Value Relevant Information Beyond Analysts. Forecasts: The Role of Growth Potential and. Bankruptcy Risk

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1 Vlue Relevnt Informtion Beyond Anlysts Forecsts: The Role of Growth Potentil nd Bnkruptcy Risk Mingyu Chen, Colin Clubb, nd Trik Driouchi ABSTRACT This pper explores the vlue relevnt informtion beyond nlysts forecsts in residul income dynmics nd equity vlution. More specificlly, we incorporte Growth Potentil (GP) nd Bnkruptcy Risk (BK) into the residul income dynmics beyond nlysts forecsts. Among the vrious proxies, we find the Present Vlue of Growth Potentil (PVGO) of Kester (1984) nd the Loss Given Defult (LGD) of Merton (1974) best cpture GP nd BK effects. We demonstrte tht GP nd BK provide dditionl informtion content beyond lgged residul income nd nlysts forecsts in the residul income dynmics. Moreover, incorporting GP nd BK in residul income dynmic beyond nlysts forecsts revels superiority in equity vlution in terms of forecst ccurcy nd explinbility. The subsmple nlysis shows tht the improvement of this model is minly reflected in the high potentil growth subsmple nd high finncil risk subsmple, in line with growth potentil nd bnkruptcy risk theories. JEL clssifiction: M40, M41, G14 Keywords: Equity Vlution, rel options, liner informtion dynmics, vlue relevnt informtion, nlysts forecst, growth potentil, bnkruptcy risk King s Business School, King s College London, University of London. Bush House, 30 Aldwych, London, WC2B 4BG, United Kingdom; Emil: mingyu.chen@kcl.c.uk King s Business School, King s College London, University of London. Bush House, 30 Aldwych, London, WC2B 4BG, United Kingdom; Emil: colin.clubb@kcl.c.uk King s Business School, King s College London, University of London. Bush House, 30 Aldwych, London, WC2B 4BG, United Kingdom; Emil: trik.driouchi@kcl.c.uk 1

2 1. Introduction Residul Income Models (RIM) hve become prominent in mrket-bsed ccounting reserch (MBAR) over the pst decde. The work of Ohlson (1995) develops the residul income model by integrting erly normtive pproch with modern finnce theory nd is considered to be one of the most importnt developments in cpitl mrket reserch (Bernrd, 1995, pp. 733). The forecsting of future residul income is importnt for implementing RIM (Dechow et l. 1999; Ohlson 2001; Cheng 2005). Anlysts forecsts re commonly used to deduce other informtion in the residul income dynmics. By cpturing forwrd-looking informtion, the nlysts forecsts re resonble nd esy to incorporte in vrious vlution models. Dechow et l. (1999) use nlysts ernings forecsts to bckwrdly deduce the other vlue relevnt informtion in Ohlson (1995). Their results generlly support the informtion dynmics in Ohlson (1995) nd confirm the superior predictive bility of the Ohlson model with nlysts forecsts. Further reserch on the informtion content of nlysts forecsts (Cheng, 2005; Rmnth et l. 2008) suggests tht nlysts forecsts might not fully includes certin types of public informtion. According to Cheng (2005), nlysts forecsts do indeed incorporte substntil informtion in the explicit informtion items nd even unique informtion beyond such items. However, it lso revels its deficiency in underestimting or ignoring the effects of conservtive ccounting nd trnsitory ernings when predicting future ernings, nd the effects of economic rents, conservtive ccounting nd risk when explining the mrketto-book rtio (Cheng, 2005, pp. 6). The im of this pper is to exmine vlue relevnce informtion beyond nlysts forecsts 2

3 in predicting residul income, nd to further explore the vlution effect of such vlue relevnt informtion. We include Growth Potentil (GP) nd Bnkruptcy Risk (BK) prmeters beyond nlysts forecsts in the Ohlson (1995) dynmics. More specificlly, we respectively incorporte R&D intensity, the direct nd indirect mesure of Present Vlue of Growth Option (PVGO) suggested in Trigeorgis nd Lmbertides (2014) nd the PVGO of Kester (1984) s proxies for GP; we respectively use Altmn s Z-Score (1968) nd the Loss Given Defult (LGD) implied in the Merton Model (1974) s proxies for BK. Following Cheng (2005) nd Tsy et l. (2008), this pper contributes to findings on vlue relevnce informtion beyond nlysts forecsts in equity vlution. We demonstrte tht GP nd BK do yield incrementl informtion in the residul income dynmic, nd incorporting GP nd BK in the residul income dynmic cn improve the vlution performnce of the equity vlution model in terms of forecst bis, forecst ccurcy nd explinbility. Moreover, this thesis contributes to the literture of non-liner equity vlution with rel options through bringing the prmeters with option chrcteristics directly into liner informtion dynmics. In the non-liner ccounting-bsed equity vlution literture, models with rel options re lwys developed from the recursion vlue (Hwng nd Sohn, 2000; Ashton et l. 2003) or the decision-mking process (Zhng, 2000; Yee,2000). In other words, the option vlue is defined s n ttchment to the estimted equity vlue from liner models (the vlue outside the liner vlution function). We investigte from different perspective, nd explore the possibility of introducing the prmeters with option chrcteristics directly into the residul income dynmics. The results suggest tht the liner model including option prmeters inside outperforms the originl liner models in equity vlution. 3

4 2. Vlution Models Trditionl Residul Income Model Ohlson (1995) with other informtion is expressed in LID1. It ssumes tht the time-series behvior of residul income is s follows: x t+1 = ω 11 x t + v t + ε 1t+1, (LID1) v t+1 = ω 22 v t + ε 2t+1. Residul income x t+1 nd the other informtion vrible v t+1 both follows first order uto regression. The persistence prmeter of residul income ω 11 is predicted to lie in the rnge of 0 ω 11 < 1. ω 22 represents the persistence prmeter of other informtion nd lso hs rnge of 0 ω 22 < 1. ε 1t+1 nd ε 2t+1 re unpredictble disturbnces with men of zero. Combining the LID1 nd the RIM vlution eqution, Ohlson (1995) with other informtion derives equity vlue s function of book vlue, residul income nd other informtion s follows: V1 t = B t + α 1 x t + α 2 v t, (V1) where α 2 = α 1 = ω 11 R ω 11, R (R ω 11 )(R ω 22 ). 4

5 Residul income is represented s x t = x t (R 1)B t 1, where x t is ernings nd B t 1 is the yer beginning book vlue of equity. R equls one plus the cost of cpitl. Ohlson (1995) with other informtion is consistent with Modiglini Miller dividend irrelevnce. It ssumes tht the expected goodwill is zero nd tht book vlue is n unbised estimtor of mrket vlue. Following Dechow et l. (1999), we dopt the nlysts consensus forecsts for future residul income s mesure of vlue relevnt informtion vrible. The other informtion vrible is deduced from nlysts forecsts for future residul income: v t = E t [x t+1 ] ω 11 x t = f t ω 11 x t, f t = f t r t b t. This other informtion vrible, v t, in Ohlson (1995), is used in ll the models in this study s proxy for nlysts forecsts. Residul Income Model with Growth Potentil Growth potentil reflects ccounting conservtism in ccounting-bsed vlution reserch. The ccounting literture identifies two brod forms of conservtism, nmely conditionl conservtism nd unconditionl conservtism (Ruch nd Tylor, 2015). Conditionl conservtism refers to the symmetric recognition of positive nd negtive economic news while unconditionl conservtism rises through the consistent under-recognition of ccounting net ssets. Reserch built on liner informtion dynmics in the residul income model mostly focuses on unconditionl conservtism, such s ccelerted deprecition methods, expensing R&D costs nd filure to recognize future positive NPV profits 5

6 (Felthm nd Ohlson, 1995; 1996). Investment opportunities might bring positive goodwill if they re chrcterized by positive NPV investment projects (Felthm nd Ohslon, 1996; Richrdson nd Tinikr, 2004). Such investment opportunities revel the growth potentil of compny. The growth prospect of specific compny is rtionlly reflected in the current stock mrkets, but not recognized in the current ccounting net ssets. The importnce of growth option in determining equity vlue hs incresingly been ddressed in the literture (Zhng, 2000; Co et l. 2008). Thus, we include the growth potentil beyond nlysts forecsts in forecsting next period residul income: x t+1 = ω 11 x t + ω 12 v t + ω 13 GP t + ε 1t+1, (LID2) v t+1 = ω 22 v t + ε 2t+1, GP t+1 = ω 33 GP t + ε 3t+1. In LID2, the GP t represents the growth potentil nd ω 33 signifies the persistence prmeter of the growth potentil. The implied vlution function is: V2 t = B t + α 1 x t + α 2 v t + α 3 GP t, (V2) where α 1 = ω 11 (R ω 11 ), α 2 = Rω 12 (R ω 11 )(R ω 22 ), α 3 = Rω 13 (R ω 11 )(R ω 33 ). 6

7 We respectively utilize four vribles to cpture growth potentil. The first is R&D intensity 1, which reflects firm s systemtic determintion to cultivte multistge growth options. It is frequently used in the literture to cpture expected economic rents in future ernings (Cheng, 2005; Shh et l. 2009). The second nd third growth potentil vribles re proxied by the direct nd indirect mesure of PVGO of Trigeorgis nd Lmbertides (2014), while the fourth mesure of growth potentil is the PVGO suggested by Kester (1984). Residul Income Model with Bnkruptcy Risk Literture on bnkruptcy risk (Ferris et l. 1997; Rose-Green nd Dwkins, 2000) indictes tht firm s probbility of bnkruptcy hs significnt effect on its stock price. High finncil risk exposes dverse informtion, which in turn lowers the mrket vlue of the ssets (Cornett nd Trvlos, 1989). According to Lim nd Tn (2007), high vlue-t-risk (VAR) tends to result in weker ernings-return reltionship. Menwhile, compny s decision to lter the degree of finncil leverge hs significnt impct on equity vlue (Cornett nd Trvlos, 1989). Following Tsy et l. (2008), this empiricl study considers the role of finncil risk in predicting next period residul income beyond nlysts forecsts: x t+1 = ω 11 x t + ω 12 v t + ω 14 BK t + ε 1t+1, (LID3) v t+1 = ω 22 v t + ε 2t+1, 1 We lso lterntively test R&D expenses, nd verge R&D expenses for the pst three yer insted of R&D intensity. In ll cses, the min results do not chnge. 7

8 BK t+1 = ω 44 BK t + ε 3t+1. BK t is the bnkruptcy risk nd ω 44 is the prmeter representing the persistence of finncil risk from one period to the next. The implied vlution function is: V3 t = B t + α 1 x t + α 2 v t + α 4 BK t, (V3) where α 1 = ω 11 (R ω 11 ), α 2 = Rω 12 (R ω 11 )(R ω 22 ), α 4 = Rω 14 (R ω 11 )(R ω 44 ). Bnkruptcy risk is respectively proxied by two vribles, the first of which is the Z-Score of Altmn (1968) nd second of which is the Loss Given Defult (LGD) inferred from the Merton Model (1974). Residul Income Model with both Growth Potentil nd Bnkruptcy Risk We lso consider both the growth potentil nd bnkruptcy risk beyond nlysts forecsts in predicting residul income nd equity vlue: x t+1 = ω 11 x t + ω 12 v t + ω 13 GP t + ω 14 BK t + ε 1t+1, (LID4) v t+1 = ω 22 v t + ε 2t+1, 8

9 GP t+1 = ω 33 GP t + ε 3t+1, BK t+1 = ω 44 BK t + ε 4t+1. GP t represents the growth potentil nd BK t represents the bnkruptcy risk. The implied vlution function is: V4 t = B t + α 1 x t + α 2 v t + α 3 GP t + α 4 BK t, (V4) where α 1 = ω 11 (R ω 11 ), α 2 = Rω 12 (R ω 11 )(R ω 22 ), α 3 = Rω 13 (R ω 11 )(R ω 33 ), α 4 = Rω 14 (R ω 11 )(R ω 44 ). 9

10 3. Reserch Methodology 3.1 Empiricl Estimtion Models To exmine vlue relevnce informtion beyond nlysts forecsts in predicting residul income, the prmeters of the residul income dynmics re estimted in pooled time-series cross-sectionl regressions (Fm-Mcbeth regressions) using ll historiclly vilble UK dt in Dtstrem. The Fm-Mcbeth pproch is widely used in the existing empiricl ccounting reserch (Dechew et l., 1999; Esten nd Pe, 2004; Cheng, 2005). It is designed to ddress concerns bout cross-sectionl correltion (Gow et l. 2010). Newey- West corrected Fm-McBeth stndrd errors re lso used in the regression to correct for seril correltion in ddition to cross-sectionl correltion. To reduce the influence of heteroscedsticity, following Choi et l. (2006), ll the regression vribles in LID re deflted by the beginning book vlue of equity. It is found tht of the vrious deflters, book vlue is the most widely used in the UK empiricl ccounting reserch (Akbr nd Strk, 2003; Dedmn et l., 2010; Rees nd Vlentincic, 2013), nd it provides the lowest bis in vlution (Shen nd Strk, 2013) Growth Potentil We comprtively utilize four vribles to mesure growth potentil: R&D intensity, the direct nd indirect mesure of PVGO of Trigeorgis nd Lmbertides (2014), nd the PVGO suggested in Kester (1984). 10

11 x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 RD GP j,t 1 + ω B 13,t j,t 1 B j,t 1 + ε t. (GP1) x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 TLDirect GP j,t 1 + ω B 13,t j,t 1 B j,t 1 + ε t. (GP2) x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 TLIndirect GP j,t + ω B 13,t j,t 1 B j,t 1 + ε t. (GP3) x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 Kester GP j,t 1 + ω B 13,t j,t 1 B j,t 1 + ε t. (GP4) In (GP1), GP RD j,t 1 represents the R&D intensity for compny j t time t 1, nd it is mesured s the verge reserch nd development expenses for the pst three yers divided by sles. In (GP2), GP TLDirect j,t 1 represents the PVGO directly clculted in Trigeorgis nd Lmbertides (2014) for compny j t time t 1. The PVGO signifies the firm s vlue rising from future potentil growth nd it is clculted by directly subtrcting the perpetul discounted operting csh flow from the mrket vlue of the firm. More specificlly, the direct PVGO of Trigeorgis nd Lmbertides (2014) cn be clculted s follows: PVGO Direct j,t = F j,t CF j,t, k j,t where F j,t is the mrket vlue of the firm, CF j,t is the csh flow from operting ctivities nd k j,t is the cost of cpitl. The indirect mesure of the PVGO of Trigeorgis nd 11

12 Lmbertides (2014) is used s the third potentil growth vrible. As illustrted below, the growth in cpitl investment nd yet-unexercised growth options is relted to eight dimensions bsed on rel options theory (Trigeogis, 1996; Smit nd Trigeorgis, 2004; Ioulinou et l. 2017): Mrket GO = f(firm specific voltility, mngeril flexibility/symmetry, orgniztionl flexibility, finncil flexibility, csh flow coverge, R&D intensity, cumultive growth, mrket power, fixed effects, industry effects, interctions). In the bove Growth Option (GO) eqution, Mrket GO represents mrket growth option score nd it is mesure s direct PVGO divided by mrket vlue of the firm. Firm-specific voltility is obtined s the residuls of the regression of the equity s returns on the FTSE 100 index return bsed on the mrket model. Skewness is estimted from the monthly stock returns over the previous three yers. R&D intensity is obtined s the verge R&D percentge (R&D divided by sles) over the previous three yers. Orgniztionl flexibility is mesured s Selling, Generl, nd Administrtive (SGA) expenses divided by sles. Finncil Leverge is estimted s book vlue of totl libilities divided by mrket vlue of the firm. Cumultive Sles Growth (SG) is clculted s the percentge chnge in firm revenues for the pst three yers. The firm s mrket power is mesured s the squre root of the Herfindhl-Hirschmn Index (HHI) if the firm s Tobin s q is bove the industry verge in the specific yer, otherwise s 0. Csh Flow Coverge (CFC) is mesured s csh flow from operting ctivities divided by totl libilities. The bove eqution is 12

13 regressed using the Fm-Mcbeth pproch from the erliest yer ll the required vribles re vilble through yer t to obtin the yerly cross-sectionl coefficients lodings to the eight option-driven vribles. An interction term between Skewness nd Leverge is included, nd industry dummies re included in the regression. Following this, the current dt for these vribles for ech firm is utilized with the coefficients to determine predicted GO j,t for ech firm. The indirect PVGO is then clculted s the product of predicted GO nd the mrket vlue of the firm: PVGO Indirect j,t = GO Predicted j,t. F j,t In (GP2) nd (GP3), the direct nd indirect PVGO of Trigeorgis nd Lmbertides (2014) is set to be zero if csh flow from opertions is negtive or the mrket vlue of the firm is lower thn the cpitlized csh flow from opertions. In (GP4), GP Kester j,t 1 represents the PVGO suggested in Kester (1984). It is determined by subtrcting the cpitlized ernings from the mrket vlue of equity: PVGO Kester j,t = V j,t E j,t, r j,t where V i,t is the mrket vlue of equity; E i,t represents ernings; nd r i,t represents the cost of equity. One yer lgged nlysts forecsts ernings were used to clculte the PVGO of Kester (1984). By using lgged nticipted ernings, Kester (1984) void the one-off compny-specific surprises tht my ffect ernings outcomes. The PVGO of Kester (1984) is set to be zero if nticipted ernings re negtive or the mrket vlue of equity is lower thn the cpitlized nticipted ernings. 13

14 3.1.2 Bnkruptcy Risk Two vribles re used to mesure the bnkruptcy risk: Altmn s Z-Score nd the LGD in the Merton Model. x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 Z Score BK j,t 1 + ω B 14,t j,t 1 B j,t 1 + ε t. (BK1) x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 Merton BK j,t 1 + ω B 14,t j,t 1 B j,t 1 + ε t. (BK2) In (BK1), BK Z Score j,t 1 represents the reciprocl of Altmn s Z-Score (1968). Altmn s Z- Score is the output of credit-strength test which is bsed on five key finncil rtios. It mesures the likelihood of bnkruptcy for compny. The clcultion used to determine the Altmn Z-score is s follows: ZSCORE t = (3.3) EBIT t TA t + (1.0) Sles t TA t + (1.4) RE t TA t + (0.6) MV t TD t + (1.2) WC t TA t, where EBIT t is the ernings before interest nd tx of the firm; TA t is the totl ssets; Sles t is the net sles; RE t is the retined ernings; MV t is the mrket vlue of equity; TD t is the totl libility; nd WC t is the working cpitl. The second proxy for the bnkruptcy risk is the LGD in the Merton (1974) Model. The loss given defult is equl to the Expected Loss (EL) divided by the Probbility of Defult (PD). LGD works better in the regression thn PD for two resons. First, LGD is the conditionl expecttions nd it reflects the finncil risk. Second, it is similr in mount terms to other regression vribles. The 14

15 empiricl implementtion of the Merton model is similr to Chritou et l. (2013). LGD(F, T) = K N( d 2 ) Fe (rf D)T N( d 1 ), d 1 = ln (F B ) + (μ D + 0.5σ v 2 )T, σ V T d 2 = d 1 σ V T = ln (F B ) + (μ D 0.5σ v 2 )T. σ V T In the model, K is the fce vlue of debt; F is the firm vlue nd it equls the sum of the mrket vlue of equity nd the fce vlue of debt; D is the totl pyout yield; σ V is the stndrd devition of firm vlue; T is the time-to-debt mturity; rf is risk-free interest rte; nd μ is the ctul firm vlue return. Due to the lck of monthly nd qurterly debt dt, the voltility of the firm is clculted s the stndrd devition of the firm return in the pst 5 yers. The time-to-debt mturity clcultion is similr to Chritou et l. (2013). The totl figure for long term debt is ssumed to hve common mturity of 5 yers, while the shortterm debt hs mturity of 1 yer. 3.2 Estimtion of Out-of-Smple Vlution Performnce Yerly regressed LID prmeters re used to clculte the cross-sectionl theoreticl implied coefficients in equity vlution (vrious α in ech model). These coefficients re pplied to ll the firms with the necessry dt to clculte the estimted mrket vlue. We contrst the vlution performnce of the models which build on vrious LID in terms of out-of-smple forecst bis, forecst ccurcy nd explinbility, following Frncis et l. (2000). The men nd medin Proportionl Vlution Error (PVE) mesures the forecst 15

16 bis while the medin Absolute Proportionl Vlution Error (APVE) mesures the forecst ccurcy. PVE t = MV t Est MV t Act MV t Act, APVE t = MV t Est MV t Act MV t Act, Est Act where MV t represents the estimted mrket vlue for firm j t time t nd MV t represents the mrket vlue for firm j t time t. The centrl tendency of the vlue estimtes is lso reported, defined s the percentge of observtions with the estimted vlue lying within 15% of the security price. Following Cheng (2005), the Fm-Mcbeth djusted R Squre is used to mesure the bility of the estimted equity vlue in explining the mrket vlue (explinbility). 3.3 Smples nd Dt The smple includes ll UK non-finncil compnies listed on the London Stock Exchnge. Ded compnies re included to void survivorship bis. Mrket dt re collected from Dtstrem, ccounting vribles re collected from Worldscope, nd nlysts forecsts dt re retrieved from I/B/E/S. All dtbses re ccessed through Thomson Reuters Dtstrem. To ensure the integrity of the dtset, ll vribles re collected from the erliest yer UK dt re vilble on Thomson Reuters Dtstrem. The estimtion of LID prmeters uses pooled time-series cross-sectionl regressions with ll historiclly vilble dt from The finl comprison of residul income dynmics nd equity vlution performnce consist of 21 yers of nnul dt from 1995 to

17 Tble 1 provides the definition for ech vrible used in empiricl nlysis. The estimtion of LID prmeters nd equity vlution re conducted on per shre bsis. The mrket vlue of equity is collected six months fter the finncil yer end (ensuring there is sufficient time for UK compnies to publish ccounting reports). Following Begley nd Felthm (2002), ernings re before extrordinry items nd it is ssumed tht they re trnsitory nd therefore unlikely to ffect the residul income. We use the medin of one yer hed forecst EPS to mesure nlysts forecsts of ernings. The eight optionmotivted vribles re mesured ccording to their definitions in Trigeorgis nd Lmbertides (2014). In terms of the Merton model, due to the lck of monthly debt dt, we clculte the voltility of firm using pst 5 period yerly dt following Hwng nd Sohn (2010). The definition of vribles in the Merton model follows Chritou et l. (2013). As for the risk-free rte, the British Government Securities Ten Yer Nominl Pr Yield is used. The cross-sectionl cost of equity hs been widely used in reltive empiricl ccounting literture (Ahmed et l. 2002; Choi et l. 2006). Following O Hnln nd Steele (2000) nd Copelnd et l. (2000), the cost of equity equls the risk-free rte plus constnt risk premium of 5%. We estimte the cost of debt to be 4% lower thn the cost of equity similr to Trigeorgis nd Lmbertides (2014). According to Co et l. (2008), the estimtion of the PVGO is insensitive to the discount rte. 17

18 Tble 1. Vrible Definitions Vribles Lbel Dt Items nd Definition Mrket Vlue of Equity MV t Mrket Vlue = Mrket Vlue Cpitl (MV) For ccounting periods ending before the 20th Jnury 2007, UK firms hd up to six months fter the finncil yer-end to publish ccounting dt. This ws reduced to four months for ccounting periods ending fter tht dte following the implementtion of the Trnsprency Directive 2004/109/EC. To mintin consistency, we collect the mrket vlue of equity (MV) six months fter the finncil yer-end (6 months fter time t). Book Vlue B t Book Vlue = Common Equity (WC03501) Ernings x t Ernings = Net Income Avilble to Common (WC01751) Residul Income x t x t = x t - r t * B t 1 Anlysts Forecsts of Ernings Csh Flow from Operting Activities f t CF t Anlysts forecsts of Ernings = Forecst Ernings Per Shre Medin Vlue FY1 (EPS1MD) * Common Shres Used to Clculte Ernings Per Shre (WC05191) Csh Flow from Operting Activities = Net Csh Flow Operting Activities (WC04860) R&D Expenses R&D t Reserch nd Development Expenses = Reserch & Development (WC01201) SGA expenses SGA t SGA expenses = Selling, Generl & Administrtive Expenses (WC01101) Sles Sles t Sles = Net Sles or Revenues (WC01001) Totl Assets TA t Totl Assets (WC02999) Totl Libilities TL t Totl Libilities (WC03351) Mrket Vlue of Firm F t Mrket Vlue of Firm = Mrket Vlue Cpitl (MV) + Totl Assets (WC02999) - Common Equity (WC03501) Deferred Txes (WC03263) Tobin s Q Q t Tobin s Q = Mrket Vlue of Firm / Totl Assets (WC02999) 18

19 Tble 1. (Continued) Firm Specific Voltility (Trigeorgis nd Lmbertides, 2014) Asymmetry (Trigeorgis nd Lmbertides, 2014) R&D Intensity (Trigeorgis nd Lmbertides, 2014) Orgniztionl Flex (Trigeorgis nd Lmbertides, 2014) Finncil Flex (Trigeorgis nd Lmbertides, 2014) Cumultive Sles Growth (Trigeorgis nd Lmbertides, 2014) Mrket Power (Trigeorgis nd Lmbertides, 2014) σ t Skewness t R&D_INT t SGA_PER t Leverge t SG t Firm Specific Voltility = The residul of the regression of the equity s returns on the FTSE 100 index return bsed on the mrket model using previous 3 yers monthly return dt Asymmetry = The skewness of the monthly stock returns for the previous three yers R&D Intensity = Averge R&D Expenses for recent three yers / Sles Orgniztionl Flex = SGA expenses / Sles Finncil Flex = Totl Libility / Mrket Vlue of Firm Cumultive Sles Growth = Percentge of Chnge in Sles over recent 3-yer period HHI t Mrket Power = The squre root of the Herfindhl-Hirschmn Index (HHI) for the compny if the firm s Tobin s q is bove the industry verge in the specific yer, nd 0 otherwise. Csh Flow Coverge (Trigeorgis nd Lmbertides, 2014) HHI for compny = {[(Sles Interntionl Sles) / Sum of Compny Sles in the Industry]*100}^2 CFC t Csh Flow Coverge = Csh Flow from Operting ctivities / Totl Libility EBIT EBIT t EBIT = Ernings Before Interest nd Txes (EBIT) (WC18191) Retined Ernings RE t Retined Ernings (WC03495) 19

20 Tble 1. (Continued) Working Cpitl WC t Working Cpitl (WC03151) Residul Income x t x t = x t - r t * B t 1 Fce Vlue of Totl Debt K t Fce Vlue of Totl Debt = [Short term debt (WC03501) + Long term debt (WC03251)] Totl Pyout Yield D t Totl Pyout Yield = Ln {[1 + Totl Pyout] / Mrket Vlue of Equity in the previous yer} Totl Pyout = [Csh Dividends (WC05376) + Interest Expense (WC01251)] Mrket Vlue of Firm in Merton Model 2 Voltility of Firm in Merton Model F t Merton σ F, t Mrket Vlue of Firm in Merton = Mrket Cpitliztion (WC08001) + Totl Debt (WC03255) Voltility of Firm is clculted s the Stndrd Devition of Firm Return in the previous 5 Yers following Hwng nd Sohn (2010) Firm Return = Ln {[Firm Vlue + Totl Pyout] / Firm Vlue in the previous yer} Time to Mturity T Time to Mturity = [Present Vlue of Short Term Debt * 1 + Present Vlue of Long Term Debt * 5] / [Present Vlue of Short Term Debt + Present Vlue of Long Term Debt] Present Vlue of Short Term Debt = Short Term Debt / Riskfree Rte Present Vlue of Long Term Debt = Long Term Debt / (Annul Averge of British Government Securities Five Yer Nominl Pr Yield) ^ 5 Cost of Equity r t Cross Sectionl: An nnul Averge of British Government Securities Ten Yer Nominl Pr Yield (10 Yer Pr Yield) plus verge risk premium rte of 5% 2 This definition of mrket firm vlue hs the dvntge of focusing directly on the mrket cp nd debt. It is used only in Merton Model. We lso use the previous definition of Mrket Vlue of Firm to test the Merton Model. The min results remin unchnged. 20

21 Tble 1. (Continued) Risk-free Rte rf t Cross Sectionl: An nnul Averge of British Government Securities Ten Yer Nominl Pr Yield (10 Yer Pr Yield) Cost of Equity r t Cross Sectionl: An nnul Averge of British Government Securities Ten Yer Nominl Pr Yield (10 Yer Pr Yield) plus verge risk premium rte of 5% Cost of Cpitl k t Cost of Cpitl = Cost of Equity * (1 Debt Rtio) + Cost of Debt * Debt Rtio * (1 Tx Rte) Cost of Debt = Cost of Equity 3% Debt Rtio = Totl Libility / Totl Assets Tx Rte = Income Txes (WC01451) / Pretx Income (WC01401) 21

22 4. Results 4.1 Results on Residul Income Dynmics In compring the results on vlue relevnce informtion beyond nlysts forecsts in the residul income dynmic, we respectively incorporte four growth potentil proxies nd two bnkruptcy risk proxies. In order to present the results in simplified nd cler mnner, the following sequences re used: (1) compring the residul income dynmics incorporting vrious growth potentil proxies (section ); (2) compring the residul income dynmics incorporting vrious bnkruptcy risk proxies (section ); (3) through using the best proxies for GP nd BK, testing the residul income dynmic with both growth potentil nd bnkruptcy risk beyond nlysts forecsts (section ) LID with Growth Potentil Tble 2 provides summry of vlue estimtes of regression vribles in the residul income dynmic with GP nd nlysts forecsts, bsed on the joint smple. All vribles re stted on per shre bsis nd deflted by one yer lgged book vlue. The medin residul income is round 0.01, close to zero. This suggests tht nerly hlf the smple hs positive residul income. The medin of other informtion vrible is round 0.04, which indictes tht, on verge, nlysts hve n optimistic view regrding the future prospect of compnies. With respect to the GP vribles, GP RD represents the R&D intensity nd it hs men of 0.44 nd medin of round zero. Further nlysis on the R&D expenses revel tht nerly hlf the smple observtions revel zero reserch nd development expenses, similr to the descriptive sttistics in Trigeorgis nd Lmbertides (2014). GP TLDirect, GP TLIndirect nd GP Kester ll mesure the present vlue of growth options. It 22

23 cn be inferred from the tble tht the direct PVGO of Trigeorgis nd Lmbertides provides the lrgest medin (round 0.77), followed by the indirect PVGO of Trigeorgis nd Lmbertides (bout 0.51). Kester s PVGO hs the lowest medin t round Tble 2. Vlue Estimtes of Growth Potentil Vribles N 0.25 Medin 0.75 Men S.D. x v GP RD GP TLDirect GP TLIndirect GP Kester Notes: Tble 2 reports the vlue estimtes of reltive GP vribles in the residul income dynmic, bsed on joint smple of x stnds for residul income nd v stnds for other informtion vrible. GP RD, GP TLDirect, GP TLIndirect nd GP Kester respectively represent the growth potentil proxies of R&D intensity, direct nd indirect PVGO of Trigeorgis nd Lmbertides (2014), nd PVGO of Kester (1984). All vribles re stted on per shre bsis nd deflted by one yer lgged book vlue. 23

24 To estimte the indirect PVGO of Trigeorgis nd Lmbertides, the coefficients from the GO eqution re needed to clculte the predicted GO. We regress the GO eqution in Trigeorgis nd Lmbertides (2014) utilizing Fm-Mcbeth regression pproch from the erliest yer tht ll the required vribles re vilble through yer t to obtin the yerly cross-sectionl coefficients lodings to the eight option-driven vribles 3. Pnel A in Tble 3 reports the summry sttistics of mrket GO nd the eight option-motivted vribles. The men of mrket GO is round 0.59, which indictes tht on verge, the direct PVGO occupies 59% of the mrket vlue of the firm. Pnel B in Tble 3 presents the Fm- Mcbeth coefficients over the period The signs of the coefficients lodings to the option-motivted vribles re the sme s the findings in Trigeorgis nd Lmbertides (2014). Among the vribles, firm specific voltility, orgniztionl flexibility, cumultive sles growth nd mrket power re significntly nd positively relted to growth option. It suggests tht higher idiosyncrtic risk, SGA expenses, sles growth nd mrket competitive power contribute to lrger growth option vlue. Menwhile, skewness hs significnt reltionship to growth option, nd revels positive interction with finncil leverge. 3 This Fm-Mcbeth pproch follows both Dechow et l. (1999) nd Choi et l. (2006). We lso directly use 1, 3, 5 yers estimtion window insted of the Fm-Mcbeth pproch to estimte the coefficients. The signs of the coefficients re similr, nd the predicted GO score re not tht sensitive to the estimtion pproch. In ll cses the min results of the study do not chnge. 24

25 Tble 3. Summry Sttistics nd Coefficient Estimtes of GO Eqution Pnel A Summry Sttistics of Growth Option Vribles Vrible Men Std.Dev. Q1 Medin Q3 Mrket GO Firm-specific voltility Asymmetry R&D Intensity Orgniztionl Flex Finncil Flex Cumultive Sles Growth Mrket Power Csh Flow Coverge N Pnel B Coefficients Estimtes of Growth Option Vribles Dependent Vrible: Mrket GO Independent Vribles Coef. t-stt. Firm-specific voltility *** 7.65 Asymmetry *** R&D Intensity Orgniztionl Flex *** 2.70 Finncil Flex Cumultive Sles Growth ** 2.55 Mrket Power * 1.65 Csh Flow Coverge *** Skewness Leverge ** 2.02 N R Notes: Tble 3 reports summry sttistics nd coefficient estimtes of GO eqution. The GO euqtion is regressed using Fm-Mcbeth regression utilizing ll vilble UK dt from 1983 to Averge R 2 is the verge R sttistic nd t vlue (in prentheses) is bsed on Newey-West corrected Fm-McBeth stndrd errors. The most extreme 1% of the regression vribles re winsorized in estimting the coefficients. Mrket GO represents mrket growth option score nd it is mesured s direct PVGO divided by mrket vlue of the firm. Firm-specific voltility is obtined through the residuls of the regression of the equity s returns on the FTSE 100 index return bsed on the mrket model. Skewness is obtined from the monthly stock returns for the previous three yers. R&D intensity is meusred s the verge R&D percentge (R&D divided by sles) for the pst three yers. Orgniztionl flexibility is mesured s Selling, Generl, nd Administrtive (SGA) expenses divided by sles. Finncil Leverge is estimted s book vlue of totl libilities divided by mrket vlue of the firm. Cumultive Sles Growth (SG) is clculted s the percentge chnge in firm revenues for the pst three yers. The firm s mrket power is mesured s the squre root of the Herfindhl-Hirschmn Index (HHI) should the firm s Tobin s q be bove the industry verge in the specific yer, nd 0 otherwise. Csh Flow Coverge (CFC) is mesured s csh flow from operting ctivities divided by totl libilities. An interction term between Skewness nd Leverge is included. Industry dummies re included in the regression 25

26 To exmine vlue relevnce of GP vribles in the residul income dynmic, regressions of the residul income dynmic re initilly conducted incorporting vrious GP proxies excluding nlysts forecsts. These results re summrized in Tble 4. Except for the R&D intensity, ll other GP proxies significntly provide incrementl explntory power beyond lgged residul income in forecsting next period residul income. More specificlly, the residul income dynmic incorporting reltive PVGO significntly provides higher Fm-Mcbeth verge R squre then the trditionl residul income dynmic in O95. There is n incrementl R squre of 4.4% for the direct PVGO of Trigeorgis nd Lmbertides, 4.4% for the indirect PVGO of Trigeorgis nd Lmbertides, nd 5.4% for the PVGO of Kester (1984). It cn be inferred from the results tht the three PVGO proxies re vlue relevnt with regrds to forecsting next period residul income. Tble 5 provides the regression results of the residul income dynmics including vrious GP vribles s well s the other informtion vrible inferred from nlysts forecsts. The coefficients on lgged residul income nd other informtion vrible in ech model re significnt t the 0.01 level. The coefficient on lgged residul income in ech model is round 0.5, which is consistent with the findings in Dechow et l. (1999) nd Cllen nd Segl (2005). Among ll GP proxies, only R&D intensity is not significnt in explining next period residul income. This finding is similr to Cheng (2005), which suggests tht R&D intensity fils to provide significnt vlue relevnt informtion beyond nlysts forecsts in the residul income dynmic. In terms of PVGO proxies, the PVGO of Kester (1984) fits best in the residul income dynmic beyond nlysts forecsts. With coefficient of 0.049, this suggests tht the current PVGO of Kester (1984) contributes 26

27 positively to next period residul income beyond nlysts forecsts. Moreover, the Fm- Mcbeth verge R squre of GP4 is round 0.450, higher thn the R squre in the trditionl O95 model with nlysts forecsts. It demonstrtes tht including the PVGO of Kester (1984) in residul income dynmic beyond nlysts forecsts does indeed improve the dynmic explinbility. In other words, the PVGO of Kester (1984) provides dditionl vlue relevnt informtion beyond the lgged residul income nd nlysts forecsts. Compred with PVGO of Kester (1984), the direct nd indirect PVGO of Trigeorgis nd Lmbertides re lso significnt in reveling vlue relevnce in the residul income dynmic beyond lgged residul income nd nlysts forecsts, but with lower incrementl explntory power. This is due to the fct tht the PVGO of Kester focuses directly on the growth option of equity, while the PVGO of Trigeorgis nd Lmbertides emphsize the growth option of the firm. As residul income is more closely relted to the cost of equity nd ernings, this suggests tht the PVGO of Kester is better for proxying the growth potentil in the residul income dynmic. 27

28 Tble 4. Residul Income Dynmics with Growth Potentil Excluding Anlysts Forecsts N ω 10 ω 11 ω 12 ω 13 Averge R 2 O95: x j,t x j,t 1 = ω B 10,t + ω 11,t + ε j,t 1 B t. j,t 1 Trditionl Liner Model Estimtions *** GP1: x j,t (-1.35) (6.61) x j,t 1 GP j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 13,t + ε j,t 1 B t. j,t 1 GP proxied by R&D intensity RD Estimtions *** GP2: x j,t x j,t 1 GP j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 13,t j,t 1 (-0.81) (6.34) (1.17) TLDirect B j,t 1 + ε t. GP proxied by PVGO Directly Mesured in Trigeorgis nd Lmbertides (2014) Estimtions *** *** *** GP3: x j,t x j,t 1 GP j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 13,t j,t 1 (-7.03) (6.60) (9.09) TLIndirect B j,t 1 GP proxied by PVGO Indirectly Mesured (estimted coefficients) in Trigeorgis nd Lmbertides (2014) + ε t. Estimtions *** *** *** GP4: x j,t x j,t 1 GP j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 13,t j,t 1 GP proxied by PVGO of Kester (1984) (-7.17) (6.81) (8.06) B j,t 1 Kester + ε t. Estimtions *** *** *** (-6.92) (7.36) (9.76) Notes: Tble 4 shows the coefficients nd R squre of the residul income dynmics excluding nlysts forecsts in vrious GP models bsed on Fm-Mcbeth regression from 1988 to Following Choi et l. (2006), the most extreme 1% of the deflted vribles re winsorized in estimting the LID prmeters. Averge R 2 is the verge R sttistic nd t vlue (in prentheses) is bsed on Newey-West corrected Fm- McBeth stndrd errors. The superscripts *, **, *** respectively indicte significnce t the 10%, 5% nd 1% level. 28

29 Tble 5. Residul Income Dynmics with Growth Potentil Beyond Anlysts Forecsts N ω 10 ω 11 ω 12 ω 13 Averge R 2 O95 with Anlysts Forecsts: Trditionl Liner Model with nlysts forecsts x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t + ε j,t 1 B t. j,t 1 Estimtions *** *** *** GP1: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 GP proxied by R&D intensity (-8.22) (16.34) (14.77) RD GP j,t 1 + ω B 13,t j,t 1 B j,t 1 + ε t. Estimtions *** *** *** GP2: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 (-7.20) (15.93) (14.14) (0.48) TLDirect GP j,t 1 + ω B 13,t j,t 1 B j,t 1 + ε t. GP proxied by PVGO Directly Mesured in Trigeorgis nd Lmbertides (2014) Estimtions *** *** *** *** GP3: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 (-10.58) (14.12) (10.87) (4.50) TLIndirect GP j,t 1 + ω B 13,t j,t 1 GP proxied by PVGO Indirectly Mesured (estimted coefficients) in Trigeorgis nd Lmbertides (2014) Estimtions *** *** *** *** GP4: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 GP proxied by PVGO of Kester (1984) B j,t 1 + ε t. (-8.71) (16.30) (13.50) (4.73) Kester GP j,t 1 + ω B 13,t j,t 1 B j,t 1 Estimtions *** *** *** *** ε t. (-9.06) (11.87) (9.07) (5.21) Notes: Tble 5 shows the coefficients nd R squre of the residul income dynmics including the other informtion vrible (nlysts forecsts) in vrious GP models bsed on Fm-Mcbeth regression from 1991 to Following Choi et l. (2006), the most extreme 1% of the deflted vribles re winsorized in estimting the LID prmeters. Averge R 2 is the verge R sttistic nd t vlue (in prentheses) is bsed on Newey-West corrected Fm-McBeth stndrd errors. The superscripts *, **, *** respectively indicte significnce t the 10%, 5% nd 1% level. 29

30 4.1.2 LID with Bnkruptcy Risk Tble 6 reports the vlue estimtes of regression vribles in the residul income dynmics with BK nd nlysts forecsts, bsed on the joint smple. The vlue estimtes use ll vilble dt in the UK over the period All vribles re stted on per shre bsis nd deflted by one yer lgged book vlue. The descriptive sttistics of residul income nd other informtion vrible in this smple is similr to those in growth potentil. With respect to the BK vribles, BK Z Score represents the reciprocl of Altmn s Z-Score (1968) nd hs men of 0.89 nd medin of round BK Merton stnds for the LGD in the Merton model. The Loss Given Defult (LGD) reflects finncil risk s it involves the conditionl expecttions on the probbility of defult. The men of BK Merton is 0.03 nd its medin is lso centered round zero. It is hypothesized tht bnkruptcy risk provides dditionl informtion beyond nlysts forecsts nd it revels negtive reltionship with the next period residul income. Tble 6. Vlue Estimtes of Bnkruptcy Risk Vribles N 0.25 Medin 0.75 Men S.D. x v BK Z Score BK Merton Notes: Tble 6 reports the vlue estimtes of reltive BK vribles in the residul income dynmic. x stnds for residul income nd v stnds for other informtion vrible. BK Z Score nd BK Merton respectively represent the bnkruptcy risk proxies of Altmn s Z-Score nd LGD in the Merton Model. All vribles re stted on per shre bsis nd deflted by one yer lgged book vlue. 30

31 Tble 7 presents the results on the residul income dynmics including vrious BK proxies excluding nlysts forecsts. It cn be inferred from this tble tht including the Merton s LGD significntly improves the explinbility of the O95 residul income dynmic. It rises the Fm-Mcbeth verge R squre from to The significntly negtive coefficient on Merton s LGD suggests this BK proxy hs negtively effect in forecsting next period residul income. Z-Score fils to provide significnt coefficient beyond lgged residul income in the residul income dynmic. Thus, only the Merton s LGD revels vlue relevnce in forecsting next period residul income. Tble 8 summrizes the results on the residul income dynmics including vrious BK proxies beyond the other informtion inferred from nlysts forecsts. It is evident from the tble tht the coefficients on lgged residul income nd other informtion vrible in ll models re significnt t the 0.01 level. In terms of the BK vribles, only the BK Merton is significnt. It indictes tht compred with the Z-Score, the loss given defult in Merton presents s the better proxy for bnkruptcy risk in residul income dynmic with nlysts forecsts. The coefficient on BK Merton is , which suggests tht the bnkruptcy risk hs significntly negtive effect in forecsting next period residul income beyond nlysts forecsts. A Fm-Mcbeth verge R squre of is observed for the residul income dynmic with BK Merton, which is higher thn the in the trditionl O95 model with nlysts forecsts. As result, it is obvious tht including the bnkruptcy risk proxy of Merton model s LGD improves the explinbility of the trditionl residul income dynmic with nlysts forecsts. In other words, Merton s LGD s proxy for bnkruptcy risk contins vlue-relevnt informtion beyond nlysts forecsts in 31

32 forecsting next period residul income. Tble 7. Residul Income Dynmics with Bnkruptcy Risk Excluding Anlysts Forecsts N ω 10 ω 11 ω 12 ω 14 Averge R 2 O95: x j,t x j,t 1 = ω B 10,t + ω 11,t + ε j,t 1 B t. j,t 1 Trditionl Liner Model Estimtions *** (0.09) (11.37) BK1: x j,t Z Score x j,t 1 BK j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 14,t + ε j,t 1 B t. j,t 1 BK proxied by Z-Score Estimtions *** (0.40) (11.55) (-0.62) BK2: x j,t Merton x j,t 1 BK j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 14,t + ε j,t 1 B t. j,t 1 BK proxied by Loss Given Defult in Merton Model Estimtions *** * (0.58) (11.72) (-2.00) Notes: Tble 7 shows the coefficients nd R squre of the residul income dynmics excluding nlysts forecsts in vrious BK models bsed on Fm-Mcbeth regression from 1995 to Following Choi et l. (2006), the most extreme 1% of the deflted vribles re winsorized in estimting the LID prmeters. Averge R 2 is the verge R sttistic nd t vlue (in prentheses) is bsed on Newey-West corrected Fm- McBeth stndrd errors. The superscripts *, **, *** respectively indicte significnce t the 10%, 5% nd 1% level. 32

33 Tble 8. Residul Income Dynmics with Bnkruptcy Risk Beyond Anlysts Forecsts N ω 10 ω 11 ω 12 ω 14 Averge R 2 O95 with Anlysts Forecsts: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t + ε j,t 1 B t. j,t 1 Trditionl Liner Model with nlysts forecsts Estimtions *** *** *** (-8.50) (18.22) (14.48) BK1: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 Z Score BK j,t 1 + ω B 14,t j,t 1 B j,t 1 + ε t. BK proxied by Z-Score Estimtions *** *** *** (-7.50) (17.95) (15.03) (-0.68) BK2: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 Merton BK j,t 1 + ω B 14,t j,t 1 B j,t 1 + ε t. BK proxied by Loss Given Defult in Merton Model Estimtions *** *** *** ** (-9.03) (17.78) (14.86) (-2.16) Notes: Tble 8 shows the coefficients nd R squre of the residul income dynmics including the other informtion vrible (nlysts forecsts) in vrious BK models bsed on Fm-Mcbeth regression from 1995 to Following Choi et l. (2006), the most extreme 1% of the deflted vribles re winsorized in estimting the LID prmeters. Averge R 2 is the verge R sttistic nd t vlue (in prentheses) is bsed on Newey-West corrected Fm-McBeth stndrd errors. The superscripts *, **, *** respectively indicte significnce t the 10%, 5% nd 1% level. 33

34 4.1.3 LID with Growth Potentil nd Bnkruptcy Risk To test the dditionl informtion content of growth potentil nd bnkruptcy risk, we include Kester s PVGO s the growth potentil proxy nd Merton s LGD s the bnkruptcy risk proxy beyond nlysts forecsts in the residul income dynmic. The test is bsed on ll vilble UK dt from 1995 to Tble 9 shows the residul income regression results on the trditionl liner model with nlysts forecsts, the model with GP, the model with BK nd the model with both GP nd BK. It cn be observed tht the coefficients of explntory vribles in ech model s residul income dynmics re significnt. Among which, the lgged residul income nd other informtion vrible re significnt t the 0.01 level in ll cses. For the model with both GP nd BK, the coefficient on growth potentil is nd the coefficient on bnkruptcy risk is which suggests tht growth potentil hs significntly positive impct while bnkruptcy risk presents significntly negtive impct in forecsting next period residul income beyond nlysts forecsts. In terms of explntory power, the trditionl liner model presents Fm-Mcbeth verge R squre of It should be further noted tht including growth potentil increses the R squre to 0.471, including bnkruptcy risk increses the R squre to 0.457, nd incorporting both the growth potentil nd bnkruptcy risk increses the R squre to It cn be inferred from these results tht incorporting both growth potentil nd bnkruptcy risk provides dditionl informtion content beyond lgged residul income nd nlysts forecsts in the residul income dynmic. As such, these findings suggest tht incorporting informtion with option chrcteristics (the growth option from Kester nd the bnkruptcy risk from Merton) into the residul income dynmic beyond nlysts 34

35 forecsts does indeed provide incrementl usefulness in predicting future residul income. Tble 9. Residul Income Dynmic with Growth Potentil nd Bnkruptcy Risk Beyond Anlysts Forecsts N ω 10 ω 11 ω 12 ω 13 ω 14 Averge R 2 O95 with Anlysts Forecsts: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t + ε j,t 1 B t. j,t 1 Trditionl Liner Model with nlysts forecsts Estimtions *** *** *** GP: x j,t (-6.76) (17.14) (13.64) x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 GP proxied by PVGO of Kester (1984) Kester GP j,t 1 + ω B 13,t j,t 1 Estimtions *** *** *** *** BK: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 BK proxied by Loss Given Defult in Merton Model B j,t 1 + ε t. (-8.81) (11.46) (8.70) (4.87) Merton BK j,t 1 + ω B 14,t j,t 1 B j,t 1 + ε t. Estimtions *** *** *** ** Model with GP nd BK: x j,t x j,t 1 v j,t 1 = ω B 10,t + ω 11,t + ω j,t 1 B 12,t j,t 1 (-6.77) (16.63) (14.04) (-2.58) Kester GP j,t 1 + ω B 13,t j,t 1 B j,t 1 Merton BK j,t 1 + ω 14,t B j,t 1 GP proxied by PVGO of Kester (1984), BK proxied by Loss Given Defult in Merton Model Estimtions *** *** *** *** ** ε t. (-8.82) (11.33) (8.90) (4.81) (-2.46) Notes: Tble 9 shows the coefficients nd R squre of the residul income dynmics in vrious models bsed on Fm-Mcbeth regression from 1995 to Following Choi et l. (2006), the most extreme 1% of the deflted vribles re winsorized in estimting the LID prmeters. Averge R 2 is the verge R sttistic nd t vlue (in prentheses) is bsed on Newey-West corrected Fm-McBeth stndrd errors. The superscripts *, **, *** respectively indicte significnce t the 10%, 5% nd 1% level. 35

36 4.2 Results on Vlution Performnce Following on from the previous section, we continue to test whether including GP nd BK in the residul income dynmic beyond nlysts forecsts improves the equity vlution performnce. We use Kester s PVGO s the growth potentil proxy nd Merton s LGD s the bnkruptcy risk proxy. To estimte the equity vlue, the yerly regressed LID prmeters re used to clculte the cross-sectionl theoreticl implied coefficients in equity vlution (vrious α in ech vlution model). These coefficients re pplied to ll the firms with dt necessry to clculte the estimted mrket vlue Out of Smple Forecst Bis nd Forecst Accurcy Tble 10 shows the results on vlution errors regrding the trditionl liner model, the model with GP, the model with BK nd the model with both GP nd BK. It cn be observed from this tble tht the model with only GP nd the model with both GP nd BK present less forecst bis thn the other models, with the men nd medin PVE of nd for the model with GP, nd the men nd medin PVE of nd for the model with GP nd BK. The negtive men nd medin PVE in the trditionl model suggests tht the O95 with nlysts forecsts underestimtes the equity vlue. This finding is consistent with Dechow et l. (1999) nd Gregory et l. (2005). In terms of the forecst ccurcy, the model with GP lone nd the model with both GP nd BK provide better forecst ccurcy then the other models. More specificlly, the medin APVE of the model with GP nd the medin APVE of the model with both GP nd BK re both centered round 0.47, lower thn the 0.48 medin APVE of the trditionl O95 with nlysts forecsts. The centrl tendency of the model with GP is 14.86% while the centrl tendency of the 36