CFA level i quick sheet 2019

CFA level i quick sheet 2019 CFA level i quick sheet 2019 CFA level i quick sheet 2019 CFA level i quick sheet 2019 CFA level i quick sheet 2019 CFA level i quick sheet 2019 CFA level i quick sheet 2019 CFA level i quick sheet 2019 CFA level i quick sheet 2019 CFA level i quick sheet 2019

2018 CRITICAL CONCEPTS FOR THE CFA EXAM CFA® EXAM REVIEW CFA LEVEL I SMARTSHEET ® FUNDAMENTALS FOR CFA® EXAM SUCCESS WCID184 efficientlearning.com/cfa ETHICAL AND QUANTITATIVE METHODS PROFESSIONAL STANDARDS TIME VALUE OF MONEY ETHICS IN THE INVESTMENT PROFESSION STANDARDS OF PROFESSIONAL CONDUCT PV = FV (1 + r) N risk (higher is better) • PV and FV of ordinary annuity and annuity due PVAnnuity Duee = PVOrdinar inary y Annuity × (1 + r) FVAnnuity Duee = FVOrdinar inary y Annuity × (1 + r) PMT I/Y 360 − (t × rBD ) R G =  n (1 + R1 ) × (1 + R ) ×…× ×… × (1 + R n )  − R MM = HPY × (360/t) Bond Equivalent Yieldmean: used to determine the average cost of • Harmonic historical performance when first claiming compliance, then add one year of compliant performance each subsequent year so that the firm eventually presents a (minimum) performance record for 10 years • Nine major sections: Fundamentals of Compliance; Input data; Calculation Methodology; Composite Construction; Disclosures; Presentation and Reporting; Real Estate; Private Equity; and Wrap Fee/Separately Managed Account (SMA) Portfolios shares purchased over time 0.5 BEY = [(1 + EAY) − 1] × Harmonic mean: X H = N N ∑x i =1 i • Variance: average of the squared deviations around the mean n σ = ∑ (X i − µ)2 i =1 n ∑ (X i − X) i =1 sp PROBABILITY CONCEPTS • Expected value and variance of a random variable (X) using probabilities E(X) = P( X1 ) X1 + P(X )X + … P(X X n )X )X n n σ (X) = ∑ P(X i ) [X [ X i − E (X)]2 i =1 • Covariance and correlation of returns Corr(R A ,R B ) = ρ(R A ,R ,RB) = Cov(R R A ,R ,RB) (σ A )(σ B ) • Expected return on a portfolio N E(R R p ) = ∑ wi E E(R (R i ) = w1E(R R1 ) + w E E(R (R ) + i =1 + w N E(R RN ) • Variance of a 2-asset portfolio Va R p ) = w2A σ ((R Var( R A ) + w2B σ ((R R B ) + 2w A w Bρ((R R A ,,R R B )σ (R A )σ ((R RB) BINOMIAL DISTRIBUTION • Probability of x successes in n trials (where the probability of success, p, is equal for all trials) is given by: P(X X = x) x) = nCx (p))x ((1 – p)n – x • Expected value and variance of a binomial random variable E(x) = n × p σ = n × p × (l-p) NORMAL DISTRIBUTION • • • • • • 50% of all observations lie in the interval µ ± (2/3)σ 68% of all observations lie in the interval µ ± 1σ 90% of all observations lie in the interval µ ± 1.65σ 95% of all observations lie in the interval µ ± 1.96σ 99% of all observations lie in the interval µ ± 2.58σ A z-score is used to standardize a given observation of a normally distributed random variable z = (obser erve ved value − population mean)/standard nda deviationn = (x à) / ndard Roys safety-rst criterion: used to compare shortfall risk of portfolios (higher SF ratio indicates lower shortfall risk) Shortf hortfal hortf tfall ratio (SF Ratio) = n s2 = rp − rf platykurtic (negative excess kurtosis), mesokurtic (same kurtosis as normal distribution; i.e zero excess kurtosis) Professionalism DISCOUNTED CASH FLOW APPLICATIONS A Knowledge of the Law • Positive net present value (NPV) projects increase B Independence and Objectivity shareholder wealth C Misrepresentation • For mutually exclusive projects, choose the project with D Misconduct the highest positive NPV II Integrity of Capital Markets • Projects for which the IRR exceeds the required rate of A Material Nonpublic Information return will have positive NPV B Market Manipulation • For mutually exclusive projects, use the NPV rule if the III Duties to Clients NPV and IRR rules conflict A Loyalty, Prudence and Care YIELDS FOR US TREASURY BILLS B Fair Dealing C Suitability • Bank discount yield D Performance Presentation D 360 rBD = × E Preservation of Confidentiality F t IV Duties to Employers • Holding period yield A Loyalty B Additional Compensation Arrangements P − P + D1 P1 + D1 HPY = = −1 P0 P0 C Responsibilities of Supervisors V Investment Analysis, Recommendations and Actions • Money market yield A Diligence and Reasonable Basis 360 × rBD B Communication with Clients and Prospective R MM = 360 − (t × rBD ) Clients C Record Retention R MM = HPY × (360/t) DiscounTeD cash floW applicaTions VI Conflicts of Interest A Disclosure of Conflicts • Effective annual yield B Priority of Transactions Effective Annual Yield C Referral Fees EAY = (1 + HPY)365/ t − VII Responsibilities as a CFA Institute Member or CFA where: Candidate HPY =STATISTICAL holding period yield CONCEPTS A Conduct as Participants in CFA Institute Programs t = numbers of days remaining till maturity • Data scales: Nominal (lowest), Ordinal, Interval, Ratio B Reference to CFA Institute, the CFA Designation, HPY = (1 + EAY) t /365 − (highest) and the CFA Program • Arithmetic Money Market Yield mean: simple average GLOBAL INVESTMENT PERFORMANCE • Geometric mean return: used to average rates of change 360 ì rBD STANDARDS (GIPSđ) (or over time = R MMgrowth) is voluntary Sharpe ar ratio = arpe • Positive skew: mode < median < mean • Kurtosis: leptokurtic (positive excess kurtosis), • PV of a perpetuity PVPerpetuity = • Compliance by investment management firms with GIPS s X • Sharpe ratio: used to measure excess return per unit of I basis in order to claim compliance Coefficient of variatio ar ariatio n= flow situational influences, focusing on the immediate rather than long-term outcomes/consequences • General ethical decision-making framework: identify, consider, decide and act, reflect • CFA Institute Professional Conduct Program sanctions: public censure, suspension of membership and use of the CFA designation, and revocation of the CFA charter (but no monetary fine) • Third-party verification of GIPS compliance is optional • Present a minimum of five years of GIPS-compliant dispersions of data sets (lower is better) • Present value (PV) and future value (FV) of a single cash • Challenges to ethical behavior: overconfidence bias, • Comply with all requirements of GIPS on a firm-wide • Standard deviation: positive square root of the variance • Coefficient of variation: used to compare relative E (RP ) − RT σP n −1 Wiley © 2018 efficientlearning.com/cfa SAMPLING THEORY TECHNICAL ANALYSIS MARKET STRUCTURES • Central limit theorem: Given a population with any • Reversal patterns: head and shoulders, inverse head • Perfect competition • Minimal barriers to entry, sellers have no pricing power • Demand curve faced by an individual firm is perfectly probability distribution, with mean, µ, and variance, σ2, the sampling distribution of the sample mean x, computed from sample size n will approximately be normal with mean, µ (the population mean), and variance, σ2/n, when the sample size is greater than or equal to 30 • The standard deviation of the distribution of sample means is known as the standard error of sample mean • When the population variance is known, the standard error of sample mean is calculated as σx = σ • When the population variance is not known, the standard error of sample mean is calculated as s sx = n • Confidence interval for unknown population parameter based on z-statistic σ n based on t-statistic Small Sample Large Sample n < 30 n > 30 When Sampling from a: Normal distribution with known variance z‐statistic z‐statistic Normal distribution with unknown variance t‐statistic t‐statistic* Non-normal distribution with known variance not available z‐statistic Non-normal distribution with unknown variance not available t‐statistic* * Use of z‐statistic is also acceptable HYPOTHESIS TESTING H0 : μ ≤ μ0 Null hypothesis Alternate hypothesis Ha : μ > μ0 One tailed (lower tail) test H0 : μ ≥ μ0 Two‐tailed H0 : μ = μ0 Fail to reject null if Reject null if Test statistic > critical value Test statistic ≤ critical value P‐value represents Probability that lies above the computed test statistic Ha : μ < μ0 Test statistic < critical value Test statistic ≥ critical value Probability that lies below the computed test statistic Ha : μ ≠ μ0 Test statistic < lower critical value Test statistic > upper critical value Lower critical value ≤ test statistic ≤ upper critical value Probability that lies above the positive value of the computed test statistic plus the probability that lies below the negative value of the computed test statistic • Type I versus Type II errors Decision Do not reject H0 H0 is True Correct decision Incorrect decision Type I error Significance level = P(Type I error) Reject H0 H0 is False Incorrect decision Type II error Correct decision Power of the test = − P(Type II error) • Hypothesis test concerning the mean of a single population x − µ0 s n • Hypothesis test concerning the variance of a normally distributed population ( n − 1) s σ 20 • Hypothesis test related to the equality of the variance of two populations F= s12 s22 pricing power • Product is differentiated through non-price strategies • Demand curve faced by the monopoly is the industry demand curve (downward sloping) • An unregulated monopoly can earn economic profits in the long run • Monopolistic competition • Low barriers to entry, sellers have some degree of pricing power non-price strategies • Own-price elasticity of demand is calculated as: • Oligopoly • High costs of entry, sellers enjoy substantial pricing power %∆Q QDx … (Equation 6) %∆Px • Product is differentiated on quality, features, equals 1, demand is said to be unit elastic • If the absolute value of price elasticity of demand lies between and 1, demand is said to be relatively inelastic • If the absolute value of price elasticity of demand is greater than 1, demand is said to be relatively elastic • Income elasticity of demand is calculated as: % change in quantity demanded % change in income marketing and other non-price strategies • Pricing strategies: pricing interdependence (kinked demand curve), Cournot assumption, game theory (Nash equilibrium), Stackelberg model (dominant firm) • Firms always maximize profits at the output level where MR = MC • Identification of market structure • N-firm concentration ratio • HHI (add up the squares of the market shares of each of the largest N companies in the market) AGGREGATE SUPPLY AND DEMAND • Cross-price elasticity of demand is calculated as: EC = make normal profits • Monopoly • High barriers to entry, single seller has considerable • Demand curve faced by each firm is downward sloping • In the long run all will make normal profits • Positive for a normal good • Negative for an inferior good • One-tailed versus two-tailed tests χ2 = ECONOMICS EI = elastic (horizontal) • Average revenue (AR) = Price (P) = MR • In the long run, all firms in perfect competition will • Product is differentiated through advertising and other • If the absolute value of price elasticity of demand • When to use z-statistic or t-statistic t-stat = • EDPx = s n Type of test One tailed (upper tail) test • DEMAND ELASTICITIES • Confidence interval for unknown population parameter x ± tα • • n x ± z α /2 • and shoulders, double top and bottom, triple top and bottom Continuation patterns: triangles (ascending/descending/ symmetrical), rectangles, flags and pennants Price-based indicators: moving averages, Bollinger bands, momentum oscillators (rate of change, relative strength index, stochastic, moving average convergence/ divergence) Sentiment indicators: opinion polls, put-call ratio, VIX, margin debt levels, short interest ratio Flow of funds indicators: Arms index, margin debt, mutual fund cash positions, new equity issuance, secondary offerings Cycles: Kondratieff (54-year economic cycle), 18-year (real estate, equities), decennial (best DJIA performance in years that end with a 5), presidential (third year has the best stock market performance) % change in quantity demanded % change in price of substitute or complement • Components of GDP • Expenditure approach GDP = C + I + G + (X (X − M M) • Income approach • Positive for substitutes • Negative for complements • Normal good: substitution and income effects reinforce one another • Inferior good: income effect partially mitigates the substitution effect • Giffen good: inferior good where the income effect outweighs the substitution effect, making the demand curve upward sloping • Veblen good: status good with upward sloping demand curve GDP = National income + Capital consumption allowance + Statistical discrepancy … (Equation 1) • Equality of Expenditure and Income S = I + (G − T) + ( X − M) … (Equation 7) • To finance a fiscal deficit (G – T > 0), the private sector must save more than it invests (S > I) and/or imports must exceed exports (M > X) • Factors causing a shift in aggregate demand (AD) PROFIT MAXIMIZATION, BREAKEVEN AND SHUTDOWN ANALYSIS An Increase in the Following Factors Shifts the AD Curve Reason Stock prices Rightward: Increase in AD Higher consumption • Profits are maximized when the difference between total Housing prices Rightward: Increase in AD Higher consumption Consumer confidence Rightward: Increase in AD Higher consumption Business confidence Rightward: Increase in AD Higher investment Capacity utilization Rightward: Increase in AD Higher investment Government spending Rightward: Increase in AD Government spending a component of AD Taxes Leftward: Decrease in AD Lower consumption and investment Bank reserves Rightward: Increase in AD Lower interest rate, higher investment and possibly higher consumption Exchange rate (foreign currency per unit domestic currency) Leftward: Decrease in AD Lower exports and higher imports Global growth Rightward: Increase in AD Higher exports revenue (TR) and total cost (TC) is at its highest The level of output at which this occurs is the point where: • Marginal revenue (MR) equals marginal cost (MC); and • MC is not falling • Breakeven occurs when TR = TC, and price (or average revenue) equals average total cost (ATC) at the breakeven quantity of production The firm is earning normal profit • Short-run and long-run operating decisions Revenue/ Cost Relationship Short-run Decision Long-run Decision TR = TC Continue operating Continue operating TR > TVC, but < TC Continue operating Exit market TR < TVC Shut down production Exit market • Factors causing a shift in aggregate supply (AS) Wiley © 2018 efficientlearning.com/cfa An Increase in Shifts SRAS Shifts LRAS Reason Supply of labor Rightward Rightward Increases resource base Supply of natural resources Rightward Rightward Increases resource base Supply of human capital Rightward Rightward Increases resource base Supply of physical capital Rightward Rightward Increases resource base Productivity and technology Rightward Rightward Improves efficiency of inputs Nominal wages Leftward No impact Increases labor cost Input prices (e.g., energy) Leftward No impact Increases cost of production Expectation of future prices Rightward No impact Anticipation of higher costs and/or perception of improved pricing power Business taxes Leftward No impact Increases cost of production Subsidy Rightward No impact Lowers cost of production Exchange rate Rightward No impact Lowers cost of production • Impact of changes in AD and AS An increase in AD A decrease in AD An increase in AS A decrease in AS Real GDP Unemployment Rate Aggregate Level of Prices Increases Falls Increases Falls Falls Increases Falls Increases Increases Falls Falls Increases • Effect of combined changes in AD and AS Change in AS Change in AD Effect on Real GDP Increase Decrease Increase Decrease Increase Decrease Decrease Increase Increase Decrease Uncertain Uncertain Effect on Aggregate Price Level Uncertain Uncertain Decrease Increase BUSINESS CYCLES • Phases: trough, expansion, peak, contraction (or recession) • Theories • Neoclassical (Say’s Law) • Austrian (misguided government intervention) • Keynesian (advocates government intervention during a recession) • Monetarist (steady growth rate of money supply) • New Classical (business cycles have real causes, no government intervention) • Neo-Keynesian (prices and wages are downward sticky, government intervention is useful in eliminating unemployment and restoring macroeconomic equilibrium) • Unemployment: natural rate vs frictional vs structural vs cyclical • Prices indices: using a fixed basket of goods and services to measure the cost of living results in an upward bias in the computed inflation rate due to substitution bias, quality bias and new product bias • Economic indicators • Leading (used to predict economy’s future state) • Coincident (used to identify current state of the economy) • Lagging (used to identify the economy’s past condition) MONETARY AND FISCAL POLICY • Quantity theory of money MV = PY • Contractionary monetary policy (reduce money supply and increase interest rates) is meant to rein in an overheating economy Expansionary monetary policy (increase money supply and reduce interest rates) is meant to stimulate a receding economy • Limitations of monetary policy: • Central bank cannot control amount of savings • Central bank cannot control willingness of banks to extend loans • Central bank may lack credibility • Contractionary fiscal policy (reduce spending and/ or increase taxes) is used to control inflation in an expansion Expansionary fiscal policy (increase spending and/or reduce taxes) is used to raise employment and output in a recession • Fiscal multiplier [1 − MPC(1 − t )] FINANCIAL REPORTING AND ANALYSIS FINANCIAL REPORTING BASICS • Types of audit opinions: unqualified, qualified, adverse, • Limitations fiscal policy: recognition, action and impact lags • Relationships between monetary and fiscal policy • Easy fiscal policy/tight monetary policy – results in higher output and higher interest rates (government expenditure would form a larger component of national income) • Tight fiscal policy/easy monetary policy – private sector’s share of overall GDP would rise (as a result of low interest rates), while the public sector’s share would fall • Easy fiscal policy/easy monetary policy – this would lead to a sharp increase in aggregate demand, lowering interest rates and growing private and public sectors • Tight fiscal policy/tight monetary policy – this would lead to a sharp decrease in aggregate demand, higher interest rates and a decrease in demand from both private and public sectors disclaimer • Accruals: unearned or deferred revenue (liability), unbilled or accrued revenue (asset), prepaid expenses (asset), accrued expenses (liability) • Qualitative characteristics of financial information: relevance, faithful representation, comparability, verifiability, timeliness, understandability (first two are fundamental qualitative characteristics) • General features of financial statements: fair presentation, going concern, accrual basis, materiality and aggregation, no offsetting, frequency of reporting, comparative information, consistency INCOME STATEMENTS • Revenue recognition methods: percentage of • INTERNATIONAL TRADE • Comparative advantage: a country’s ability to produce a good at a lower opportunity cost than its trading partners • Ricardian model: labor is the only variable factor of production and differences in technology are the key source of comparative advantage • Heckscher-Ohlin model: capital and labor are variable factors of production and differences in factor endowments are the primary source of comparative advantage • Effect of tariffs, import quotas, export subsidies and voluntary export restraints • Price, domestic production and producer surplus increase • Domestic consumption and consumer surplus decrease • Balance of payments components • Current account (merchandise trade, services, income receipts and unilateral transfers) • Capital account (capital transfers and sales/purchases of non-produced, non-financial assets) • Financial account (financial assets abroad and foreignowned financial assets in the reporting country) • Current account surplus or deficit • • • completion, completed contract, installment method, cost recovery method Discontinued operations: reported net of tax as a separate line item after income from continuing operations Unusual or infrequent items: listed as separate line items, included in income from continuing operations, reported before-tax Accounting changes • Change in accounting principle (applied retrospectively) • Change in an accounting estimate (applied prospectively) • Correction of prior-period errors (restate all priorperiod financial statements) Basic EPS Basic EPS = Net incomee − Preferred dividends Weighted average number of share s outstanding hare • Diluted EPS (taking into account all dilutive securities) Diluted EPS = Conver Convertible Conver  Convertible  prefe pref eferred rred +  × (1 − t) debt  interest  dividends Shares from Shares from Weighted Shares conversion conve convers rsio ion n of of conversion of + issuable from + average + convertible convertible conver convertible stock options shares prefe ef rred shares efe debt Net income − Preferred  + dividends   BALANCE SHEETS • Accounting for gains and losses on marketable securities CA = X – M = Y – (C + I + G) CURRENCY EXCHANGE RATES Balance Sheet Held‐to‐Maturity Securities Reported at cost or amortized cost • Exchange rates are expressed using the convention A/B; i.e number of units of currency A (price currency) required to purchase one unit of currency B (base currency) USD/GBP = 1.5125 means that it will take 1.5125 USD to purchase GBP • Real exchange rate Real exchange rate DC/FCC = SDC/ PFC //P PDC ) C/FC FC × ((P • Forward exchange rate (arbitrage-free) FDC/FC = SFC/DC × (1 + rDC ) (1 + rDC ) or FDC/FC = SDC/FC C/FC × (1 + rFC ) (1 + rFC ) • Exchange rate regimes: dollarization, monetary union, fixed parity, target zone, crawling pegs, fixed parity with crawling bands, managed float, independently floating rates Items recognized on the income statement Interest income Realized gains and losses Available‐for‐Sale Securities Reported at fair value Trading Securities Reported at fair value Unrealized gains or losses due to changes in market values are reported in other comprehensive income within owners’ equity Dividend income Dividend income Interest income Interest income Realized gains and losses Realized gains and losses Unrealized gains and losses due to changes in market values • Common-size balance sheet: expresses each balance sheet as a % of total assets to allow analysts to compare firms of different sizes CASH FLOW • CFO (direct method) • Step 1: Start with sales on the income statement • Step 2: Go through each income statement account and adjust it for changes in all relevant working capital accounts on the balance sheet • Step 3: Check whether changes in these working capital accounts indicate a source or use of cash Wiley © 2018 efficientlearning.com/cfa • Step 4: Ignore all non-operating items and non-cash charges • CFO (indirect method) • Step 1: Start with net income • Step 2: Go up the income statement account and remove the effect of all non-cash expenses and gains from net income • Step 3: Remove the effect of all non-operating activities from net income • Step 4: Make adjustments for changes in all working capital accounts • Free cash flow to the firm (FCFF) FCFF = NI + NCC C + [In [[Int Intt * (1 − tax rate)]] − FCI FCInv F CInv nv − WCInv FCFF = CFO CFO + [[Int * (1 − tax tax rat rrate)] ate) e)]] − F FCInv • Profitability ratios Operating profit of margin = ofit Pretax margin = reserve • Net income under FIFO = Net income under LIFO + Change in LIFO reserve × (1 – tax rate) • Equity under FIFO = Equity under LIFO + LIFO reserve ì Operating profit Revenue (1 tax rate) Liabilities under FIFO = Liabilities under FIFO + LIFO EBT (earnings ear earnings before tax, but afte af r interes nter t) nteres Revenue Net profit margin = reserve × tax rate LONG-LIVED ASSETS Net profit Revenue • Capitalizing vs expensing Net income ROA = Average total assets Adjusted ROA = • Free cash flow to equity (FCFE) FCFE = CFO − FCInv + Net borrowing • COGS under FIFO = COGS under LIFO – Change in LIFO Gross profit Gross profit margin = Revenue Net incomee + Inter nteres est expense (1 − Tax rate) Average total assets Operating ROA = Operating income or EBIT Average total assets FINANCIAL ANALYSIS TECHNIQUES • Activity ratios Return on total capital = Cost of goods sold Average inventory nventor nventory Inventory y tturnover = Days of inventor invent y on hand (DOH) = Receivabless tturnover = 365 Inventory nventory turnove nventor ur r Revenue Average receivables 365 Days of sales outstanding (DSO) = Receivables turnove tur r Payabless tturnover = Purchases Averagee ttrade payables Depreciation expense = Net income Return on equity = Average total equity Revenue Average working or orking capital Revenue Average total assets • Liquidity ratios Current ratio at = atio Quick ratio at = atio Cash ratio = Current assets Current liabilities Cash + Shor ortt-term marketable investments + Receivables Current liabilities Cash + Shorthor term mark hortma etable investments Current liabilities Defensive interval ratio = Cash + Shor hortt-term marketable investments + Receivables Daily cash expenditures Cash conversion cycle = DSO + DOH − Number of days of payables • Solvency ratios Debt -to-assets ratio = Net incomee − Preferred dividends Average common equity DDB depreciatio depr n in Year X = Depreciation Components ROE = ↓ ↓ ROA Leverage Net income Average total assets Revenue × × Revenue Average total assets Average share holders’ equity hare ↓ ↓ Net profit margin ROE = Interest burden Assett ttur urnover urnove ↓ ↓ Leverage Accumulated depreciation Annual depreciation expense Remaining useful life lif = Net investment in fixed assets Annual depreciation expense model under US GAAP) Net income EBT Average total assets EBIT Revenue × × × × EBT EBIT Revenue Average total assets Avg shareholders eholde ’ equity eholders ↓ ↓ ↓ Tax burden EBIT margin Leverage • Dividend-related measures Dividend payout ratio at = atio Retention Rate = Common share dividends hare Net income attributable ttr ttributable to common share s hare Net income attributable ttr ttributable to common share s − C hare Common share dividends hare Net income attributable ttr ttributable to common share s hare Sustainable growth rate = Retention rate ì ROE INVENTORIES If revaluation initially decreases the asset’s carrying amount, the decrease is recognized as a loss on the income statement • If revaluation initially increases the asset’s carrying amount, the increase goes directly to equity • Impairment of property, plant and equipment • IFRS: asset is impaired when its carrying amount exceeds its recoverable amount (impairment loss is the difference between these two amounts) • US GAAP: asset is impaired when its carrying value exceeds the total value of its undiscounted expected future cash flows (impairment loss is the difference between the asset’s carrying value and its fair value) DEFERRED TAXES (DUE TO TEMPORARY DIFFERENCES) • A deferred tax liability (asset) arises when: • Taxable income is lower (higher) than pretax accounting profit • Taxes payable is lower (higher) than income tax expense • If a company has a DTL, a reduction (increase) in tax rates Total debt Shareholders eholde ’ equity eholders EBIT Interest coverage ratio = Interest payments Average age of asset = • Revaluation of long-lived assets • IFRS allows revaluation model or cost model (only cost • LIFO vs FIFO with rising prices and stable inventory levels Average total assets Average total equity Gross investment in fixed assets Annual depreciation expense ↓ Assett ttur urnover urnove Total debt Total assets Financial leverage ratio = Estimated useful ef life eful lif = Net income Average total assets ROE = × Average total assets Average share holders’ equity hare Total debt Debt -to-capital ratio at = atio Total debtt + S Share holders’ equity hare Debt -to-equity ratio = × Book value att tthe beginning of Year X Depreciable life lif • Depreciation components Revenue Fixed assett tturnover = Averagee ffixed assets Total assett tturnover = Original cost − Salvage value Depreciable life lif • Double declining balance (DDB) • DuPont decomposition of ROE 365 Number of days of payables = Payables turnove tur r Working capital turnover = Expensing Lower Higher Lower Lower Lower Higher Higher Higher • Depreciation expense • Straight line EBIT Shorthor term debt + Long-term debt + Equity hort- Return on common equity = Capitalizing Higher Lower Higher Higher Higher Lower Lower Lower Net income (first year) Net income (future years) Total assets Shareholders’ equity Cash flow from operations Cash flow from investing Income variability Debt-to-equity • LIFO to FIFO conversion with rising prices and stable or rising inventory quantities • Inventory under FIFO = Inventory under LIFO + LIFO reserve would reduce (increase) liabilities, reduce (increase) income tax expense, and increase (reduce) equity • If a company has a DTA, a reduction (increase) in tax rates would reduce (increase) assets, increase (reduce) income tax expense, and reduce (increase) equity • DTA carrying value should be reduced to the expected recoverable amount using a valuation allowance Wiley © 2018 efficientlearning.com/cfa ACCOUNTING FOR BONDS • Dividend discount model RISK MANAGEMENT • Effective interest method required under IFRS and D re = + g P0 • Financial risks: market, credit (default or counterparty • Bond yield plus risk premium • Non-financial risks: settlement, legal, compliance preferred under US GAAP • Interest expense for a given period is calculated as the book value of the liability at the beginning of the period multiplied by market interest rate at bond issuance • Coupon payments are classified as cash outflows • Book value of the bond liability at any point in time is the PV of the bond’s remaining cash flows (discounted at the market interest rate at issuance) LEASES • Lease accounting from lessee’s perspective: treating a lease as a finance lease (compared to an operating lease) results in: • Higher assets, current liabilities, long-term liabilities, EBIT, CFO, leverage ratios • Lower net income (early years), CFF, asset turnover, current ratio, ROA (early years), ROE (early years) • Same total cash flow FINANCIAL REPORTING QUALITY • Conditions conducive to issuing low quality financial reports: opportunity, motivation, rationalization • Mechanisms that discipline financial reporting quality: markets, regulatory authorities, registration requirements, auditors, private contracting CORPORATE FINANCE CORPORATE GOVERNANCE • Key areas of interest: economic ownership and voting control, board of directors representation, remuneration and company performance, investors in the company, strength of shareholders’ rights, managing long-term risks CAPITAL BUDGETING • Consider incremental after-tax cash flows, externalities • • • • • and opportunity costs Ignore sunk costs and financing costs from calculations of operating cash flows For mutually exclusive projects, use the NPV rule if the NPV and IRR rules conflict Payback period ignores time value of money, risk of the project and cash flows that occur after the payback period is reached Discounted payback period ignores cash flows that occur after the payback period is reached Average Accounting Rate of Return (ratio of project’s average net income to its average book value) is based on accounting numbers and ignores the time value of money Profitability index (PI): PI exceeds when NPV is positive PI = (including regulatory, accounting and tax risks), model, operational, solvency • Methods of risk modification: risk prevention/avoidance, risk acceptance (self-insurance and diversification), risk transfer, risk shifting/modification re = rd + risk premium • Project beta • unleveraged beta for a comparable asset     β ASSET  ASSET = β E EQUITY  D    + (1 − t )    E   PORTFOLIO RISK AND RETURN • Beta for a project using a comparable asset releveraged • Weighted average cost of capital (WACC) WACC = (wd )(r )(rd ))(1 (1 − t) + (wp )(r )(rp ) + (we )(r )(re ) • Cost of preferred stock dp vp • Cost of equity • Capital asset pricing model (CAPM) re = R F + β i [E(R M ) − R F ] • Utility function U = E(R E(R) E (R)) − Aσ 2 for target company D    β PROJEC PROJECT PR OJECT T = β ASSET ASSET 1 +  (1 − t )   E   • The higher the correlation between the individual assets, MEASURES OF LEVERAGE • Degree of operating leverage (DOL) • Percentage change in operating income DOL = Percentage change in units sold • • Degree of financial leverage (DFL) DFL = Percentage change in net income Percentage change in operating income • • Degree of total leverage (DTL) DTL = • Percentage change in net income Percentage change in the number of units sold DTL = DOL × DFL • • Breakeven quantity of sales = (Fixed operating costs + the higher the portfolio’s standard deviation and the lower the diversification benefits (no diversification benefits with a correlation coefficient of +1) The Markowitz efficient frontier contains all the possible portfolios in which rational, risk-averse investors will consider investing Optimal capital allocation line: line drawn from the riskfree asset to a portfolio on the efficient frontier, where the portfolio is at the point of tangency The optimal CAL offers the best risk-return tradeoff to an investor The point where an investor’s indifference (utility) curve is tangent to the optimal CAL indicates the investor’s optimal portfolio With homogenous expectations, the capital market line (CML) becomes a special case of the optimal CAL, where the tangent portfolio is the market portfolio CML equation (slope of line is called the market price of risk) Equation of CML Fixed financial costs) ÷ Contribution margin per unit E(R Rp ) = Rf + • Operating breakeven quantity of sales = Fixed operating costs ÷ Contribution margin per unit unsystematic risk A well-diversified investor expects to be compensated for taking on systematic risk • Beta captures an asset’s systematic risk (relative to the risk of the market) • Sources of liquidity: primary (e.g cash balances and short-term funds) and secondary (e.g negotiating debt contracts, liquidating assets, filing for bankruptcy protection) • Additional liquidity measures βi = Purchases = Ending inventory + COGS − Beginning inventory calculate an asset’s required return given its beta (the security market line) Net operating cycle = Number of days of inventory + Number of days of receivables − Number of days of payables E(R R i ) = R f + β i [E( [E(R E(R m ) − R f ] • Trade discounts (e.g “2/10 net 30” means a 2% discount is available if the amount owed is paid within 10 days, otherwise full amount is due by the 30th day)  365  Number of days  beyond discount period  σσ ρi,m σ i Cov(R R i ,R , R m ) ρi,m = i,m 2i m = i,m σm σm σ 2m • The capital asset pricing model (CAPM) is used to Operating cycle = Number of days of inventory + Number of days of receivables Discount   Im Implicit rate = Cost Cost of trad trade tr adee cre ccredit redi ditt =  11+   1− D Discount  E(R Rm ) Rf ì p m Complete diversication of a portfolio eliminates WORKING CAPITAL MANAGEMENT • If an asset’s expected return using price and dividend forecasts is higher (lower) than its CAPM required return, the asset is undervalued (overvalued) • Portfolio performance evaluation measures • Sharpe ratio (uses total risk) −1 Sharpe ratio PV of future cash h fflows NPV = 1+ Initial investment Initial investment COST OF CAPITAL rp = risks), liquidity (or transaction cost risk) Sharpe ar ratio = arpe PORTFOLIO MANAGEMENT OVERVIEW σp • Treynor ratio (uses beta) Treynor ratio • Steps in the portfolio management process: planning (includes developing IPS), execution (includes asset allocation, security analysis and portfolio construction), feedback (includes portfolio monitoring/rebalancing and performance measurement/reporting) INVESTMENT POLICY STATEMENT • Investment objectives: risk objectives and return Rp − Rf objectives • Investment constraints: liquidity, time horizon, tax concerns, legal/regulatory factors, unique circumstances Treynor ratio = Rp − Rf βp • M-squared (uses total risk) M2 = (R (R p − R f ) σm (R m − R f ) − (R σp • Jensen’s alpha (uses beta) α p = R p − [R [R f + β p ((R R m − R f )] Wiley © 2018 efficientlearning.com/cfa EQUITY INVESTMENTS MARKET ORGANIZATION AND STRUCTURE • Purchasing stock on margin (leveraged position) • Leverage ratio is the reciprocal of the initial margin • Price at which the investor receives a margin call (1 − Initial margin) P0 × (1 − Maintenance margin) • Types of orders • Execution instructions, e.g market orders, limit orders • Exposure instructions, e.g hidden orders, iceberg orders • Validity instructions, e.g day orders, good till cancelled orders, immediate or cancel orders, good on close orders, stop orders • Clearing instructions, e.g how final settlement should be arranged (security sale orders must also indicate whether the sale is a long sale or a short sale) • Execution mechanisms • Pure auction (order-driven) market: ranks buy and sell orders on price precedence, then display precedence, then time precedence • Dealer/quote-driven/price-driven market: dealers create liquidity by purchasing and selling against their own inventory of securities • Brokered market: brokers arrange trades among their clients • Features of a well-functioning financial system: timely and accurate disclosure, liquidity (which facilitates operational efficiency), complete markets and external (or informational) efficiency INDICES • Price-weighted index: value equals the sum of the security prices divided by the divisor (typically set to the number of securities in the index at inception) • Equal-weighted index: each security is given an identical weight in the index at inception (over-represents securities that constitute a relatively small fraction of the target market and requires frequent rebalancing) • Market-capitalization weighted index: initial market value is assigned a base number (e.g 100) and the change in the index is measured by comparing the new market value to the base market value (stocks with larger market values have a larger impact on the index) MARKET EFFICIENCY • Cumulative preference shares are less risky than noncumulative preference shares as they accrue unpaid dividends INDUSTRY ANALYSIS RISKS OF EQUITY SECURITIES • Preference shares are less risky than common shares • Putable common shares are less risky than callable or non-callable common shares • Callable common and preference shares are more risky than their non-callable counterparts BASIC FEATURES OF BONDS • Types of collateral backing: collateral trust bonds, • Porter’s five forces: threat of substitute product, bargaining power of customers, bargaining power of suppliers, threat of new entrants, intensity of rivalry • Industry life-cycle analysis • Embryonic (slow growth, high prices, high risk of failure) • Growth (sales grow rapidly, improved profitability, lower prices, relatively low competition) • Shakeout (slower growth, intense competition, declining profitability, focus on cost reduction, some failures/mergers) • Mature (little or no growth, industry consolidation, high barriers to entry, strong cash flows) • Decline (negative growth, excess capacity, price competition, weaker firms leave) • Competitive strategies: cost leadership, product/service differentiation EQUITY VALUATION • Dividend discount model (DDM) for common stock • One-year holding period V0 = dividend to be received year-end pric pr e + (1 + k e )1 (1 + k e )1 • Gordon growth model (constant growth rate of dividends to infinity) V0 = D0 (1 (1 + gc )1 D1 = k e − gc (k e − gc )1 • Multi-stage DDM D1 D2 Dn Pn Value = + + …+ + (1 + k e )n (1 + k e )n (1 + k e )1 (1 + k e )2 where: D n +1 Pn = k e − gc Dn = Last dividend of the supernormal growth period Dn+1 = First dividend of the constant growth period • Valuation of preferred stock • Non-callable, non-convertible preferred stock with no maturity date • Weak form EMH: current stock prices reflect all security market information Abnormal risk-adjusted returns cannot be earned by using trading rules and technical analysis • Semi-strong form EMH: current stock prices reflect all security market information and other public information Abnormal risk-adjusted returns cannot be earned by using important material information after it has been made public • Strong form EMH: current stock prices reflect all public and private information Abnormal risk-adjusted returns cannot be earned (assuming perfect markets where information is cost-free and available to all) • Behavioral biases that may explain pricing anomalies: loss aversion, herding, overconfidence, information cascades, representativeness, mental accounting, conservatism, narrow framing FIXED INCOME V0 = D0 r • Non-callable, non-convertible preferred stock with maturity at time n n Dt F t + (1 + r)n t =1 (1 + r) V0 = ∑ • Price multiples: price-to-earnings, price-to-sales, priceto-book, price-to-cash flow • Justified P/E ratio P0 D1 //E E1 = E1 r−g • Enterprise value (EV): market value of the company’s common stock plus the market value of outstanding preferred stock (if any) plus the market value of debt, less cash and short-term investments (EV can be thought of as the cost of taking over a company) • EV/EBITDA multiple is useful for comparing companies with different capital structures and for analyzing lossmaking companies • • • • equipment trust certificates, mortgage-backed securities, covered bonds Credit enhancements • Internal: subordination, overcollateralization, excess spread (or excess interest cash flow) • External: surety bonds, bank guarantees, letters of credit Covenants • Affirmative: requirements placed on the issuer • Negative: restrictions placed on the issuer Repayment structures • Bullet: entire principal amount repaid at maturity • Amortizing: periodic interest and principal payments made over the term of the bond • Sinking fund: issuer repays a specified portion of the principal amount every year throughout the bond’s life or after a specified date Bonds with contingency provisions • Callable: issuer has the right to redeem all or part of the bond before maturity • Putable: bondholders have the right to sell the bond back to the issuer at a pre-determined price on specified dates • Convertible: bondholders have the right to convert the bond into a pre-specified number of common shares of the issuer (can also have callable convertible bonds) • Contingent convertible bonds (CoCos): convert automatically upon occurrence of a pre-specified event FIXED INCOME MARKETS • Public offering mechanisms: underwritten, best efforts, auction, shelf registration • Corporate debt • Bank loans and syndicated loans (mostly floating-rate loans) • Commercial paper (unsecured, up to a maturity of one year) • Corporate notes and bonds • Medium-term notes (short-term, medium- to longterm, structured segments) • Short-term wholesale funds: central bank funds, interbank funds, certificates of deposits • Repurchase agreements (repos) • Repo: seller is borrowing funds from the buyer and providing the security as collateral • Reverse repo: buyer is borrowing securities to cover a short position • Repo margin or haircut: the percentage difference between the market value of the security and the amount of the loan • Repo rate: annualized interest cost of the loan • Any coupon income received from the bond provided as security during the repo term belongs to the seller/ borrower FIXED INCOME VALUATION • Bond pricing with yield-to-maturity (uses constant interest rate to discount all the bond’s cash flows) • If coupon = YTM, the bond’s price equals par value • If coupon > YTM, the bond’s price is at a premium to par • If coupon < YTM, the bond’s price is at a discount to par • Price is inversely related to yield: when the yield increases (decreases), the bond’s price decreases (increases) • Bond pricing with spot rates (uses the relevant spot rates to discount the bond’s cash flows) Wiley © 2018 efficientlearning.com/cfa • Spot rate: yield on a zero-coupon bond for a given maturity • Accrued interest when a bond is sold between coupon payment dates • Full price: calculated as the PV of future cash flows as of the settlement date • Accrued interest (AI) included in full price: seller’s proportional share of the next coupon, where t is the number days from last coupon date to the settlement date and T is the number of days in the coupon period (actual/actual for government bonds, 30/360 for corporate bonds) SMMt = • Prepayment risk: contraction risk occurs when interest AI = t/T ì PMT Flat or clean or quoted price: full price less AI, or equivalently • Flat PV Full = PV Flat + AI • Yield measures • Effective annual yield depends on periodicity of the • • • • • • stated annual yield Annual-pay bond: stated annual yield for periodicity of one = effective annual yield Semiannual-pay bond: stated annual yield for periodicity of two = semiannual bond basis yield = semiannual bond equivalent yield = yield per semiannual period × Current yield: annual cash coupon payment divided by the bond price Yield-to-call: computed for each call date Yield-to-worst: lowest yield among the YTM and the various yields to call Money market pricing on a discount rate basis  Days  ys PV = FV ×  − × DR    year  Year   FV − PV  DR =  ×  Days   FV  • Money market pricing on an add-on rate basis PV= FV ys  + Days × AOR    Year  Year   FV − PV  AOR =  ×  Days   PV  365-day year on an add-on basis • Forward rate • Interest rate on a loan originating at some point in the future • Implied forward rates can be computed from spot rates (1 + y s0 ) y (1 + x fy )x = (1 + x+ ys0 ) • • • rates fall (leading to an increase in prepayments), while extension risk occurs when interest rates rise (leading to a decrease in prepayments) CMOs (backed by pool of mortgage pass-through securities): sequential-pay tranches (shorter-term tranches receive protection from extension risk, longerterm tranches receive protection from contraction risk); PAC/support tranches (support tranche provides protection against contraction and extension risk to the PAC tranche); floating rate tranches (floater and inverse floater) Credit enhancements for non-agency RMBS: internal (cash reserve funds, excess spread accounts, overcollateralization, senior/subordinate structure) and external (monoline insurers) Commercial MBS (backed by non-recourse commercial mortgage loans): investors have significant call protection but are exposed to balloon risk (like extension risk) Non-mortgage asset-backed securities: auto-loan receivable-backed securities (backed by amortizing auto loans) and credit card receivable-backed securities (with lockout period before principal amortizing period sets in) CDOs: structured as senior, mezzanine and subordinated bonds (or equity class) CDO manager engages in active management of the collateral to generate the cash flow required to repay bondholders and to earn a competitive return for the equity tranche x+ y PVBP = • Two types of interest rate risk • Reinvestment risk: future value of any interim bond cash flows increases (decreases) when interest rates rise (decline) Matters more to long-term investors • Market price risk: selling price of a bond decreases (increases) when interest rates rise (decline) Matters more to short-term investors • Macaulay duration: weighted average of the time it would take to receive all the bond’s promised cash flows • Modified duration: estimated percentage price change for a bond in response to a 100 bps (1%) change in yields MacDur 1+ r • If Macaulay duration is not known, annual modified duration can be estimated using the following formula: (PV V− ) − (PV (PV+ ) ApproxModDur = × ( ∆Yield) × (PV V0 ) • Effective duration: measures the sensitivity of a bond’s price to a change in the benchmark yield curve (appropriate measure for bonds with embedded options) EffDur = (PV V− ) − (PV V+ ) × ( ∆Curve) × (PV V0 ) option-free bonds based on duration to bring them close to their actual values ApproxCon = • Yield spreads • G-spread: spread over government bond yield • I-spread: spread over the swap rate • Z-spread: spread over the government spot rate • Option-adjusted spread: z-spread less option value (bps per year) • Asset-backed securities • Residential MBS: agency RMBS vs non-agency RMBS (require credit enhancements) • Mortgage pass-through securities (backed by pool of residential mortgage loans): single monthly mortality rate (SMM) MoneyDur = AnnModDur ì PVFull Price value of a basis point (PVBP): estimates the change (PV V− ) + (PV (PV+ ) − [2 × (PV (PV0 ))] ( ∆Yield Yield) Y ield))2 ì ((PV PV0 ) The percentage change in a bond’s full price for a given change in yield based on duration with convexity adjustment is estimated as follows: Full ll %∆PV PV Fu ≈ (− (− AnnM AnnModDur An nMod odDu Durr × ∆Yield Yield) Y ield)) +  × AnnConvexity AnnConvexity × ( ∆Y Yield)2   2 • Effective convexity: use for bonds with embedded options instead of approximate convexity • Callable bonds can exhibit negative convexity when benchmark yields decline Putable bonds always exhibit positive convexity CREDIT ANALYSIS • Two components of credit risk: default risk (or default probability) and loss severity (or loss given default) Loss severity equals minus the recovery rate • Expected loss Expected loss = Defaul Default Defa ultt pr pprobability robability obability × Loss severity ver given default verity ef efault • Spread risk consists of downgrade risk (or credit migration risk) and market liquidity risk • • • • Corporate family rating (CFR): issuer rating Corporate credit rating (CCR): rating for a specific issue Four Cs: capacity, collateral, covenants, character Return impact of a change in the credit spread (includes convexity adjustment for larger changes) Return impact ≈ −(MDurr × ∆S Spread)) + (1/ ((1/2 1/22 × C Convexity × ∆Spread ) DERIVATIVES TYPES OF DERIVATIVES • Forward commitments: forwards, futures, interest rate swaps • Contingent claims: options, credit derivatives DERIVATIVE PRICING AND VALUATION • Derivative pricing is based on risk-neutral pricing • Forward contracts • Price at contract initiation (assuming underlying asset entails benefits and costs) • Key rate duration: measure of a bond’s sensitivity to a change in the benchmark yield for a given maturity (used to assess yield curve risk, i.e non-parallel shifts in the yield curve) • Portfolio duration: weighted average of the durations of the individual bonds held in the portfolio, where each bond’s weight equals its proportion of the portfolio’s market value • Money duration: measure of the dollar price change in response to a change in yields (PV V− ) − (PV V+ ) • Approximate convexity: used to revise price estimates of INTEREST RATE RISK ModDur = • Bond-equivalent yield: money-market rate stated on a in the full price of a bond in response to a bp change in its YTM Prepayment in month mont t Beginning mortgage balancee ffor mont month ht−S Scheduled cheduled principa principal payment payment in month month t F(0,T) = (S0 − γ + θ)(1 )(1 + rr))T oor F(0,T)) = S0 (1 + r)T − ( γ − θ))(1 (1 + r)T *Note that benefits (γ) γγ) and costs (θ) are expressed in terms of present value • Value of a forward contract during its life (long position) Vt (0, ((0,T) 0,T) T) = St − ( γ − θ)(1 + r ) t − [F(0, T) / (1 + r )T− t ] • Value of a forward contract at expiration (long position) VT (0, ((0,T) 0,T) T) = ST − F (0,T) • Forward rate agreement (FRA) • Long (short) position can be viewed as the party that Wiley © 2018 efficientlearning.com/cfa has committed to take (give out) a hypothetical loan • If LIBOR at FRA expiration > FRA rate, the long benefits • If LIBOR at FRA expiration < FRA rate, the short benefits • Futures: similar to forwards but standardized, exchange- traded, marked-to-market daily, clearinghouse guarantees that traders will meet their obligations • Forward vs futures prices • If underlying asset prices are positively (negatively) correlated with interest rates, the futures price will be higher (lower) than the forward price • If futures prices are uncorrelated with interest rates or if interest rates are constant, forwards and futures would have the same price • Interest rate swaps • The swap fixed rate represents the price of the swap (swap has zero value to the swap counterparties at swap initiation) • If interest rates increase after swap initiation, the swap will have positive value for the fixed-rate payer • If interest rates decrease after swap initiation, the swap will have positive value for the floating-rate payer • An interest rate swap can be viewed as a combination of FRAs • Options • Call (put) option gives the holder/buyer the right to buy (sell) the underlying asset at the exercise price • European option: can only be exercised at the option’s expiration • American option: can be exercised at any point up to the option’s expiration • Call (put) option is in-the-money when the stock price is higher (lower) than the exercise price • Intrinsic or exercise value: the amount an option is in-the-money by (minimum value of 0) • Put-call parity for European options (options and bond have the same time to expiration/maturity T) X c0 + = p + S0 (1 + R F )T • Put-call parity formula can be rearranged to create synthetic call, put, underlying asset and bond, e.g synthetic call = long put + long underlying stock + short bond) • Factors affecting the value of an option Impact of an increase in: Call Put Value of the underlying Increase Decrease Exercise price Decrease Increase Risk-free rate Increase Decrease Time to expiration Increase Increase (except for deep in-the-money European puts) Volatility of the underlying Increase Increase Benefits from the underlying Decrease Increase Cost of carry Increase Decrease • One-period binomial model for a call option (based on risk-neutral probability π) c= πc + + (1 − π)c − (1 + r) π= (1 + r − d) (u − d) Wheree u = S1+ S− and d = S0 S0 ALTERNATIVE INVESTMENTS • Potential benefits of alternative investments: low correlations with returns on traditional investments and higher returns than traditional investments • Hedge funds • Event-driven strategies: merger arbitrage, distressed/ restructuring, activist, special situations • Relative value strategies: fixed income convertible arbitrage, fixed income asset backed, fixed income general, volatility, multi-strategy • Macro strategies: long and short positions in broad markets (e.g equity indices, currencies, commodities, etc.) based on manager’s view regarding overall macro environment • Equity hedge strategies: market neutral, fundamental growth, fundamental value, quantitative directional, short bias, sector specific • Two types of fees: management fee (based on assets under management) and incentive fee (which may be subject to a hurdle rate or high water mark provision) • Private equity • Leveraged buyouts (LBOs): management buyouts (MBOs) and management buy-ins (MBIs) • Venture capital: formative stage financing (angel investing, seed-stage financing, early-stage financing), later-stage financing, mezzanine-stage financing • Development capital: includes private investment in public equities (PIPEs) • Distressed investing: buying debt of mature companies in financial distress • Exit strategies: trade sale, IPO, recapitalization, secondary sale, write-off/liquidation • Valuation methods for portfolio company: market or comparables approach, discounted cash flow approach, asset-based approach • Real estate • Investment categories: residential property, commercial real estate, REITs, timberland/farmland • Performance measurement: appraisal indices (tend to understate volatility), repeat sales indices (sample selection bias), REIT indices (based on prices of publicly traded shares of REITs) • Real estate valuation approaches: comparable sales approach, income approach (direct capitalization method and discounted cash flow method), cost approach • REIT valuation approaches: income-based approaches, asset-based approaches (NAV) • Commodities • Investors prefer to trade commodity derivatives to avoid costs of transportation and storage for physical commodities • Price of a commodity futures contract Futures price = Spot pr pric ice × (1 + Risk-free shorthor term rate) hort+ Storage costs − Convenience yield • When the futures price is higher (lower) than the spot price, prices are said to be in contango (backwardation) • Sources of return on a commodity futures contract: roll yield, collateral yield, spot prices • Infrastructure • Investments in real, capital intensive, long-lived assets • Economic infrastructure: assets such as transportation and utility assets • Social infrastructure: assets such as education, healthcare and correctional facilities • Brownfield investments: investments in existing infrastructure assets • Greenfield investments: investments in infrastructure assets to be constructed • Risk-return measures • Sharpe ratio is not appropriate risk-return measure since returns tend to be leptokurtic and negatively skewed • Downside risk measures more useful, e.g value at risk (VAR), shortfall risk, Sortino ratio Smarter Test Prep The secret is out CFA® EXAM REVIEW MORNING SESSION LEVEL II CFA ® MOCK EXAM Wiley’s materials are a better way to prep www.efficientlearning.com/cfa Sign up for your Free Trial today CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by Wiley CFA Institute, CFA® and Chartered Financial Analystđ are trademarks owned by CFA Institute Wiley â 2018 Wiley © 2018 C r it ic a l C o n c e pt s f o r t h e 2019 l r ETHICAL AND PROFESSIONAL , STANDARDS I Professionalism I (A) Knowledge of the Law I (B) Independence and Objectivity I (C ) Misrepresentation I (D) Misconduct 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) Integrity o f Capital Markets Material Nonpublic Information Market Manipulation Duties to Clients Loyalty, Prudence, and Care Fair Dealing Suitability Performance Presentation Preservation o f Confidentiality Duties to Employers Loyalty Additional Compensation Arrangements Responsibilities o f Supervisors Investment Analysis, Recommendations, and Action Diligence and Reasonable Basis Communication with Clients and Prospective Clients Record Retention Conflicts o f Interest Disclosure o f Conflicts Priority o f Transactions Referral Fees Responsibilities as a CFA Institute Member or CFA Candidate Conduct in the CFA Program Reference to CFA Institute, CFA Designation, and CFA Program QUANTITATIVE METHODS Machine learning: Gives a computer the ability to improve its performance o f a task over time Distributed ledger: A shared database with a consensus mechanism, ensuring identical copies Simple Linear Regression Correlation: Ny = covXY (sx )( sy ) t-test for r (n —2 df): t = r>/n —2 V l-r cov xy Estimated slope coefficient: CFA® E x a m M SR = RSS / k • M SE = SSE / (n - k - 1) • Test statistical significance o f regression: F = M SR / M SE with k and n - k — df (1-tail) Risk Types: Appropriate m ethod D istribution o f risk Sequential? Accommodates Correlated Variables? • Standard error o f estimate (SEE = >/MSE ) Smaller SEE means better fit • Coefficient of determination (R = RSS / SST) % o f variability o f Y explained by Xs; higher R means better fit Simulations Continuous Does not matter Yes Scenario analysis Discrete No Yes Decision trees Discrete Yes No Regression Analysis— Problems • Heteroskedasticity Non-constant error variance Detect with Breusch-Pagan test Correct with White-corrected standard errors • Autocorrelation Correlation among error terms Detect with Durbin-Watson test; positive autocorrelation if D W < dl Correct by adjusting standard errors using Hansen method • Multicollinearity High correlation among Xs Detect if F-test significant, t-tests insignificant Correct by dropping X variables M odel M isspecification • Omitting a variable • Variable should be transformed • Incorrectly pooling data • Using lagged dependent vbl as independent vbl • Forecasting the past • Measuring independent variables with error Effects o f M isspecification Regression coefficients are biased and inconsistent, lack o f confidence in hypothesis tests o f the coefficients or in the model predictions Supervised machine learning: Inputs, outputs are identified Relationships modeled from labeled data Unsupervised machine learning: Algorithm itself seeks to describe the structure o f unlabeled data Linear trend model: Yt = b + b jt + £t Log-linear trend model: ln(yt) = b0 + bjt + et Covariance 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 = Series with unit root is not covariance stationary First differencing will often eliminate the unit root Autoregressive (AR) model: specified correctly if autocorrelation o f residuals not significant Mean reverting level for AR(1): Estimated intercept: b0 = Y —b jX Confidence interval for predicted Y-value: A (1 - b j ) RM SE: square root o f average squared error Y ± t c x SE of forecast Random W alk T im e Series: M ultiple Regression Yi = b + ( b , x X li) + (b x X 2i) + (b X X jiJ + Ej • Test statistical significance o f b; H0: b = xt = x t-i + £t Seasonality: indicated by statistically significant lagged err term Correct by adding lagged term ARCH: detected by estimating: = ao + Reject if |t| > critical t or p-value < a • Confidence Interval: bj ± • SST = RSS + SSE + Mr Variance o f ARCH series: A9 A A A9 CTt+l = a0 “b alet (tcX Sb, _ k ECONOMICS bid-ask spread = ask quote - bid quote Cross rates with bid-ask spreads: Currency arbitrage: “Up the bid and down the ask.” Forward premium = (forward price) - (spot price) Value o f fwd currency contract prior to expiration: (FPt — FP) (contract size) 1+ Ra days 360 , Covered interest rate parity: + Ra + Rb days) 360 j So days [3 , Uncovered interest rate parity: E (% A S)wb, = R a - R , Fisher relation: R nominal = R real + E(inflation) v ' International Fisher Relation: R nominal A —R nominal IR = E(inflation.) —EfinflationJ B v A' v B' Relative Purchasing Power Parity: High inflation rates leads to currency depreciation %AS(A/B) = inflation^ - inflation(B) where: % AS(AJB) = change in spot price (A/B) Profit on FX Carry Trade = interest differential change in the spot rate o f investment currency Mundell-Fleming model: Impact o f 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)Q Growth Accounting: growth rate in potential GDP = long-term growth rate o f technology + Oi (long-term growth rate o f capital) + (1 - a ) (long-term growth rate of labor) growth rate in potential GDP = long-term growth rate o f labor force + long-term growth rate in labor productivity 最新CFA、FRM、AQF、ACCA资料欢迎添加微信zyz786468331 continued on next page ECONOMICS continued ••• Classical Growth T heory • Real GDP/person reverts to subsistence level Neoclassical Growth T heory • Sustainable growth rate is a function of population growth, labor’s share o f income, and the rate o f technological advancement • Growth rate in labor productivity driven only by improvement in technology • Assumes diminishing returns to capital g** = (1 - a ) G* = — - — + A L (1 - a ) Endogenous Growth T heory • Investment in capital can have constant returns • | in savings rate —» permanent j in growth rate • R & D expenditures j technological progress Classifications o f Regulations • Statutes: Laws made by legislative bodies • Administrative regulations: Issued by government • Ju d icial law : Findings of the court Classifications o f Regulators • Can be government agencies or independent • Independent regulator can be SRO or non-SRO Self-Regulation in Financial M arkets • Independent SROs are more prevalent in common-law countries than in civil-law countries Econom ic Rationale for Regulatory Intervention • Inform ationalfrictions arise in the presence of information asymmetry • Externalities deal with provision of public goods Regulatory Interdependencies and T h eir 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 o f a regulation Tools o f Regulatory Intervention • Price mechanisms, restricting or requiring certain activities, and provision of public goods or financing o f private projects Financial m arket regulations: Seek to protect investors and to ensure stability o f financial system Securities m arket 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 Anticom petitive Behaviors and A ntitrust Laws • Discriminatory pricing, bundling, exclusive dealing • Mergers leading to excessive market share blocked N et regulatory burden: Costs to the regulated entities minus the private benefits o f 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: 50% owned, control Acquisition method required under U.S GAAP and IFRS Goodwill not amortized, subject to annual impairment test All assets, liabilities, revenue, and expenses o f subsidiary are combined with parent, excluding intercomp, trans If firm contribution, diff = borrowing (reclassify difference from CFO to CFF after-tax) M ultinational Operations: Choice o f M ethod For self-contained sub, functional ^ presentation currency; use current rate method: • Assets/liabilities at current rate • Common stock at historical rate • Income statement at average rate • Exposure = shareholders’ equity • Dividends at rate when paid For integrated sub., functional = presentation currency, use temporal method: • Monetary assets/liabilities at current rate • Nonmonetary assets/liabilities at historical rate • Sales, SGA at average rate • CO G S, depreciation at historical rate • Exposure = monetary assets - monetary liabilities Net asset position & depr foreign currency = loss Net liab position & depr foreign currency = gain Original F/S vs All-Current • Pure BS and IS ratios unchanged • If LC depreciating (appreciating), translated mixed ratios will be larger (smaller) Hyperinflation: GAAP vs IFR S Hyperinfl = cumul infl > 100% over yrs GAAP: use temporal method IFRS: 1st, restate foreign curr st for infl nd, translate with current rates Net purch power gain/loss reported in income 最新CFA、FRM、AQF、ACCA资料欢迎添加微信286982279 Beneish model: Used to detect earnings manipulation based on eight variables H igh-quality earnings are: Sustainable: Expected to recur in future Adequate: Cover company’s cost o f capital IF R S A N D U S GAAP D IF F E R E N C E S Reclassification o f 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 o f 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 • IFRS permits either the “partial goodwill’’ or “full goodwill” methods to value goodwill and noncontrolling interest U.S GAAP requires the full goodwill method Goodwill impairment processes: IFRS - step (recoverable amount vs carrying value) U.S GAAP - 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 R O E decomposed (extended D uPont equation) Tax Interest E B IT Burden Burden Margin NI EBT E B IT RO E = - x - x x E B T E B IT revenue T otal Asset T urnover Financial Leverage revenue average assets x average assets average equity Accruals Ratio (balance sheet approach) accruals ratio85 = (N O A END - N O A BEG) (N O A e n d + N O A BEG) / Accruals Ratio (cash flow statem ent approach) accruals ratk) = (NI - C FO - CFI) (N O A e n d + N O A BEG) / Financial institutions differ from other companies due to systemic importance and regulated status Basel III: Minimum levels o f capital and liquidity CAMELS: Capital adequacy, Asset quality, Management, Earnings, Liquidity, and Sensitivity Liquidity coverage ratio = Net stable funding ratio = highly liquid assets expected cash outflows available stable funding required stable funding IN SU R A N C E C O M PA N Y K EY R A T IO S: Underwriting loss ratio claims paid + A loss reserves net premium earned continued on next page FINANCIAL STATEMENT ANALYSIS continued •• Expense ratio underwriting expenses inch commissions net premium written Loss and loss adjustment expense ratio loss expense + loss adjustment expense net premiums earned Dividends to policyholders dividends to policyholders net premiums earned Combined ratio after dividends = combined ratio - dividends to policyholders Total investment return ratio = total investment income / invested assets Life and health insurers’ ratios total benefits paid / (net premiums written and deposits) commissions + expenses / (net premiums written + deposits) CORPORATE FINANCE Capital Budgeting Expansion • Initial outlay = FCInv + WCInv • CF = (S - C - D ) ( l - T ) + D = (S - C )(l - T ) + D T • T N O C F = SalT + NWCInv - T(SalT - BT) Capital Budgeting Replacem ent • Same as expansion, except current after-tax salvage o f old assets reduces initial outlay • Incremental depreciation is A in depreciation Evaluating Projects w ith Unequal Lives • Least common multiple o f lives method • Equivalent annual annuity (EAA) method: annuity w/ PV equal to PV o f project cash flows Effects o f Inflation • Discount 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 • If positive NPV projects > available capital, choose the combination with the highest NPV Real O ptions • Timing, abandonment, expansion, flexibility, fundamental options Econom ic and Accounting Incom e • Econ income = AT CF + A in projects MV • Econ dep based on A in investment’s MV • Econ income is calculated before interest expense (cost o f capital is reflected in discount rate) • Accounting income = revenues - expenses • Acc dep’n based on original investment cost • Interest (financing costs) deducted before calculating accounting income Valuation Models • Economic profit = NOPAT - $W ACC oo EP • Market Value Added = X I t = i (1 + W A C C ) M M Prop II (No Taxes): increased use o f cheaper debt increases cost o f equity, no change in WACC re = < b + f ( r o - r d) E M M Proposition I (With Taxes): tax shield adds value, value is maximized at 100 % debt VL = Vu + ( t x d ) M M Proposition II (With Taxes): tax shield adds value, WACC is minimized at 100 % debt re = r + ^ ( r - r d )(1 - T c ) E Investor Preference Theories • M M ’s dividend irrelevance theory: In a no-tax/ no-fee world, dividend policy is irrelevant because investors can create a homemade dividend • Dividend preference theory says investors prefer the certainty o f current cash to future capital gains • Tax 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 o f 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: AP = d (i - t d ) {l - t c g ) Target Payout Adjustm ent Model expected increase in dividends = ■ target expected b „ \ previous ^ x payout I —K , , earnings r ' -q / dividend Corporate Governance Objectives • Mitigate conflicts of interest between (1) managers and shareholders and (2 ) directors and shareholders • Ensure 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, 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 (H H I): market power = sum o f 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 H H I = ^ ( M S j xlOO): i=l M ethods to D eterm ine Target Value D C F method: target proforma FCF discounted at adjusted WACC Com parable company analysis: based on relative valuation vs similar firms + takeover premium Com parable transaction analysis-, target value from takeover transaction; takeover premium included M erger Valuations C om binedfirm : VAT = VA+ VT + S - C adjustment factor Dividend Coverage Ratios dividend coverage ratio = net income / dividends FCFE coverage ratio = FCFE / (dividends + share repurchases) Share Repurchases • Share repurchase is equivalent to cash dividend, assuming equal tax treatment • Unexpected share repurchase is good news • Rationale 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 • Residual dividend: dividends based on earnings less funds retained to finance capital budget • Longer-term residual dividend: forecast capital budget, smooth dividend payout • Dividend stability: dividend growth aligned with sustainable growth rate • Target payout ratio: long-term payout ratio target Stakeholder impact analysis (SLA): Forces firm to identify the most critical groups Ethical D ecision M aking Friedman Doctrine: Only responsibility is to increase profits “within the rules o f the game.” • Residual income: = NI - equity charge; Utilitarianism: Produce the highest good for the discounted at required return on equity largest number o f people • Claims valuation separates CFs based on equity Kantian ethics: People are more than just an claims (discounted at cost o f equity) and debt economic input and deserve dignity and respect holders (discounted at cost o f debt) Rights theories: Even if an action is legal, it may M M Prop I (No Taxes): capital structure irrelevant violate fundamental rights and be unethical (no taxes, transaction, or bankruptcy costs) Justice theories: Focus on a just distribution of VL= VU 最新CFA、FRM、AQF、ACCA资料欢迎添加 economic output (e.g., “veil o f ignorance”) 微信zyz786468331 Takeover prem ium (to target): GainT = TP = PT —VT Synergies (to acquirer): GainA= S - TP = S - (PT - VT) M erger 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 o f divestitures: equity carve-outs, spin-offs, split-offs, and liquidations EQUITY Holding period return: P i— P o + C F , o P i+ C F , -1 Required return: Minimum expected return an investor requires given an asset’s characteristics Internal rate o f 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: = -yr forecasted dividend yield on market index + consensus long-term earnings growth rate - long-term government bond yield Ibbotson-C hen equity risk premium [1 + i] x [1 + rEg] x [1 + PEg] - + Y - RF Models o f required equity return: • CAPM\ r = RF + (equity risk premium x (3.) • M ultifactor m odel: required return = RF + (risk premium) + (risk premium) n Fam a-French: r.j = RF + 13 mkt,j x (R mkt —RF) + ^SMB,j x ( P'small — 'big' + ^H HML.j M U X ^ H B M “ ^ LBM ) continued on next page EQUITY continued • Pastor-Stambaugh model: Adds a liquidity factor to the Fama-French model • M acroeconom ic m ultifactor models: Uses factors associated with economic variables • 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 0) WACC = weighted average cost of capital M Vequity MV.debt ^Xdebt+equity > a (i-T )+ ^ ^ d e b t -(-equity Discount cash flows to firm at WACC, and cash flows to equity at the required return on equity Discounted Cash Flow (D C F) M ethods Use dividend discount models (DDM ) when: • Firm has dividend history • Dividend policy is related to earnings • Minority shareholder perspective Use free cash flow (FCF) models when: • Firm lacks stable dividend policy • Dividend policy not related to earnings • FCF is related to profitability • Controlling shareholder perspective Use residual income (RI) when: • Firm lacks dividend history • Expected FCF is negative Gordon Growth M odel (G G M ) Assumes perpetual dividend growth rate: V0 = r~g Most appropriate for mature, stable firms Limitations are: • Very sensitive to estimates of r and g • Difficult with non-dividend stocks • Difficult with unpredictable growth patterns (use multi-stage model) Present Value o f Growth Opportunities V0 = + PVGO H -M odel _ D x(l + gL)] | [P x H x ( gs —gL)] v0= r ~gL r ~gL Sustainable Growth Rate: b x ROE Required Return From Gordon Growth Model: r = (D, / P0) + g Free Cash Flow to Firm (FC FF) 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 = C FO + [Int x (1 - tax rate)] - FCInv ;ree Cash Flow to Equity (FC FE) 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 FC FF/FC FE Models • For FCFF valuation: V = • For FCFE valuation: V = FCFFj W ACC- g FC FE r~g 2-Stage FC FF/FC FE 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: • If earnings < 0, P/E meaningless • Volatile, transitory portion o f earnings makes interpretation difficult • Management discretion over accounting choices affects reported earnings Justified P/E leading P/E = -r~g trailing P/E = !+ g + / ( j.k ) ] Price to Sales (P/S) Ratio Advantages: • Meaningful even for distressed firms • Sales revenue not easily manipulated • Not as volatile as P/E ratios • Useful for mature, cyclical, and start-up firms Disadvantages: • High sales ^ imply high profits and cash flows • Does not capture cost structure differences • Revenue recognition practices still distort sales justified P /S = PMo X (1 - b)(1 + g) r~g D uPont M odel X sales total 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 M ethod o f Comparables Firm multiple > benchmark implies overvalued Firm multiple < benchmark implies undervalued Fundamentals that affect multiple should be similar between firm and benchmark Residual Incom e Models • RI = Et —(r x Br-i) = (ROE —r) x Bt_i • Single-stage RI model: V0 = B + T F(i,k) = justified P / B = R Q E ~ g r~g sales (l + ST ) Forward price of zero-coupon bond: Price to Book (P/B) Ratio Advantages: • BV almost always > • BV more stable than EPS • Measures NAV of financial institutions Disadvantages: • Size differences cause misleading comparisons • Influenced by accounting choices • BV ^ M V due to inflation/technology net income 1+Control Premium Total discount = - [(1 - D L O C )(l - DLOM)] The DLO M varies with the following • An impending IPO or firm sale [ DLOM • The payment o f dividends J, DLOM • Earlier, higher payments { DLOM • Restrictions on selling stock | DLOM • A greater pool of buyers J, DLOM Greater risk and value uncertainty | DLOM rT= f-g Normalization M ethods • Historical average EPS • Average ROE RO E = D LO C = — Price o f a T-period zero-coupon bond: Justified dividend yield: Private Equity Valuation FIXED INCOME ( l - b ) ( l + g) r~g Do Econom ic Value Added® • EVA - NOPAT - $WACC; NOPAT - E B I T ( - 1) (RO E —r ) x B r~g • Multistage RI valuation: Vo = Bo + (PV of interim high-growth RI) + (PV o f continuing RI) Forward pricing model: p0+k) F(i.k) = P; J Forward rate model: [i +y(j>k)]k = [i + S(j+k)](j+k) / (i + s.)j “Riding the yield curve”: Holding bonds with maturity > investment horizon, with upward sloping yield curve swap spread = swap rate - treasury yield T E D spread: = (3-month LIBO R rate) —(3-month T-bill rate) Libor-OIS spread = LIBO R rate —“overnight indexed swap” rate Term Structure o f 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)^r + a\[tdz Vasicek model: dr = a(b - r)dt + ad z Ho-Lee model: drt = 0t dt + ad z t Managing yield curve shape risk: AP/P = - D l A x l - D sA xs - D c;Axc (L = level, S = steepness, C = curvature) Yield volatility: Long-term c)