CFA 2018 - Level 2 Schweser-s Quicksheet


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CFA 2018 L2 quick sheet
  LEVEL II SCHWESER' C ritical  C oncepts   for   the   2018  CFA® E xam ETHICAL AND PROFESSIONAL STANDARDS I I (A) I (B) I (C) I (D) II II (A) II (B) III HI (A) HI (B) HI (C) HI (D) HI (E) IV IV (A) IV (B)IV (C) V v (A)V (B)V (C) VI VI (A) VI (B)VI (C) VII VII (A) VII (B) ProfessionalismKnowledge of the Law Independence and Objectivity Misrepresentation MisconductIntegrity of Capital MarketsMaterial Nonpublic InformationMarket ManipulationDuties to ClientsLoyalty, Prudence, and CareFair DealingSuitabilityPerformance Presentation Preservation of Confidentiality Duties to Employers LoyaltyAdditional Compensation Arrangements Responsibilities of Supervisors Investment Analysis, Recommendations, and ActionDiligence and Reasonable Basis Communication with Clients and Prospective Clients Record Retention Conflicts of Interest Disclosure of Conflicts Priority of Transactions Referral FeesResponsibilities as a CFA Institute Member or CFA CandidateConduct in the CFA Program Reference to CFA Institute, CFA Designation, and CFA Program QUANTITATIVE METHODS Simple Linear RegressionCorrelation:covXY rXY = ( sx )( sy ) t-test for r (n - 2 df): t =rVn —2Estimated slope coefficient:cov xy <J\ Estimated intercept: b0 = Y —bjX Confidence interval for predicted Y-value:  A  Y ± tc x SE of forecast Multiple Regression Yi = b0+(b1xXli) + (b2xX2l) + (b3 XX3i) + £;ãTest statistical significance of b; H(): b = 0, A/ t = y , n —k —1dfReject if |t|> critical t or p-value < a. Confidence Interval: bj ± |tc X sgSST = RSS + SSE.MSR = RSS /k.MSE = SSE /(n-k - 1).Test statistical significance of regression:F = MSR /MSE with k and n —k —1df (1-tail)Standard error of estimate (SEE = VMSE ). Smaller SEE means better fit.ãCoefficient of determination (R2= RSS /SST). % of variability of Y explained by Xs; higher R2means better fit. Regression Analysis—Problems ãHeteroskedasticity. Non-constant error variance. Detect with Breusch-Pagan test. Correct with White-corrected standard errors.ãAutocorrelation. Correlation among error terms. Detect with Durbin-Watson test; positive autocorrelation if DW < d(. Correct by adjusting standard errors using Hansen method.ãMulticollinearity. High correlation among Xs. Detect if F-test significant, t-tests insignificant. Correct by dropping X variables.Model MisspecificationãOmitting a variable.ãVariable should be transformed.ãIncorrectly pooling data.ãUsing lagged dependent vbl. as independent vbl.ãForecasting the past.ãMeasuring independent variables with error. Effects of MisspecificationRegression coefficients are biased and inconsistent, lack of confidence in hypothesis tests of the coefficients or in the model predictions.Linear trend model: yt = b0 + b,t + £tLog-linear trend model: ln(yt) = b0 + b,t + £tCovariance stationary: mean and variance don’t change over time. To determine if a time series is covariance stationary, (1) plot data, (2) run an AR model and test correlations, and/or (3) perform Dickey Fuller test.Unit root: coefficient on lagged dep. vbl. = 1. Series with unit root is not covariance stationary. First differencing will often eliminate the unit root. Autoregressive (AR) model: specified correctly if autocorrelation of residuals not significant.Mean reverting level for AR(1):bo(1 —bj)RMSE: square root of average squared error. Random Walk Time Series:xt = xt-i + £tSeasonality: indicated by statistically significant lagged err. term. Correct by adding lagged term. ARCH: detected by estimating:= ao+ ai^t-i + Bt Variance of ARCH series: A2 AAA2 CTt+l = a0 + al£tRisk Types:  AppropriatemethodDistribution   of riskSequential ?  Accommodates   Correlated Variables' SimulationsContinuousDoes not matterYesScenarioanalysisDiscreteNoYesDecision treesDiscreteYesNo ECONOMICS bid-ask spread = ask quote - bid quote Cross rates with bid-ask spreads:'A' vC, 'A' vC, bid 'A'B,n > X bid .B C offer /AX\B,V^ / /T-x\ X offerbid BC\^ / offer Currency arbitrage: “Up the bid and down the ask.”Forward premium = (forward price) - (spot price) Value of fwd currency contract prior to expiration:(FPt —FP)(contract size)Vt = 1+ R A days360\Covered interest rate parity:1+ R a  F = ^  -------- days360/ã0 1+ R Bdays 360Uncovered interest rate parity: e (% asw , = R, - K  Fisher relation:R = R . + E(inflation) nominal real International Fisher Relation:R . —R .= E(inflation.) nominal A nominal B vA' E(inflationB)Relative Purchasing Power Parity: High inflation rates leads to currency depreciation.%AS(A/B) = inflation Xj - inflation,B) where: %AS(A/B)  = change in spot price (A/B)  Profit on FX Carry Trade = interest differential - change in the spot rate of investment currency. Mundell-Fleming model: Impact of monetary and fiscal policies on interest rates & exchange rates. Under high capital mobility, expansionary monetary policy/restrictive fiscal policy —>low interest rates —> currency depreciation. Under low capital mobility, expansionary monetary policy/ expansionary fiscal policy —>current account deficits —»currency depreciation.Dornbusch overshooting model: Restrictive monetary policy —»short-term appreciation of currency, then slow depreciation to PPP value.Labor Productivity:output per worker Y/L = T(K/L)‘'Growth Accounting:growth rate in potential GDP= long-term growth rate of technology + a (long-term growth rate of capital)+ (1 - a) (long-term growth rate of labor) growth rate in potential GDP= long-term growth rate of labor force + long-term growth rate in labor productivityClassical Growth TheoryãReal GDP/person reverts to subsistence level.Neoclassical Growth TheoryãSustainable growth rate is a function of population growth, labor’s share of income, and the rate of technological advancement.ãGrowth rate in labor productivity driven only by improvement in technology.  Assumes diminishing returns to capital. 0   0 g* =(1-a)G* =(1-a)+ AL Endogenous Growth Theory ãInvestment in capital can have constant returns.ã| in savings rate —>permanent T in growth rate.ãR&D expenditures  ]  technological progress. Classifications of Regulations ã Statutes:  Laws made by legislative bodies.ã  Administrative regulations:  Issued by government.ã  Judicial law:  Findings of the court. Classifications of Regulators ãCan be government agencies or independent.ãIndependent regulator can be SRO or non-SRO. Self-Regulation in Financial Markets ãIndependent SROs are more prevalent in common-law countries than in civil-law countries. Economic Rationale for Regulatory Intervention ã Informational  frictions  arise in the presence of information asymmetry.ã Externalities  deal with provision of public goods. Regulatory Interdependencies and Their Effects Regulatory capture theory:  Regulatory body is influenced or controlled by industry being regulated. Regulatory arbitrage:  Exploiting regulatory differences between jurisdictions, or difference between substance and interpretation of a regulation. Tools of Regulatory Intervention ãPrice mechanisms, restricting or requiring certain activities, and provision of public goods or financing of private projects. Regulations Covering Commerce ãCompany law, tax law, contract law, competition law, banking law, bankruptcy law, and dispute resolution system. Financial market regulations:  Seek to protect investors and to ensure stability of financial system. Securities market regulations:  Include disclosure requirements, regulations to mitigate agency conflicts, and regulations to protect small investors. Prudential supervision:  Monitoring institutions to reduce system-wide risks and protect investors. Anticompetitive Behaviors and Antitrust Laws ãDiscriminatory pricing, bundling, exclusive dealing.ãMergers leading to excessive market share blocked. Net regulatory burden:  Costs to the regulated entities minus the private benefits of regulation. Sunset clauses:  Require a cost-benefit analysis to be revisited before the regulation is renewed. FINANCIAL STATEMENT ANALYSIS Accounting for Intercorporate Investments   Investment in Financial Assets: <20% owned, no significant influence.ãHeld-to-maturity at cost on balance sheet; interest and realized gain/loss on income statement.ãAvailable-for-sale at FMV with unrealized gains/ losses in equity on B/S; dividends, interest, realized gains/losses on I/S.ãHeld-for-trading at FMV; dividends, interest, realized and unrealized gains/losses on I/S.ãDesignated as fair value —like held for trading. Investments in Associates: 20—50% owned, significant influence. With equity method, pro-rata share of the investee’s earnings incr. B/S inv. acct., also in I/S. Div. received decrease investment account (div. not in I/S). Business Combinations: >50% owned, control. Acquisition method required under U.S. GAAP and IFRS. Goodwill not amortized, subject toannual impairment test. All assets, liabilities, revenue, and expenses of subsidiary are combined with parent, excluding intercomp, trans. If <100%, minority interest acct. for share not owned.  Joint Venture: 50% shared control. Equity method. Financial Effect of Choice of Method Equity, acquisition, & proportionate consolidation:ãAll three methods report same net income.ãAssets, liabilities, equity, revenues, and expenses are higher under acquisition compared to the equity method. Differences between IFRS and U.S. GAAP   treatment of intercorporate investments include: ãUnrealized FX gains and losses on available-for-sale debt securities recognized on income statement under IFRS and as OCI under U.S. GAAP.ãIFRS permits either the “partial goodwill” or “full goodwill” methods to value goodwill and noncontrolling interest. U.S. GAAP requires the full goodwill method. Pension Accounting  ãPBO components: current service cost, interest cost, actuarial gains/losses, benefits paid. Balance Sheet ãFunded status = plan assets —PBO = balance sheet asset (liability) under GAAP and IFRS. Income Statement ãTotal periodic pension cost (under both IFRS and GAAP) = contributions —A funded status.ãIFRS and GAAP differ on where the total periodic pension cost (TPPC) is reflected (Income statement vs. OCI).ãUnder GAAP, periodic pension cost in P&L= service cost + interest cost ± amortization of actuarial (gains) and losses + amortization of past service cost —expected return on plan assets.ãUnder IFRS, reported pension expense = service cost + past service cost + net interest expense.ãUnder IFRS, discount rate = expected rate of return on plan assets. Net interest expense = discount rate x beginning funded status. If funded status was positive, a net interest income would be recognized. Total Periodic Pension Cost TPPC = ending PBO —beginning PBO + benefits paid - actual return on plan assets TPPC = contributions —(ending funded status - beginning funded status) Cash Flow Adjustment If TPPC < firm contribution, difference = A in PBO (reclassify difference from CFF to CFO after-tax). If TPPC > firm contribution, diff = borrowing (reclassify difference from CFO to CFF after-tax). Multinational Operations: Choice of Method For self-contained sub, functional ^ presentation currency; use current rate method:ãAssets/liabilities at current rate.ãCommon stock at historical rate.ãIncome statement at average rate.ãExposure = shareholders’ equity.ãDividends at rate when paid.For integrated sub., functional = presentation currency, use temporal method:ãMonetary assets/liabilities at current rate.ãNonmonetary assets/liabilities at historical rate.ãSales, SGA at average rate.ãCOGS, depreciation at historical rate.ãExposure = monetary assets - monetary liabilities. Net asset position & depr. foreign currency = loss. Net liab. position & depr. foreign currency = gain. Original F/S vs. All-Current ãPure BS and IS ratios unchanged.ãIf LC depreciating (appreciating), translated mixed ratios will be larger (smaller). Hyperinflation: GAAP vs. IFRS Hyperinfl. = cumul. infl. > 100% over 3 yrs. GAAP: use temporal method. IFRS: 1st, restate foreign curr. st. for infl. 2nd, translate with current rates. Net purch. power gain/loss reported in income. Beneish model: Used to detect earnings manipulation based on eight variables. High-quality earnings are: 1. Sustainable: Expected to recur in future.2. Adequate: Cover company’s cost of capital. IFRS AND U.S. GAAP DIFFERENCESReclassification of passive investments:IFRS —Restricts reclassification into/out of FVPL. U.S. GAAP —No such restriction. Impairment losses on passive investments:IFRS —Reversal allowed if due to specific event. U.S. GAAP —No reversal of impairment losses. Fair value accounting, investment in associates:   IFRS —Only for venture capital, mutual funds, etc. U.S. GAAP —Fair value accounting allowed for all. Goodwill impairment processes: IFRS - 1 step (recoverable amount vs. carrying value) U.S. GAAP —2 steps (identify; measure amount) Acquisition method contingent asset recognition:   IFRS —Contingent assets are not recognized.U.S. GAAP —Recognized; recorded at fair value. Prior service cost:IFRS —Recognized as an expense in P&L.U.S. GAAP - Reported in OCI; amortized to P&L. Actuarial gains/losses: IFRS —Remeasurements in OCI and not amortized. U.S. GAAP —OCI, amortized with corridor approach. Dividend/interest income and interest expense:   IFRS —Either operating or financing cash flows. U.S. GAAP —Must classify as operating cash flow. ROE decomposed (extended DuPont equation)Tax Interest EBIT   Burden Burden Margin NI EBT EBITROE =  ------- x  --------- x  ------------ xEBT EBIT revenue T otal Asset   T urnover revenue X FinancialLeverage average assetsaverage assets average equity Accruals Ratio (balance sheet approach) (NOAE nd  —NOABE g )accruals ratio ^ =(NOA end  + NOABE g ) /2 Accruals Ratio (cash flow statement approach) (NI - CFO - CFI)accruals ratio ^ =(NOA end  + NOABE g ) /2 CORPORATE FINANCE Capital Budgeting Expansion ãInitial ouday = FCInv + WCInvãCF = (S - C -D)(l -T) + D = (S - C)(l -T) + DTãTNOCF = SaLr + NWCInv - T(Salr - B.r) Capital Budgeting Replacement ãSame as expansion, except current after-tax salvage of old assets reduces initial outlay.ãIncremental depreciation is A in depreciation. Evaluating Projects with Unequal Lives ãLeast common multiple of lives method.ãEquivalent annual annuity (EAA) method: annuity w/PV equal to PV of project cash flows.  Effects of Inflation ãDiscount nominal (real) cash flows at nominal (real) rate; unexpected changes in inflation affect project profitability; reduces the real tax savings from depreciation; decreases value of fixed payments to bondholders; affects costs and revenues differently. Capital Rationing  ãIf positive NPV projects > available capital, choose the combination with the highest NPV. Real Options ãTiming, abandonment, expansion, flexibility, fundamental options. Economic and Accounting Income ãEcon income = AT CF + A in project’s MV.ãEcon dep. based on A in investment’s MV.ãEcon income is calculated before interest expense (cost of capital is reflected in discount rate).ãAccounting income = revenues - expenses.ãAcc. dep’n based on original investment cost.ãInterest (financing costs) deducted before calculating accounting income. Valuation Models ãEconomic profit = NO PAT - $WACCãMarket Value Added =t=i (1 + WACC)rãResidual income: = NI —equity charge; discounted at required return on equity.ãClaims valuation separates CFs based on equity claims (discounted at cost of equity) and debt holders (discounted at cost of debt).MM Prop I (No Taxes): capital structure irrelevant (no taxes, transaction, or bankruptcy costs). V = V VL VU MM Prop II (No Taxes): increased use of cheaper debt increases cost of equity, no change in<b+fOb-rd)MM Proposition I (With Taxes): tax shield adds value, value is maximized at 100% debt.VL = Vu + (txd)MM Proposition II (With Taxes): tax shield adds value, WACC is minimized at 100% debt. re = *0 +^0b -rd)(!-Tc) E Investor Preference Theories ãMM’s dividend irrelevance theory: In a no-tax/ no-fee world, dividend policy is irrelevant because investors can create a homemade dividend.ãDividend preference theory says investors prefer the certainty of current cash to future capital gains.ãTax aversion theory: Investors are tax averse to dividends; prefer companies buy back shares. Effective Tax Rate on Dividends Double taxation  or split rate  systems:eff. rate = corp. rate + (1 - corp. rate)(indiv. rate) Imputation  system: effective tax rate is the shareholder’s individual tax rate. Signaling Effects of Dividend Changes Initiation:  ambiguous signal. Increase:  positive signal. Decrease:  negative signal unless management sees many profitable investment opportunities. Price change when stock goes ex-dividend:Ar = °(1-T°) (1_  t cg) Target Payout Ratio Adjustment Model If company earnings are expected to increase and the current payout ratio is below the target payout ratio, an investor can estimate future dividends through the following formula:expected dividend =previousdividend+expected increase in EPS \ X/target payout ratio\xadjustment factor/ Dividend Coverage Ratios dividend coverage ratio = net income /dividendsFCFE coverage ratio= FCFE /(dividends + share repurchases) Share Repurchases ãShare repurchase is equivalent to cash dividend, assuming equal tax treatment.ãUnexpected share repurchase is good news.ãRationale for: (1) potential tax advantages, (2) share price support/signaling, (3) added flexibility, (4) offsetting dilution from employee stock options, and (5) increasing financial leverage. Dividend Policy Approaches ãResidual dividend: dividends based on earnings less funds retained to finance capital budget.ãLonger-term residual dividend: forecast capital budget, smooth dividend payout.ãDividend stability: dividend growth aligned with sustainable growth rate.ãTarget payout ratio: long-term payout ratio target. Stakeholder impact analysis (SIA): Forces firm to identify the most critical groups. Ethical Decision Making    Friedman Doctrine: Only responsibility is to increase profits “within the rules of the game. ” Utilitarianism: Produce the highest good for the largest number of people. Kantian ethics: People are more than just an economic input and deserve dignity and respect. Rights theories: Even if an action is legal, it may violate fundamental rights and be unethical.  Justice theories: Focus on a just distribution of economic output (e.g., “veil of ignorance”). Corporate Governance Objectives ãMitigate conflicts of interest between(1) managers and shareholders, and (2) directors and shareholders.ãEnsure assets used to benefit investors and stakeholders. Merger Types: horizontal, vertical, conglomerate. Merger Motivations: achieve synergies, more rapid growth, increased market power, gain access to unique capabilities, diversify, personal benefits for managers, tax benefits, unlock hidden value, achieving international goals, and bootstrapping earnings. Pre-Offer Defense Mechanisms: poison pills and puts, reincorporate in a state w/restrictive takeover laws, staggered board elections, restricted voting rights, supermajority voting, fair price amendments, and golden parachutes. Post-Offer Defense Mechanisms: litigation, greenmail, share repurch, leveraged recap, the “crown jewel,” “Pac-Man,” and “just say no” defenses, and white knight/white squire. The Herfindahl-Hirschman Index (HHI):  market power = sum of squared market shares for all industry firms. In a moderately-concentrated industry (HHI 1,000 to 1,800), a merger is likely to be challenged if HHI increases 100 points (or increases 50 points for HHI >1,800). n HHI = ^(MSiXl00)2 i=l Methods to Determine Target Value DCF method:  target proforma FCF discounted at adjusted WACC. Comparable company analysis-,  target value from relative valuation metrics on similar firms + takeover premium. Comparable transaction analysis : target value from takeover transaction; takeover premium included. Merger Valuations Combinedfirm: Y at  = V a  + V t  + S —C Takeover premium (to target): GainT = TP = PT —VT Synergies (to acquirer): GainA= S —TP = S —(PT —VT) Merger Risk & Reward Cash offer:  acquirer assumes risk & receives reward. Stock offer:  some of risks & rewards shift to target. If higher confidence in synergies; acquirer prefers cash & target prefers stock. Forms of divestitures: equity carve-outs, spin-offs, split-offs, and liquidations. EQUITY  Holding period return: = r=Pl~ p 0+ cfi = p 1+ cfl   x Po Po Required return: Minimum expected return an investor requires given an asset’s characteristics. Internal rate of return (IRR): Equates discounted cash flows to the current price. Equity risk premium: required return = risk-free rate + ((3 x ERP) Gordon growth model equity risk premium: = 1 -yr forecasted dividend yield on market index + consensus long-term earnings growth rate - long-term government bond yield Ibbotson-Chen equity risk premium [1 + i] x [1 + rEg] x [1 + PEg] -1 + Y —RF + ^SMB.j X ^ Models of required equity return: ã CAPM:   r. = RF + (equity risk premium x 0.)ã  Multifiactor model:  required return = RF + (risk premium) j + ... + (risk premium) nã Fama-French : r. = RF + 0 , . x (R —RF)  j 1mkt,j xmkt ' small _ Pyg) + ^HML.j X ~~ Pastor-Stambaugh model:  Adds a liquidity factor to the Fama-French model.ã  Macroeconomic multifiactor models:  Uses factors associated with economic variables.ã Build-up method:  r = RF + equity risk premium + size premium + specific-company premium Blume adjustment: adjusted beta = (2/3 x raw beta) + (1/3 x 1.0)  WACC = weighted average cost of capital MVdebt ^^debt+equity rd (l - T) + MV. equity M Vdebt+equity Discount cash flows to  firm  at WACC,  and cash flows to equity  at the required return on equity. Discounted Cash Flow (DCF) Methods  Use dividend discount models (DDM) when:ãFirm has dividend history.ãDividend policy is related to earnings.ãMinority shareholder perspective.Use free cash flow (FCF) models when:ãFirm lacks stable dividend policy.ãDividend policy not related to earnings.  ãFCF is related to profitability.ãControlling shareholder perspective.Use residual income (RI) when:ãFirm lacks dividend history.ãExpected FCF is negative. Gordon Growth Model (GGM) Assumes perpetual dividend growth rate:V„=-^r-gMost appropriate for mature, stable firms. Limitations are:ãVery sensitive to estimates of r   and  g. ãDifficult with non-dividend stocks.ãDifficult with unpredictable growth patterns (use multi-stage model). Present Value of Growth Opportunities V0 = + PVGOr 2-Stage Growth Model Step 1: Calculate high-growth period dividends. Step 2: Use GGM for terminal value at end of high-growth period.Step 3: Discount interim dividends and terminal value to time zero to find stock value. H-Model V0 = Dox(l + gL)] |[D q  xHx(gs r~gL r~gL gL ) Sustainable Growth Rate: b x ROE. Solving for Required Return For Gordon (or stable growth) model:Dir = ^ + gAo Free Cash Flow to Firm (FCFF) Assuming depreciation is the only NCC:FCFF = NI + Dep + [Int x (1 —tax rate)] - FCInv- WCInv.FCFF = [EBIT x (1 —tax rate)] + Dep —FCInv- WCInv.FCFF = [EBITDA x (1 —tax rate)] + (Dep x tax rate) —FCInv - WCInv.FCFF = CFO + [Int x (1 —tax rate)] —FCInv. Tee Cash Flow to Equity (FCFE) FCFE = FCFF —[Int x (1 —tax rate)] + Net borrowing.FCFE = NI + Dep - FCInv - WCInv + Net borrowing.FCFE = NI - [(1 - DR) x (FCInv - Dep)]- [(1 - DR) x WCInv]. (Used to forecast.) Single-Stage FCFF/FCFE Models FCFFãFor FCFF valuation: V0 =  -----------  - —WACC-gFCFFãFor FCFE valuation: V0 =  -------- -r~g 2-Stage FCFF/FCFE Models Step 1: Calculate FCF in high-growth period.Step 2: Use single-stage FCF model for terminal value at end of high-growth period.Step 3: Discount interim FCF and terminal value to time zero to find stock value; use WACC for FCFF, r for FCFE. Price to Earnings (P/E) Ratio  Problems with P/E:ãIf earnings < 0, P/E meaningless.ãVolatile, transitory portion of earnings makes interpretation difficult.ãManagement discretion over accounting choices affects reported earnings.  Justified P/E leading P/E =1-br“gtrailing P/E = ^-b)(1 + g)r-g Justified dividend yield:Do _ r - g0! + g Normalization Methods ãHistorical average EPS.ãAverage ROE. Price to Book (P/B) Ratio Advantages:ãBV almost always > 0. ãBV more stable than EPS.ãMeasures NAV of financial institutions. Disadvantages:ãSize differences cause misleading comparisons.ãInfluenced by accounting choices.ãBV ^ MV due to inflation/technology. j ustified P /B = —&r“g Price to Sales (P/S) Ratio Advantages:ãMeaningful even for distressed firms.ãSales revenue not easily manipulated.ãNot as volatile as P/E ratios.ãUseful for mature, cyclical, and start-up firms. Disadvantages:ãHigh sales ^ imply high profits and cash flows.ãDoes not capture cost structure differences.ãRevenue recognition practices still distort sales. justified P/S = PMox(1~b)(1 + g)r-g DuPont Model ROE =net income sales x salestotal assets x total assets equity Price to Cash Flow Ratios Advantages:Cash flow harder to manipulate than EPS.More stable than P/E.Mitigates earnings quality concerns, disadvantages:Difficult to estimate true CFO.FCFE better but more volatile. Method of Comparables Firm multiple > benchmark implies overvalued. Firm multiple < benchmark implies undervalued. Fundamentals that affect multiple should be similar between firm and benchmark. Residual Income Models ãRI = Et —(r x Bt_i) = (ROE —r) x Bt_iãSingle-stage RI model:(ROE —r)xB0V0=B0 +r“gãMultistage RI valuation: Vo = Bo + (PV of interim high-growth RI) + (PV of continuing RI) Economic Value Added® ãEVA = NOPAT - $WACC; NOPAT = EBIT(1-1) Private Equity Valuation 1DLOC = 1 -1 + Control PremiumTotal discount = 1 - [(1 - DLOC)(l - DLOM)]. The DLOM varies with the following.ãAn impending IPO or firm sale [   DLOM.The payment of dividends J, DLOM.Earlier, higher payments J, DLOM. Restrictions on selling stock J DLOM.A greater pool of buyers J, DLOM.Greater risk and value uncertainty | DLOM. FIXED INCOME Price of a T-period zero-coupon bond:Py =  ------------ y-(! + S t )Forward price of zero-coupon bond: Sno=—  i + ZO’k))Forward pricing model:B P()+k>F0’k) p. AJ Forward rate model: [1 +/j,k)]k=[l+S((<10]«*k»/(l+S()i “Riding the yield curve”: Holding bonds with maturity > investment horizon, with upward sloping yield curve.swap spread = swap rate - treasury yield TED spread:= (3-month LIBOR rate) —(3-month T-bill rate) Libor-OIS spread= LIBOR rate - “overnight indexed swap” rate Term Structure of Interest Rates   Traditional theories: Unbiased (pure) expectations theory.Local expectations theory.Liquidity preference theory.Segmented markets theory.Preferred habitat theory.Modern term structure models:Cox-Ingersoll-Ross: dr   = a(b-r)^ + afrdz  Vasicek model: dr =  a(b - r  )dt+ adz  Ho-Lee model: dr =Qdt+ adz t t t Managing yield curve shape risk:AP/P » -D l A xl  - DsAxs -DcAxc (L = level,  S = steepness , C = curvature) Yield volatility: Long-term  <— uncertainty regarding the real economy and inflation. Short term  <— uncertainty re: monetary policy. Long-term yield volatility is generally lower than volatility in short-term yields.Value of option embedded in a bond:V = V -V call straight bond callable bond V = V -V put putable bond straight bond When interest rate volatility increases:  v. .T,v . T>v  call option 1put option 1 V t 1'k 5putable bond 1callable bond' Upward sloping yield curve: Results in lower call value and higher put value.When binomial tree assumed volatility increases :ãcomputed OAS of a callable  bond decreases. ãcomputed OAS of a  putable  bond increases. effective duration = _ BV Ay - BV h Ay 2 x BV0 x Ay. . BV Ay + BV+Ay - (2 >errective convexity =  --------------------------  - —BV0 x Ay2Effective duration:ãED (callable bond) < ED (straight bond).ãED (putable bond) < ED (straight bond).ãED (zero-coupon) « maturity of the bond.ãED fixed-rate bond < maturity of the bond.ãED of floater « time (years) to next reset.
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