CFA Level I 2025 Cheat Sheet

University:
CFA Institute
Course:
CFA Level 1 | Quantitative Methods
Academic year:

2025
Views:

231

Pages:

12
Author:

Ed Farmingtoner

Level I CF1 Education CheatSheet Concept for CFA® Program Exam-2025 QUANTITATIVE METHODS TIME VALUE OF MONEY BASICS Future value (FV): amount to which investment grows after one or more compounding periods. Future value: FV=PV (1 + 1 / Y) ^ prime prime . Present value (PV): current value of some future cash flow PV + - F * V / ((1 + 1 / Y) ^ N) Annuities: series of equal cash flows that occur at evenly spaced intervals over time. Ordinary annuity: cash flow at end-of-time period. Annuity due: cash flow at beginning-of-time period. Perpetuities: annuities with infinite lives. PV PMT/(discount rate). REQUIRED RATE OF RETURN Components: 1. Real risk-free rate (RFR). 2. Expected inflation rate premium (IP). 3. Risk premium. E(R)=(1+RF Rrgoal ) (1 + 1P)(1 + RP) - 1 Approximation formula for nominal required rate: E(R) cong RFR + IP + RP Means Arithmetic mean: sum of all observation values in sample/population, divided by # of observations. Geometric mean: used when calculating investment returns over multiple periods or to measure compound growth rates. Geometric mean return: R G =[(I+R 1 )*....* (I + R_{N}) ^ (1 / H) - 1 Harmonic mean = overline X Hi = N sum i=1 ^ M 1 X i Trimmed mean (x%): Exclude highest and lowest x/2 percent of observations. Winsorized mean (x%): Substitute values for highest and lowest x/2 percent of observations. VARIANCE AND STANDARD DEVIATION Variance: average of squared deviations from mean. sample variance = S ^ 2 = sum i=1 ^ n (x i - overline x )^ 2 n-1 Standard deviation: square root of variance. TARGET DOWNSIDE DEVIATION Starget= Σ allX, =), Alternative hypothesis (H₂): concluded if there is sufficient evidence to reject the null hypothesis. DIFFERENCE BETWEEN ONE-AND TWO-TAILED TESTS One-tailed test: tests whether value is greater than or less than a given number. Two-tailed test: tests whether value is equal to a given number. TYPE I AND TYPE II ERRORS Type I error: rejection of null hypothesis when it is actually true. Type II error: failure to reject null hypothesis when it is actually false. HYPOTHESIS TESTS Test of: Stat d.f. Mean forz n - 1 Difference in means. n - 1 Mean differences t n - 1 Variance x ^ 2 Equal variances F n - 1 Correlation n_{1} - 1, n_{2} - 1 Independence x ^ 2 n - 2 (r - 1)(c - 1) Regression slope: Significance Value F t 1, n - 2 n - 2 ECONOMICS ELASTICITY %Aquantity demanded %Aprice Own price elasticity= If absolute value > 1 s demand is elastic. If absolute value < 1, demand is inelastic. On a straight line demand curve, total revenue is maximized where price elasticity = - 1 , Income elasticity= %Aquantity demanded %Aincome If positive, the good is a normal good. If negative, the good is an inferior good. XAquantity demanded Cross price elasticity= %Aprice of related good If positive, related good is a substitute. If negative, related good is a complement. BREAKEVEN AND SHUTDOWN Breakeven: total revenue = total cost. Operate in short run if total revenue is greater than total variable cost but less than total cost. Shut down in short run if total revenue is less than total variable cost. MARKET STRUCTURES Perfect competition: Many firms with no pricing power; very low or no barriers to entry; homogeneous product. Monopolistic competition: Many firms; some pricing power; low barriers to entry; differentiated products; large advertising expense. Oligopoly: Few firms that may have significant pricing power; high barriers to entry; products may be homogeneous or differentiated. Monopoly: Single firm with significant pricing power; high barriers to entry; advertising used to compete with substitute products. In all market structures, profit is maximized at the output quantity for which marginal revenue marginal cost. GROSS DOMESTIC PRODUCT Real GDP = consumption spending investment + government spending + net exports. SAVINGS, INVESTMENT, FISCAL BALANCE, AND TRADE BALANCE Fiscal budget deficit (GT) excess of saving over domestic investment (S-1)-trade balance (X-M) EQUATION OF EXCHANGE MV=PY, where M = real money supply, V = velocity of money in transactions, P = price level, and Y = real GDP BUSINESS CYCLE PHASES Expansion; peak; contraction; trough. ECONOMIC INDICATORS Leading: Turning points occur ahead of peaks and troughs (stock prices, initial unemployment claims, manufacturing new orders) Coincident: Turning points coincide with peaks and troughs (nonfarm payrolls, personal income, manufacturing sales) Lagging: Turning points follow peaks and troughs (average duration of unemployment, inventory/ sales ratio, prime rate) FACTORS AFFECTING AGGREGATE DEMAND Consumers' wealth; business expectations; consumers' income expectations; capacity utilization; monetary and fiscal policy; exchange rates; global economic growth. FACTORS AFFECTING SR AGGREGATE SUPPLY Input prices; labor productivity; expectations for output prices; taxes and subsidies; exchange rates; all factors that affect LR aggregate supply. FACTORS AFFECTING LR AGGREGATE SUPPLY Size of labor force; human capital; supply of natural resources; stock of physical capital; level of technology. TYPES OF UNEMPLOYMENT Frictional: time lag in matching qualified workers with job openings. Structural: unemployed workers do not have the skills to match newly created jobs. Cyclical: economy producing at less than capacity during contraction phase of business cycle. POLICY MULTIPLIERS 1 money multiplier = reserve requirement 1 money multiplier = 1-MPC(1-1) where MPC marginal propensity to consume, t = tax rate. EXPANSIONARY AND CONTRACTIONARY POLICY Monetary policy is expansionary when the policy rate is less than the neutral interest rate (real trend rate of economic growth + inflation target) and contractionary when the policy rate is greater than the neutral interest rate. Fiscal policy is expansionary when a budget deficit is increasing or surplus is decreasing, and contractionary when a budget deficit is decreasing or surplus is increasing. BALANCE OF PAYMENTS Current account: merchandise and services; income receipts; unilateral transfers. Capital account: capital transfers; sales/purchases of nonfinancial assets. Financial account: government-owned assets abroad; foreign-owned assets in the country. REGIONAL TRADING AGREEMENTS Free trade area: Removes barriers to goods and services trade among members. Customs union: Members also adopt common trade policies with non-members. Common market: Members also remove barriers to labor and capital movements among members. Economic union: Members also establish common institutions and economic policy. Monetary union: Members also adopt a common currency. FOREIGN EXCHANGE RATES For the exam, FX rates are expressed as price currency/base currency and interpreted as the number of units of the price currency for each unit of the base currency. REAL EXCHANGE RATE nominal FXrate X base currency CPI price currency CPI NO-ARBITRAGE FORWARD EXCHANGE RATE forward 1+price currency interest rate spot 1+base currency interestrate EXCHANGE RATE REGIMES Formal dollarization: country adopts foreign currency. Monetary union: members adopt common currency. Fixed peg: 1% margin versus foreign currency or basket of currencies. Target zone: Wider margin than fixed peg. Crawling peg: Pegged exchange rate adjusted periodically. Crawling bands: Width of margin increases over time. Managed floating: Monetary authority acts to influence exchange rate but does not set a target. Independently floating: Exchange rate is market determined. FINANCIAL STATEMENT ANALYSIS REVENUE RECOGNITION Two requirements: (1) completion of earnings process and (2) reasonable assurance of payment. Five-step revenue recognition model: 1. Identify contracts 2. Identify performance obligations 3. Determine transaction price 4. Allocate price to obligations 5. Recognize when (as) obligations are satisfted UNUSUAL OR INFREQUENT ITEMS Gains/losses from disposal of a business segment. Gains/losses from sale of assets or investments in subsidiaries. Provisions for environmental remediation. Impairments, write-offs, write-downs, and restructuring costs. Integration expenses associated with businesses recently acquired. DISCONTINUED OPERATIONS To be accounted for as a discontinued operation, a business-assets, operations, investing, financing activities-must be physically/operationally distinct from rest of firm. Income/losses are reported net of tax after net income from continuing operations. COMPUTE CASH FLOWS FROM OPERATIONS (CFO) Direct method: start with cash collections (cash equivalent of sales); cash inputs (cash equivalent of cost of goods sold); cash operating expenses; cash interest expense; cash taxes. Indirect method: start with net income, subtracting back gains and adding back losses resulting from financing or investment cash flows, adding back all noncash charges, and adding and subtracting asset and liability accounts that result from operations. FREE CASH FLOW Free cash flow (FCF) measures cash available for discretionary purposes. It is equal to operating cash flow less net capital expenditures. CRITICAL RATIOS Common-size financial statement analysis: Common-size balance sheet expresses all balance sheet accounts as a percentage of total assets. Common-size income statement expresses all income statement items as a percentage of sales. Common-size cash flow statement expresses each line item as a percentage of total cash inflows (outflows), or as a percentage of net revenue. Horizontal common-size financial statement analysis: expresses each line item relative to its value in a common base period. current assets Liquidity ratios: current ratio = current liabilities quick ratio cash+marketable securities+receivables current liabilities cash+marketable securities cash ratio-current liabilities cash+mkt.sec.+receivables defensive interval= daily cash expenditures Receivables, inventory, payables turnover, and days supply ratios-all of which are used in the cash conversion cycle: annual sales average receivables receivables turnover =- average inventory cost of goods sold inventory turnover = purchases average trade payables payables turnover ratio = days of sales outstanding = 365 receivables turnover. days of inventory onhand= 365 inventory turnover number of days of payables 365 payables turnover ratio cash conversion cycle= days of inventory onhand story) days of sales outstanding )-( number of days of payables Total asset, fixed-asset, and working capital turnover ratios: total asset turnover = revenue average total assets fixed asset turnover = revenue average fixed assets revenue working capital turnover = average working capital Gross, operating, and net profit margins: gross profit margin gross profit revenue operating profit margin= operating profit EBIT revenue net sales netincome net profit margin= revenue Return on assets [return on total capital (ROTC)): EBIT return on assets (total capital)= average total capital Debt to equity ratio and total debt ratio: total debt debt-to-equity ratio total equity total debt total-debt-ratio= total assets Interest coverage and fixed charge coverage: interest coverage EBIT interest fixed charge coverage = EBIT +lease payments interest+lease payments dividends declared retentionrate=1-operatingincome after taxes Liquidity ratios indicate company's ability to pay its short-term liabilities. Operating performance ratios indicate how well management operates the business. DUPONT ANALYSIS Traditional DuPont equation: netincome sales assets return on equity-sales assets equity You may also see it presented as: return on equity margin turnover multiplier, netprofit asset equity Extended DuPont equation further decomposes net profit margin: netincome EBT EBIT ROE= EBT EBIT revenue revenue avg. avg.totale total assets, avg. total assets avg.equity ROE = tax burden x interest burden x EBIT margin x asset turnover x leverage MARKETABLE SECURITY CLASSIFICATIONS Held-for-trading: fair value on balance sheet;dividends, interest, realized and unrealized G/L recognized on income statement. Available-for-sale: fair value on balance sheet; dividends, interest, realized G/L recognized on income statement; unrealized G/L is other comprehensive income. Held-to-maturity: amortized cost on balance sheet; interest, realized G/L recognized on income statement. INVENTORY ACCOUNTING In periods of rising prices and stable or increasing inventory quantities: LIFO results in: Higher COGS Lower gross profit Lower COGS Higher gross profit Lower inventory Higher inventory balances FIFO results in: balances Basic EPS calculation does not consider effects of any dilutive securities in computation of EPS: basic EPS = netincome-preferred dividends wtd.avg.no.of common shs.outstanding diluted EPS = adj.income avail, for common shares wtd.avg.common shares plus potential common shares outstanding Growth rate (g): g = RR x ROE Therefore, diluted EPS is: net income-pfddiv + debt convertible interest convertible preferred + dividends (1-1) wtd sharesfrom avg conversionof sh's conv.pfd.sh's sh'sfrom conversion + conv.debt share issuablefrom stockoptions LONG-LIVED ASSETS CAPITALIZING VS. EXPENSING Capitalizing: lowers income variability and increases near-term profits. Increase assets, equity. Expensing: opposite effect. DEPRECIATION cost-residual value Straight-line: usefullife Double declining balance: You may also see it presented as: 2 usefullife (cost-accum.depreciation) Units of production: cost-salvage value xoutput units useful life in units REVALUATION OF LONG-LIVED ASSETS IFRS: revaluation gain recognized in net income only to the extent it reverses previously recognized impairment loss; further gains recognized in equity as revaluation surplus. (For investment property, all gains and losses from marking to fair value are recognized as income.) U.S. GAAP: revaluation is not permitted. DEFERRED TAXES Created when taxable income (on tax return) ≠ pretax income (on financial statements) due to temporary differences. Deferred tax liabilities are created when taxable income < pretax income. Treat DTL as equity if not expected to reverse. Deferred tax assets are created when taxable income > pretax income. Must recognize valuation allowance if more likely than not that DTA will not be realized. LONG-TERM LIABILITIES Premium bond: coupon rate > market rate at issuance. Discount bond: coupon rate

Related Documents

Recommended Documents

Description

Related Documents

Almost There!

Free up your schedule!

Take 5 seconds to unlock