A biplot perspective on market-based valuations in an emerging market

Transcription

1 A biplot prspctiv on markt-basd valuations in an mrging markt Nil l Roux (Dpt Statistics & Actuarial Scinc) Soon Nl & Wilna Bruwr (Dpt Accountancy) Stllnbosch Univrsity, South Africa SASA Confrnc, Rhods Univrsity, Grahamstown, Octobr 28-30,

2 Singl Factor Multipl Modl (SFM) V it t = λ α it V it λ t α it Actual quity valu of ntity i at tim t Actual quity-basd multipl at tim t Spcific actual valu drivr at tim t Aim: Quantify ability of abov quation to approximat actual shar prics on th JSE 3

3 SFM (continu) Lt Thn λˆpt V ˆ it stimatd pr group multipl at tim t = ˆ λ pt α rprsnts stimatd quity valu and ε it Vit V = ˆ V is takn as th valuation rror it it it 4

4 SFM (continu) Th valuation rror ε it Vit V = ˆ V it it and th quantitis it contains ar dfind for EQUITY-BASED MULTIPLES Similar formula ar dfind for ENTITY-BASED MULTIPLES 5

5 Composit Multipls Modls Equity valu stimat givn by ˆ λ jpt α jit 0 2 Vˆ it is jth singl factor quity valu stimat to b stimatd such that k j= 1 k = β j= 1 β1 it, β it,..., βkit 1 β jit = 1 jit ˆ λ jpt α jit st of wights 6

6 Data Slction Entitis listd on JSE 2001 to 2010 Yar Data xtractd from McGrgor BFA Databas: Markt Pric Variabls MCap Markt Capitalisation MVIC Markt Valu of Invstd Capital Valu Drivrs: 16 Groupd as: Earnings-basd; Rvnu-basd; Asst-basd; Cash - Flow-basd 7

7 Data Slction: Valu Drivrs GP Gross Profit EBITDA Earnings Bfor Intrst, Tax, Dprciation and Amortisation EBIT Earnings Bfor Intrst and Tax PBT Profit Bfor Tax PAT Profit Aftr Tax HE Hadlin Earnings TA Total Assts IC Invstd Capital BVE Book Valu of Equity R Turnovr CgbO Cash gnratd by Oprations NCIfOA Nt Cash Inflow from Oprating Activitis NCIfIA Nt Cash Inflow from Invstmnt Activitis OD Ordinary Dividnds FCFF Fr Cash Flow to th Firm FCFE Fr Cash Flow to Equity 8

8 Data Slction: Gnral Industry Classification rcordd: IND: Industry SUP: Suprsctor SEC: Sctor SUB: Subsctor Critria for slction Multipls must b positiv Entity must hav 3 or mor yars of pos multps Industry catgory at last 4 ntitis Obsrvations outsid 1 st to 99 th prcntils of poold obsrvations rmovd 9

9 Data Slction: Obsrvations Multipls: Diffrnt Population Sizs Vary btwn 759 and ach Total numbr of obs: Rprsntation of Obsrvations usd: 71% of total numbr of listd ntitis on JSE 91% of markt capitalisation 10

10 Slcting th Pr Groups Basd on Industry Classification: IND, SUP, SEC, SUP Out-of-sampl pr group multipl for ntity Estimatd: Harmonic Man of rmaining ntitis in industry classification group 11

11 Rsarch hypothss 1. Multipls with pr group slction basd on narrowr industry classifications offr mor accurat valuations 2. Multipls with pr group slction basd on a combination of valuation fundamntals offr mor accurat valuations 3. Equity-basd valuation modls offr mor accurat valuations than ntity-basd valuation modls 4. Equity-basd valuation modls offr mor accurat valuations whn constructd on arnings-basd valu drivrs than using asst-, rvnu-, dividnd- or cash flow-basd valu drivrs. 5. Valuation accuracy of quity-basd multipls is industry-spcific 6. Industry-spcific composit multipls modls offr mor accurat valuations than corrsponding singl factor multipls modls 12

12 What is a biplot? Simultanous graphical rprsntation of th rows and th columns of a data matrix Approximation of a data matrix in 1D, 2D or 3D Gnralizing a scatttrplot Rows as points; columns as calibratd axs 14

13 What is a monoplot? Gowr t al (2011) Approximation of a symmtric matrix.g. corrlation matrix 15

14 1. Narrowr industry classifications offr mor accurat valuations Narrowing byond SEC adds littl Multipls hav diffrnt optimal industry classifications 16

15 P/EBITDA P/PBT P/EBIT FRE 0.25 FRE 0.15 N=2393 N=2376 N=2277 N= FRE 0.25 FRE 0.15 N=2215 N=2198 N=2099 N= FRE 0.25 FRE 0.15 N=2330 N=2313 N=2215 N=1789 IND SUP SEC SUB P/PAT IND SUP SEC SUB P/GP IND SUP SEC SUB P/TA FRE 0.25 FRE 0.15 N=2173 N=2157 N=2059 N= FRE 0.25 FRE 0.15 N=2261 N=2228 N=2097 N= FRE 0.25 FRE 0.15 N=2747 N=2727 N=2650 N=2224 IND SUP SEC SUB IND SUP SEC SUB IND SUP SEC SUB P/IC P/OD P/R FRE 0.25 FRE 0.15 N=2745 N=2725 N=2649 N=2223 IND SUP SEC SUB FRE 0.25 FRE 0.15 N=1721 N=1700 N=1539 N=1202 IND SUP SEC SUB FRE 0.25 FRE 0.15 IND SUP SEC SUB 17 N=2441 N=2421 N=2318 N=1884

16 P/ NCIfOA P/BVE P/FCFE FRE 0.25 FRE 0.15 N=2002 N=1987 N=1888 N= FRE 0.25 FRE 0.15 N=2467 N=2447 N=2356 N= FRE 0.25 FRE 0.15 N=1413 N=1401 N=1277 N=941 IND SUP SEC SUB IND SUP SEC SUB IND SUP SEC SUB P/HE P/ CgbO P/FCFF FRE 0.25 FRE 0.15 N=2225 N=2209 N=2110 N= FRE 0.25 FRE 0.15 N=2217 N=2201 N=2060 N= FRE 0.25 FRE 0.15 N=1586 N=1574 N=1427 N=1053 IND SUP SEC SUB IND SUP SEC SUB IND SUP SEC SUB P/ NCIfIA FRE 0.25 FRE 0.15 N=1144 N=1129 N=1042 N= IND SUP SEC SUB

17 2. Mor accurat valuations with pr group slction using combination of valuation fundamntals Bnchmark valuation fundamntal.g. TA Prgroup for Targt company: All companis with TA within 30% of that of Targt company PCA biplot: Valuation rrors for ach PGV rsulting from diffrnt Multipls 19

18 PCA Biplot (Quality=89%) Multipl Prdictivity GP 0.80 EBITDA 0.90 EBIT 0.87 PAT 0.98 PBT 0.99 HE 0.96 TA 0.95 IC 0.95 BVE 0.74 R 0.78 CgbO 0.72 NCIfOA 0.96 NCIfIA 0.99 OD 0.57 FCFE 0.99 FCFF

19 Corrlation Monoplot of Multipls 21

20 Corrlation Monoplot of PGVs 22

21 3. Equity-Basd Multipls dlivr mor accurat valuations than Entity-Basd Multipls Valu drivrs Earnings Assts Rvnu Cash flow MPV MCap or MVIC GP TA R CgbO EBITDA IC FCFF EBIT 23

22 FCFF GP CgbO (12.86%) N=1430 N=1428 * (11.88%) N=2284 N= (11.22%) N=2057 N=2055 * Entity Equity Entity Equity Entity Equity R EBIT EBITDA (9.99%) N=2316 N= (8.52%) N=2216 N= (7.48%) N=2278 N=2276 Entity Equity IC Entity Equity TA Entity Equity (5.55%) N=2647 N=2643 Entity * Equity (2.82%) N=2648 N=2644 Entity Equity 24

23 4. Earnings-basd Valu Drivrs outprform Asst-, Rvnu-, Dividnd- or Cash Flow-basd Valu Drivrs for Equity-basd Multipls Modls Poold valuation accuracy of th fiv valu drivr catgoris Valuation rrors Earnings Dividnds Assts Rvnu Cash flow 25

24 4. Earnings-basd Valu Drivrs (continu... ) Biplot: Multidimnsionality takn into account Quality: 96.2% Axis Prdictivitis: 86% to 99.9% 26

25 4. Earnings-basd Valu Drivrs (continu... ) First PC: Optimal On-Dimnsional Scaling of Rlativ Valuation Prformanc Earnings Dividnds Assts Rvnu Cashflows Scal Valuation Accuracy within Earnings Valu drivr Catgory * * * * * * N=2064 N=2043 N=2015 N=2161 N=2229 N=2235 HE PBT PAT EBIT EBITDA GP 27 (0.00%) (22.29%) (24.64%) (27.99%) (33.61%) (48.92%)

26 4. Earnings-basd Valu Drivrs (continu... ) Biplot: Prformanc of Individual Valu Drivrs ovr Study Priod Quality: 93.6% Axis Prdictivitis: 82% to 99% 28

27 4. Earnings-basd Valu Drivrs (continu... ) First PC: Optimal On-Dimnsional Scaling of Rlativ Valuation Prformanc of all 16 Valu Drivrs HE PBT PAT EBIT EBITDA CgbO OD TA BE IC NCIfOA GP R FCFF FCFE NCIfIA Scal Earnings Cash flows Dividnds Assts Rvnu BVE TA IC Scal NCIfOA FCFF GP R Scal

28 4. Earnings-basd Valu Drivrs (continu... ) Monoplot: Corrlations btwn th Yars Axis Prdictivitis: 92% to 100% 30

29 5. Valuation Accuracy of Equity-basd Multipls Industry-spcific 22 Sctors 10 PGVs Quality: of Display 75% 31

30 5. Industry-spcific (continu... ) Monoplot: Corrlations btwn th 10 PGVs 32

31 5. Industry-spcific (continu... ) 22 Sctors 16 Valu Drivrs Quality: of Display 63% 33

32 5. Industry-spcific (continu... ) Monoplot: Corrlations btwn th 16 Valu Drivrs 34

33 What Larnd from Invstigating H1 to H5? Modls to Look for: Optimal Industry-Spcific Composit Multipls Equity-Basd 35

34 Sarch for Optimal, Industry-Spcific, Equity- Basd, Composit Multipls Modls Starting Point: Equity-Basd SFMs MPV MCap Valu Drivrs Earnings Assts Dividnds Cash flow PBT BVE OD NCIfOA PAT HE NCIfIA FCFE Nxt: Optimally Wightd Equity-Basd SFMs with Vˆ it = k j= 1 ˆ β λ jt jpt α jit (0 β, 1t β,..., β 1; = 1) th Wightd Sum of k Singl-factor Equity valu prdictions 2t kt k j= 1 β jt 36

35 Finding th Optimal Wights First Stp St Minimiz d i w.r.t. β i= 1 using function lp from R packag lpsolv with qual starting wights Scond Stp d n i V = ˆ i V V i i Us optimum wights from Stp I in gosolnp of R packag Rsolnp to finally optimiz = V i m β V i i V 1 m1β V2 m1β Vn m1β Minimum Mdian,,, Constraintd β V1 V2 Vn 37

36 Nxt: Optimally Wightd Equity-Basd SFMs Sctors: 22 Wights z 38

37 Composits 2010 Valu Drivrs Earnings-basd Asst Dividnd Cash flow-basd PBT PAT HE BVE OD NCIfOA NCIfIA FCFE Basic Matrials Initial Optimal I Optimal II Consumr Goods Initial Optimal I Optimal II Consumr Srvics Initial Optimal I Optimal II Financials Initial Optimal I Optimal II Industrials Initial Optimal I Optimal II Tchnology Initial Optimal I Optimal II

38 Biplot: Basic Matrials z 40

39 Biadditiv Intraction biplot: Basic Matrials z 41

40 Biadditiv Modl: Anova Tabl ANOVA TABLE Sourc Sum_of_squars DF Man_ss 1 Row main ffct Column main ffct Intraction Man Total (Uncor) Row:Column Intraction Multiplicativ trm 1 z Multiplicativ trm Multiplicativ trm Multiplicativ trm Multiplicativ trm Multiplicativ trm Multiplicativ trm Multiplicativ trm Man ss intraction: Man ss rror: F.intraction: P.valu=

41 WS Nl, BW Bruwr & NJ l Roux. (2013). Th impact of industry classification on th valuation accuracy of multipls in th South African capital markt, Intrnational Businss & Economics Rsarch Journal, 12:1, WS Nl, BW Bruwr & NJ l Roux. (2013). Equity- and ntity-basd multipls in mrging markts: vidnc from th JSE scuritis xchang, Th Journal of Applid Businss Rsarch, 29:3, WS Nl, BW Bruwr & NJ l Roux. (2013). Th valuation prformanc of quitybasd multipls in South African contxt. Risk govrnanc and control: financial markts and control, 3 (3), WS Nl, BW Bruwr & NJ l Roux. (2014). An mrging markt prspctiv on pr group slction basd on multipls. Applid financial conomics, 24(9), WS Nl, BW Bruwr & NJ l Roux. (2014). An mrging markt prspctiv on ky valu drivrs in th valuation of cross-bordr transactions into South Africa. Economics, managmnt and financial markts, (9)4. [Forthcoming] WS Nl, BW Bruwr & NJ l Roux. (2014). Prcision, consistncy and bias in mrging markts. Journal of conomics and bhavioural studis, 6(5), THANK YOU FOR YOUR ATTENTION 43