-to-book ratios is that there are firms with egative book values of equity the result of cotiuously losig moey where price to book ratios caot be computed. I this sample of 5,928 firms, there were 843 firms where this occurred. I cotrast, though, 2,512 firms had egative earigs ad PE ratios could ot be computed for them. pbvdata.xls: This dataset o the Web summarizes price-to-book ratios ad fudametals by idustry group i the Uited States for the most recet year. Aalysis The price book value ratio ca be related to the same fudametals that determie value i discouted cash flow models. Sice this is a equity multiple, we will use a equity discouted cash flow model the divided discout model to explore the determiats. The value of equity i a stable growth divided discout model ca be writte as: P 0 DPS1 = k g e Dy To 0 0 To To To To To 1 1 To To To To 2 2 To To To To 3 3 To To 4 4 To To 5 5 To 10 More Cout FIGURE 19.1 Price to Book Value U.S. Compaies i Jauary 2011

5 ch19_p511_541.qxd 12/5/11 2:22 PM Page 515 Price-to-Book Equity 515 where P 0 = Value of equity per share today DPS 1 = Expected divideds per share ext year k e = Cost of equity g = Growth rate i divideds (forever) Substitutig for DPS 1 = EPS 1 (Payout ratio), the value of the equity ca be writte as: P 0 EPS = 1 Payout ratio k g e Defiig the retur o equity (ROE) = EPS 1 /Book value of equity 0, the value of equity ca be writte as: P 0 BV0 ROE Payout ratio = k g e Rewritig i terms of the PBV ratio, P0 BV ROE Payout ratio = PBV = k g 0 e If we defie retur o equity usig cotemporaeous earigs, ROE = EPS 0 /Book value of equity 0, the price-to-book ratio ca be writte as: P0 BV ROE ( 1 + g) Payout ratio = k g 0 e The PBV ratio is a icreasig fuctio of the retur o equity, the payout ratio, ad the growth rate, ad a decreasig fuctio of the riskiess of the firm. 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 BV ( ROE g ) = (k g ) e The price book value ratio of a stable firm is determied by the differetial betwee the retur o equity ad its cost of equity. If the retur o equity exceeds the cost of equity, the price will exceed the book value of equity; if the retur o equity is lower tha the cost of equity, the price will be lower tha the book value of equity. The advatage of this formulatio is that it ca be used to estimate price book value ratios for private firms that do ot pay out divideds.

6 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES ILLUSTRATION 19.1: Payig Firm Estimatig the Itrisic Price-to-Book Ratio Stable Growth, Divided- I Chapter 13, we valued Vodafoe with the H-Model, where we assumed a slightly higher growth rate iitially that scaled dow i liear icremets to a stable growth rate. I this illustratio, we will assume that Vodafoe is already i stable growth ad estimate the price to book ratio for the firm. Vodafoe paid out 4,468 millio BP i divideds o et icome of 7,968 millio BP i 2010, givig it a payout ratio of 55.82%: Payout ratio = Divideds/ Net icome = 4,468/7,968 = 55.82% Based o its book value of equity of 90,810 millio BP at the ed of 2009, the retur o equity geerated by the firm i 2010 was 8.77%: Retur o equity = Net icome 2010 Book value of equity 2009 = 7,968 90,810 = 8.77% The expected growth rate, based upo maitaiig this payout ratio ad retur o equity, is 3.88%, which we will assume is the growth rate forever. To estimate the cost of equity, we will use the riskfree rate i British pouds (4%), a equity risk premium of 5% ad assume a beta of 1 for the compay: Cost of equity = 4% + 1(5%) = 9% There are two ways i which we ca estimate the price-to-book ratio for the firm. PBV ratio = ROE Payout ratio Cost of equity Expected growth rate = = 0.96 PBV ratio = ROE Expected growth rate Cost of equity Expected growth rate = = 0.96 The stock will trade at slightly below book value, because its retur o equity is less tha its cost of equity. ILLUSTRATION 19.2: Estimatig the Price Book Value Ratio for a Privatizatio Cadidate: Jeapharm (Germay) i 1991 Oe of the by-products of Germa reuificatio was the Treuhadastalt, the Germa privatizatio agecy set up to sell hudreds of East Germa firms to other Germa compaies, idividual ivestors, ad the public. Oe of the hadful of firms that seemed to be a viable cadidate for privatizatio was Jeapharm, the most respected pharmaceutical maufacturer i East Germay. Jeapharm, which was expected to have reveues of 230 millio DM i 1991, also was expected to report et icome of 9 millio DM i that year. The firm had a book value of assets of 110 millio DM ad a book value of equity of 58 millio DM at the ed of 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 1.05, though may of these firms had much more diversified product portfolios ad less volatile cash flows. Allowig for the higher leverage ad risk i Jeapharm, a beta of 1.25 was used for Jeapharm. The 10-year bod rate i

7 ch19_p511_541.qxd 12/5/11 2:22 PM Page 517 Price-to-Book Equity 517 Germay at the time of this valuatio i early 1991 was 7%, ad the equity risk premium for stocks over bods was assumed to be 3.5%. Expected et icome = 9 millio DM Retur o equity = Expected et icome/book value of equity = 9/58 = 15.52% Cost of equity = 7% (3.5%) = % Price book value ratio = (ROE g)/(k e g) = ( )/( ) = 1.65 Estimated MV of equity = BV of equity Price/BV ratio = = millio DM PBV Ratio for a High-Growth Firm The price book value 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. The value of equity of a high-growth firm i the two-stage divided discout model ca be writte as: Value of equity = Preset value of expected divideds + Preset value of termial price Whe the growth rate is assumed to be costat after the iitial high-growth phase, the divided discout model ca be writte as follows: P 0 = ( 1+ g) EPS0 Payout ratio ( 1+ g) 1 ( 1+ ke,hg) k g e,hg EPS0 Payout ratio ( 1+ g) ( 1+ g) + (k g )( 1+ k ) e,st e,hg where g = Growth rate i the first years Payout = Payout ratio i the first years g = Growth rate after years forever (stable growth rate) Payout = Payout ratio after years for the stable firm k e = Cost of equity (hg: high-growth period; st: stable-growth period) Rewritig EPS 0 i terms of the retur o equity, EPS 0 = BV 0 ROE, ad brigig BV 0 to the left-had side of the equatio, we get: P0 BV 0 ( 1+ g) Payout ratio ( 1+ g) 1 ( 1+ ke,hg) = ROE k g e,hg Payout ratio ( 1+ g) ( 1+ g) + ROE ( k g )( 1+ k ) e,st e,hg where ROE is the retur o equity ad k e is the cost of equity.

8 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES The left-had side of the equatio is the price book value ratio. It is determied by: Retur o equity. The price book value ratio is a icreasig fuctio of the retur o equity. Payout ratio durig the high-growth period ad i the stable period. The PBV ratio icreases as the payout ratio icreases, for ay give growth rate. Riskiess (through the discout rate r). The PBV ratio becomes lower as riskiess icreases; the icreased risk icreases the cost of equity. Growth rate i earigs, i both the high-growth ad stable phases. The PBV icreases as the growth rate icreases, i either period, holdig the payout ratio costat. This formula is geeral eough to be applied to ay firm, eve oe that is ot payig divideds right ow. Note, i additio, that the fudametals that determie the price-to-book ratio are the same as they were for a stable growth firm the payout ratio, the retur o equity, the expected growth rate, ad the cost of equity. Chapter 14 oted that firms may ot always pay out what they ca afford to ad recommeded that the free cash flows to equity be substituted i for the divideds i those cases. You ca, i fact, modify the equatio to state the price-tobook ratio i terms of free cash flows to equity. P0 BV 0 FCFE ( 1+ g) g Earigs ( 1+ ) 1 hg + k = ROEhg ( 1 ) k e,hg FCFE g g Earigs ( 1 + ) ( 1 + ) + ROE (k g )( 1+ k ) e,st e,hg e,hg The oly substitutio that we have made is the replacemet of the payout ratio by the FCFE as a percet of earigs. ILLUSTRATION 19.3: Two-Stage Model Estimatig the PBV Ratio for a High-Growth Firm i the Assume that you have bee asked to estimate the PBV ratio for a firm that is expected to be i high growth for the ext five years. The firm has the followig characteristics: EPS growth rate i first five years = 20% Payout ratio i first five years = 20% EPS growth rate after five years = 8% Payout ratio after five years = 68% Beta = 1.0 Risk free rate = T-bod rate = 6% Retur o equity = 25% Cost of equity = 6% + 1(5.5%) = 11.5%

9 ch19_p511_541.qxd 12/5/11 2:22 PM Page 519 Price-to-Book Equity (.)( ) 1 PBV = ( 068. )( 120. )( 108. ) = (.. )(. ) The estimated PBV ratio for this firm is ILLUSTRATION 19.4: Estimatig the Itrisic Price-to-Book Ratio (with High Growth) To exted the reach of the itrisic valuatio model, we will use a two-stage model to estimate the price-to-book ratio for Nestle, a compay we valued with a two stage FCFE model i Chapter 14. Rather tha use the actual divideds paid (ad payout ratio), we will the FCFE as potetial divideds ad measure a payout ratio accordigly. Potetial Payout ratio = 1 FCFE/ Net Icome Usig the illustratio i Chapter 13, we summarize the iputs for Nestle: High Growth Stable Growth Legth of Growth 5 Forever ROE 21.35% 10% Equity Reivestmet Rate 37.17% 25.00% Potetial Payout ratio 62.83% 75.00% Expected growth rate 7.94% 2.50% Cost of equity 6.90% 6.90% Expected growth rate = ROE (1 Potetial Payout ratio) Pluggig back ito the two stage model, we get: ( ) 5 ( )(1.0794) 1 ( 1.069) 5 PBV = ( ) ( ) ( 0.75)(1.0794) ( ) ( ) ( ) = I this illustratio, we assumed that Nestle s expected ROE for the ext five years will be equal to its curret ROE of percet. Lowerig the expected future retur o equity will reduce the price-tobook ratio for the firm, but it will stay high as log as the ROE o existig assets stays high. If the ROE o existig assets drops, the price-to-book ratio will drop precipitously. PBV Ratios ad Retur o Equity The ratio of price to book value is strogly iflueced by the retur o equity. A lower retur o equity affects the price book value ratio directly through the formulatio specified i the prior sectio ad idirectly by lowerig the expected growth or payout. Expected growth rate = Retetio ratio Retur o equity The effects of lower retur o equity o the price book value ratio ca be see by goig back to Illustratio 19.3 ad chagig the retur o equity for the firm valued i that example.

10 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES ILLUSTRATION 19.5: Retur o Equity ad Price Book Value I Illustratio 19.3, we estimated a price to book ratio for the firm of 7.89, based o a retur o equity of 25%. This retur o equity, i tur, allowed the firm to geerate growth rates of 20% i high growth ad 8% i stable growth: Growth rate i first five years = Retetio ratio ROE = % = 20% Growth rate after year 5 = Retetio ratio ROE = % = 8% If the firm s retur o equity drops to 12%, the price book value ratio will reflect the drop. The lower retur o equity will also lower expected growth i the iitial high-growth period: Expected growth rate (first five years) = Retetio ratio Retur o equity = % = 9.6% After year 5, either the retetio ratio has to icrease or the expected growth rate has to be lower tha 8%. If the retetio ratio is adjusted, New retetio ratio after year 5 = Expected growth/roe = 8%/12% = 66.67% New payout ratio after year 5 = 1 Retetio ratio = 33.33% The ew price book value ratio ca the be calculated as follows: PBV = (. 012) 5 ( ) (.)( ) ( ) ( )( )(. 1 08) + (. 012) = ( )( ) The drop i the ROE has a two-layered impact. First, it lowers the growth rate i earigs ad/or the expected payout ratio, thus havig a idirect effect o the PBV ratio. Secod, it reduces the PBV ratio directly. The price book value ratio is also iflueced by the cost of equity, with higher costs of equity leadig to lower price book value ratios. The ifluece of the retur o equity ad the cost of equity ca be cosolidated i oe measure by takig the differece betwee the two a measure of excess equity retur. The larger the retur o equity relative to the cost of equity, the greater is the price book value ratio. I Illustratios 19.3 ad 19.5, for istace, the firm, which had a cost of equity of 11.5 percet, wet from havig a retur o equity that was 13.5 percet greater tha the required rate of retur to a retur o equity that barely broke eve (0.5 percet greater tha the required rate of retur). Cosequetly, its price book value ratio declied from 7.89 to Figure 19.2 shows the price book value ratio as a fuctio of the differece betwee the retur o equity ad cost of equity. Note that whe the retur o equity is equal to the cost of equity, the price is equal to the book value. Determiats of Retur o Equity The differece betwee retur o equity ad the cost of equity is a measure of a firm s capacity to ear excess returs i the busiess

11 ch19_p511_541.qxd 12/5/11 2:22 PM Page 521 Applicatios of Price Book Value Ratios 521 FIGURE 19.2 Price Book Value as a Fuctio of Retur Differetial i which it operates. Corporate strategists have examied the determiats of the size ad expected duratio of these excess profits (ad high ROE) usig a variety of frameworks. Oe of the better kow is the five forces of competitio framework developed by Porter. I his approach, competitio arises ot oly from established producers producig the same product but also from suppliers of substitutes ad from potetial ew etrats ito the market. Figure 19.3 summarizes the five forces of competitio. I Porter s framework, a firm is able to maitai a high retur o equity because there are sigificat barriers to etry by ew firms or because the firm has sigificat advatages over its competitio. The aalysis of the retur o equity of a firm ca be made richer ad much more iformative by examiig the competitive eviromet i which it operates. There may also be clues i this aalysis to the future directio of the retur o equity. eqmult.xls: This spreadsheet allows you to estimate the price-earigs ratio for a stable-growth or high-growth firm, give its fudametals. APPLICATIONS OF PRICE BOOK VALUE RATIOS There are several potetial applicatios for the priciples developed i the precedig sectio, ad we will cosider three i this sectio. We will first look at what causes price-to-book ratios for etire markets to chage over time, ad whe a low (high) price-to-book ratio for a market ca be viewed as a sig of udervaluatio or overvaluatio. We will ext compare the price-to-book ratios of firms withi a sector, ad exted this to look at firms across the market ad what you eed to

12 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES FIGURE 19.3 Forces of Competitio ad Retur o Equity Source: Porter. cotrol for i makig these comparisos. Fially, we will look at the factors that cause the price-to-book ratio of a idividual firm to chage over time ad how this ca be used as a tool for aalyzig restructurigs. PBV Ratios for a Market The price-to-book value ratio for a etire market is determied by the same variables that determie the price-to-book value ratio for a idividual firm. Other thigs remaiig equal, therefore, you would expect the price-to-book ratio for a market to go up as the equity retur spread (ROE mius cost of equity) eared by firms i the market icreases. Coversely, you would expect the price-to-book ratio for the market to decrease as the equity retur spread eared by firms decreases. Chapter 18 oted the icrease i the price-earigs ratio for the S&P 500 from 1960 to Over that period, the price-to-book value ratio for the market also icreased. Figure 19.4 reports o the price-to-book ratio for the S&P 500 ad the retur o equity for S&P 500 firms. The icrease i the price-to-book ratio over betwee

13 ch19_p511_541.qxd 12/5/11 2:22 PM Page 523 Applicatios of Price Book Value Ratios 523 Price-to-Book Ratio Year 20.00% 18.00% 16.00% 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% ROE PBV ROE FIGURE 19.4 Price-to-Book Ratios ad ROE S&P ad 2000 ca be at least partially explaied by the icrease i retur o equity over the same period. The last decade ( ) has bee more rocky, with a sigificat declie i the price-to-book ratio ad the retur o equity i the early years, followed by a icrease of both measures, util a collapse durig the 2008 bakig crisis. Comparisos across Firms i a Sector Price book value ratios vary across firms for a umber of reasos differet expected growth, differet payout ratios, differet risk levels, ad most importatly, differet returs o equity. Comparisos of price book value ratios across firms that do ot take ito accout these differeces are likely to be flawed. The most commo approach to estimatig PBV ratios for a firm is to choose a group of comparable firms, to calculate the average PBV ratio for this group, ad to base the PBV ratio estimate for a firm o this average. The adjustmets made to reflect differeces i fudametals betwee the firm beig valued ad the comparable group are usually made subjectively. There are several problems with this approach. First, 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 complete 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. Secod, 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. Adjustig for differeces subjectively does ot provide a satisfactory solutio to this problem, sice these judgmets are oly as good as the aalysts makig them. Give the relatioship betwee price book value ratios ad returs o equity, it is ot surprisig to see firms that have high returs o equity sellig for well above book value ad firms that have low returs o equity sellig at or below book value. The firms that should draw attetio from ivestors are those that provide mismatches of price book value ratios ad returs o equity low PBV ratios

14 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES ad high ROE, or high PBV ratios ad low ROE. There are two ways i which we ca brig home these mismatches a matrix approach ad a sector regressio. Matrix Approach If the essece of misvaluatio is fidig firms that have price-tobook ratios that do ot go with their equity retur spreads, the mismatch ca be brought home by plottig the price-to-book value ratios of firms agaist their returs o equity. Figure 19.5 presets such a plot. If we assume that firms withi a sector have similar costs of equity, we could replace the equity retur spread with the raw retur o equity. Though we ofte use curret returs o equity, i practice, the matrix is based o expected returs o equity i the future. Regressio Approach If the price-to-book ratio is largely a fuctio of the retur o equity, we could regress the former agaist the latter: PBV = a + b ROE If the relatioship is strog, we could use this regressio to obtai predicted priceto-book ratios for all of the firms i the sector, separatig out those firms that are udervalued from those that are overvalued. Overvalued High Price to Book Low Equity Retur Spread High Price to Book High Equity Retur Spread Price-to-Book Ratio Low Price to Book Low Equity Retur Spread Udervalued Low Price to Book High Equity Retur Spread Retur o Equity Cost of Equity FIGURE 19.5 Price-to-Book Ratios ad Retur o Equity

15 ch19_p511_541.qxd 12/5/11 2:22 PM Page 525 Applicatios of Price Book Value Ratios 525 This regressio ca be eriched i two ways. The first is to allow for oliear relatioships betwee price-to-book ad retur o equity; this ca be doe either by trasformig the variables (atural logs, expoetials, etc.) or by ruig oliear regressios. The secod is to expad the regressio to iclude other idepedet variables such as risk ad growth. ILLUSTRATION 19.6: Comparig Price-to-Book Value Ratios: Itegrated Oil Compaies i 2000 The followig table reports o the price-to-book ratios for itegrated oil compaies listed i the Uited States i September 2000: Ticker Price-to- Retur o Stadard Compay Name Symbol Book Ratio Equity Deviatio Crow Cetral Petroleum A CNPA % 59.36% Giat Idustries GI % 38.87% Harke Eergy Corp. HEC % 56.51% Getty Petroleum Mktg. GPM % 58.34% Pezoil Quaker State PZL % 51.06% Ashlad Ic. ASH % 21.77% Shell Trasport SC % 31.61% USX Maratho Group MRO % 45.31% Lakehead Pipe Lie LHP % 19.56% Amerada Hess AHC % 26.89% Tosco Corp. TOS % 34.51% Occidetal Petroleum OXY % 39.47% Royal Dutch Petroleum RD % 29.81% Murphy Oil Corp. MUR % 27.80% Texaco Ic. TX % 27.78% Phillips Petroleum P % 29.51% Chevro Corp. CHV % 26.44% Repsol-YPF ADR REP % 26.82% Uocal Corp. UCL % 34.90% Kerr-McGee Corp. KMG % 42.47% Exxo Mobil Corp. XOM % 19.22% BP Amoco ADR BPA % 27.00% Clayto Williams Eergy CWEI % 26.31% Average % The average price-to-book ratio for the sector is 2.30, but the rage i price-to-book ratios is large, with Crow Cetral tradig at 0.29 times book value ad Clayto Williams Eergy tradig at 5.57 times book value. We will begi by plottig price-to-book ratios agaist returs o equity for these firms i Figure While there are o firms that show up i the overvalued quadrat, firms such as Pezoil (P), Occidetal (OXY), Amerada Hess (AHC), ad Murphy (MUR) look udervalued relative to the rest of the sector. Regressig the price-to-book ratio agaist retur o equity for oil compaies, we obtaied the followig: PBV = ROE R 2 = 48.6% [2.97] [4.46]

16 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES FIGURE 19.6 Price to Book versus Retur o Equity: Oil Compaies If we exted this regressio to iclude stadard deviatio i stock prices as a measure of risk, we get: PBV = ROE 2.63 Stadard deviatio R 2 = 52% [2.16] [2.92] [1.21] This regressio ca be used to estimate predicted price-to-book ratios for these compaies i the followig table: Compay Name Price-to-Book Ratio Predicted PBV Uder- or Overvalued Crow Cetral Petroleum A NMF Giat Idustries % Harke Eergy Corp % Getty Petroleum Mktg % Pezoil Quaker State % Ashlad Ic % Shell Trasport % USX Maratho Group % Lakehead Pipe Lie % Amerada Hess %

17 ch19_p511_541.qxd 12/5/11 2:22 PM Page 527 Applicatios of Price Book Value Ratios 527 Compay Name Price-to-Book Ratio Predicted PBV Uder- or Overvalued Tosco Corp % Occidetal Petroleum % Royal Dutch Petroleum % Murphy Oil Corp % Texaco Ic % Phillips Petroleum % Chevro Corp % Repsol-YPF ADR % Uocal Corp % Kerr-McGee Corp % Exxo Mobil Corp % BP Amoco ADR % Clayto Williams Eergy % The most udervalued firm i the group is Giat Idustries, with a actual price-to-book ratio of 0.54 ad a predicted price-to-book ratio of 1.80, ad the most overvalued is Harke Eergy, with a actual price-to-book ratio of 0.64 ad a predicted price-to-book ratio of Comparig Firms across the Market I cotrast to the comparable firm approach, you could look at how firms are priced across the etire market to predict PBV ratios for idividual firms. The simplest way of summarizig this iformatio is with a multiple regressio, with the PBV ratio as the depedet variable, ad proxies for risk, growth, retur o equity, ad payout formig the idepedet variables. Past Studies The relatioship betwee price book value ratios ad the retur o equity has bee highlighted i other studies. Wilcox (1984) posited a strog relatioship betwee the price-to-book value ratio (plotted o a logarithmic scale) ad retur o equity. Usig data from 1981 for 949 Value Lie stocks, he arrived at the followig equatio: log(price/book value) = (Retur o equity) He also foud that this regressio has much smaller mea squared error that competig models usig price-earigs ratios ad/or growth rates. These PBV ratio regressios were updated i the first editio of this book usig data from 1987 to The Compustat database was used to extract iformatio o price book value ratios, retur o equity, payout ratios, ad earigs growth rates (for the precedig five years) for all NYSE ad AMEX firms with data available i each year. The betas were obtaied from the CRSP tape for each year. All firms with egative book values were elimiated from the sample, ad the regressio of PBV o the idepedet variables yielded the followig for each year:

18 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES Year Regressio R-squared 1987 PBV = Payout Beta EGR ROE PBV = Payout Beta EGR ROE PBV = Payout Beta EGR ROE PBV = Payout Beta EGR ROE PBV = Payout Beta EGR ROE where PBV = Price/book value ratio at the ed of the year Payout = Divided payout ratio at the ed of the year Beta = Beta of the stock EGR = Growth rate i earigs over prior five years ROE = Retur o equity = Net icome/book value of equity Updated Regressios I Jauary 2011, we regressed the price-to-book ratios agaist the fudametals idetified i the precedig sectio the retur o equity, the payout ratio, the beta, ad the expected growth rate over the ext five years (from aalyst forecasts): PBV = (ROE) (Payout ratio) Beta (Expected growth rate) [0.45] [39.61] [4.09] [4.29] [17.60] The regressio has a R-squared of 43.2%. The strog positive relatioship betwee price to book ratios ad returs o equity is ot uique to the Uited States. I fact, Table 19.1 summarizes regressios for of price-to-book ratios agaist returs o equity for compaies globally. TABLE 19.1 Price-to-Book Value Regressios Global i Jauary 2011 Regio Regressio : Jauary 2010 R Squared Europe PBV = Expected growth 44.0% Payout 0.55 Beta ROE Japa PBV = ROE 28.2% Emergig markets PBV = Expected growth 28.1% Payout ROE ILLUSTRATION 19.7: Valuig Coca-Cola Usig the Cross-Sectioal Regressio Assume that you had bee asked to value Coca-Cola early i Jauary 2011 ad that you had obtaied the followig data o the compay: Book value of equity per share = $14.11 Payout = 50.00% Earigs growth rate = 10.00%

19 ch19_p511_541.qxd 12/5/11 2:22 PM Page 529 Applicatios of Price Book Value Ratios 529 Retur o equity = 30% Beta = 0.90 Predicted price book value ratio = (.30) (.50) (.90) (.10) = 4.87 Predicted market value of firm = $ = $68.64 The stock was tradig at a price to book value ratio of 4.83, suggestig that it was fairly valued. pbvreg.htm: This dataset o the Web reports the results of the latest regressio of PBV ratios agaist fudametals, usig all firms i the market. CURRENT VERSUS EXPECTED RETURNS ON EQUITY I all of the comparisos that we have made i this sectio, we have used a firm s curret retur o equity to make judgmets about valuatio. While it is coveiet to focus o curret returs, the market value of equity is determied by expectatios of future returs o equity. To the extet that there is a strog positive correlatio betwee curret ROE ad future ROE, usig the curret retur o equity to idetify uder- or overvalued compaies is appropriate. Focusig o the curret ROE ca be dagerous, however, whe the competitive eviromet is chagig, ad ca lead to sigificat errors i valuatio. I such cases, you should use a forecast retur o equity that ca be very differet from the curret retur o equity. There are two ways to obtai this forecast: 1. Compute a historical average (over the past three or five years) of the retur o equity eared by the firm ad substitute this value for the curret retur o equity, whe the latter is volatile. 2. Push the firm s curret retur o equity toward the idustry average to reflect competitive pressures. For istace, assume that you are aalyzig a computer software firm with a curret retur o equity of 35 percet ad that the idustry average retur o equity is 20 percet. The forecast retur o equity for this firm would be a weighted average of 20 percet ad 35 percet, with the weight o the idustry average icreasig with the speed with which you expect the firm s retur to coverge o idustry orms. Comparig a Firm s Price-to-Book Ratio across Time As a firm s retur o equity chages over time, you would expect its price-to-book ratio to also chage. Specifically, firms that icrease their returs o equity should icrease their price-to-book ratios ad firms that see their returs o equity deteriorate should see a fall i their price-to-book ratios as well. Aother way of thikig about this is i terms of the matrix preseted i Figure 19.5, where we argued that firms with low (high) returs o equity should have low (high) price-to-book ratios. Thus, oe way to measure the effect of the restructurig of a poorly performig firm (with low retur o equity ad low price-to-book ratio) is to see where it moves o the matrix. If it succeeds i its edeavor, it should move from the low PBV/low ROE quadrat toward the high PBV/high ROE quadrat. (See Figure 19.7.)

20 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES Price-to-Book Ratio As retur o equity drops, the price-to-book ratio will drop Droppig ROE Low Price to Book Low Equity Retur Spread High Price to Book High Equity Retur Spread Icreasig ROE As retur o equity icreases, the price-to-book ratio will icrease Retur o Equity Cost of Equity FIGURE 19.7 Chages i ROE ad Chages i PBV Ratio ILLUSTRATION 19.8: ROE ad PBV Ratios: The Case of IBM IBM provides a classic example of the effects of returs o equity o price book value ratios. I 1983, IBM had a price which was three times its book value, oe of the highest price book value multiples amog the Dow 30 stocks at that time. By 1992, the stock was tradig at roughly book value, sigificatly lower tha the average ratio for Dow 30 stocks. This declie i the price book value ratio was triggered by the declie i retur o equity at IBM, from 25% i 1983 ad 1984, to egative levels i 1992 ad I the years followig Lou Gerster becomig CEO, the firm has recovered dramatically ad was tradig at ie times book value i Eve after the dot-com crash, IBM has bee able to sustai a strog record of high ROE ad high price-to-book ratios from 2001 to Figure 19.8 illustrates both PBV ad ROE betwee 1983 ad 2010 for IBM. A ivestor buyig IBM at its low poit would have obtaied a stock with a low price to book ad a low retur o equity, but her bet would have paid off. As the retur o equity improved, IBM migrated from the bottom-left quadrat to the top-right quadrat i the matrix. As its price-to-book ratio improved, the ivestor would have see substatial price appreciatio ad profits. USE IN INVESTMENT STRATEGIES Ivestors have used the relatioship betwee price ad book value i a umber of ivestmet strategies ragig from the simple to the sophisticated. Some have used low price book value ratios as a scree to pick udervalued stocks. Others

21 ch19_p511_541.qxd 12/5/11 2:22 PM Page 531 Use i Ivestmet Strategies % Price-to-Book Value % 60.00% 40.00% 20.00% 0.00% 20.00% 40.00% Retur o Equity PBV Year ROE 60.00% FIGURE 19.8 IBM: The Fall ad Rise Agai combie price-to-book value ratios with other fudametals to make the same judgmet. Fially, the sheer persistet of higher returs eared by low price-tobook stocks is viewed by some as a idicatio that price-to-book value ratio is a proxy for equity risk. The Lik to Excess Returs Several studies have established a relatioship betwee price book value ratios ad excess returs. Roseberg, Reid, ad Lastei (1985) foud that the average returs o U.S. stocks are positively related to the ratio of a firm s book value to market value. Betwee 1973 ad 1984, the strategy of pickig stocks with high book price ratios (low price book values) yielded a excess retur of 36 basis poits a moth. Fama ad Frech (1992), i examiig the cross sectio of expected stock returs betwee 1963 ad 1990, established that the positive relatioship betwee book-to-price ratios ad average returs persists i both the uivariate ad multivariate tests, ad is eve stroger tha the small firm effect i explaiig returs. Whe they classified firms o the basis of book-to-price ratios ito 12 portfolios, firms i the lowest book-to-price (highest PBV) class eared a average mothly retur of 0.30 percet, while firms i the highest book-to-price (lowest PBV) class eared a average mothly retur of 1.83 percet for the 1963 to 1990 period. Cha, Hamao, ad Lakoishok (1991) foud that the book-to-market ratio has a strog role i explaiig the cross sectio of average returs o Japaese stocks. Capaul, Rowley, ad Sharpe (1993) exteded the aalysis of price book value ratios across other iteratioal markets betwee 1981 ad 1992, ad cocluded that value stocks (stocks with low price book value ratios) eared excess returs i every market that they aalyzed. Their aualized estimates of the retur

22 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES differetial eared by stocks with low price book value ratios, over the market idex, were as follows: Coutry Added Retur to Low PBV Portfolio Frace 3.26% Germay 1.39% Switzerlad 1.17% Uited Kigdom 1.09% Japa 3.43% Uited States 1.06% Europe 1.30% Global 1.88% While this study is dated, the coclusio that lower price-to-book stocks ear higher returs tha higher price-to-book stocks looks robust. Usig Price Book Value Ratios as Ivestmet Screes The excess returs eared by firms with low price book value ratios have bee exploited by ivestmet strategies that use price book value ratios as a scree. Bejami Graham, for istace, i his classic book o security aalysis, listed price beig less tha two-thirds of book value as oe of the criteria to be used to pick stocks. The discussio i the precedig sectio emphasized the importace of retur o equity i determiig the price book value ratio, ad oted that oly firms with high retur o equity ad a low price book value ratio could be cosidered udervalued. Price to Book as a Proxy for Risk The persistece of excess returs eared by firms with lower price-to-book ratios idicates either that the market is iefficiet or that the price-to-book ratio is a proxy for equity risk. I other words, if lower price-to-book ratio stocks are viewed by the market as riskier tha firms with higher price-to-book ratios, the higher returs eared by these stocks would be a fair retur for this risk. I fact, this is the coclusio that Fama ad Frech (1992) reached after examiig the returs eared by lower price-to-book stocks. While you caot reject this hypothesis out of had, you would eed to put it to the test. What is the additioal risk that low price-to-book stocks are exposed to? It is true that some low price-to-book ratio compaies are highly levered ad may ot stay i busiess. For the most part, though, a portfolio composed of low price-to-book ratio stocks does ot seem ay more risky tha a portfolio of high price-to-book stocks their leverage ad earigs variability are similar. VALUE-TO-BOOK RATIOS Istead of relatig the market value of equity to the book value of equity, the valueto-book ratio relates the firm value to the book value of capital of the firm. Cosequetly, it ca be viewed as the firm value aalogue to the price-to-book ratio.

23 ch19_p511_541.qxd 12/5/11 2:22 PM Page 533 Value-to-Book Ratios 533 Defiitio The value-to-book ratio is obtaied by dividig the market value of both debt ad equity by the book value of capital ivested i a firm: (Market value of equity + Market value of debt) Value-to-book ratio = (Book value of equity + Book value of debt) If the market value of debt is uavailable, the book value of debt ca be used i the umerator as well. Needless to say, debt has to be cosistetly defied for both the umerator ad deomiator. For istace, if you choose to covert operatig leases to debt for computig market value of debt, you have to add the preset value of operatig leases to the book value of debt as well. There are two commo variats of this multiple that do ot pass the cosistecy test. Oe uses the book value of assets, which will geerally exceed the book value of capital by the magitude of curret liabilities, i the deomiator. This will result i price-to-book ratios that are biased dow for firms with substatial curret liabilities. The other uses the eterprise value i the umerator, with cash etted from the market values of debt ad equity. Sice the book value of equity icorporates the cash holdigs of the firm, this will also bias the multiple dow. If you decide to use eterprise value i the umerator, you would eed to et cash out of the deomiator as well. Nettig out cash from book capital creates a measure called ivested capital: Ivested capital = BV of equity + BV of debt Cash Eterprise value to Ivested capital (Market value of equity + Market value of debt Cash) = (Book value of equity + Book value of debt Cash) I additio, the multiple will eed to be adjusted for a firm s cross holdigs. The adjustmet was described i detail for the eterprise value to EBITDA multiple i Chapter 18 ad will require that you et out the portio of the market value ad book value of equity that is attributable to subsidiaries. Descriptio The distributio of the value-to-book ratio resembles that of the price-to-book ratio. Figure 19.9 presets the distributios for EV/Ivested Capital ad Value/Book capital ratios for U.S. compaies i Jauary As with the other multiples, it is a heavily skewed distributio. As with the other multiples, the average values are much higher tha the medias: The media EV/Ivested capital for U.S. firms i Jauary 2011 was 1.68 while the average price-to-book ratio was Note that there are 102 firms where eterprise value is egative (because cash exceeds the combied market values of debt ad equity).

24 ch19_p511_541.qxd 12/5/11 2:22 PM Page BOOK VALUE MULTIPLES EV/Ivested Capital Value/Book <0 0 To To To To To 1 1 To To To To 2 2 To To To To 3 3 To To 4 4 To To 5 5 To 10 More FIGURE 19.9 EV/Ivested Capital ad Value to Book: U.S. Firms i Jauary 2011 Oe of the iterestig by-products of switchig from price-to-book ratios to value-to-book is that we lose o firms i the sample with value to book ratios ad oly 102 firms with EV/Ivested capital. pbvdata.xls: This dataset o the Web summarizes value to book multiples ad fudametals by idustry group i the Uited States for the most recet year. Aalysis The value-to-book ratio is a firm value multiple. To aalyze it, we go back to a free cash flow to the firm valuatio model, ad use it to value a stable growth firm: Substitutig i FCFF = EBIT 1 (1 t)(1 Reivestmet rate), we get: EBIT1 ( 1 t)( 1 Reivestmet rate) Eterprise value = (Cost of capital g) Dividig both sides by the book value of capital, we get: 2 Eterprise value Ivested capital FCFF1 Eterprise value = (Cost of capital g) ROC(1 Reivestmet rate) = (Cost of capital g) 2 As with the retur o equity, if retur o capital is defied i terms of cotemporaeous earigs (ROC = EBIT 0 /Book capital), there will be a extra (1 + g) i the umerator.

25 ch19_p511_541.qxd 12/5/11 2:22 PM Page 535 Value-to-Book Ratios 535 The value-to-book ratio is fudametally determied by its retur o capital firms with high returs o capital ted to have high value-to-book ratios. I fact, the determiats of value-to-book mirror the determiats of price-to-book equity, but we replace equity measures with firm value measures the ROE with the ROC, the cost of equity with the cost of capital, ad the payout ratio with (1 Reivestmet rate). I fact, if we substitute i the fudametal equatio for the reivestmet rate: Reivestmet rate = g/ ROC Eterprise value Ivested capital (ROC g) = (Cost of capital g) The aalysis ca be exteded to cover high-growth firms, with the value-to-book capital ratio determied by the retur o capital, cost of capital, growth rate, ad reivestmet i the high-growth ad stable-growth periods: ( 1+ g) ( 1 RIRhg) ( 1+ g) 1 Eterprise value 1 k 0 ( + c,hg) = ROChg Ivested capital 0 k g ( 1 RIRst) ( 1+ g) ( 1+ g) + ROC hg ( k g )( 1+ k ) where ROC = Retur o capital (hg: high-growth period; st: stable-growth period) RIR = Reivestmet rate (hg: high-growth period; st: stable-growth period) k c = Cost of capital (hg: high-growth period; st: stable-growth period) c,hg c,st c,hg firmmult.xls: This spreadsheet allows you to estimate firm value multiples for a stable-growth or high-growth firm, give its fudametals. ROC, ROIC, ROA, AND ROE We have emphasized the importace of measurig the returs geerated by a firm o its ivestmets through both the DCF ad relative valuatio sectios, but we have used differet measures of accoutig returs: retur o equity, retur o capital, ad retur o ivested capital. I fact, there are may who also compute retur o assets as a measure. So, how do they relate to each other, ad which oe should you use? Let s start with what they share i commo. They all relate curret earigs i the umerator to the book value i the deomiator, but they measure earigs ad book value differetly. With retur o equity, we divide earigs to equity ivestors (et icome) by the book value of equity to get a measure of how much retur is beig eared by equity ivestors. This is the measure we use whe our compariso metric is the cost of equity ad to get growth rates i equity earigs (for the divided discout ad FCFE models). (cotiued)