CFA Formula sheet, Cheat Sheet of Financial Accounting

Download CFA Formula sheet and more Cheat Sheet Financial Accounting in PDF only on Docsity! 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 11 RMM= 360/days*HPY RMM=Money market yield 12 Bond equivalent yield= {(1+ effective annual yield)1/2-1} * 2 13 Geometric Mean= [(1+R1)(1+R2)…. (1+Rn)]1/n-1 Geometric mean return is also known as compound annual rate of return 14 Harmonic Mean= N n 15 Position of observation at a given percentile 16 Range= Maximum Value- Minimum Value 18 Population Variance 19 Standard Deviation σ = square root of variance 20 Sample Variance Coefficient of Variation 17 Mean Absolute Deviation (MAD)= N (∑(Xi-μ)2) σ2 = N-1 (∑(Xi-μ)2) σ2 = (standard deviation of x) (average value of x) CV= (Rp-RFR) σp 3) S3 Sharpe Ratio= s =sample standard deviation Ly=(n+1) y 100 21 Chebyshev’s Inequality Percentage of observations that lie within k standard deviations of the mean is at least= 1-1/k2 Rp= Portfolio Return RFR= Risk Free Rate σp= standard deviation of portfolio return 22 Excess Kurtosis= Sample Kurtosis - 326 23 Sample Skewness (Sk) = 24 4) S4Sample Skewness (Sk) = 25 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 Centre for Financial Learning 80 Interest Rate Parity, 81 Accounting Equation, (Balance Sheet) Assets= liabilities + equity Assets=liabilities+ contributed capital+ ending retained earnings Assets=liabilities+ contributed capital+ beginning retained earnings+ revenue-expens- es-dividends 87 Free Cash flow to firm, FCFF= NI+ NCC+ Interest(1-Tax Rate) –FC Inv-WC Inv FCFF=CFO+ Interest(1-Tax Rate)-FC Inv NI= Net income NCC= Non cash charges FC Inv= Fixed capital investment WC Inv= Working Capital Investment 88 Free cash flow to equity, FCFE=CFO-FC Inv + net borrowing Net borrowing= debt issued- debt repaid 82 Income statement equation, Net income=revenues-expenses 84 Accelerated depreciation- double declining balance method DDB depreciation= 2 (cost-accumulated depreciation) useful life 85 83 Straight line depreciation expense= foward spot (1+interest rate (domestic) (1+interest rate (foreign) (cost-residual value) (useful life) (net income-preferred dividends) (weighted average number of common shares outstanding) = FINANCIAL STATEMENT ANALYSIS: AN INTRODUCTION Basic EPS= 86 (Adjusted income for common shareholders) (weighted average commom and potential common shares outstanding) ([Net income-preferred dividends]+[convertible preferred dividends] +[convertible debt interest](1-tax rate)) ([Weighted average shares]+[shares from conversion of converted preferred shares] +[shares from conversion of debt]+[shares issuable from stock options]) Diluted EPS= Diluted EPS= UNDERSTANDING CASHFLOW STATEMENTS 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 141 Capital asset pricing model (CAPM) Kce=RFR+β[E(Rm)-RFR] Kce=Cost of equity capital RFR= Risk free rate E(Rm)= Expected return on market. 142 Dividend discount model, 143 Bond yield plus risk premium approach, Kce=bond yield + risk premium D/E= Comparable company’s debt to equity ratio 144 Asset Beta, 145 Project Beta, 146 147 Revised CAPM using country risk premium, Kce=Rf+β[E(Rm)-RFR+CRP CRP= Country risk premium Sovereign yield spread= difference between the yields of government bonds in in the developing country and treasury bonds of similar maturities D1= Next year dividend. K=Required rate of return on common equity. g = Firm’s expected constant growth rate. D1 (k-g)Po= ΒAsset=βEquity (1+(1-t) D E ΒProject=βAsset 1 (1-t)D E1+ CRP= Break Points= (Annualised standard deviation of equity index of developing country) (Annualised standard deviation of sovereign bond Market in terms of the developed market currency) 148 Break Point (any time the cost of one of the components of the company’s WACC changes.) (Amount Of Capital at which the components cost of capital changes) (weight of the he component in the capital structure) ) 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 185 Portfolio duration= W1D1 + W2D2 +……… +WnDn W= Weight= Full price/total value D=Duration on bond 186 Money duration= annual modified duration *full price of bond position Money Duration per 100 units of par value= annual modified duration * full price per 100 of par value 187 Price value of a basis point (PVBP)= Average of decrease in value of bond when YTM increases and increase in value of bond when YTM decreases 188 Approximate Convexity= V_-V+ -2Vo / 2Vo 190 Duration Gap= Macaulay duration-Investment horizon 192 Yield spread = liquidity premium + credit spread 193 Payment to the long at settlement, 194 Intrinsic value of call option, C= Intrinsic Value of Call option S= Spot price 195 Intrinsic value of a put option, P=intrinsic value of put Days= number of days in the loan term 191 Return impact (%change in bond price) For small spread changes, For larger spread changes, ⁄ 189 % change in Bond Price (when duration and convexity are given) ⁄ (notional principal) days 360 (floating-foward) 1+[(floating) days 360 Centre for Financial Learning