The appendix presents a cash flow forecasting model that is

Transcription

1 Free Cash Flow and Shareholder Yield: New Prioriies for he Global Invesor By William W. Pries and Lindsay H. McClelland Copyrigh 27 by William W. Pries and Lindsay H. McClelland APPENDIX Coninuous-Time Free Cash Flow Valuaion Framework The appendix presens a cash flow forecasing model ha is currenly under developmen a Epoch Invesmen Parners.* The following analysis will provide some quaniaive deails abou our securiy selecion process. Free Cash Flow Valuaion and he Epoch Core Model The purpose of securiy analysis for invesing in a firm is o research he risk and reurn characerisics of he underlying business process employed by he firm o generae profi. Following he Modigliani-Miller Theory and Meron s srucural model, a firm is reaed as an ineres rae derivaive whose payoff is coningen upon is underlying business risk; is capial srucure is designed o maximize he shareholder value; is enerprise valuaion can be deermined by a replicaing sraegy based on no-arbirage assumpion. For firms compeing in *We are graeful o he Epoch Invesmen Parners quaniaive research eam for providing his analysis, paricularly Thomas Yiien Hu. 143

2 144 Appendix he same business environmen, he rue valuaion merics ha differeniae hem are he firm s disribuion policy and invesmen sraegy wih respec o is cash flow. We recognize here are only five opions 1 a firm can explore wih is excess cash in order o maximize shareholder value: 1. Pay cash dividends; 2. Repurchase ousanding shares; 3. Reduce ousanding debs; 4. Engage in mergers & acquisiions; 5. Reinves in inernal projecs wih favorable reurns. By his consrucion, free cash flow, or he cash available for disribuion o invesors afer all planned capial invesmen and axes, is he key driver in assessing he value of a firm. To wi, a free cash flow discoun model posulaes ha he firm value V can be derived by discouning a perpeual free cash flow generaed by he firm as follows: FCP V = S + D = IÊ ρ f, T, ( ( ) R M ) where S and D represen he value of he firm s equiy and deb, and IÊ denoes a valuaion measure adjused by he firm s weighed average cos of capial (WACC), ρ, given by ρ= k S + ( τ ) S + D k D S + D E D 1 where τ is he effecive ax rae and k E and k D denoe he firm s cos of equiy and cos of deb, whose value can be esimaed from marke-observable parameers f (, T) and R M, he risky

3 Appendix 145 corporae yield curve and he benchmark reurn via mulifacor 2 Capial Asse Pricing Model (CAPM). If hese parameers can be reliably exraced from liquid marke daa, hen securiy analysis is essenially forecasing he firm s fuure free cash flow and conemplaing he viabiliy of he firm s capial srucure. Principal invesmen and rading decisions can hus be made according o such a forecas. An invesor can express his or her views on he firm s business oulook by posiioning in an appropriae ranche in he firm s capial srucure via rading relaed financial insrumens. I has been a well-known fac ha forecasing free cash flow using publicly available informaion is hard due o he difficuly in disinguishing capial expendiure for business expansion and essenial mainenance. For firms going hrough special siuaions such as leveraged recapializaion, leveraged buyous, spin-offs, carve-ous, financial disress, and IPOs, or experiencing regime shif in he compeiive environmen, he free cash flow implied by he financial saemens and pricing informaion observed in he markes mus be used wih cauion. Recognizing ha securiy analysis is more of an ar han science, we have developed he Epoch Core Model: an evolving proprieary research plaform ha blends he fundamenal insighs and quaniaive rigor for forecasing free cash flow. In he Epoch Core Model, he forecasing procedure is buil ino he selecion algorihm ha seeks o idenify firms ha are forward cash-rich and exhibi financial flexibiliy in exploring sraegic real opions. A firm s common sock will be issued a favorable rank by he Core Model if i shows: 3 High median forecas of earnings per share for he nex welve monhs; High dividend yield for he las welve monhs; Sable rend in capial expendiure for he las welve quarers;

4 146 Appendix Low deb-o-equiy raio; Low dividend payou raio. This procedure, hough qualiaively feasible, produces no measurable quaniy relaed o he firm s free cash flow. To enhance his procedure, we propose a forward free cash flow model based on forecasing a firm s revenues. By saring from he op line, we believe his mehodology provides a scalable framework for analyss o issue recommendaions based on forecas of he firm s business risk and is free cash flow implicaions given he firm s incumben capial srucure. Free Cash Flow Forecasing Model: A Coninuous-Time Approach We define a firm s free cash flow as follows: 4 R c : firm'srevenuesaime ; + c R : firm's operaing overheads, assumed linearly dependen on revenues; 1 τ : effecive ax rae; DA : depreciaion and amorizaion; ΔNWC : increase (decrease) in ne working capial; CapEx : capial expendiure; ( )( FCF = 1 τ R c c R 1 ) + DA ΔNWC CapEx EBIT ( )( ) ( ) + Δ = 1 τ 1 c R 1 τ c DA NWC CapEx = α+ β R 1 We assume ha he fixed porion of he firm s operaing overhead c and oher accrual iems can be approximaed by a consan a for analyical racabiliy.

5 Appendix 147 By decomposing a firm s free cash flow in his form, we have separaed is risk exposure ino a sysemic componen, βr, and an idiosyncraic componen, α. The firm s enerprise value under free cash flow discoun model given is WACC hen becomes V α = ( 1 τ) k D βr + ρ g where g is he growh rae of revenues. We discoun he fixed componen of free cash flow a he afer-ax cos of deb because his componen is assumed o have no exposure o marke risk and can be collaeralized o service he firm s deb issuance. To deermine R, he revenue process of a firm, we assume i obeys geomeric Brownian moion wih consan 5 drif g and consan volailiy σ under suiable probabiliy measure: R = R + grds RdW s + σ ˆ s s or in sochasic differenial equaion form: dr R = gd +σdwˆ whose soluion is given by 1 2 R = R exp g W σ + σ ˆ 2

6 148 Appendix hanks o Iô s lemma. Since he Wiener process Wˆ is normally disribued wih mean and variance, we can esimae g and σ by using Mean and Var ln R ln R = gd =σ 2 d. R R d d Thus we can derive a discreized model of R in he following form: Δ R = R R = grδ + σr Δ +Δ where denoes a series of independen and idenically disribued normal random variables. We hus have he Δ-ahead predicor of he revenue process a +Δ condiional on he observed revenue a ime : ( ) + Δ R = 1 + g Δ R σ R +Δ where Δ is he naural reporing frequency of he firm s financials in erms of year fracion, i.e., Δ = 1 4 for quarerly and 1 12 for monhly revenue series. The Δ-ahead predicor of he firm s free cash flow process is herefore FCF +Δ = α+ βr +Δ ( ) + Δ = α+ β 1 + gδ R βσr and is expeced forward enerprise value under he WACCadjused probabiliy measure:

7 Appendix 149 Vˆ = IEˆ ( FCF ) ρ +Δ +Δ ( 1 τ) kd = α e d + β e The nex key sep is o find he appropriae discoun rae given he firm s business risk. We briefly ouline he mehodology o esimae hese parameers from marke informaion in he following secions. Consruc Defaul-Free Discoun Curve α = ( 1 τ) k D βrˆ +Δ + ρ g We boosrapp he discoun facors from marke prices of insrumens raded in he iner-bank markes: (i) cash insrumens in money markes (1 day o 9 monhs); (ii) ineres rae fuures (e.g., Eurodollar fuures) conracs (6 monhs o 2 years); (iii) ineres rae swap conracs (1 year o 3 years). Cash securiies are quoed on a simple spo rae basis f(, ). The quoed price simply indicaes he annualized simple ineres rae he borrower will pay o he lender according o Ac/36 day-coun convenion. The discoun facor is given by 1 D(, ) = 1 f, + ( ) ρ IÊ R +Δ 36 ( ) d where is he enor of he securiies. Eurodollar fuures conracs are quoed on a simple forward rae basis f(, T, T +δ) and sele according o he Inernaional Moneary Markes daes, i.e., he 3rd Wednesday of March, June, Sepember, and December. The lender (fuures buyer) can agree o place funds wih he borrower (fuures

8 15 Appendix seller) during a fuure period [T, T +δ] (e.g., for hree monhs beween June 21, 26 and Sepember 2, 26 for EDM6 Eurodollar fuures conrac) a a cerain annualized simple ineres rae f(t, T +δ). The price quoed needs o be adjused for forward rae convexiy. The calculaion formula is given by Convexiy f ( T, T + δ) = 1, P quoed 1, The discoun facor implied is herefore (Ac/36 daycoun) ( ) D, T D(, T + δ) = 1 + f T, T + δ ( ) δ 36 Ineres rae swap conracs are quoed in swap raes, which is he fixed rae he Payer (Receiver) needs o pay (receive) in a swap ransacion o receive floaing rae paymen (e.g., 3-monh LIBOR quarerly money) from he Receiver(Payer) on a noional amoun ill conrac mauriy. A rade incepion he swap rae is so deermined such ha he ransacion has ne presen value of zero. I can be shown ha he swap rae of a liquid vanilla swap can be deermined by he following relaionship: ( ) = s, T, T n ( ) ( n) DT (, i) D, T D, T n δ i = 1 n where is he valuaion dae of a swap saring a T and erminaes a T n wih paymen dae T 1, T 2,..., T n 1 and δ n := T i T i 1 is he enor beween paymen daes according o given day-coun convenion.

9 Appendix 151 Modeling Defaul Probabiliies and Corporae Credi Spread To esimae a firm s credi risk, we place ourselves on a filered probabiliy space Ω, F, ( ), IP and a fixed ime horizon T*. ( F ) Consider he hazard rae {h(, ω)} T* as a non-negaive, coninuous, adaped sochasic process. The defaul ime is defined as a random sopping ime { } ( ) Δ = ( ) τ ω inf, T * : h s, ωds θ where θ is an exponenial random variable wih rae 1, independen of he hazard rae process. The survival probabiliy S() unil ime is given by ( ) Δ = ( ) = S IP τ > IE 1 { τ > } If we assume h() o be piecewise consan (or consan if we are courageous), hen he survival probabiliy simplifies o S exp( h u du ) ( ) = ( ) and he defaul arrival becomes an inhomogenous Poisson process. If h is consan, hen he survival ime follows an exponenial disribuion wih parameer h and he defaul arrival is homogenous Poisson. These assumpions will no normally hold in pracice bu can serve as a reasonable approximaion for analyical racabiliy. Under his model we can esimae a firm s credi spread from is credi defaul swap (CDS) conracs. CDS is a bilaeral conrac ha enables an invesor o buy proecion agains he

10 152 Appendix risk of defaul of an asse issued by a specified reference eniy. The Proecion Buyer pays a running premium (CDS spread) and receives coningen paymen (loss given defaul, LGD) when a cerain credi even 6 occurs, and mus deliver he defauled deliverable obligaion referenced by he CDS o he proecion Seller, who in principle can sell he defauled obligaion a recovery value. Le 1, 2,..., M be he paymen daes for he premium leg. The proecion buyer mus pay his cash flow unil defaul occurs, herefore he presen value of he premium leg is ( ) = ( ) PL N s δ IE D, 1 cds m m { τ > m } m where T = M is he CDS mauriy, δ m : = ( m m 1 ) he enor beween paymens, N he noional amoun and D(, m ) he discoun facor beween [, m ]. The presen value of he defaul leg is DL ( ) = N IE ( R ( )) D ( ) { T 1 ζ, τ, τ 1 τ } LGD where R(ζ, τ) is he recovery value, which may be dependen on defaul ime τ and oher economic or legal facor ζ. In pracice we ofen assume R o be consan. The fair CDS spread is found by equaing he wo legs such ha he ransacion has ne presen value of zero a incepion: s cds IE ( 1 R) D(, τ) 1 { τ T} = δ IE D m (, m) 1 m { τ> } m

11 Appendix 153 In pracice we are given he informaion in he form of a CDS curve so ha we may evaluae he mark-o-marke value of a CDS via boosrapping procedure 7 in order o back ou he implied survival probabiliies a each paymen dae. Because of is increasing populariy and liquidiy, CDS has become acceped as he lead indicaor of a firm s credi oulook. This approach allows us o build he implied hazard rae as well as a firm s credi curve f (, T) ha can be used as proxy o infer is cos of deb. We hen combine his esimae wih he firm s cos of equiy based on CAPM o derive is weighed average cos of capial for valuaion. Implemenaion We consruc a simple screening algorihm in our proprieary research sysem o implemen his forecas procedure as follows: Esimae g and σ using repored quarerly LTM revenues over rolling five-year horizon; Derive curren free cash flow and esimae α and β using he mos recen LTM revenues; Compue 1Q-ahead predicor of free cash flow using he esimaed parameers. To evaluae he effeciveness of his forecas procedure, we FCF +Δ calculae he forward free cash flow yield, i.e., Marke Value as well as he spo free cash flow yield for firms in our coverage universe and perform backesing over he ranked universe 8 o see if i has any predicive power for he subsequen sock reurns. We repor he informaion coefficien 9 and -saisics over various reurn horizons as follows:

12 154 Appendix FCF Yield IC/T-Sa Spo Forward 1M.5/3.2.5/3. 3M.8/4.67.8/4.6 6M.11/ / M.14/ /7.13 We can see he spo and he forward FCF yield have very similar predicive power; all are saisically significan a 5 percen level. This is no surprising because he forward free cash flow is inferred from he spo free cash flow and he mos recenly repored revenue. Since he forecas horizon is one quarer, he FCF process is unlikely o diffuse oo far from is spo level. The correlaion beween he spo FCF yield and he forward FCF yield is.96 over he backesing ime frame, corroboraing he above empirical observaion. Fuure Work The need for improvemen is obvious. By modeling he firm s revenues as a lognormal process, we are ignoring he nonsaionary effec inheren in he economic environmen. A robus FCF forecas model mus ake ino consideraion he sensiiviies of he firm s business process o he macroeconomic parameers. Also, he linear relaionship beween revenues and free cash flow will break down 1 during corporae resrucuring and regime shif in he compeiive environmen. To capure hose effecs we may consruc a mulivariae model based on balance shee iems. Poenial problems exis due o he difficuly in specifying coheren disribuions for hose iems and over-fiing migh be hard o avoid. For his we mus rely on experienced human judgmen o idenify caalyss likely o drive sock price movemen. Finally, o furher

13 Appendix 155 check is viabiliy as in any derivaives pricing problem, he model should be able o calibrae o he firm s enerprise value observable in he marke, given he cos of deb (esimaed from is liquid deb securiies or CDS curve) and he cos of equiy (esimaed under CAPM assumpions using proper equiy benchmark). We defer he calibraion and model enhancemen seps o fuure research. The free cash flow valuaion framework presened here, hough idealisic, provides he foundaion for evaluaing he firm s fair value consisen wih he heory of modern corporae finance. By adoping a parsimonious approach, our esimaion mehodology allows qualiaive judgmen o be incorporaed ino quaniaive framework in a robus manner. Furhermore, when evaluaing he firm s enry/exi opions, as well as oher scenarios under special siuaions, his model can be more powerful han he radiional earnings-based mehodology.