Financial Analysis and Investment: Formulas and Concepts, Cheat Sheet of Econometrics and Mathematical Economics

Download Financial Analysis and Investment: Formulas and Concepts and more Cheat Sheet Econometrics and Mathematical Economics in PDF only on Docsity! Handbook for Formulas List of formulas for Level 1 CFA® Program TIME VALUE OF MONEY 1 Nominal interest rate= real risk-free rate + expected inflation rate 2 Required interest rate on security= nominal risk-free rate + default risk premium+ liquidity premium + maturity risk premium 3 Effective Annual Return (EAR)= EAR=(1+periodic rate)m -1 Periodic rate= stated annual rate/m M= number of compounding periods per year FV= future value PV= Present value I/Y=Rate of return per compounding period N=Number of compounding periods CF= Expected cash flow r =Discount rate IRR= Internal rate of return. HPR= Holding period return RBD= D/F*360/t RBD= Annualised yield on a bank discount basis D=Dollar discount= purchase price - face value F=Face value t=Number of days until maturity 360=Bank convention of number of days in a year 4 FV= PV(1+ I/Y)N 5 PV perpetuity = PMT (I/Y) 6 PV= N Y1+ I FV PMT= Fixed periodic cash flow DISCOUNTED CASH FLOW APPLICATION CF (1+r)t 7 IRR 8 9 Effective Annual Yield (EAY)= (1+HPY)365/t -1 HPY= Holding period yield 10 HPR= CF1 (1+IRR) CF2 (1+IRR)2 (Ending Value-Beginning Value) (Beginning Value) CF3 (1+IRR)30=CF+ + + Centre for Financial Learning 43 Roy’s safety first criteria, 44 Continuously compounded rate of return, Rcc=ln(1+HPR) 45 Standard Error of sample Mean, σx= σ σ= Standard deviation of population n=Size of the sample 46 t-distribution to construct a confidence interval, When variance is unknown, x=tα/2 When variance is known, x=tα/2*σ x= Point estimate of population mean tα/2=The t-reliability factor 48 t-statistic When population variance is unknown, 49 When population variance is known, 47 **Choose the portfolio with largest SFR SFR= ([E(Rp)-Rl]) (σ p) Test Statistic= (Sample Mean - Hypothesized Mean) (Standard Error of Sample Mean) TRIN= (Number of advancing Issues / Number of declining issues) (Volume of advancing issues / Volume of declining issues) SAMPLING AND ESTIMATION SAMPLING AND ESTIMATION TECHNICAL ANALYSIS (x-μ) (s/√n) Tn-1= (x-μ) (σ/√n) Tn-1= (n-1)s2 σ2 X2=Chi-square test: 50 F-distribution test, F=s12/s22 51 Arms Index or Short Term Trading Index, Centre for Financial Learning Centre for Financial Learning DEMAND AND SUPPLY ANALYSIS: INTRODUCTION DEMAND AND SUPPLY ANALYSIS: THE FIRM AGGREGATE OUTPUT, PRICES AND ECONOMIC GROWTH 52 Qdx=f(Px,I,Py,….) Py=Prices of related goods 53 54 55 56 Accounting profit=total revenue-total accounting costs 57 Economic profit=accounting profit-implicit opportunity costs Or Economic profit=total revenue-total economic costs 58 Normal profit, Economic profit=accounting profit-normal profit=0 Normal profit is the accounting profit that makes economic profit equal to zero 59 Marginal Cost, MC=change in total cost/change in output 60 Pi,t= Price of good i in year t. Qi,t=Quantity of good I produced in year t 61 GDP deflator= (nominal GDP/value of year t output at year t)*100 62 Per Capita Real GDP= GDP/population 63 GDP by expenditure approach, M=Imports 64 GDP by Income Approach, GDP=national income+ capital consumption allowance+ statistical discrepancy 65 National Income= compensation of employees (wages and benefits) + corporate and government enterprise profits before taxes +Interest Income +Unincorporated business net income (business owner’s income) +rent +indirect business taxes-subsidies 66 Personal Income= national Income +transfer payments to households -indirect business taxes -corporate income taxes -undistributed corporate profits 67 Personal disposable income=personal income-personal taxes 68 Quantity Theory Of Money, MV=PY M=Money Supply, V=Velocity of money in transactions, P=Price level Y=Real GDP 69 Recessionary Gap or Output Gap=Real GDP-Full Employment GDP 70 Potential GDP=aggregate hours worked*labour productivity In terms of economic growth, Growth in potential GDP=growth in labour force+ growth in labour productivity 71 Production Function, Y=A*f(L,K) Y=Aggregate economic output, L=Size of labour force, K=Amount of capital available, A=Total factor productivity 72 CPI= (Cost of basket at current prices/cost of basket at base period prices)*100 73 Total amount of money that can be created, Money created= new deposit/reserve requirement 74 Money Multiplier=1/Reserve Requirement 75 Fisher Effect, Rnom=Rreal+E(I)+RP Rnom=Nominal interest rate, Rreal=Real Interest rate RP=Risk premium for uncertainty 76 Neutral Interest Rate= Real trend rate of economic growth + inflation target 77 Fiscal Multiplier= 1/[1-MPC(1-t)] 78 Relation between trade deficit, saving and domestic investment, Exports-imports= private savings+ government savings+ domestic investment 79 Real Exchange Rate= Nominal Exchange Rate(d/f)* UNDERSTANDING BUSINESS CYCLES CURRENCY EXCHANGE RATES (CPI foreign) (CPI domestic) Centre for Financial Learning 104 Payables turnover= Purchases (Average trade payables) 105 Number of days of payables= 365 (Payable turnover) 106 Total asset turnover= (Revenue ) (Average total assets) 107 Fixed asset turnover= Revenue (Average net fixed assets) 108 Working capital turnover= Revenue (Average working capital) 109 Current Ratios= (Current Assets) (Current Liabilities) 110 Quick Ratio= (Cash+Marketable Securities+Receivables) (Current Liabilities) 111 Cash Ratio= (Cash+Marketable Securities) (Current Liabilities) 112 Defensive Interval= (Cash+Marketable Securities+Receivables) (Average Daily Expenditures) 114 Debt to equity ratio= (Total debt) (Total Shareholders Equity) 115 Debt To Capital= (Total debt) (Total Debt+Total Shareholders Equity) 116 Debt To Assets= (Total Debt) (Total Assets) 117 Financial Leverage= (Average Total Assets) (Average Total Equity) 118 Interest Coverage Ratio= (Earnings Before Interest and taxes) (Interest payments) 119 Fixed Charge Coverage= (Earnings Before Interest & Taxes+Lease Payments) (Interest payments+Lease payments) 113 LIQUIDITY RATIOS SOLVENCY RATIOS Cash Conversion Cycle= (Days sales outstanding)+(days on inventory on hand)-(number of days of payables) Centre for Financial Learning PROFITABILITY RATIOS 120 Net income= earnings after taxes but before dividends Net profit margin= (Net Income) Revenue 121 Gross profit= Net Sales- COGS Gross Profit Margin= (Gross profit) Revenue 122 Operating profit margin= (Operating Income (EBIT)) Revenue 123 Pretax margin= EBT Revenue 124 Return on assets (ROA)= (Net Income) (Average Total Assets) 125 Operating return on assets= (Operating Income) (Average Total Assets) 128 Return on common equity= 129 Sustainable growth rate= RR*ROE RR= Retention rate =1-dividend payout (Net Income-Preferred Dividends) (Average Common Equity) 126 Return on Total Capital= EBIT (Average Total Capital) 127 Return On Equity= = Net Profit Margin * Equity Turnover =Net Profit Margin*Asset Turnover*Leverage Ratio =Tax Burden *Interest Burden*EBIT Margin*Asset turnover*financial leverage Return On Equity By Du Pont Equation, ROE By Extended Dupont Equation, Or (Net Income) (Average Total Equity) Return On Equity= Return On Equity= (Net Income) Revenue (Net Income) Sales ROE= (Net Income) EBT EBIT Revenue Revenue (Total Assets) EBT EBIT (Sales ) Assets Revenue Equity * * * * (Total Assets ) (Total Equity)* (Assets) Equity* * Centre for Financial Learning Centre for Financial Learning 130 Coefficient of variation sales= (Standard deviation of operating income) (Mean sales) 131 CV Operating Income= (Standard deviation of operating income) (mean operating income) 132 CV Net Income= 133 134 COGS= beginning inventory + purchases - ending inventory (Standard deviation of net income) (Mean net income) 135 Effective tax rate= (Income tax expense) (Pretax income) 137 Profitability Index (PI)= (PV Of future cash flows) CF0 =1+ NPV CF0 (Original cost-salvage value) (life in output units) Output units in the period INVENTORIES LONG LIVED ASSETS INCOME TAXES CAPITAL BUDGETING COST OF CAPITAL Depreciation methods, i) straight line and ii) ddb covered earlier. Ii) units of production depreciation= 136 DTL= Deferred tax liability DTA= Deferred tax asset 138 WACC= (wd)[kd(1-t)]+(wps)(kps)+(wcc)(Kcc) Wd= percentage of debt in capital structure. Wps=percentage of preferred stock in the capital structure. Wcc=percentage of common stock in the capital structure 139 After tax cost of debt= kd(1-t) 140 Cost of preferred stock (kps) Kps= Dps/p * Centre for Financial Learning PORTFOLIO RISK AND RETURN: PART II 155 Expected return when one asset is invested in risky asset and one asset in risk free asset E(Rp)= WAE(RA)+wBE(RB) WB=1-WB 157 Total Risk= systematic risk + unsystematic risk 158 General form of multifactor model, E(Ri)-Rf=βil*E(Factor 1) + βi2*E(factor 2)+………. Βik*E(Factor k) 159 Equation of SML, 162 Jenson’s Alpha= αp=Rp-[Rf+βp(Rm-Rf)] 164 Compounded Returns, Rp= (1+R1)(1+R2)(1+R3)……. (1+Rk)-1 K= last sub period 167 Equal weighting index, New index value= Initial index value (1+Change in index) 163 161 160 M Square= (Rp-Rf) 156 SECURITY MARKET INDICES MARKET ORGANISATION AND STRUCTURE Capital market line equation, E(Rp)= Rf+ σ p(E(Rm)-Rf) (σ m) E(Ri)=RFR+ (Cov i,mkt) (E(Rm)-RFR) (Variance of Market) (Std Dev of m) (Std Dev of p) (Rp-Rf) βp ((1-initial margin)) ((1-maintenance margin)) – (Rm-Rf) Treynor Measure= Margin call price= Po 165 (Sum of stock prices) (Number of stocks in index adjusted for splits)Price weighted Index= 166 (Current total market value of index stocks) (Base year total market value of index stocks)Current index value= Market weighted Index, *Base year index value Po= initial purchase price Centre for Financial Learning EQUITY VALUATION: CONCEPTS AND BASIC TOOLS 168 Dividend discount model, One year holding period: 169 Free cash to equity, FCFE= net income+ depreciation-increase in working capital-fixed capital investment-debt principal repayments+ new debt issues FCFE=CFO-FC investment + net borrowing CFO= Cash flow from operations. 171 Enterprise Value (EV) EV= market value of common and preferred stock + market value of debt –cash and short term investment Book value of equity= common shareholders equity = (total assets- total liabilities)-pre- ferred stock Vo= Current stock value Dt=Dividend at time t Ke=Required rate of return Two year holding period DDM, Vo= Dt ((1+ke) ) Value= D1 ((1+ke) ) Value= D1/ (1+ke) ) Pn= (Dn+1) (Ke-gc) Preferred stock value= Dp= Fixed dividend Kp=Required rate of return Dp kp D2 (1+ke)2 D2 (1+ke)2 P2 ((1+ke)2) (Year End Price) ((1+ke)) + + + Dn ((1+ke)n )+ Pn ((1+ke)n)+ + Multi-stage dividend discount model: 170 Trailing P/E= (Market price per share) (EPS over previous 12 months) 172 Leading P/E= (Market price per share) (Forecast EPS over next 12 months) 173 P/B Ratio= (Market value of equity) (Book value of equity) (Market price per share) (Book value per share) 174 = 175 INTRODUCTION TO FIXED INCOME VALUATION UNDERSTANDING FIXED INCOME RISK AND RETURN Modified duration, For annual pay bond: Modified duration= Macualay duration/ (1+YTM) For semi-annual bond, ModDursemi=MacDur/(1+ YTM/2 ) V¬_ = price increase V+=price decrease V0=current price P/S Ratio= 177 Price of annual coupon bond, 179 Current Yield= 178 Full Price= Flat price + Accrued interest 181 182 Option Value= z spread –OAS 183 180 Relation between forward rates and spot rates, (1+s2)=(1+S1)(1+1y1y) YTM= Yield to maturity Price of semi-annual coupon bond, (Market value of equity) (Total sales) (Annual cash coupon payment) (Bond price) 184 Effective duration= (V_ -V+) 176 P/CF Ratio (Market value of equity) (Cash flow) Price= Coupon ((1+YTM)) YTM 2 Approximate modified duration = (V¬_ -V+) Price= 1+ Coupon YTM 2 Principal+ Coupon YTM 2 1+ 1+2 Coupon Coupon ((1+YTM)2) (Principal+ Coupon) ((1+YTM)n)+ +……… + +……… + n*2 Centre for Financial Learning