Finance Formula Study Guide

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 4 FV= PV(1+ I/Y)N FV PV= N 1+ I Y FV= future value PV= Present value I/Y=Rate of return per compounding period N=Number of compounding periods 5 PV perpetuity = PMT (I/Y) PMT= Fixed periodic cash flow DISCOUNTED CASH FLOW APPLICATION CF (1+r)t 6 CF= Expected cash flow r =Discount rate 7 IRR 0=CF+ CF1 CF2 + + (1+IRR)2 (1+IRR) CF3 (1+IRR)3 IRR= Internal rate of return. 8 HPR= (Ending Value-Beginning Value) (Beginning Value) HPR= Holding period return 9 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 10 Effective Annual Yield (EAY)= (1+HPY)365/t -1 HPY= Holding period yield 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= 15 Position of observation at a given percentile y Ly=(n+1) 100 16 Range= Maximum Value- Minimum Value 17 Mean Absolute Deviation (MAD)= 18 Population Variance (∑(Xi-µ)2) σ2 = N 19 Standard Deviation σ = square root of variance 20 Sample Variance σ2 = N n (∑(Xi-µ)2) N-1 21 Chebyshev9s Inequality Percentage of observations that lie within k standard deviations of the mean is at least= 1-1/k2 22 Coefficient of Variation (standard deviation of x) CV= (average value of x) 23 24 (Rp-RFR) σp Rp= Portfolio Return RFR= Risk Free Rate σp= standard deviation of portfolio return Sharpe Ratio= Sample Skewness (Sk) = S3 s =sample standard deviation 3 ) 4 25 Sample Skewness (Sk) = 26 Excess Kurtosis= Sample Kurtosis - 3 S4 ) PROBABILITY CONCEPTS 27 Multiplication Rule Of Probability, P(AB)=P(A/B)*P(B) 28 Addition Rule Of Probability, P(A or B)= P(A)+P(B)-P(AB) 29 Total Probability Rule (Used to determine unconditional probability of an event) P(A)=P(A/B1)P(B1)+P(A/B2)P(B2)+&&&+P(A/BN)P(BN) 30 Expected value of random variable= weighted average of possible outcomes, Weights = probabilities that the outcome will occur 31 Covariance Cov(Ri, Rj)= E{[Ri-E(Ri)][(Rj-E(Rj)]} Cov(Ri, Rj)= Corr(Ri, Rj) σ(Ri)σ(Rj) 32 Correlation Cofficient (Cov(Ri,Rj)) Corr(Ri,Rj)= (σ(Ri)σ(Rj)) 33 Weight of asset in portfolio, w= market value of investment in asset i/market value of the portfolio 34 Portfolio Expected Value E(Rp)=w1E(R1) + w2E(R2)+&& wnE(Rn) 35 Variance of 2 Asset Portfolio 36 Variance of 3 asset Portfolio 37 Bayes Formula, Updated Probability=( Probability of new information for a given event / unconditional probability of new event )*(prior probability of event) 38 Factorial n! = n*(n-1)*(n-2)*(n-3)&& *1 0!=1 39 Labelling, n! / (n1!)*(n2!)*&. ( nn!) 40 Combination, n Cr=n! /(n-r)!r! Permutation, n! /(n-r)! 41 COMMON PROBABILITY DISTRIBUTIONS 42 To standardize a normal variable, z= (Observation - Population Mean) (Standard Deviation) 43 Roy9s safety first criteria, ([E(Rp)-Rl]) SFR= (σ p) **Choose the portfolio with largest SFR 44 Continuously compounded rate of return, Rcc=ln(1+HPR) SAMPLING AND ESTIMATION 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 SAMPLING AND ESTIMATION 47 48 (Sample Mean - Hypothesized Mean) Test Statistic= (Standard Error of Sample Mean) t-statistic When population variance is unknown, (x-µ) Tn-1= (s/√n) When population variance is known, (x-µ) Tn-1= (σ/√n) 49 50 Chi-square test: X2= (n-1)s2 σ2 F-distribution test, F=s12/s22 TECHNICAL ANALYSIS 51 Arms Index or Short Term Trading Index, (Number of advancing Issues / Number of declining issues) TRIN= (Volume of advancing issues / Volume of declining issues) DEMAND AND SUPPLY ANALYSIS: INTRODUCTION                                        55     54     53   Qdx=f(Px,I,Py,&.)  Py=Prices of related goods  52 DEMAND AND SUPPLY ANALYSIS: THE FIRM 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 AGGREGATE OUTPUT, PRICES AND ECONOMIC GROWTH 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 owner9s 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 UNDERSTANDING BUSINESS CYCLES 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 Neutral Interest Rate= Real trend rate of economic growth + inflation target Fiscal Multiplier= 1/[1-MPC(1-t)] 76 77 78 Relation between trade deficit, saving and domestic investment, Exports-imports= private savings+ government savings+ domestic investment CURRENCY EXCHANGE RATES 79 Real Exchange Rate= Nominal Exchange Rate(d/f)* (CPI foreign) (CPI domestic) 80 Interest Rate Parity, (1+interest rate (domestic) foward = (1+interest rate (foreign) spot FINANCIAL STATEMENT ANALYSIS: AN INTRODUCTION 81 Accounting Equation, (Balance Sheet) Assets= liabilities + equity Assets=liabilities+ contributed capital+ ending retained earnings Assets=liabilities+ contributed capital+ beginning retained earnings+ revenue-expenses-dividends 82 Income statement equation, Net income=revenues-expenses 83 84 Straight line depreciation expense= Accelerated depreciation- double declining balance method DDB depreciation= 85 86 (cost-residual value) (useful life) 2 (cost-accumulated depreciation) useful life (net income-preferred dividends) Basic EPS= (weighted average number of common shares outstanding) Diluted EPS= (Adjusted income for common shareholders) (weighted average commom and potential common shares outstanding) Diluted EPS= ([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]) UNDERSTANDING CASHFLOW STATEMENTS 87 Free Cash flow to firm, FCFF= NI+ NCC+ Interest(1-Tax Rate) 3FC 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 89 Performance Ratio: Cash flow to revenue= CFO/Net Revenue CFO= Cash flow from operations 90 Performance Ratio: Cash return on asset ratio= CFO/Average total assets 91 Performance Ratio: Cash return on equity ratio=CFO/Average total equity 92 Performance Ratio: Cash to income ratio: CFO/Operating Income 93 94 Cash flow per share= Coverage Ratio: Debt coverage= 95 (CFO-Preferred Dividends) (Weighted Average Number Of Common Shares) CFO (Total Debt) Coverage Ratio: (CFO+interest paid+taxes paid) Interest coverage ratio: (interest paid) If interest paid is classified as a financing activity under ifrs, no interest adjustment is necessary 96 Reinvestment Ratio= CFO (Cash paid for long term assets) 97 Debt payment Ratio= CFCFO (Cash long term debt repayment) 98 CFO Dividend Payment Ratio= (Dividends paid) 99 Investing and Financing Ratio= CFO (Cash outflow from investing and financing activities) FINANCIAL ANALYSIS TECHNIQUES ACTIVITY RATIOS: 100 Receivables Turnover=net annual sales /average receivables 101 Days of sales outstanding= 102 Inventory Turnover= 103 Days of inventory in hand= 365 (Receivables turnover) (Cost of goods sold) (Average inventory) 365 (Inventory turnover) 104 105 106 107 108 Payables turnover= Purchases (Average trade payables) 365 Number of days of payables= (Payable turnover) Total asset turnover= (Revenue ) (Average total assets) Fixed asset turnover= Revenue (Average net fixed assets) Revenue Working capital turnover= (Average working capital) LIQUIDITY RATIOS 109 110 111 112 113 Current Ratios= Quick Ratio= Cash Ratio= (Current Assets) (Current Liabilities) (Cash+Marketable Securities+Receivables) (Current Liabilities) (Cash+Marketable Securities) (Current Liabilities) Defensive Interval= (Cash+Marketable Securities+Receivables) (Average Daily Expenditures) Cash Conversion Cycle= (Days sales outstanding)+(days on inventory on hand)-(number of days of payables) SOLVENCY RATIOS 114 115 116 117 118 119 Debt to equity ratio= (Total debt) (Total Shareholders Equity) Debt To Capital= (Total debt) (Total Debt+Total Shareholders Equity) Debt To Assets= (Total Debt) (Total Assets) Financial Leverage= (Average Total Assets) (Average Total Equity) Interest Coverage Ratio= (Earnings Before Interest and taxes) (Interest payments) Fixed Charge Coverage= (Earnings Before Interest & Taxes+Lease Payments) (Interest payments+Lease payments) PROFITABILITY RATIOS 120 121 122 123 124 125 (Net Income) Revenue Net income= earnings after taxes but before dividends Net profit margin= (Gross profit) Revenue Gross profit= Net Sales- COGS Gross Profit Margin= Operating profit margin= Pretax margin= (Operating Income (EBIT)) Revenue EBT Revenue (Net Income) Return on assets (ROA)=(Average Total Assets) Operating return on assets= (Operating Income) (Average Total Assets) 126 EBIT Return on Total Capital=(Average Total Capital) 127 (Net Income) Return On Equity= (Average Total Equity) Or (Net Income) Revenue Return On Equity= * Revenue Equity = Net Profit Margin * Equity Turnover Return On Equity By Du Pont Equation, (Net Income) (Sales ) Return On Equity= Sales * Assets (Assets) * Equity =Net Profit Margin*Asset Turnover*Leverage Ratio ROE By Extended Dupont Equation, ROE= EBIT Revenue (Net Income) EBT (Total Assets ) EBT * EBIT * Revenue * (Total Assets) * (Total Equity) =Tax Burden *Interest Burden*EBIT Margin*Asset turnover*financial leverage 128 129 Return on common equity= (Net Income-Preferred Dividends) (Average Common Equity) Sustainable growth rate= RR*ROE RR= Retention rate =1-dividend payout 130 131 132 Coefficient of variation sales= CV Operating Income= (Standard deviation of operating income) (Mean sales) (Standard deviation of operating income) (mean operating income) (Standard deviation of net income) CV Net Income= (Mean net income) INVENTORIES 133 COGS= beginning inventory + purchases - ending inventory LONG LIVED ASSETS 134 Depreciation methods, i) straight line and ii) ddb covered earlier. Ii) units of production depreciation= (Original cost-salvage value) * (life in output units) Output units in the period INCOME TAXES 136 Effective tax rate= (Income tax expense) (Pretax income)  DTL= Deferred tax liability DTA= Deferred tax asset  135 CAPITAL BUDGETING 137 Profitability Index (PI)= (PV Of future cash flows) CF0 =1+ NPV CF0 COST OF CAPITAL 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 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, D1 Po= (k-g) D1= Next year dividend. K=Required rate of return on common equity. g = Firm9s expected constant growth rate. 143 Bond yield plus risk premium approach, Kce=bond yield + risk premium 144 Asset Beta, 1 ΒAsset=βEquity 1+ (1-t)D E D/E= Comparable company9s debt to equity ratio 145 Project Beta, ΒProject=βAsset (1+(1-t) D ) E 146 147 Revised CAPM using country risk premium, Kce=Rf+β[E(Rm)-RFR+CRP CRP= Country risk premium CRP= (Annualised standard deviation of equity index of developing country) (Annualised standard deviation of sovereign bond Market in terms of the developed market currency) Sovereign yield spread= difference between the yields of government bonds in in the developing country and treasury bonds of similar maturities 148 Break Point (any time the cost of one of the components of the company9s WACC changes.) Break Points= (Amount Of Capital at which the components cost of capital changes) (weight of the he component in the capital structure) MEASURES OF LEVERAGE 149 Degree of operating leverage, (Percentage change in EBIT) DOL= (Percentage change in sales) DOL for a particular level of units, DOL= Q(P-V) = (Q(P-V)-F) (S-TVC) (S-TVC-F) Q= Quantity of units sold P=Price per unit V= Variable cost per unit F= Fixed costs S= Sales TVC=Total variable costs 150 Degree of financial leverage, DFL= (Percentage change in EPS) (Percentage change in EBIT) DFL for particular level of operating units, DFL= 151 EBIT (EBIT-Interest) Degree Of Total Leverage DTL=DOL+DFL 152 DTL= (% change in EBIT) (% change in EPS) (% change in EPS) = (% Change in Sales) (% change in Sales)* (% change in EBIT) DTL= Q(P-V) = (Q(P-V)-F-I) (S-TVC) (S-TVC-F-I) Breakeven Quantity Of Sales, (Fixed perating costs+Fixed financing costs) QBE= (Price-Variable cost per unit) DIVIDENDS AND SHARE REPURCHASE BASICS 153 Eps after buyback= (Total earnings-After tax cost of funds) (Shares outstanding after buyback) WORKING CAPITAL MANAGEMENT 154 Cost of trade credit=(1+ (%discount) 365/days past discount -1 (1-%discount) 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 156 Capital market line equation, E(Rp)= Rf+ (E(Rm)-Rf) σp (σ m) 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, E(Ri)=RFR+ 160 161 162 (E(Rm)-RFR) (Cov i,mkt) (Variance of Market) M Square= (Rp-Rf) (Std Dev of m) 3 (Rm-Rf) (Std Dev of p) Treynor Measure= (Rp-Rf) βp Jenson9s Alpha= αp=Rp-[Rf+βp(Rm-Rf)] MARKET ORGANISATION AND STRUCTURE 163 Margin call price= Po ((1-initial margin)) ((1-maintenance margin)) Po= initial purchase price SECURITY MARKET INDICES 164 Compounded Returns, Rp= (1+R1)(1+R2)(1+R3)&&. (1+Rk)-1 K= last sub period 165 166 Price weighted Index= Market weighted Index, Current index value= 167 (Sum of stock prices) (Number of stocks in index adjusted for splits) (Current total market value of index stocks) *Base year index value (Base year total market value of index stocks) Equal weighting index, New index value= Initial index value (1+Change in index) EQUITY VALUATION: CONCEPTS AND BASIC TOOLS 168 Dividend discount model, One year holding period: Dt (Year End Price) + ((1+ke) ) ((1+ke)) Vo= Current stock value Dt=Dividend at time t Ke=Required rate of return Vo= Two year holding period DDM, D2 P2 D1 + + Value= ((1+ke) ) (1+ke)2 ((1+ke)2) Multi-stage dividend discount model: Dn Pn D2 D1/ + + + Value= (1+ke) ) (1+ke)2 ((1+ke)n ) ((1+ke)n) Pn= 169 (Dn+1) (Ke-gc) 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. 170 Preferred stock value= Dp kp Dp= Fixed dividend Kp=Required rate of return 171 Enterprise Value (EV) EV= market value of common and preferred stock + market value of debt 3cash and short term investment 172 Trailing P/E= (Market price per share) (EPS over previous 12 months) 173 Leading P/E= (Market price per share) (Forecast EPS over next 12 months) 174 P/B Ratio= (Market value of equity) (Market price per share) = (Book value of equity) (Book value per share) Book value of equity= common shareholders equity = (total assets- total liabilities)-preferred stock 175 176 P/S Ratio= P/CF Ratio (Market value of equity) (Total sales) (Market value of equity) (Cash flow) INTRODUCTION TO FIXED INCOME VALUATION 177 Price of annual coupon bond, Price= Coupon Coupon + +&&& + ((1+YTM)) ((1+YTM)2) (Principal+ Coupon) ((1+YTM)n) YTM= Yield to maturity Price of semi-annual coupon bond, Coupon Coupon YTM YTM +&&& + Price= 1+ 1+ 2 2 2 178 179 180 Principal+ Coupon YTM n*2 1+ 2 Full Price= Flat price + Accrued interest Current Yield= (Annual cash coupon payment) (Bond price) Relation between forward rates and spot rates, (1+s2)=(1+S1)(1+1y1y) 181 Option Value= z spread 3OAS UNDERSTANDING FIXED INCOME RISK AND RETURN 182 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 (V¬_ -V+) Approximate modified duration =  183  184 (V_ -V+) Effective duration=  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 189 % change in Bond Price (when duration and convexity are given) ⁄ 190 Duration Gap= Macaulay duration-Investment horizon 191 Return impact (%change in bond price)  For small spread changes,   For larger spread changes, ⁄ 192 Yield spread = liquidity premium + credit spread 193 Payment to the long at settlement, (floating-foward) (notional principal) 1+[(floating) days 360 days 360 Days= number of days in the loan term 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 196 Option value= intrinsic value+ time value 197 Put-call parity:  C= Call P=Put S=Stock  198 Put call parity with assets cashflows,  199 Plain vanilla interest rate swap, (Net fixed rate payment)t = (Swap rate- LIBORt-1) ((Number of days) notional principal 360)*