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

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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^ - 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)

PV=

N 1+ Y

I

FV

PMT= Fixed periodic cash flow

DISCOUNTED CASH FLOW APPLICATION

139 ™

CF

(1+r) t

7 IRR

Effective Annual Yield (EAY)= (1+HPY) 365/t^ - HPY= Holding period yield

HPR=

CF

(1+IRR)

CF

(1+IRR) 2

(Ending Value-Beginning Value) (Beginning Value)

CF

(1+IRR) 3

0=CF+ + +

PROBABILITY CONCEPTS

COMMON PROBABILITY DISTRIBUTIONS

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

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)…… * 0!=

39 Labelling, n! / (n1!)(n2!)…. ( nn!)

40 Combination, n Cr=n! /(n-r)!r!

41 Permutation, n! /(n-r)!

42 To standardize a normal variable,

Corr(Ri,Rj)= (Cov(Ri,Rj)) (σ(Ri)σ(Rj))

z= (Observation - Population Mean) (Standard Deviation)

43 Roy’s safety first criteria,

44 Continuously compounded rate of return, Rcc=ln(1+HPR)

45 Standard Error of sample Mean, σx= σ¥Q 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 V¥Q

When variance is known, x=tα/2*σ¥Q x= Point estimate of population mean tα/2=The t-reliability factor V¥Q 6WDQGDUGHUURURIVDPSOHPHDQ

48 t-statistic When population variance is unknown,

When population variance is known,

**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)s σ

Chi-square test: X2=

50 F-distribution test, F=s12/s

51 Arms Index or Short Term Trading Index,

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)*

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)

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

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

Payables turnover=

Purchases (Average trade payables)

105 Number of days of payables=

(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)

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)

LIQUIDITY RATIOS

SOLVENCY RATIOS

Cash Conversion Cycle= (Days sales outstanding)+(days on inventory on hand)-(number of days of payables)

PROFITABILITY RATIOS

Net income= earnings after taxes but before dividends

Net profit margin= (Net Income) Revenue

Gross profit= Net Sales- COGS

Gross Profit Margin= (Gross profit) Revenue

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)

Return on common equity=

129 Sustainable growth rate= RR*ROE RR= Retention rate =1-dividend payout

(Net Income-Preferred Dividends) (Average Common Equity)

Return on Total Capital=

EBIT

(Average Total Capital)

127 Return On Equity=

= Net Profit Margin * Equity Turnover

=Net Profit MarginAsset TurnoverLeverage Ratio

=Tax Burden Interest BurdenEBIT MarginAsset turnoverfinancial 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

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,

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.

D

Po=(k-g)

ΒAsset =βEquity

(1+(1-t)

D

E

Β (^) Project=βAsset

1 (1-t)D 1+E

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)

MEASURES OF LEVERAGE

DIVIDENDS AND SHARE REPURCHASE BASICS

WORKING CAPITAL MANAGEMENT

Degree of operating leverage,

Q= Quantity of units sold P=Price per unit V= Variable cost per unit F= Fixed costs S= Sales TVC=Total variable costs

DOL=

(Percentage change in EBIT) (Percentage change in sales)

Degree of financial leverage,

151 Degree Of Total Leverage

152 Breakeven Quantity Of Sales,

DFL for particular level of operating units,

DFL=

(Percentage change in EPS) (Percentage change in EBIT)

DFL=

EBIT

(EBIT-Interest)

QBE=

(Fixed perating costs+Fixed financing costs) (Price-Variable cost per unit)

Eps after buyback= (Total earnings-After tax cost of funds) (Shares outstanding after buyback)

(^154) Cost of trade credit=(1+ (%discount) 365/days past discount - (1-%discount)

DTL=

Q(P-V)

(Q(P-V)-F-I)

(S-TVC)

(S-TVC-F-I)

DTL=

(% change in EBIT) (% change in Sales)

(% change in EPS) (% change in EBIT)

(% change in EPS) (% Change in Sales)

DOL for a particular level of units,

DOL= =

Q(P-V)

(Q(P-V)-F)

(S-TVC)

(S-TVC-F)

DTL=DOL+DFL

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=

D

((1+ke) )

Value=

D1/

(1+ke) )

Pn= (Dn+1) (Ke-gc)

Preferred stock value= Dp= Fixed dividend Kp=Required rate of return

Dp kp

D

(1+ke)

D

(1+ke)

P

((1+ke)2)

(Year End Price) ((1+ke))

Dn ((1+ke)n )

Pn ((1+ke)n)

Multi-stage dividend discount model:

Trailing P/E= (Market price per share) (EPS over previous 12 months)

Leading P/E= (Market price per share) (Forecast EPS over next 12 months)

P/B Ratio= (Market value of equity) (Book value of equity)

(Market price per share) (Book value per share)

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

Option Value= z spread –OAS

183 $SSUR[LPDWHFKDQJHLQERQGSULFH 0RG'XU ¨<

180 Relation between forward rates and spot rates,

(1+s 2 )=(1+S^1 )(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+) 9R¨&XUYH

P/CF Ratio (Market value of equity) (Cash flow)

Price= Coupon ((1+YTM))

YTM

Approximate modified duration =

(V¬_ -V+)

92¨\WP

Price= 1+

Coupon YTM 2

Principal+ Coupon YTM 2

Coupon

Coupon ((1+YTM)2)

(Principal+ Coupon)

• +……… + ((1+YTM)n)

+……… + n*

196 Option value= intrinsic value+ time value

197 Put-call parity: &; 5)5 W 6 C= Call P=Put S=Stock ; 3UHVHQWYDOXH

198 Put call parity with assets cashflows, &; 5)5 W 6R²39FI 

199 Plain vanilla interest rate swap,

(Net fixed rate payment)t = (Swap rate- LIBORt-1) ((Number of days) 360)*

notional principal

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