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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))
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)
+……… + 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
