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CFA Formula sheet, Cheat Sheet of Financial Accounting

Formula sheet with time value of mony, Discounted cash flow application, probability concept, Sampling and estimation.

Typology: Cheat Sheet

2021/2022

Uploaded on 02/07/2022

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TIME VALUE OF MONEY
1Nominal interest rate= real risk-free rate + expected inflation rate
2Required interest rate on security= nominal risk-free rate + default risk premium+ liquidity
premium + maturity risk premium
3Effective 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
4FV= PV(1+ I/Y)N
5PV perpetuity = PMT
(I/Y)
6
PV= N
Y
1+ I
FV
PMT= Fixed periodic cash flow
DISCOUNTED CASH FLOW APPLICATION
139  CF
(1+r)t
7IRR
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)3
0=CF+ ++
Centre for Financial Learning
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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+ + +

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- Geometric mean return is also known as compound annual rate of return

14 Harmonic Mean= N ™ [

n

™;L;

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 ) σ^2 =

N-

(∑(Xi-μ)^2 ) σ^2 =

(standard deviation of x) (average value of x)

CV=

(Rp-RFR) σp

™ ;L[ 3 )

S^3

Sharpe Ratio=

s =sample standard deviation

; $ULWKPHWLFPHDQ

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/k 2

Rp= Portfolio Return RFR= Risk Free Rate σp= standard deviation of portfolio return

26 Excess Kurtosis= Sample Kurtosis - 3

Sample Skewness (Sk) =

™ ;L[ 4 )

S^4 25 Sample Skewness (Sk) =

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,

DEMAND AND SUPPLY ANALYSIS: INTRODUCTION

DEMAND AND SUPPLY ANALYSIS: THE FIRM

AGGREGATE OUTPUT, PRICES AND ECONOMIC GROWTH

52 'HPDQGIXQFWLRQIRUJRRG;

Qdx=f(Px,I,Py,….) 3[ 3ULFHRIJRRG;, 6RPHPHDVXUHRIDYHUDJHLQFRPHSHU\HDU Py=Prices of related goods

53 3ULFH(ODVWLFLW\RI'HPDQG^ ¨4XDQWLW\'HPDQGHG¨3ULFH ¨ FKDQJH

54 &URVV3ULFH(ODVWLFLW^ ¨4XDQWLW\'HPDQGHG¨3ULFH2I5HODWHG*RRGV ¨ FKDQJH

55 ,QFRPH(ODVWLFLW^ ¨4XDQWLW\'HPDQGHG¨LQ,QFRPH ¨ FKDQJH

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= 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 1RPLQDO*'3 ™3LW4LW

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)*

62 Per Capita Real GDP= GDP/population

63 GDP by expenditure approach, '3 &, ; & &RQVXPSWLRQVSHQGLQJ, %XVLQHVVLQYHVWPHQW* *RYHUQPHQWSXUFKDVHV; ([SRUWV 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

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

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

100 Receivables Turnover=net annual sales /average receivables

94 Coverage Ratio:

Coverage Ratio:

If interest paid is classified as a financing activity under ifrs, no interest adjustment is necessary

Cash flow per share=

Interest coverage ratio:

(CFO-Preferred Dividends) (Weighted Average Number Of Common Shares)

(CFO+interest paid+taxes paid) (interest paid)

Reinvestment Ratio=

CFO

(Cash paid for long term assets)

(^97) Debt payment Ratio= CFCFO (Cash long term debt repayment)

(^98) Dividend Payment Ratio= CFO (Dividends paid)

(^99) Investing and Financing Ratio= CFO (Cash outflow from investing and financing activities)

(^101) Days of sales outstanding= 365 (Receivables turnover)

(^102) Inventory Turnover= (Cost of goods sold) (Average inventory)

(^103) Days of inventory in hand= 365 (Inventory turnover)

Debt coverage= CFO (Total Debt)

FINANCIAL ANALYSIS TECHNIQUES

ACTIVITY RATIOS:

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

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=

COGS= beginning inventory + purchases - ending inventory

(Standard deviation of net income) (Mean net income)

Effective tax rate= (Income tax expense) (Pretax income)

Profitability Index (PI)=

(PV Of future cash flows) CF

NPV

CF

(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 ,QFRPHWD[H[SHQVH^ WD[HVSD\DEOH¨'7/¨'7$

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 (k^ ps ) Kps = D (^) ps /p

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

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 )= W (^) AE(RA)+w (^) B E(RB ) W (^) B =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)+………. ΒikE(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)- K= last sub period

167 Equal weighting index,

New index value= Initial index value (1+Change in index)

M Square= (Rp-Rf)

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=

(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

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*

185 Portfolio duration= W^1 D1^ + W^2 D 2 +……… + W^ nDn 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+ -2V^ o / ¨FXUYH^2 Vo

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,

& PD[>6;@ C= Intrinsic Value of Call option S= Spot price ; 6WULNHSULFH

195 Intrinsic value of a put option,

3 PD[>;6@ P=intrinsic value of put

Days= number of days in the loan term

191 Return impact (%change in bond price)

For small spread changes, 5HWXUQLPSDFW§0RGLILHGGXUDWLRQ ¨6SUHDG

For larger spread changes, 5HWXUQLPSDFW§0RGLILHGGXUDWLRQ ¨6SUHDG⁄FRQYH[LW\ ¨VSUHDG 

189 % change in Bond Price (when duration and convexity are given)

¨%RQG9DOXH GXUDWLRQ ¨VSUHDG ⁄FRQYH[LW\ ¨VSUHDG 

(notional principal)

days 360 (floating-foward)

1+[(floating) days 360