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# Class Note for FINA 221 at GW (2)

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Date Created: 02/07/15

PrintScreen wwwjansfreewarecom fgt Capiche Sachlis39s Lecture Notes for Fin 274 These notes link to specific topics Use the Syllabus Menu for all assignments Course 1ntro Focus syllabus hardcopy amp ElFian Conceptual Causal Tree Topic 1 Valuation Theory 11 Purpose To 1 PO must understand determinants of P0 in eqs 10 in equation panel WhyOwner 12 Perspective Four quotStepsquot to estimate Current Market Value CMV of an asset 1 Estimate E0 CFtgt0 CFt lt 0 gt cash outflow else cash in Prob distn 2 quot E0 SECFtgt0 or risk of CF stream by year of CF stream 3 Set RR Rf RiskPrmo risk premfrisk estimate above risk aversion 4 Calc CMV PV eq 1 in equation panel 13 PV CMV buyer39s view 1FF if and only if MktValValGen NPVvs1RR ltr numerical proof a Recoup cost CMV PV paid for asset b ER eq 3 general eq 42 for stock RR eqs 4 in general amp 47 via CAPM c Apply to Stocks 14 Mechanically 1dentify appropriate variables for a common stock for n CF amp RR in eq 1 Two Viewpoints 15 1 Whole market n infinity forever for quotgoing concernquot 25 yrs Ok in practice CF CD inflow amp CS outflow eqs 22 a 24 RR RRo quot0quot for owners eqs47 via CAPM MktValwhlmkt Gives eqs 10 on perishare basis gCDt embedded varies yearfbyfyear except eq 10a 16 1F gCDt amp RRo constant forever eq l0 rgt eq 10a Gordon model Tradeoff of simplicity vs validity Goranod amp pchplot 17 Explicit cash OUTflow mkt to firm rgt eq 10b lt7 FUNDAMENTAL ThrySim 18 2 Individual n 39HP39 yrs holding pd gt don39t hold forever MktERo1ndMkt CF CDt to year HP then plus PHP gt div39s 39cap gains39 POGenPlot ltr 19 Gives eq 10c but PHP PVfuture cash flows after year HP from buyer39s viewpoint 110 Conclusion 1 and 2 above give same P0 gt 1nternal consistency We use eq 10b 111 Security analysts tend to use 2 above with HP between 1 amp 5 yrs then eq 10a at HPth year 112 Real meaning of a quotGquotrowth stock ValngG ltfffff 113 Use eq 10b amp add and subtract EATSO amp break into two pieces cont39d current EATSO gt forever and new future CHANGEd CDt39s Via new invest fgt eq 10d CMVcont39d current ops real quotGquotrowth 114 CMV of expected future quotgquotrowth in size is quotGquot PVNPV39s of future new invest ValngGNPVisG amp quotGquot NPVquotgquot can be lt 0 even though quotgquotsales profits assets gt 0 Four ways 115 Wall Street measures gt compare over firms GNPVMkBk amp AllSumPlot Are just NPV disguised PriceEarnings PE Just take any eq10d formulation amp divide by EATSShO 1RRo NPVEATSShO MarketBook MktBook 1 NPVOE on balance sheet mvbvplot EVA EATS a RRo OE on balance sheet gt NPV PVEVA RRo in eq 2 Vary over firms due mostly to diff39s bt future quotriskquot via RRo and quotgquotrowth gt quotGquot NPV in eq 10d 116 From Accounting to OwnerltltfgtgtFirm Cash Flows r The numerator of P0 in eq 10b OwnFrmCF ltr Combine 2 acct eqns 1S and SCF to get E50 CD a CS fgt eq 24 Eqs 10 PO PVeq 24 E50 flows by year discounted at eq 47 RRo required return 117 Simulation ElFian Base Case 0 Objectives are Show numerically that 13 is guaranteed by PV calc NPVPurePlot Sim amp NPVvs1RR simple Show numerically that NPV quotGquot CHANGE in P0 due to invest i also NPVPurePlot ltfffff 1ntroduction to Sim info and analytical system BCRtn amp ValSum Overview AllSumPlot ltfffff ElFian Demo in Class NPVvs1RR simple for 13 NPVPurePlot amp AllSumPlot Sim for 11215 amp 117 ConcTreefgtAnalysis TreefgtPlumPlotfgtBusPlotfgtEquotfgt gtptcfplot lt7 117 1f time Causal Layer amp Line Trees deeper into Analysis Tree Detailed output Linkages between ltf 117 Tiefins Capital Budgeting CB in 11 uses NPV criterion gt quotGquot above Determinants of CAPM in 111 is one explanation of risk to owner fgt RRo above quotStreetquot ratios in 115 Financing now only via CS new stock later allow TD debt 1V and RE retentions V Topic 11 Capital Budgeting CB Long Term Funds Uses Sources in 1V Put up eq 10 amp review Master ConcSymb Causal Tree 111 Nature CapBud Longfterm not cheaplyquickly reversible Bus Dec39s Mktg Prod RampDtech pers major effect on PO risky 112 Tiefin to Valuation Theory Erom Valuation 17 amp related eq lOb amp eq lOd in 1l3fl5 take CHANGES fgt NPV quotGquot which measures CHANGE in P0 due to changes in ESo amp RRo ValngG amp GNPVMkBk NPV is the best financial criterion for CE amp virtually all decisions CBThry 113 Desired characteristics for financial decisionfmaking WANT fgt CF TVM Price Risk Payback Yes no no Avg Acct RO1 no no no DCE methods 1RR ER Yes Yes Yes 1RR vs RR f efficiency measure NPV Snow Yes Yes Yes CE disc RR f power measure vs efficiency 114 Problems with 1RR not shared by NPV gt NPV is quotbestquot vs popular Multiple 1RR39s ltf multiple flipfflops in CEt stream beware of softwares that quotsolvequot problem Unnecessary compexity amp multiple 1RR39s with mutually exclusive decisions Psychological avoidance of estimating RR gt use quotgutquot 1s 1RR quothigh enoughquot Only via RR 115 1E time Caveat with NPV amp 1RR Reinvestment rate problem 1 Assumption about reinvestment of future cash inflows 7gt TV approach 1110 done if time mutually excl unequal lives 2 Capital rationing Prof1ndex linear prog better dynamic integer prog best possible 116 Conclude NPV is quotbestquot bc fewest problems amp direct bc NPV quotGquotrowth stock ValngG amp GNPVMkBk 117 NPV connection to 1RR if 1RR is valid f 114 above Eq 2 NPV1RRPlot ltfffff 118 Keep in mind a CE39s are relevant measuring unit fgt ESo CD f CS in eq 24 b 1ncremental CHANGEs in CEt39s ESo are focus for CHANGE in P0 c Explicit estimates of risk rgt explicit RRo vs proxy or quotgutquot d Separate the investment decision here from its financing 1V bc are independent 119 Sim ElFian BC 7gt C1 dPOCBRtn amp AllSumPlot ltrrrrr a only verbal summary show in demo at end Effects of Mkt amp Prod ie business decisions on RETURN determinant of CHANGE in P0 Note financing DOE CD amp WC decisions are SAME as BC gt pure effect of Bus dec39s ie CB 11l0 First exposure to analytical system to link decisions rgt CHANGE in expected future performance fgt change in ESo return amp risk 111 next fgt change in P0 current stock price Eirst exposure to issue of market Efficiency amp Competitiveness CBThryNPVCompEff 11ll Components of efficcomp Equal access to info inputs equal technology to produce process infoprodservice equal access to trade output in market 1112 quotPerfectquot efficcomp gt NPV 0 tie to econ theory of MR MC amp eq 2 11l3 Contrast Real markets productservice tech human capital vs Financial markets RlEiant 11l4 Real mkt performance expected in future reflected in current fin mkt prices mvbvplot ltfffff ElFlan Demo in Class mvbvplot ltf 1114 NPV1RRPlot ltf 115 1112 Real mkts AllSumPlot ltrrrrr ConcTree rgt Analysis Tree ltrrrrr AnlyzReturn rgt PlumPlot rgt BusPlot rgt rgt p0cfplot ltf 119 amp 10 1f time PlumPlot Causal Layer amp Line plots deeper Analysis Tree Detailed Outputs Tiefins 11l amp 117 above to Valuation theory 1 amp esp 1l2fl4 for NPV quotGquot CHANGE in P0 118c above to Risk topic next 111 for RRo fgt PO 118d above to financing topics TD debt 1V and RE retentions V 1ntroduce topic of Risk Main question and outline of approach to answer it Topic 111 Risk f Chances quotthings turn out badlyquot 111l Purpose Understand what risk of a firm39s REAL investment is relevant to owners and how that risk is priced out in eqs l07 fgt dPO via RRo in eqs 477 1112 Risk of an isolated investmenti gt held by itself RiskThryrskdef Estimate benchmark mean of prob dist39n of ERi expected return of investi over different possible eventse gt eq 30 Estimate quotriskquot via dispersion of dist39n gt VarRi in eq 31 famt of deviation and prob of that dev Note Risk vs uncertainty VarRi CovRiRi ERie f ERi2 SERi SERi rRiRi assume possible actual Rie normally distributed pretty realistic Sum Probe must l Risk ADDED by investi to portfolio of other investments RiskThryoffdev 1113 Benchmark ERp is wtd avg over investmentsi gt eq 32 Notes Each ERi is in turn wtd avg of Rie over eventse gt 2 dimensions e events for each of 1 members Sum Xi l0 and investi ADDS all of its return to portfolio 1114 Estimate VarRp risk of port via dispersion of portfolio Rpe for different possible eventse around ERp gt eq 33 1115 Each event affects each member39s Rie which in turn affects ERp gt key in Rie a ERi in eq 33 gt risk ADDED by memberi still famt of member39s dev under evente and probe above amp noW also fXi allocation over investsi and the prob that members39 deviations from their respective means Will OFFSET each other under the same evente KEY features added by port building are CHOICE of Xi AND chance that members39 deviations Will offset each other via the rRiRj correlation between each ij pair of members in Eq 33a amp b Summarizing both dimensions eventse and member investsl egt Eq 33a for port risk VarRp feach member39s SERi risk hoW We Xi allocate funds over members AND the probmembers39 deviations OEESET reflected by rRiRj in eq 33c PortRiskPlot ltfffff 1116 Result Eq 34 ConRiRp risk ADDED by investi to port is Xijeighted CovRiRj in Eq 33b which is less than its CovRiRi isolation risk 1EE the probability of its deviations being offset by other members is gt o gt rRiRp lt 10 because some rRiRj 39s lt 10 in eq 33c Points 1113 and 1116 gt FREE LUNCH of diversification bc all of ERi added to port but only rRiRp portion of its risk survives in portfolio vs 100 of risk in point 1112 above 1117 Generalize Stability of system increases With the independance gt loW corr of its members 1mplications for centralized quotmanagementquot vs devolution Optimal efficient portfolio Weights Xi 1118 Remembering We can choose Xi39s in eqs 32 amp 33 can We improve on naive divers Xi 1n 1119 Balance investi39s return added to port vs its risk BOTH Within each investi AND across all memberi39s given constraint gt eq 35 EffSetGenPlot ltfffff 11110 Solution MarkoWitz efficient SET of port all having same members but different Xi39s over membi39s gt diff EfficPort of same members gt xi39s Via k in eq 35 identify specific port on SET 11111 Result Are MANY EfficPort39s one for each risk level gt Question Which ONE is quotbestquot Which single effic risky port is quotbestquot Need to knoW bc CovRiRp depends on port investi added to 11112 Perspective VieWpoint is mgr inside firm deciding on REAL invest BUT mgr must take oWners39 perspective to 1 PO gt What is single quotbestquot risky effic port of oWner gt stocks 11113 What portfolios of stocks do our firm39s oWners have so We can estimate the return amp risk added to it by this REAL investi made by the firm 11113a HoW many stocks held by oWner and Which ones 11113a1 i n number of stocks as long as rRneWRp lt 10 gt all return but part of risk 1116 11113a2 Find as n increases rRneWRp fgt 1 gt searchtrans costs limit n 11113a3 But mutual funds neutralize 13a2 costs gt EULL divers SPSOO is standard proxy 11113b What is allocation Xi39s across oWners39 fully divers stock port RiskThy2addrf 11113b1 Same MarkoWitz analysis as 111810 noW on stocks gt same problem for oWner as 11111 above 11113b2 Theory solution Add riskless Rf asset fgt ansWer to 11111 single best risky effic port of stocks held by oWner Rp Note irony Every oWner holds combination of Rf and Rp depending on personal returnrisk preferences But ALL hold same Xi in Rp 11113c What 1S allocation of Xi in Rp in quotrealquot World RiskThy2index 1E stock mkt is quotinfoquot efficient amp rational gt Rp is quotmktquot port gt xi CapiCapSPSOO 11113c1 quot1nfoquot effic gt hoW quickly and fully stock prices reflect investors39 expectations and their changes due to neW info Weak rejected bc rPtPt1 near 0 autocorrero ltfffff Semifstrong accepted bc prof mgrs Strong rejected bc insider trading empirical tests Weight of academic evidence favors semifstrong stock markets So centralized financial markets are quothighlyquot efficient Anomalies VL Small firm January Weekend 11113c2 Conclusion 1f you can39t consistently beat it then BUY it gt quotmktquot port ansWers 11113c question gt all stock investors are someWhere on Capital Market Line CML Real World proxy for Rp quotmarketquot porfolio is 1ndex mutual fund eg SP500 11113c3 1rony 1nfo efficient mkts depend on you believing that it is info NOT info efficient Result CAPM in eqs 47 11113 above argues that 11114 Eirm39s oWners hold quotmktquot port With Rm and SERm including the stock of our company gt they CAN GET returnrisk tradeoff of CML gt oWner W111 REQUIRE a RRO return of our co commensurate With return they CAN GET already for risk taken on CML gt eqs 47 OWners of our firmi39s stock Will required same return they can earn With same risk ADDED to their port Which is SEERo rERoRm portion of total isolation risk that is UNdiverifiable systematic RiskThy2syst 11115 For our firm making a neW REAL investi it adds total risk of SEgS agt SEERa agt SEERe agt SEERo to our stock Via the Causal chain But only rgSgE fgt rERoRm portion of SEERo is borne by oWners the rest being diversified aWay 1115 and 1116 above The net result of the transmission of risk from our co39s real investi to the oWners39 fully diversified portmkt is SEERo rERoRm risk added gt eqs 47 or any variation 1 f rERoRm portion of our stock39s risk is not borne by oWners as it39s OEESET via eq 33c 11116 Real investi by firm affects SEERo rERoRm risk taken by oWners Who charge eqs 47 as RRo required return Which is the discount rate applied to the invest39s ESO CD f CS cash floWs to get P0 in eqs 10 hence quotpricing outquot the firm39s real investment risk in the financial stock market RiskEmpPlot ltfffff 11117 Sim ElFian BC 7gt C1 dCBRsk dCBPO amp LTUseRsk AllSumPlot Effects of Mkt amp Prod ie business decisions on R1SK determinant of CHANGE in P0 Analysis Tree fgt Summary lt for explanation of Tree amp application to Decision Set amp Cases selected Also AllSum for summary over all ElEian Cases Note financing DOE CD amp WC decisions are SAME as BC gt pure effect of Bus dec39s ie CB ElFian Demo in Class PortRiskPlot lt 1115 EffSetGenPlot lt 1118 ll ConcTree gt Analysis Tree AnlyzRisk lt 11117 AllSumPlot 1f time Evidence erseerbusmkt autocorrero PlumPlot Causal Layer amp Line plots Detailed Outputs TleilDS 12 3 via RRo on company39s stock in Valuation 118 in Capital Budgeting RRo will also be affected by financial leverage in 1V next Topic 1V Financing gt Debt vs Retentions vs New Common Stock 1Vl Purpose Understand when debt or equity financing is cheaper than new stock gt 1 PO 1V2 Perspective Firm has GIVEN LT use of funds Bus dec39s rgt investment NOW decide LT sources Evaluate PURE financing effects gt same LT Bus USEs TA total assets amp O1 profits over time Now change to debt financing from equity gt 1 TD 1 OE Ein dec is indep of invest Overview effects of 1 TD vs 1 CS via eq lOb Financial mkt compeffic 11ll 111l3cl will play role in TDBSOEBS debtequity effect on PO 1V3 Effect of i TDBSOEBS on ERe equity return ELThryere eredoeplot dERe dTDBSOEBS ERa a RRTD l 7 Tx Vla eq 41 gtquotfavorabiltyquot reflects ERa left for owners after paying RRTD for debt eredoeplot ltccccc EinLevPlot Works for personal leverage same as corporate Home mortgage gt same effect of CHANGEd debtequity on ERe real asset Link to CML of CAPM eqs 47 Rp XRf Rf l a XRf Rm financial asset CML above Rm gt borrow rgt Rp Rm Rm 7 Rf XRf eq 41 structure XRf above TDBSOEBS debtequity of eq 4l 1V4 Effect of i TDBSOEBS on SEERe ONGO1NG equity risk RRTD fixed for now dSEERe dTDBSOEBS SEERa l 7 Tx Vla eq 44 ELThryseere seeredoeplot ltr EinLevPlot 1ntuition Same equity profit risk SEEATS relative to lower OEBS equity investment General OE owners39 equity takes all ONGO1NG invest risk after taxes lender takes none Works same for personal leverage Home mortgage gt same Owner takes full gain or loss on real asset lender takes none Link to CML stp XRf SDRf l a XRf SDRm SDRm l a XRf eq 44 structure bc XRf above TDBSOEBS debtequity of eq 44 1V5 Effect of i TDBSOEBS on PO current stock price bottom line CostCapPlot ltccccc 1V5a Change to indirect Viewpoint dTDBSOEBS rgt dRRa eq 46 7gt dVA eq 11 7gt dTPO rgt dPO 1V5b Perfect Markets Txcd txcoe txpdtxpeq O Prdefault039 Pers Corp leverage 1V5bl Net1ncome theory RRTD lt RRo gt i RRa W i TDBSOEBS dRRo dRRTD 0 gt i TDBSOEBS gt i RRa eq 46gt 1 VA eq 11 gt i TPO eq 10b shO gt 1 P0 1V5b2 MM Agree W RRTD lt RRo but argue dRRo gt 0 dRRTD still 0 Justify dRRo gt 0 Risk route eq 44 gt 45 gt 47 ampor Return route pers eq 4l gt i RRo gt opposing forces of lst amp 2nd terms on dRRa ELThryperfmkt Qst Which larger Ans Equal in PerkatsgtdRRaO eq 46gtdVAO eq ll gt dPO O Justify 1nvestors pay premium only if they can39t use leverage as well as firms can Ein mkts quotperfectlyquot efficcompetitive gt no competitive advant relaxed in 1V5c Risk route Risk due to dTDBSOEBS is same 1V4 above cgt CAPM 111 Return route RRTD debt cost same for firm amp person 1V3 in perfect markets MM is received theory today 200l 1V5c Add market imperfections in real world to MM in perfect mkts 1V5cl Taxes Corporate Txcd vs Txcoe expense shield differential ELThrytaxes Personal Txpd vs Txpoe income differential KEY Net differential of above differentials on aftercallctax RRTD in eq 46 RRTD l Txcd Txcoe l Txpoel Txpd 1f ratio l gt 1V5b2 result gt no net effect Current law fgt tax effect on P0 Complication Tax exempts39 arbitrage int39i rgt unknown net tax effects 1V5c2 Bankruptcy PrDef and cost on dRRTD in eq 46 ELThryOngoDeath amp ELThryprdef 3rd dRRTD term now gt 0 via lender risk aversion to bankruptcy risk vs ONGO1NG risk in 1V4 2nd dRRo term has secondcorder lt 0 shift via Option Pricing Theory OPT other course 1ntuition Owner limited loss lender risk gt offsetting effect Unknown net effect ELThryopmlev but not required for this course 1V5c3 Personal vs Corp leverage opp and cost recent WSJ quotes Long term Home mort vs corp longcterm fixedcrate bonds Short term OPT gt high personal debtequity at Rf vs corp 1V5d Add across all effects from 1V5b2 fgt 1V5c3 for each term of CHANGE in eq 46 and then add across 3 terms dRRa gt dPO ELThryaddem Empirical evidence dRRa gt dP0 gt probably small Conclusion Major dP0 is via invest use in II amp esp II13 not dTDBSOEBS mvbvdoeplot lt 1 1V6 Sim Results C1 gt C2 MMSImEL amp following topics through ELSum AllSumPlot Used principally to provide numerical example for various points above quotImperfectionsquot in Sim Txcd 0400 Txcoe Txpd Txpoe 0 no tax exempts or int39l flotation costs diff39s no inflation yet ad hoc OPT tho w same reasoning ElEian Demo in Class Evidence eredoeplot lte IV339 seeredoeplot lte IV439 mvbvdoeplot lte IV5d ConcTree rgt Analysis Tree PlumPlot AllSumPlot lt7 If time Causal Layer amp Line plots deeper Analysis Tree ereeraplot seereseeraplot TleilDS I III have replaced NCS financing with debt here in IV I2 debt financing changes all 4 elements from owners39 view but net effect on P0 probably small II12 amp 13 NPV of transactions small in quothighlyquot compeffic mkts eg financing decisions esp in IV5c3 III14 CML of CAPM plays role via personal leverage in IV4 and IV5b2 risk route above Option Pricing Theory Options not req39d plays role in IV5c2 amp IV5c3 above Other major financing alternative Retaining Earnings next Other issues if time permits CAPM can39t handle bankruptcy risk even though BR risk quotsomewhatquot systematic Interactions Real investment tax shields agency eitherboth avoid invest risk andor pursue it Agency issues Costs of monitoring pecking order mgt vs lenders vs owners Dividend Policy other main possible source of funds vs debt above via RE SUMMARIZE POINTS BELOW via eg 10b vs cover in detail IV7 Question What is the effect of the firm39s dividend policy on it owners39 total current wealth IV8 Perspective Like financial leverage look at PURE financing effect gt SAME Investment 1V2 financed VIa RE vs NCS Overview via eg 10b Must broaden measure of owners39 current W0 wealth to include current cash dividend paid as well as exedividend amp diluted P0 stock price Dividend vs Dilution in Perfect Mkts a simple numerical example via Gordon eg 10a for easy calcs IV9 12312001 for existing firm Current amp future no growth Balance Sheet Investment TA 1000 TD 0 gt OE 1000 Expected Profit ERe 15 perpetual gt EATS2001 150 amp future 150yr forever Expected Risk RRo 15 Valuation Sh2001 1000 gt P12312001 115 via eg 10b t start 0 not 1 P is quotdividendseonquot and divs from 2001 EATS will be paid on 122002 to holders of record Behavior of Pt when stock goes quoteXleldeDdquot on 122002 Drop by CDsh122002 IV10 NEW investment announced on 112002 TA 100 ERe 20 perpetual gt new added EATS2002 amp future 20yr RRo 15 dP112002 NPVsh 51002015 1001000Sh 033 via eq 10b CDThryNewInv gtP112002 divion 150 1502015 1001000Sh 1183 115 033 gt P1l2002 P12312001 dPll2002 115 033 1183 033 is INVESTMENT effect gt W1l2002 gt W12312001 by NPVsh 0033 due to INVESTMENT ON 122002 pay div from 2001 EATS BEEORE issuing new stock if any NOW the FINANCING effect W122002 CDSh122002 P122002 closing price IV11 IE RE RetEarn to finance new TA 100 CDThryRE W122002 15010010008h 1701510008h 1183 IV8 cash CDsh 05 Pexediv 1133 same as W112002 though composition changed IV12 IE instead issue new CS 100 to finance TA after 122002 div paid to current owners IV12a Eair price to current owners 17015 1001000Sh 1033 via eg 10b or equivalently 170 10015151000Sh same 1033 gt eg same 10b gt need to issue 1001033 968 new shares gt 10968 TotShrs CDThryDilSh0 IV12b Eair price to NEW owners CDsh starting 122003 517010968sh 155yr forever PV of CDsh 15515 1033 gt ok to new shareholders Equivalently have 96810968 7 883 of shs gt will get total CD39s of 1700883 15yr on 100 paid for CS gt ERo 15 RRo gt 1033 is Eair price for new shs Also 100 via new1133 total Cap value 883 is another way Note 1033 is Pl22002 100 exidiv wo new invest NPVsh 033 of new invest IV12c W122002 of current shareholders with new CS stock issued is 1501000sh 1701510968sh cash CDsh of 15 Pexidiv of 1033 1183 Same as IV11 if RE retain earnings IV13 Conclusion Current owner wealth unaffected by CD policy in Perkat bc W0 IV11 IV12c same Current owner pays same to finance new invest either via reduced div39s or dilution IV14 Market quotimperfectionsquot and their incremental effects on IV13 result CDThryRlWld IV14a Taxes Txccg lt Txccd due to tax level and timing of payment gt prefer RE Complications legal avoidance via borrowing tax exempts int39l differentials IVl4b Transaction costs Investment Banker fees on new CS vs indiv broker fees IVl4c Birdsinshand argument confuses invest effect with financing Is invalid Conclusion wimperfections or some preference to RE RetEarn vs new CS due to tax diff Empirical evidence to slight pref for RetEarn when Txccg lt Txccd by quotlarge enoughquot gap IV15 Theory vs Practice MngCDStm Acad IV13 amp 14 gt prefer to RetEarn gt residual CDpol diVidend policy gt manage RE gt CD residual to avoid NCS flotation fees excess RetEarn Personal Tax disadvantage of div39s vs CapGains Pract Stable S or growth CD policies gt manage CD39s gt RE residual Args BirdsinsHandrisk perceptions info contentsignalling Counterpargs Issue remains one of major differences bt Acad amp Pract Stock buybacks a way to reconcile Sim Results c2 7gt C3 dCDRtn amp following topics through CDSum AllSumPlot ltaaaaa Focus on effects of replacing residual CD policy with a managed CD policy Sim quotimperfectionsquot in IV6 Cost of managed policy sgt quotoverquots andor quotunderquotsretaining earnings No pers tax diff penalty ElEian Demo in Class ConcTree gt Analysis Tree PlumPlot If time Causal Layer amp Line plots deeper Analysis Tree Tiesins To other major financing alternative IV2 5d Leverage To issue of financial market compeffic gt corp vs personal access IIlZ13 amp IV5c3 Topic V Working Capital a Principal Concepts amp Forecasting Vl Define the area Short term uses current assets amp sources curr liab gt deClSlOnS are quickly amp cheaply reversible gt decisions are small dynamic Motivations Liquidity cash amp MS vs curr liab and marketing AR amp inventory Returnrisk tradeoffs Objective same 1 PO f CD Dil RR over far future eqs 10 Practice gt EATS O Rf for coming year OK due to short term Effects on dPO usually small due to incremental decisions quick competitor response except possibe BR risk via insufficient liquidity Theory is not well developed bc is quothardquot area dynamic amp BR risk poorly understood WCGenConNoThry and dPO effect should be quotsmallquot just above Result Many narrow highly specialized tools EOQ ECQ l Computercomm technology sgt iefficiency and iinvestment gt 1 PO V2 Example of dynamic nature of decisions if time Grant credit even though Prpay only 5 PprodlOO V6 n50 2pd Bayesian approach reflects dynamic nature of decision V3 Three Underlying Concepts WCGenConspont V3a Spontaneous uses amp sources a linked to sales bc of internal policy eg cash AR or external constraints eg AP taxpayable Sim uses simple models vs many indep vars nonslinear Used extensively in cash budgeting ST financing needs forecasting AcRecSlsPlot ltsssss V3b quotPermanentquot working capital V18 8 permanent sales patent supply contract good marketing V3c Given V3a amp 3b igt quotpermquot NWC need match term of sources with uses Demonstrate via UseLT vs SourceST sgt irisk amp ireturn Worth it Recommendation has no rigorous logical basis ie theory gt quotrule of thumbquot Sim Results C3 7gt c4 dWCRtn amp follOWlng topics through WCSum AllSumPlot ltaaaaa Analysis Tree Main purpose is to show simple modeling of WC and why firm39s policy decisions end up in equations Shows concept of spontaneous U amp S amp tie to policies Reflects dynamic interactive feedback nature of WC decisions Effects of some WC policies are exaggerated in Sim to make them stand out from rounding error amp other quotnoisequot and would be dynamically altered in real world gt dPO exaggerated Tiesins Contrast short term in Vl above to longsterm perpsective of I5 Contrast lack of unified theory here to topics I IV Bankruptcy via illiquidity in Vl above may be addressed in options course Options not req39d Nature of decisions in here gt application of Bayesian statistics amp AIExpert Systems amp neural networks V4 Integration do ONLY if time General and Business Financial theory Revisit Master Causal Tree All one integrated theory centered on eqs 10 V5 Modeling of forecasting of WC items WCCtrlARPol WCCtrlInvPol amp fcst errors SE AcRec ltsssssl Use mkt mgr39s forecast of Salestl with regression parms agt WCitl WCEcstEcstAR AcRecSlsPlot Reasons for fcst errors Sales economy comp SElepe SEreg error Estimating quotlikelyquot size of WC item fcst error WCEcstAREcstErr Estimating quotlikelyquot size of total NetWC fcst error below WCEcstAREcstErr MktSecEcstErrPlot Estimating needed precautionary MS to absorb NetWC fcst error x of the time Intro to Model Building broaden V5 Master gt Full ConcTree PRs dec igt PO result Topic VI Model Building in General and in Sim Specifically VIl Why do Extensive use in applied financial research Financial engineering swaps etc for multinationals unbundling Predictive models eg Wharton for macroeconomy business firm s performance eg Sim environment Improve system s performance trading timing amp rebalancing strategies Computer cost amp speed amp software amp data availability make it much more feasible VI2 Model domain Ultimate ENDOgenous LHS variables to EXOGenous variables Master Conc gt Full Tree Model building CAUSAL model generates data vs Statistical modeling data gt infer causal model Eg quotreverse engineeringquot on Wall St Link eqs from exogenous egt endogenous intermediate egt endogenous final Master Causal Tree VI3 Principal ideasconcepts VI3a Simplicity analytical ANLY vs realism numerical NUM modeling Goranod solution optimize vs flexibility VI3b Modeling of stochastic processes statistical modeling tries to take it back out RN7t VI3c Likely presence of simultaneous feedback relationships Mitigating vs Exacerbating Simult VI3d Possible need to model individual behavior to model aggregate system 39s behavior EinStEct Sims an example of ideas applied You39re NOT responsible for Sim details only VI3 Ideas applied in Sim Sequence of eqn panel is in order of vars in basic equations vs sequence of causal relations gt modeling VI4 P0 current stock price Eq lOa ANLY vs lOb NUM lti VI3a above Goranod eqs 1 VI5 Modeling the firm s expected cashflow performance Summarize via Acct model OwnErmCE ltiiiii ANLY given var values but many var values GOTTEN via NUM methods lti VI3a eg PO Only need 1 NUM eq to kill ANLY strengths Eqs 2 in eqn panel VI6 Modeling the unpredictable variability of the firm s performance RN7t lti VI3b CovCorrProbCorr priced out in eqs 3 VI7 Modeling the causes of VI5 amp 6 and hence 4 above use Eull ConcTree VI7a Sales Sales growth PRs dec agt EgS agt gSt amp SES eqs 2Ala and sales capacity AEA dec agt SCap BusPlot amp ascapafaplot Eqs 2Alc Modeling gSt lt7 EgS BgS SEgS amp RN t gstsulplot amp gstOlplot lt7 VI3a amp 3b Eqs 2Ala VI7b Variable operating costs v lt7 AEA decision vafaplot ltaaaaa Eqs 2Alb VI7c Fixed operating costs EC lt7 AEA decision cfcafaplot Eqs 2Alc VI7d Working capital policies WCPol decisions vacpayplot Eqs 2Bla d 2B2a c Financial Structure policy TDBSOEBS decision RRd Simult Eqs 2B2 vs 2B3 Dividend policy CDpol decision manage CD vs RE Eqs 2A2 VI8 quotInsidequot model of mgt forecasting Vl3d done within quotoutsidequot model Vl4i7g igt forecast errors Mgt fcsts based only on EgS vs actual gSt egt forecast errs VI7a for all vars affected by sales EinStEct plus stochastic elements in AR amp Inv SEAcRec VI8a Modeling marketable securities balances MSpol decision amp cash crises MSBS affected by all forecasting errors AcRecSlsPlot gt MktSecEcstErrPlot Eqs 2B4 CrisisCsh ltiiiii VI9 Transmitting above to the firmquots stock s volatility amp pricing it out gt RRo VI9a The main source SES sales volatility results from VI7a modeling Eqs 2Ala igt 3ClalAl VI9b Resulting dividend amp capital gains risks Causal Chain is in eqs 3C SES agt SEERa agt SEERe agt SECD amp SETPrh amp SETPRf agt SEEo agt SEERo VI9c Pricing it out Vla CAPMAPT SEERo amp rERoRm lt7 rgSgE amp rERoRf agt RRo Eqs 3Di3G VI9d Simultaneous feedback effects Simult lt in VI3c SimSimulPlot ltiiiii SimSimul Eqs lB VIlO Endogenous determination of PO VIlOa Going concern SimSimul VIlOb Trouble Ad hoc Option Pricing Model for exacerbating P0 ltegt RRo feeback SimSimulAdHocOPM Eqs lB4alBl amp lB4alE ElEian demo in class Done with points explained above Topic VII Portfolio Optimization Reasoning amp Math VIIl Why do this Prep for future courses amp centrality to Finance amp generalizeability to other areas v112 Generality of portfolio behavior gt insight amp mathematics Portfolio Group of members which when members39 performances are ADDED SUMMED together determine the performance of the group portfolio quotPerformancequot gt the average mean and dispersion standard deviation or variance of its behavior NO synergies causally interactive effects allowed the performance must be a linear algebraic sum or weighted sum of its members39 performances Applications Exam grade is the weighted sum of question grades and course grade is weighted sum of exam grades PortRskGPortRskGrd amp PortAppsgrades gSt sales growth is weighted sum of EgS EgE and RN7t VI7a Working capital item eg AcRec is sum of policy effects WCPol sales levels and management inside Sim model forecasting errors VI8 Actual total working capital sum of working capital items and their forecasting errors PortAppsWCEcstErr Profit is sum of revenues and costs Eirm39s income statement 01 Business and EATS equity income PortAppsvarcst amp PortAppsindxrrd Investor39s stock income ESo for whole market plus dPO for cap gains for indiv PortAppsseedr Inferential stat Mean of a sample is the weighted by probability sum of the sample39s observations gt SE Mean of X SDXsqrtn via random sample gt rXiXil 0 for obsi Linear Regression Dependent variable behavior is sum of intercept independent variables39 slopes and values and residual error Eg gSt modeling above in VI7a gstsulplot Portfolio of securities behavior return is allocationiweighted sum of member securities39 returns A perfect hedge is a portfolio of 2 members with perfect positivenegative correlation PortAppshedge General systems theory WITHOUT quotsynergiesquot feedback VII3 Portfolio behavior Math follows intuition ERp portfolio return weighted sum of member returns fERi member returns amp Xi weights in eq 32 SDRp portfolio risk coiweighted sum of members39 covariance risks fSDRi member risks Xi weights amp rRiRj probdeviations of memberi will be offset by deviations of member agt coiweighted avg of SDRi SDRj rRiRj CovRiRj 39s in eqs 33 Probdevs offset Lg l rRiRj in eq 33c RiskThryoffdev rRiRj l gt EULL Cov risk added gt port risk linear fmember risks as in port BetaSyst amp in SECD SETPrh portion of SEEo PortRskGperfcorr rRiRj O gt NO Cov risk added bc members devs offset half the time thus nullifying other half when they don39t PortRskGUNcorr rRiRj l gt NEGATIVE Cov risk added so members39 offsetting pairwise devs occuring EVERY time CovRiRj lt O for i not equal to j gt different members offsetting each member39s own added risk as well as the other member39s risk CovRiRi must be gt 0 i ne 3 form in eq 33a This also known as a quotperfectquot hedge egt VarRp SDRp o in eqs 33 PortAppshedge rRiRj Undefined igt special role of riskless asset SDRf 0 PortRiskPlot has a simple 2member portfolio showing graphically and explaining the roles played by the above variables as they affect portfolio return and risk VII4 Portfolio optimization Efficient Xi allocation across members i EffPort VII4a Max 2 k ERp a VarRp a L X1 x2 x3 Xn a 10 in eq 35 ojective function VarRp risk is quotbadquot and constraints have a cost gt they39re subracted from quotgoodquot ERp return k quotutilityquot of return relative to risk implied quot1quot weight on risk Importance of return vs risk k O gt return UNimportant gt min VarRp risk 1k gt increased value to person of return vs risk Is a quotrisk aversionquot measure for the individual to choose their personal quotbestquot effic port from the SET of effic port39s that result one effic port for each different possible VarRp risk level k dVarRp dERp is also reciprocal of slope of efficient set Port return eq 32 and risk eqs 33 defined above in VII3 L is Lagrange multiplier to enforce full investment constraint sum Xi39s 10 Is an equality constraint IS neat trick to make constraint part of the solution gt forces solution to obey the constraints VII4b Optimization usual general steps in finding any maximum or minimum gt optimize 1 Take lst derivative of eq 35 Z wrt each Xi amp L express how changing control var each Xi affects objective function in eq 35 2 Set lst deriv O gt balance each member within itself See steps 1 amp 2 in VII4c below for eqns dZdL is Lagrange39s trick to force Sum Xi l 3 Solve system of Nl equations n Xi deriv eqns plus deriv for L simultaneously for Nl variables gt balance every member39s contribution to Z with every OTHER member39s cont to Z due to full invest constraint while enforcing full invest constraint via dZdL VII4c Easiest case a Only equality constraints ie L has sum Xi39s 10 General steps VII4bl amp 2 above in equation form focus of EffPort as is foundation for cases below dZdXi k ERi Sum igtn 2 CovRiRj Xj W L 0 one for each member i dZd L o a Sumjlgtn l Xj a l o In matrix form k R a a V X a C 7 O Rearrange to v x ac k R Step VII4b3 Solve inverse gt X Val C k Val R a k b gt Xi is linear fVl risk amp R return Xi MinVarRp k dXdk generates memi alloc39s for diff k values Need only solve ONCE for full effic set via a amp b with quotkquot tracing out X vector of effic ports over whole effic set from quotkquot 0 Min Var port to infinity Max Return port e vs 1 effic port at a time many softwares vs numerical approach eg Excel Solver Is called UNconstrained effic set even though has equality constraint of full investment via L EffSetGenPlot choose UNConstrained lt alternative to see the above applied VII4d Harder cas No short sales gt INequalityiconstrained efficient set All Xi gt or O gt Xi lt or 10 added to L constraint for Xi allocations over members Method in ElEian is Critical Line Algorithm EffSetGenPlot choose CONstrained lt alternative to see the above applied Is selection algorithm to determine which members are quotINquot the portfolio amp hence the others are quotOUTquot gt Xi O or 10 Wrapped around the optimization steps VII4bl 3 above Start at top of effic set max return gt max k in eq 35 amp work Way quotiteratequot down to min var port adding secs that reduce risk most for return given up or deleting ones that violate the Xi gt or O gt Xi lt or 10 inequality constraints on each memberi A initial iteration Eind Max ERp port gt XI 10 IN for Max ERl memberi All other Xi39s 0 DOWN gt OUT This is port w k infinity since return completely dominates risk Remember from VII4a above that k is also k dVarRp dERp the change in risk vs return of the efficient set E Working down from the Max ERp port toWard the k o gt Min VarRp risk port calc each memberi39s Kcriti critical k value the max one Will be the next member to quotchange basisquot gt be added to or deleted from the portfolio for the next quotiterationquot For each memberi if memberi is in the current iteration DOWN or UP Kcriti dVarRpdXi dERpldXi decline in port risk relative to port return lt39S actually a bit more complex but a diversion gt hoW much it contributes to port risk reduction relative to return given up or memberi is IN Kcriti K value to drive XI 0 or 1 gt OUT DOWN or UP Find the memberi that has Max Kcriti bc is lst closest to current k to cause a change in basis added or deleted for next iteration c IE Max Kcriti gt 0 THEN go to step D gt change basis gt add or delete memberi amp do next iteration ELSE go to step H done bc canquott reduce risk anymore bc k O gt min VarRp risk port gt the other end of the noishortisale efficient set D IE current basis of Max Kcriti member i is DOWN Xi O or UP Xi 10 THEN change ltS baSlS to IN gt ADD lt ELSEIE current basis of Max Kcriti member i is IN 0 lt Xi lt 1 THEN change its basis to DOWN or UP depending on dXdkl gt which way it was going gt DELETE E Reset matrices R V and C from general optimization steps 1 amp 2 above VII4b general and VII4c UNconstrained gt include only IN members in quotUNquotconstrained solution for this iteration section of the constrained efficient set E Do optimization step 3 invert gt simult solution for IN members for this iteration section of the norshortrsale constrained efficient set gt UNconst opt only on IN members G Since Max Kcriti gt 0 return to step B for the next iteration until Max Kcriti lt 0 in step c H Done because Max Kcriti dVarRpdXi dERpldXi O or less means that cannot reduce port risk any more With reduced return or risk would increase With reduced return gt have Min Var port k O in eq 35 Which is other end of effic set from Which We started in step A Max Return port gt max k Note that the algorithm steps A a E just determine Which memberi39s are IN or OUT of the portfolio for the next iteration amp whether to do another iteration Max Kcriti gt 0 in step c step E does the exact same optimization matrix inversion to get Val and hence Xi Xi39s for MinVarRp k dXdk in VII4c for the current iteration With the memberi39s that are IN the iteration basis the current segment of the constrained effic set VII4e Still harder case ANY set of INequality constraints lnflnlty lt Xi39 lt infinity UNconstrained in VII4c can have Xi39 a or infinity EG 35 lt Xi lt 157 Initial Step A above solution gotten via Linear Programming Max Rp ST above inequalities then go through steps B thru H above VII4f Still harder cases Subset constraints eg Sum specific xi39s gt 756 amp lt 237 say to avoid industry or country exposure Taxes transactions costs a different members may face different handling Dynamic Bajoux Adding modeling of evolution of expectations as neW info changes expectations depending on What last neW info Was andor hoW market reacted to last info andor Etc

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