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In SFM





In SFM



EARNING PER SHARE (EPS)

(EPS)SharePerEarning SharesEquityofNumbersTotalrsShareholdeEquityforAvailableEarnings Total

DIVIDEND PER SHARE (DPS)

Dividend Per Share (DPS) = SharesEquityofNumber TotalrShareholde Equity To PaidDividendTotal

MARKET PRICE PER SHARE (MPS)

Market Price Per Share (MPS) = SharesEquityofNumber TotalCap Market /tionCapitaliza Market /Value MarketTotal

DIVIDEND RATE

Dividend Rate = 100ValueFace

SharePerDividend

DIVIDEND YIELD ( RETURN )

Dividend Yield ( Return ) = 100SharePerPriceMarket

SharePerDividend

DIVIDEND PAYOUT RATIO (D/P RATIO)

Dividend Payout Ratio = 100SharePerEarningSharePerDividend

RETENTION RATIO

Retention Ratio = 100EPS

DPS-EPS

or (1 - Dividend Payout Ratio) or 100EPS

Share Per Earning Retained

EARNING YIELD (EY)

Earning Yield = SharePerPriceMarketSharePerEarnings

WALTER'S MODEL

Symbolically : Po = eK

DPS +

eK

DPS)–(EPSeKr

OPTIMUM DIVIDEND PAYOUT OR OPTIMUM RETENTION RATIOWalter suggested that optimum dividend payout ratio or optimum retention ratio depends on the relationshipof Ke & r OptimumNature of Firm Relation Dividend Payout Retention RatioGrowth Company Ke<r 0% 100%Declining Company Ke>r 100% 0 %Normal Company Ke =r Indifferent Indifferent



In SFM



GORDON'S GROWTH MODEL

Symbolically :Po= g – eK1DPS

or Po = geKg)1(0DPS

or geKb)EPS(1

0P

or [ If EPS(1-b) is considered as D1]

geKg)b)(1EPS(1

0P

[ If EPS(1-b) is considered as Do] Where b=Retention Ratio (%)

PRICE/EARNING RATIO

Price Earning Ratio = EPSMPS

RELATIONSHIP BETWEEN GROWTH RATE ; RETURN ON EQUITY ; RETENTION RATIOg = b x rNote:Other things remaining constant"g" and "b" are directly related to each other

DETERMINATION OF GROWTH RATE (g)Assuming growth rate to be constant , we can find the growth rate by using any of the following two relation :

(a) g = b r (b) 1-ng)(1BaseD Current or LatestD ZERO GROWTH RATE

When company is distributing all its earning as dividend i.e when EPS = DPS [i.e no retention], growth rate willbe NIL.In such case growth model will become :

eKEPS

0P

VALUE OF DECLINING FIRM/NEGATIVE GROWTH FIRMMarket Price Per Share of a firm whose dividend is declining at a constant rate p.a forever is given by

geKg)(10D

0P

UNEQUAL GROWTH RATE/VARIABLE GROWTH RATE CONCEPTDividend Growth Model cannot be applied directly in case where dividend is not growing at a constant ratefrom year 1 onwards .In such case we will modify Dividend Growth Model and calculate Current Market Price inthe following manner

0P [ Assuming Dividend is growing constantly from year 4 onwards ]

4Ke)(1

1g–Ke

5D4Ke)(1

4D3Ke)(1

3D2Ke)(1

2D1Ke1

1D

OVERVALUED & UNDERVALUED SHARESWhen Current Market Price[i.e price prevailing in stock market] and Theoretical(Fair OR Present Value)Market Price [i.e price which we calculate by applying present value concept] are not same we will undertakefollowing decision :Case Valuation DecisionIf Current Market Price > Present Value Market Price Overvalued SellIf Current Market Price < Present Value Market Price Undervalued BuyIf Current Market Price = Present Value Market Price Correctly Valued Hold



In SFM



RELATIONSHIP BETWEEN KE & PE RATIO

Ratio P/E1

eK

ASSET TURNOVER RATIO (ATR)

Asset Turnover Ratio = Asset Total

Sales Net

Decision:Higher the betterRETURN ON EQUITY (ROE )

Return On Equity (ROE ) ( r) = 100 Fund sr'Shareholde Equity Total

rShareholde Equity For Available EarningsTotal

BOOK VALUE PER SHARE (BVPS)

Book Value Per Share ( BVPS ) = Share EquityOf Number TotalFund sr'Shareholde Equity Total

RELATIONSHIP BETWEEN ROE,BVPS & EPSEPS = Book Value Per Share Return on Equity..

CALCULATION OF HOLDING PERIOD RETURN(HPR)

Holding Period Return or Total Yield

Yield Gain CapitalYield Dividend0P

0P1P

0P1D

0P0P1P1D

CAPITAL GAIN YIELD

Capital Gain Yield = 1000P

0P1P

PRICE AT THE END OF YEAR 1

P1 is normally calculated by using thi 1000P

0P1P

STRATEGY WHEN INVESTOR IS ALREADY HOLDING SHARESActual Po > Fair Po - Overvalued SellActual Po < Fair Po - Undervalued Hold

E/P RATIO OR EARNING PRICE OR YIELD RATIO

E/P Ratio = SharePerPriceMarketSharePerEarnings

VALUE AS PER PE MULTIPLE APPROACH AND EARNING GROWTH MODEValue of stock under the PE Multiple ApproachMarket Price per Share = EPS x PEWhere PE Multiple = (1/Return on Equity)Value of the Stock under the Earnings Growth Model



In SFM



Market Price per Share = gKeg)EPS(1

VALUE AT THE END OF “N” YEAR FROM WHERE GROWT RATE BECOMES CONSTANT

Assuming that growth rate becomes constant after 3 years price will be:P3 = g–Ke4D

VALUE OF STRAIGHT COUPON BOND OR EQUAL COUPON BOND

)0(B Bond of Value = nYield)(1

Value MaturitynYield)(1

Interest..................2Yield)(1

Interest1Yield)(1

Interest

= Interest x PVAF ( Yield %, n years) + Maturity Value x PVF ( Yield %, n years) Where n = Number of Years toMaturity

VALUE OF PERPETUAL BOND OR IRREDEEMABLE BOND

YieldInterest Annual )0(B BondOf Value

VALUE OF ZERO COUPON BOND OR DEEP DISCOUNT BOND

nYield)(1

Value Maturity

VALUE OF SEMI ANNUAL INTEREST BOND

Meaning : Semi Annual Interest Bonds are those bonds which pay interest semiannually .To value such bonds we have to make three changes :

1. 2

Amount Interest Annual2. 2 Maturity To Years 3.

2p.a Yield

HOLDING PERIOD RETURN (HPR)

Holding Period Return (R) or Total Return = 0B

)0B1(B1I or

0B)0B1(B

0B1I or Current Interest Yield + Capitalal

Gain YieldWhere oB is the Price of bond as on today , and 1B is the price of the bond at the end of the holding periodNote : The holding period is generally assumed to be of one year period unless otherwise specially stated .

CAPITAL GAIN YIELD

Capital Gain Yield = 1000B

)0B1(B

CURRENT YIELD / FLAT YIELD /CURRENT INTEREST YIELD/BASIC YIELD

Current Yield = OB 1I

Where 1I = Interest To Be Paid at Year End 1



In SFM



YIELD ( dK ) OR YIELD TO MATURITY (YTM) OR COST OF DEBTSymbolically : It can be calculated by using two method :

Trial n Error Method : )0(B Bond of Value nYield)(1

Value MaturitynYield)(1

Interest..................2Yield)(1

Interest1Yield)(1

Interest

Now for finding Yield we should use IRR Technique :

Kd = Lower Rate + Rates in DifferenceNPVRateHigher–NPVRateLower

NPVRateLower

Approximation Method : 2

ValueIssueValueMaturityn

Bo–ValueMaturityp.a Interestp.a Kd

Where Bo is current value of bond in case of existing bond or issue price or new proceeds in case of new issue ofbond

RELATIONSHIP BETWEEN BOND VALUE AND YTMYTM and the Bond Value has inverse relationship.

RELATIONSHIP BETWEEN YTM AND COUPON RATECase Nature Of BondCoupon Rate = YTM Par Value Bond i.e Bo = Par ValueCoupon Rate > YTM Premium Bond i.e Bo > Par ValueCoupon Rate < YTM Discount Bond i.e Bo < Par Value

TAXATION EFFECT ON INTEREST INCOMEIf income tax rate is given in question then Interest should be taken after tax .

TAXATION EFFECT ON CAPITAL GAIN INCOMEIf Capital Gain Tax Rate is given then Maturity Value should be taken after tax i.e after adjusting it for CapitalGain Tax

DURATION OF PERPETUAL BOND

Duration Of Perpetual Bond =YTM

YTM1

YIELD TO CALL ( YTC )

2oBValueCall

Years CalloB–ValueCallInterest

YTC

YIELD TO PUT ( YTP )

2oBValuePut

Years PutoB–ValuePutInterest

YTP



In SFM



KD OF PERPETUAL BOND

Bo

Interest Annual Kd or Yield

DURATION OF NORMAL BOND OR FREDRICK MACAULAY 'S DURATION

Symbolically : Duration =

nKd)(1

ValueMaturitynnKd)(1

Interest..n..........2Kd)(1

Interest21Kd)(1

Interest1

oB1

Short Cut Formula:

YTM1]nYTM)[(1 Rate Coupon

YTM)Rate (Coupon nYTM)(1YTM

YTM1Duration

DURATION OF A ZERO COUPON BONDFor a zero coupon bond , the duration is simply equal to the maturity of the bondWhile the duration of a normal coupon bond will always be less than the maturity.

VOLATILITY /SENSITIVITY/MODIFIED DURATIONMeaning : Modified Duration is a measure of volatility.In other words , Modified Duration is a measure of %change in bond value for every 1 % change in Yield to Maturity.

Symbolically :Volatility or Modified Duration or Sensitivity [ % ] =

Maturity To Yield1

BondOf Duration

Note : % Change in Bond Price = - Modified Duration Change In Yield To MaturityNote : The Modified Duration will always be lower than the Macaulay Duration.

FAIR VALUE OF CONVERTIBLE BONDS AS ON TODAY/STOCK VALUE OF BONDFair Conversion Value or Stock Value Of Bond = Number Of Equity Shares Received on Conversion x Market Price Per Share prevailing at the time of conversionDecision:If Fair Conversion Value Of Convertible Bond is greater than Basic Bond Value Of Debenture,investorwill convert otherwise not.

CONVERSION RATIOConversion Ratio directly specifies the number of equity shares we get in place of one convertible bond.

PERCENTAGE OF DOWNSIDE RISKDownside Risk = Market Value Of Convertible Bond - Market Value Of Non Convertible Bond or Straight Cou-pon BondIt should be further divided by Market Value Of Convertible Bond to calculate answer in %.

CONVERSION PREMIUMConversion Premium or Premium Over Conversion Value= Market Price Of Convertible Bond-Fair Conversion Value Of Convertible Bond As On TodayIt should be further divided by Fair Value Of Convertible Bond to calculate answer in %.

CONVERSION PARITY PRICE

Conversion Parity Price =Conversion on SharesNo.of

Bond eConvertiblOf Price Market

It is the price at which premium will be 0.



In SFM



CONVERSION PARITY PRICE PREMIUM PER EQUITY SHAREIN Rs: [Also Known As Conversion Premium Per Share ] = Conversion Parity Price of Equity - Actual Market Priceof EquityIN %: [Also Known As Ratio Of Conversion Premium ]

= Equityof Price Market ActualEquityof Price Market Actual - Equityof Price Parity Conversion

FAVOURABLE INCOME DIFFERENTIAL PER SHARE

Shares EquityOf No. i.e Ratio ConversionShare Per DividendRatio ConversionDebenture From Interest Coupon

PREMIUM PAY BACK PERIOD

Share Per alDifferenti Income Favourableshare Equity per premium Conversion

COST OF REDEEMABLE PREFERENCE SHARES

20PSCValueMaturity

n0PSC–ValueMaturityDividend Annual

pK

Note On PSCo: 0PSC = Current Market Price [In case of existing preference share];and

0P = Net Proceeds Where Net Proceeds = Face Value + Premium - Discount - Flotation Cost [ In case of newwpreference share ]

COST OF IRREDEEMABLE PREFERENCE SHARES

Kp = OPSC

Dividend Annual

Sometimes when relevant information is not given for calculation of Kp then we simply useKp = Rate Of Preference Dividend

VALUE OF IRREDEEMABLE PREFERENCE SHARES

Value Of Irredeemable Preference Shares(PSCo) = pKDividend Annual

VALUE OF REDEEMABLE PREFERENCE SHARES

)0(PS Share Preference of Value = n)PK(1

Value Maturityn)PK(1

Dividend..................2)PK(1

Dividend1)PK(1

Dividend

VALUE OF BOND UNDER REINVESTMENT CONCEPT

In such case our equation is nYTM)(1

Value Face n x Amount Coupon0B



In SFM



DIRTY PRICE AND CLEAN PRICEDirty Price = Clean Price + Accrued Interest

BASIS POINT1 % = 100 basis points

CALCULATION OF BO WHEN ENTIRE PRINCIPAL & INTEREST AMOUNT IS RECEIVED AT MATURITY YEARS

In such case our equation is : nYTM)(1

nRate) CouponValue(1 Face0B

CALCULATION OF YTM OF HALF YEARLYINTEREST PAYMENT BOND

2BoValueMaturity

2 x nBo–ValueMaturity

months 6 per Interest6monthOf Kd

Now Kd p.a = Kd for 6 month x 2

NET ASSET VALUE (NAV)

Symbolically : NAV =UnitsOf Number

Asset Net =

UnitsOf NumberLiability External Total-Asset Total

Where net assets of the scheme will normally be: Total Asset - Total External Liability =[ Market Value of Investments + Receivables + Accured Income + Other Assets ] - [ Accured Expenses + Payables+ Other Liabilities ]

EXPENSE RATIO

NAV AverageUnit Per Incurred ExpensesRatio Expense Where Average NAV =

2 NAV Closing NAV Opening

HOLDING PERIOD RETURN(HPR)

Return Period Holding =

beginning the at NAVReceived Gain CapitalReceived Dividendbeginning NAVend NAV

RELATIONSHIP BETWEEN RETURN OF MUTUAL FUND, RECURRING EXPENSES , INITIAL EXPENSES ANDRETURN DESIRED BY INVESTORS

Investors By Required Return Expenses) Initial(1 Expenses RecurringFund MutualOf Return

DIVIDEND YIELD METHOD OR DIVIDEND CAPITALIZATION VALUATION METHOD

Dividend Yield = (MPS)SharePerPriceMarket(DPS)SharePerDividend



In SFM



Market Price Per Share =Yield Dividend

(DPS)SharePerDividend

EARNING YIELD METHOD OR INCOME OR EARNING CAPITALIZATION VALUATION METHOD

Earning Yield = (MPS)SharePerPriceMarket(EPS)SharePerEarning

Market Price Per Share = Yield Earning(EPS)SharePerEarning

PRESENTATION OF INCOME STATEMENT TO CALCULATE MPSSales xxxLess: Variable cost xxxContribution xxxLess: Fixed cost xxxEBIT xxxLess: Interest xxxEBT xxxLess: Tax xxxEAT xxxLess:Preference Dividend xxxEFE(Earning for Equity) xxxNo. of Equity Shares xxxEPS xxxPE Ratio xxxMPS (EPS x PE Ratio) xxx

VALUE OF FIRM USING FUTURE MAINTAINABLE PROFITS(FMP)

Value Of Business = Rate tionCapitaliza RelevantProfit leMaintainab Future

Calculation Of Future Maintainable Profits :Average Past Year Profits xxxxAdd :All Actual Expenses and Losses not likely to occur in future xxxxAll Profits likely to arise in Future xxxxLess : All Expenses and Losses expected to arise in future (xxxx)Less : All Profits not likely to occur in future (xxxx)Future Maintainable Profits ( FMP ) xxxx

PRICE EARNING [P/E] RATIO VALUATION METHOD

Price Earning Ratio [ P/E Ratio ] = EPSMPS

EPS Ratio P/EMPS

Note : Total Market Value can be calculated by multiplying MPS with Number of Equity Share .Note : If we take total earning in the above formula we will directly get Market Value .

NET ASSET VALUATION METHODNet Assets Value = [ Total Assets - Total External Liability ]



In SFM



Net Asset Value Per Equity Shareholder = Share EquityOf Number TotalAsset Net

Note : Total Asset and Total External Liability may be taken on the basis of Market Value , Liquidation Value orBook Value as the case may be .Note:If question is silent always use Market Value Approach.

DISCOUNTED CASH FLOW(DCF) APPROACH/FREE CASH FLOW APPROACHIt is a method of evaluating an investment by estimating future cash flows and taking into consideration thetime value of money.Note : How To Calculate Free Cash Flow :EBDITA xxx(-)Depreciation xxx(-)Amortization xxx(-)Interest xxxEBT xxx(-)Tax xxxEAT xxx+ Deprecciation xxx+Amortization xxx-Increase In Working Capital xxx+Decrease In Working Capitalxxx-Capital Expenditure xxxFree Cash Flow xxx

VALUATION OF COMPANY/FIRMValue Of Firm = Value Of Equity + Value Of Debt

CHOICE OF CORRECT DISCOUNT RATE WHILE CALCULATING VARIOUS VALUESUse Of Discount Rate

Value Of Firm KoValue Of Equity KeValue Of Debt Kd

CALCULATION OF CAPITAL EMPLOYEDCapital employed can be calculated in two waysone way is to calculate from liabilities side andother way is to calculate through asset side.Let’s look at both waysLiabilities sideCapital employed = Equity Share Capital + Preference Share Capital + Reserves – Fictitious Assets + Debentures+ Long Term LoansAssets SideCapital Employed = Fixed assets (excluding Fictitious Assets) + Current assets – Current liabilities

SHARE EXCHANGE RATIO BASED ON EPS

Share Exchange Ratio = Ltd) Firm(AAcquiringofEPSLtd) (B FirmTargetofEPS



In SFM



SHARE EXCHANGE RATIO BASED ON MPS

Share Exchange Ratio = Ltd) (A FirmAcquiringofMPSLtd) (B FirmTargetofMPS

SHARE EXCHANGE RATIO BASED ON BOOK VALUE PER SHARE (BVPS)

Share Exchange Ratio = Ltd) (A Firm Acquiringof Share Per Value BookLtd) (B Firm Targetof Share Per Value Book

SHARE EXCHANGE RATIO BASED ON NET ASSET VALUE PER SHARE(NAV)

Share Exchange Ratio = Ltd) (A Firm Acquiringof Value Asset NetLtd) (B Firm Targetof Value Asset Net

TOTAL NO. OF EQUITY SHARES AFTER MERGERERBNAN

EPS (A+B) WHEN SHARES ARE ISSUED

ERBNANGain SynergyBEAE

Merger After Shares EquityOf No. TotalMerger After Earning Total

Merger after Firm Combined theof EPS

MPS (A+B) WHEN SHARES ARE ISSUED1st Preference :[to be used when PE A+B is given or any hint regarding this is given]

BARatio P/EBAEPSMerger after Firm Combinedof MPS or2nd Preference :

Merger After Shares EquityOf No. TotalMerger After Value Market TotalMerger after Firm Combinedof MPS

ERBNANAny)(If Gain SynergyBMV AMV

MARKET VALUE OF MERGED FIRM1st Preference :MV (A+B) = ER]BNA[NBARatio P/EBAEPS

2nd Preference :MV (A+B) = MV A + MV B + Synergy

EQUIVALENT EPS OF B LTD IN A NEW COMPANYEPS ( A+B ) x ER

EQUIVALENT MPS OF B LTD IN A NEW COMPANYMPS ( A+B ) x ER

NEW NO. OF EQUITY SHARES ISSUED TO B LTD.ERBN

CALCULATION OF % HOLDING IN MERGED COMPANYFor ALtd :

= Ltd B To Issued Shares NewOf No. Total Shares Ltd AOf No. Total

Shares Ltd AOf No. Total

For BLtd :



In SFM



= Ltd B To Issued Shares NewOf No. Total Shares Ltd AOf No. Total

Ltd B To Issued Shares NewOf No. Total

EPS A+B WHEN SYNERGY IS EXPRESSED IN AMOUNT

EPSA+B =

ER xBNAN

Gain)SynergyBEarningA(Earning

EPS A+B WHEN SYNERGY IS EXPRESSED IN %

EPSA+B =

ER xBNAN

Gain)Synergy(1)BEarningA(Earning

MAXIMUM EXCHANGE RATIO TAKING EPS BASE-FOR A LTDMaximum Exchange Ratio ( i.e the Exchange Ratio at which EPS of Firm’s A shareholder before and after mergerwill be same )EPS Before Merger = EPS after Merger

ERBNANSynergyBEAE

AEPS

Now by solving the above equation keeping Exchange Ratio constant we can find desired Exchange Ratio.

MINIMUM EXCHANGE RATIO TAKING EPS BASE-FOR B LTDMinimum Exchange Ratio ( i.e the Exchange ratio at which EPS of Firm ’s B shareholder before and after mergerwill be same )EPS Before Merger = Equivalent EPS after Merger ERBAEPSBEPS

ERERBNAN

SynergyBEAEBEPS


IF DECISION IS BASED ON MPS [ AND IF P/E RATIO AFTER MERGER FOR A LTD IS GIVEN OR ANY HINT INTHE QUESTION IS GIVEN REGARDING THIS ] :For A Ltd :

Maximum Exchange Ratio ( i.e the Exchange Ratio at which MPS of Firm ’s A shareholder before and aftermerger will be same )MPS Before Merger = MPS After Merger BAMPSAMPS

BAEPSBARatio P/EAMPS

ERBNANSynergyBEAE

BARatio P/EAMPS


IF DECISION IS BASED ON MPS [ AND IF P/E RATIO AFTER MERGER FOR A LTD IS GIVEN OR ANY HINT INTHE QUESTION IS GIVEN REGARDING THIS ] For B Ltd :

Minimum Exchange Ratio ( i.e the Exchange ratio at which MPS of Firm ’s B shareholder before and after merger



In SFM



will be same )MPS Before Merger = Equivalent MPS after Merger BAMPSERBMPS

BARatio P/EBAEPSERBMPS

ERBNANSynergyBEAE

BARatio P/EERBMPS


IF DECISION IS BASED ON MPS [ AND IF P/E RATIO AFTER MERGER IS NOT GIVEN ] :For A Ltd :Maximum Exchange Ratio ( i.e the Exchange Ratio at which MPS of Firm ’s A shareholder before and aftermerger will be same )MPS Before Merger = MPS After Merger BAMPSAMPS

Ratio ExchangeBShares EquityOf No.AShares Equityof No.Gain SynergyBNBMPSANAMPS

AMPS


IF DECISION IS BASED ON MPS [ AND IF P/E RATIO AFTER MERGER IS NOT GIVEN ] :For B Ltd :Minimum Exchange Ratio ( i.e the Exchange Ratio at which MPS of Firm ’s B shareholder before and aftermerger will be same ) :MPS Before Merger = Equivalent MPS after Merger BAMPSERBMPS

ERBShares EquityOf No.AShares Equityof No.Gain SynergyBNBMPSANAMPS

ERBMPS


COMPONENTS OF MARKET PRICE PER SHAREMarket Price Per Share(MPS) =Earning Per Share (EPS) Price Earning Ratio (PE Ratio)

= ShareEquityofNo.rShareholde Equity ForEarning

Share Per EarningsShare Per Price Market

=Return on Equity(ROE) Book Value / Intrinsic Value Per Share ] Share Per EarningsShare Per Price Market

= Fundsr'ShareholdeEquityrShareholde Equity ForEarning SharesEquityofNo.

Fund sr'ShareholdeEquity Share Per Earnings

Share Per Price Market

Where Equity Shareholder's Fund = Equity Share Capital + Reserves - P/L account ( Dr.)EPS A+B WHEN CASH IS PAID OUT OF BORROWED MONEY

EPSA+B =

ANRate) Tax(1Rate InterestAmount BorrowedBEarningA(Earning

EPS A+B WHEN CASH IS PAID OUT OF BUSINESS MONEYEPSA+B



In SFM



=

ANtax)-(1InterestOf Cost yOpportunitPaid CashBEarningA(Earning

MARKET VALUE AFTER MERGER WHEN GROWTH RATE OF B LTD UNDER NEW MANAGEMENT INCREASESMarket Value After Merger = MPS A x No. Of Equity Share A + New MPS B Taking new growth rate x No. OfEquity Share B + Synergy to be taken as zero

NPV OF A LTD UNDER MERGERPV Of Cash Flows Received By A Ltd From B Ltd xxxLess: Cost of Acquisition Paid By A Ltd To B Ltd xxxNPV Of A Ltd if B Ltd is acquired xxxDecision:If NPV is positive, Altd should takeover Bltd.

COST OF MERGER-WHEN CASH IS PAID-FOR A LTDCost = Cash Paid - Market Value Of B received

COST OF MERGER-WHEN SHARES ARE ISSUED-FOR A LTDCost =Value of shares given – Value Of B Received = Combined Value Of A & B –Value Of B receivededWhere represents the % holding of B Ltd. in merged firm

SYNERGY GAIN-BASED ON EARNINGSMerger Gain or Synergy Based On Earnings = Total Combined Earning Of Merged Firm -[Earning Of A + EarningOf B]

SYNERGY GAIN-BASED ON MARKET VALUESMerger Gain or Synergy Based On Market Value= Total Combined Market Value Of Merged Firm -[Market Value Of A + Market Value Of B]

EFFECT OF CASH TAKEOVER IN EARNINGS AND MARKET VALUETotal Earning After Merger= Earning A + Earning B - Opportunity/Borrowing Cost Of Cash Paid Adjusted For TaxTotal Market Value After Merger = Market Value A + Market Value B - Cash Paid

GROSS NPA(%)

100Bank By Given Deposit or Advance Gross

NPA GrossRatio GNPA

CAR [CAPITAL ADEQUACY RATIO] OR CRWAR [ CAPITAL TO RISK WEIGHTED ASSET RATIO]

CAR or CRWAR or Total Capital To Risk Weight Asset Ratio = Assets Weighted RiskyCapital Total

CALCULATION OF SWAP RATIO IN CASE OF NEGATIVE FACTOR LIKE GROSS NPA

Ltd. BOf NPA GrossLtd. AOf NPA GrossRatio Swap

CALCULATION OF RETURN OF A SECURITY OR ASSET



In SFM



Holding Period Return

Beginning The At PriceonDistributi Income AnyBeginning The At PriceEnd The At Price

STANDARD DEVIATION (σ ) BASED ON PAST DATA

Standard Deviation (σ ) = n

2Return) AverageReturn (Given

STANDARD DEVIATION (σ ) BASED ON PROBABILITY

Standard Deviation ( ) = 2Return) ExpectedReturn (Givenyprobabilit

VARIANCE

Variance = 2Deviation Standard = 2σDecision:Higher the variance,higher the risk.

COEFFICIENT OF VARIATION (CV ):-PAST DATACoefficient Of Variation measures Risk Per Unit Of Return.

CV= Return AverageDeviation Standard

Decision:Higher the CV , higher the risk.

COEFFICIENT OF VARIATION (CV ) BASED ON PROBABILITY

CV = Return ExpectedDeviation Standard

Decision:Higher the CV , higher the risk.

RETURN OF PORTFOLIO-BASED ON PAST DATAThe Return of the portfolio is the weighted average return of individual security .Return Of Portfolio = A's Average Return AWeight + B's Average Return BWeight

RETURN OF PORTFOLIO ON THE BASIS OF PROBABILITYReturn Of Portfolio = A's Expected Return AWeight + B's Expected Return BWeightNote : Sum of Weights used in Portfolio for different security will always be equal to 1 .

STANDARD DEVIATION OF THE PORTFOLIO CONSISTING OF TWO SECURITY

Standard Deviation ]21[σ 1,2 r 2w 2σ 1w 1σ 222w 2

2σ2

1w 21σ

Where , 21σ = Standard Deviation of Portfolio consisting of Security 1 & 2

1 SecurityOf Deviation Standard1σ ; 2 SecurityOf Deviation Standard2σ ;

1 SecurityOf Weight1W ; 2 SecurityOf Weight2W ;

2 Security and 1 Security Between nCorrelatioOf tCoefficien1,2 r



In SFM



COEFFICIENT OF CORRELATION (r)

Coefficient of Correlation between A & B : ( B,Ar ) BσAσ

) B , (A Covariance

COVARIANCE -BASED ON PAST DATA

B) , (A Covariance =

nBReturn AverageBReturn GivenAReturn AverageAReturn Given

nBdAd

COVARIANCE BASED ON PROBABILITYB) , (A Covariance BReturn ExpectedBReturn GivenAReturn ExpectedAReturn Givenyprobabilit

WHEN RISK REDUCTION IS ACHIEVED BY BUILDING A PORTFOLIO/CONCEPT OF RISK REDUCTIONRisk Reduction is achieved when Portfolio Standard Deviation is less than Weighted Average Standard Devia-tion Of Individual Security.

MEANING OF r=+1It is a Perfect Positive Correlated Portfolio Portfolio Risk will be MaximumStandard Deviation Of Portfolio will become BWBσAWAσ)BA(σ

MEANING OF r=-1It is a Perfect Negative Correlated Portfolio Portfolio Risk will be minimumStandard Deviation Of Portfolio will become BWBσAWAσ)BA(σ

MEANING OF r=0It is a No Correlated Portfolio .Portfolio Risk will be between minimum and maximum range

Standard Deviation Of Portfolio will become = B2WB2σA2WA2σ)BA(σ

RANGE OF ‘R’ OR COEFFICIENT OF CORRELATIONRange of r is between -1 to +1

DECISION ON THE BASIS OF VALUE OF ‘R’Higher the r, higher the risk.As r increases, risk also increases When r = -1 : Minimum Risk When r =+1:Maximum RiskOverall Decision : Lower the Standard Deviation , Coefficient Of Variation , Variance or Range Lower will bethe Risk Of Security .

STANDARD DEVIATION OF PORTFOLIO CONSISTING OF THREE SECURITIES

ABCσ BCrCσBσCwB2wABrBσBwAσA2w2Cw2

Cσ2Bw2

Bσ2Aw2

Aσ

When r = +1 we can use short cut formula : CwCσBwBσAwAσABCσ

CAPITAL ASSET PRICING MODEL (CAPM) BASED RETURNSymbolically : Expected Return /Required Return /Equilibrium Return /Desired Return =

Rf)–(RmMarketBetaSecurityBeta

Rf = Rf)–(RmSecurityBetaRf



In SFM



CAPITAL ASSET PRICING MODEL (CAPM) BASED DECISION OR UNDERVALUED /OVERVALUED CONCEPTCase Valuation Decision

If CAPM Return > Given Return Overvalued or Overpriced SellIf CAPM Return < Given Return Undervalued or Underpriced BuyIf CAPM Return = Given Return Correctlyvalued or Correctly priced Hold

BETA OF A SECURITY BASED ON % RETURN CHANGESBeta is the degree of the responsiveness of the security's return with the market return .

Hence Beta may also be defined by using following relation : Return Market in ChangeReturn Security in ChangeBeta

This equation is normally applicable when two return data is given.

CALCULATION OF BETA USING COVARIANCE FORMULABeta is a ratio of " Covariance Of Security with the Market " and "Variance Of Market"

Beta of an Asset or Security = market theof Variance

Market and Security between Covariance= 2mσ

m)(s, Covariance

BETA OF A SECURITY USING CORRELATION

mσ

sσms,rSecurityOf Beta

ARBITRAGE PRICING THEORY [ STEPHEN ROSS'S APT MODEL ] /MULTI FACTOR MODELSymbolically : Overall Return in case of APT will be = Risk Free Return + (Beta x Risk Premium ) Of Each Factor= Risk Free Return + { InflationBeta Inflation Differential or Premium }+ { GNPBeta GNP Differential or Pre-mium} ....+ and so onWhere , Differential or Premium = [ Actual Value - Expected/Estimated Value ]

PORTFOLIO EVALUATION TECHNIQUE-SHARPE RATIOIt indicate the amount of return earned per unit of risk. It is also known as Reward to Risk Ratio or Reward toVariability Ratio .

Symbolically :Sharpe Ratio = SecurityOf Deviation StandardInvestment Free RiskOf ReturnSecurityOf Return

Decision : Higher the ratio, Better the performance

TREYNOR RATIOThis ratio measures the return earned per unit of systematic risk. It is also known as the Reward to VolatilityRatio.

Symbolically : Treynor Ratio = SecurityOf BetaInvestment Free RiskOf ReturnSecurityOf Return

Decision : Higher the ratio, Better the performance

JENSEN’S ALPHA / JENSEN'S INDEXSymbolically : Jensen’s Alpha = Actual or Given or Expected or Average Return - CAPM Returnwhere, CAPM Return = Rf + Beta ( Rm - Rf )Decision : If Alpha is positive it shows that the portfolio has performed better and it has out performed the



In SFM



market. If Alpha is negative, it means that the portfolio has underperformed as compared to the market. If Alphais zero, it indicates that the portfolio has just performed what it is expected to.

STANDARD DEVIATION OF PORTFOLIO CONSISTING OF FOUR SECURITIES

BDrDσBσDwB2wDArAσDσAwD2wCDrDσCσDwC2wBCrBσCσCwB2w

ACrCσAσCwA2wBArBσBwAσA2w

2Dw2

Dσ2Cw2

Cσ2Bw2

Bσ2Aw2

Aσ

ABCDσ

When r = +1 we can use short cut formula DwDσcwCσBwBσAwAσABCσ

STANDARD DEVIATION OF PORTFOLIO CONSISTING RISK FREE & RISKY SECURITY

AWAσ)BA(σ Where A is risky security & B is risk free security

STANDARD DEVIATION OF PORTFOLIO CONSISTING RISK FREE & RISKY SECURITY

AWAσ)BA(σ Where A is risky security & B is risk free security

BETA OF A PORTFOLIOBeta of a portfolio is the weighted average beta of individual securities .Symbolically : Beta Of Portfolio =

BOf WeightB SecurityOf BetaAOf WeightA SecurityOf Beta = BWB β AWA β

SECURITY MARKET LINE (SML)A Graphical representation of CAPM is known as Security Market Line .Expected Return under SML is calculated by using following equation :

Rf)–(RmMarketBetaSecurityBeta

Rf = Rf)–(RmSecurityBetaRf

Note:Beta of market assumed to be 1.Decision :If a security lie on SML:Efficient Security Correctly Priced Hold Security giving Optimum Return as expectedIf a security lie below SML:Inefficient Security Over Priced Sold Security giving Low Return than expectedIf a security lie above SML:Inefficient Security Under Priced Buy Security giving High Return than expected

CAPITAL MARKET LINE (CML)Capital Market Line shows the relationship between Return & Standard Deviation of security.Capital Market Line takes into account Total Risk .

Return under CML is calculated by using following equation : fRmRmσSσ

fR

Decision : Same as SML

CHARACTERISTICS LINE (CL)The Characteristic Line shows the relationship between the Return Of an Investment in Security and Return OfMarket Portfolio.



In SFM



Equation Of Characteristics Line : Y = X βa , Where

Y = Average or Expected Return for the Security ;X = Average or Expected Return of the Market Portfolio ;β = Betaaof Security ;a = Intercept or alpha which can be calculated as XβY

SLOPE OF CHARACTERISTICS LINE (CL)Beta of a security is a slope of Characteristics Line .

SLOPE OF SML

Slope Of SML may be obtained as follows : fRmRmB

fRmR

SLOPE OF CML

Slope Of CML may be obtained as follows : mσ

fRmR

COVARIANCE FORMULA USING CORRELATION

BσAσ BA,r) B , (A Covariance

CALCULATION OF OPTIMUM WEIGHTS TO MINIMIZE PORTFOLIO RISK WHEN WEIGHTS ARE MISSINGUnder this concept we will try to find out that " What percentage in each of the security consisting in theportfolio would result into lowest possible risk " . Hence if we are asked to calculate optimum weights which willreduce our portfolio risk then we will use following formula :

B)(A, Covariance22Bσ

2Aσ

B)(A, Covariance2Bσ

BσAσB , A r22Bσ

2Aσ

BσAσB , A r2

BσAW

and AW1BW (Since 1BWAW )

SHORT CUT FORMULA FOR OPTIMUM WEIGHTS WHEN 1r When r = -1 then we can also use the following formula for finding Optimum Weights

XW1 or YσXσ

XσyW ; YσXσ

YσXW

(Since 1YWXW )

Note : If we find the Standard Deviation ( risk ) from this optimum weights when r = -1 then portfolio risk will bezero .

COVARIANCE OF A SECURITY WITH THE SAME SECURITYAOf VarianceA)(A,Covariance

Note: Covariance with oneself is variance.

CORRELATION OF A SECURITY WITH SAME SECURITY (RA,B)rA,B = 1

COVARIANCE MATRIXA B C

A cov(A,A) cov(A,B) cov(A,C)B cov(A,B) cov(B,B) cov(B,C)C cov(A,C) cov(C,B) cov(C,C)



In SFM



NEW FORMULA OF COVARIANCE USING BETA

Covariance between any 2 stocks = m2σ2β1β

RISK RETURN RATIO (TRADE OFF) OF MARKET

Risk Return Trade Off Of Market = mσ

fRmR

HOW TO CALCULATE SYSTEMATIC RISK AND UNSYSTEMATIC RISK / SHARPE INDEX MODEL

FOR A SECURITY :Total Risk = 2sσ ;

Systematic Risk Of a Security = 2sβ2mσ ;Unsystematic Risk Of a Security = Total Risk - Systematic Risk = 2sσ -

2sβ2mσ

FOR A PORTFOLIO: Total Risk = 2Pσ

Systematic Risk Of a Portfolio= 2Pβ

2mσ ;

Unsystematic Risk Of a Portfolio = Total Risk - Systematic Risk = 2Pσ - 2

Pβ2

mσ or 2w2

USRσn

1i

CALCULATION OF SYSTEMATIC & UNSYSTEMATIC RISK USING COEFFICIENT OF DETERMINATION

Coefficient Of Determination = )2(r 2n)correlatioof nt(coefficie Use of Coefficient of Determination in calculating Systematic Risk & Unsystematic Risk

Explained by the index (Systematic Risk)= Variance of Security Return x Co-efficient of Determination of Securityor

Variance of Security Return x 2r or ms,2rs2σ

Not explained by the index(Unsystematic Risk) = Variance of Security Return (1- Co-efficient of Determinationof Security)

or Variance of Security Return (1 – 2r ) or or

ms,2r-1s2σ

CONVERTING DIRECT QUOTE INTO INDIRECT QUOTE AND VICE-VERSA-WHEN BID & ASK RATE ARE SAMEDirect Quotes can be converted into Indirect Quotes by taking reciprocals of each other, which can be math-

ematically expressed as follows: Direct Quote = Quote Indirect1

or Indirect Quote = Quote Direct1

For Example : 1 DM = Rs. 20 is a direct quote for India. 1 Re. = DM 201

is indirect quote for India

CONVERTING DIRECT QUOTE INTO INDIRECT QUOTE AND VICE-VERSA -WHEN BID AND ASK RATE ARE DIF-FERENTDirect Quotes can be converted into Indirect Quotes by taking reciprocals of each other and then switching theposition.For Example : Direct Quote wih reference to India : 1 $ = Rs. 46.10 / 46.20.



In SFM



Indirect Quote with reference to India : 46.10

1$46.20

1$ 1 Re or Re 1 = $ .02165 - $ .02170

CALCULATION OF CONTRIBUTION TO SALES RATIO UNDER FOREX

Contribution to Sales Ratio = 100Sale

onContributi

Decision-Higher the C/S Ratio better the situation

CONTRIBUTIONContribution is the selling price minus the variable cost.

EXCHANGE MARGINExchange Margin is the extra amount or percentage charged by the bank over and above the rate quoted by bank.It represents commission , transaction related expenses etc .In case of Buying Rate Quoted by bank : Deduct Exchange Margin : i.e Actual Buying Rate =Bid Rate( 1-Exchange Margin )In case of Selling Rate Quoted by bank : Add Exchange Margin : i.e Actual Selling Rate = Ask Rate ( 1+Exchange Margin )S

PREMIUM AND DISCOUNTHow to Calculate Premium or Discount : Rate of Premium or Discount of Left Hand Currency is given by :

100Period Forward

12Rate Spot

Rate SpotRate Forward

PURCHASE PRICE PARITY THEORY [PPPT]-CALCULATION OF SPOT RATE

Spot Rate (Rs. / $ )= ] USA in Price Current [ B] India in Price [Current A

PURCHASE PRICE PARITY THEORY [PPPT ]-CALCULATION OF FORWARD RATE-USING INFLATION

Symbolically :As per PPP Theory we have : (Rs./$) Rate SpotInflation Dollar1Inflation Rupee1(Rs/$) Rate Forward

or

Inflation Dollar1Inflation Rupee1

(Rs./$) Rate Spot(Rs/$) Rate Forward

DETERMINATION OF PREMIUM & DISCOUNT USING PPPTHigher Rate of Inflation in one country (as compared to the other country) results in discount of currency of thatcountry and vice-versa.

INTEREST RATE PARITY THEORY (IRPT)Meaning :IRPT is based on the concept that investment opportunity in any two given country will always besame.

Symbolically : Rate Interest Dollar1Rate Interest Rupee1

(Rs./$) Rate Spot(Rs/$) Rate Forward



In SFM



DETERMINATION OF PREMIUM & DISCOUNT USING IRPTHigher Rate of Interest in one country (as compared to the other country) results in discount of currency of thatcountry and vice-versa.

SPREADThe difference between Ask and Bid Rates is called the Spread , representing the profit margin of the dealer .Spread = Ask Rate - Bid Rate

CALCULATION OF NET EXPOSURE USING FORWARD RATE AND SPOT RATENet exposure we mean advantage of using Forward Contract over Spot Contract .Net exposure = Net Cash Flow x ( Forward Rate - Spot Rate ) = Net Cash Flow x Swap PointsDecision:A positive Net Exposure indicates benefit of Forward Rate over Spot Rate.

INTERNATIONAL FISHER EFFECT (IFE)It analyses the relationship between the Interest Rates and the Inflation .As per IFE we have(1+Money Interest Rate )=(1+Real Interest Rate)(1+Inflation Rate )

INTEREST RATE DIFFERENTIAL-NO ARBITRAGEWhen Difference in Interest Rates Between The Two Countries is equal to Premium Or Discount - No ArbitrageIs PossibleInterest Rate Differential is just another name of premium or discount of one currency in relation to anothercurrency i.e

100Period Forward

12SR[Rs/$]

SR[Rs/$]-FR[Rs/$] DollarOf Rate InterestRupeeOf Rate Interest

GAIN OR LOSS UNDER FUTURE CONTRACT-LONG POSITIONPosition Actual Price On Expiration Profit/LossLong Increase ProfitLong Decrease Loss

GAIN OR LOSS UNDER FUTURE CONTRACT-SHORT POSITIONShort Increase LossShort Decrease Profit

HOW SETTLEMENT IS DONE UNDER LONG POSITIONLong Position is settled by taking Short Position at the time of settlement

HOW SETTLEMENT IS DONE UNDER SHORT POSITIONShort Position is settled by taking Long position at the time of settlement

POSITIONS UNDER STOCK MARKETLong Position : If a person buys or holds an asset , he is said to be in a Long Position .Short Position : If a person sells an asset , he is said to be in a Short Position .

INITIAL MARGINInitial Margin deposited is not an expense it is just like security deposit .Sometimes when initial margin is not given in question it can be calculated by using following equation:



In SFM



Initial Margin = Daily Absolute Changes + 3 x Standard Deviation

MARK TO MARKET MARGINIt is like a profit and loss account.

WHEN INTEREST RATE IS COMPOUNDED CONTINUOUSLY OR INFINITY

tre Value PresentValue Future

tr -e Value Futuretre

Value FutureValue Present

PRESENT VALUE WHEN INTEREST RATE IS DISCOUNTED CONTINIOUSLY

tr -e Value Futuretre

Value FutureValue Present

FAIR FUTURE PRICE OF SECURITIES Basic Principle While Calculating Fair Future Price :1.Cost:If Given In Rs.: Add in CMP ; If Given In % :Add in rate2.Dividend:If Given In Rs.: Deduct in CMP ; If Given In % :Deduct in rate

HOW TO CALCULATE ARBITRAGE PROFIT ? WHEN-ACTUAL FUTURE VALUE > FAIR FUTURE VALUECase Valuation Borrow/Invest Cash Future

Market MarketActual Future Value > Fair Future Value Overvalued Borrow Buy Sell

PRINCIPLE OF CONVERGENCEThe process by which the futures price and the cash price of an underlying asset approach one another asdelivery date nears. The futures and cash prices should be equal on the delivery date.

HOW TO CALCULATE ARBITRAGE PROFIT ? WHEN-ACTUAL FUTURE VALUE < FAIR FUTURE VALUECase Valuation Borrow/Invest Cash Future

Market MarketActual Future Value < Fair Future Value Undervalued Invest Sell* Buy* here we are assuming that arbitrageur holds one share in cash market.

POSITION TO BE TAKEN FOR HEDGINGIf you are Short on any Security You should go Long in Index [Sensex or Nifty]If you are Long on any Security You should go Short in Index [Sensex or Nifty]

VALUE OF INDEX TO BE HEDGED FOR COMPLETE HEDGINGThe extent or value of hedging ( hedge ratio ) is determined by the beta of a security and value of current portfolioExtent Of Hedging or Total Value to be hedged or Value of Perfect Hedge = Existing Beta Of The Stock Value OfTransaction or Value Of Exposure or Current Value Of Portfolio which requires hedging

VALUE OF HEDGING FOR INCREASING & REDUCING BETA TO A DESIRED LEVEL(ASSUMING LONG POSITION)When Existing beta > Desired beta



In SFM



Objective:Reducing RiskPosition To Be Taken:Take Short PositionAmount Of hedging Required = Value of Existing Portfolio x (Existing Beta - Desired Beta)When Existing beta < Desired betaObjective:Increasing RiskPosition To Be Taken:Take Long PositionAmount Of hedging Required = Value of Existing Portfolio x (Desired Beta - Existing Beta )

BETA OF CASH & CASH EQUIVALENTBeta of Cash & Cash equivalent is always assumed to be zero.

DETERMINATION OF NUMBER OF FUTURE CONTRACTS TO BE TAKENThe number of futures contract to be taken for increasing and reducing beta to a desired level is given by the

following formula : =Contract Future Index OneOf ValuePosition Future Index TotalOf Value

HEDGE RATIO UNDER FUTURE CONTRACT

Hedge Ratio i.e Existing Beta for complete hedge purpose= fσsσ

s.fr

sσ =Standard Deviation of the Spot Price ; fσ = Standard Deviation of the Future Price; fs,r = Correlation Coeffi-cient between the two

OPTION- AN UNDERSTANDINGIn Forward Contract : Both parties are obliged to performIn Future Contract : Both the parties are obliged to performIn Option Contract : Only one party is obliged to perform

TYPES OF OPTION-CALL & PUT(i) Call Option Contract (ii) Put Options Contract

PARTIES OF OPTION CONTRACT(i) Call Option (i) Call Writer / Call Seller (ii) Call Holder/Call Buyer(ii)Put Option (i) Put Writer / Put Seller (ii) Put Holder/Put Buyer

DIFFERENCE BETWEEN CALL BUYER AND CALL SELLERCALL BUYER CALL SELLERPay Premium Receive PremiumPurchase Right Sell RightBuy Share Sell Share

DIFFERENCE BETWEEN PUT BUYER AND PUT SELLERPUT BUYER PUT SELLERPay Premium Receive PremiumPurchase Right Sell RightSell Share Buy Share

PAY OFF/PROFIT & LOSS OF A CALL BUYER



In SFM



Pay off means Profit and Loss.Call Option :Profit : When Cash Market Price As On Expiry > Strike PriceIn such case Call Buyer will exercise the Option.Net Profit = Cash Market Price As On Expiry - Strike Price - Option PremiumLoss : When Cash Market Price As On Expiry < Strike PriceIn such case Call Buyer will not exercise the option .His loss is limited to the amount of Call Premium. i.e Loss = Amount Of Premium Paid

PAY OFF/PROFIT & LOSS OF A PUT BUYERPay off means Profit and Loss.Put Option :Profit : When Cash Market Price As On Expiry < Strike PriceIn such case Put Buyer will exercise the option .Net Profit = Strike Price - Cash Market Price as on expiry - Option PremiumLoss: When Cash Market Price As On Expiry > Strike PriceIn such case Put Buyer will not exercise the Option.His Loss will be limited to the amount of premium.

BREAK EVEN PRICE OF CALL OPTIONBreakeven price is the market price at which the option parties neither makes a profit nor incur any losses.Break-Even Market Price for Buyer and Seller of Call Option :Exercise Price + Option Premium

BREAK EVEN PRICE OF PUT OPTIONBreakeven price is the market price at which the option parties neither makes a profit nor incur any losses.Break-Even Market Price for Buyer and Seller of Put Option :Exercise Price Option Premium

POINT OF MAXIMUM PROFIT & LOSS- FOR CALL BUYER & SELLERCall Buyer maximum loss--the amount of premium paidCall Seller maximum profit will be equal to the amount of premium receivedCall Buyer maximum profit will be unlimitedCall Seller maximum loss will be unlimited

POINT OF MAXIMUM PROFIT & LOSS- FOR PUT BUYER & SELLERPut Buyer maximum loss is the amount of premium paidPut Seller maximum profit will be equal to the amount of premium receivedPut Buyer maximum profit will be equal to Strike Price - Premium PaidPut Seller maximum loss will be Strike Price - Premium Received

TYPES OF RIGHTRight To Buy Shares-Call Buyer ; Right To Sell Shares-Put Buyer

IN / OUT /AT THE MONEY OPTION-FOR CALL BUYERMarket Scenario IN/OUT/ATCash Market Price as on expiry > Strike Price In the MoneyCash Market Price as on expiry < Strike Price Out Of The MoneyCash Market Price as on expiry = Strike Price At The MoneyNote : The above position is reversed for the Writer of the Option .



In SFM



IN / OUT /AT THE MONEY OPTION-FOR PUT BUYERMarket Scenario IN/OUT/ATCash Market Price as on expiry > Strike Price Out Of The MoneyCash Market Price as on expiry < Strike Price In the MoneyCash Market Price as on expiry = Strike Price At The MoneyNote : The above position is reversed for the Writer of the Option .

FAIR VALUE/PREMIUM/PRICE OF CALL OPTION AS ON EXPIRYValue(Premium) of Call Option at expiration= Maximum of ( Cash Market Price As On Expiry - Strike Price , 0)

FAIR VALUE/PREMIUM/PRICE OF PUT OPTION AS ON EXPIRYValue(Premium) of Put Option at expiration= Maximum of ( Strike Price - Cash Market Price As On Expiry , 0)

FAIR VALUE OF CALL OPTION BEFORE EXPIRY DATE MINIMUM THEORETICAL PRICE OF CALL OPTIONTheoretical Minimum Value of Call Option : = Spot Price – Present Value of Strike Price =Spot Price – StrikePrice e–rt

FAIR VALUE OF PUT OPTION BEFORE EXPIRY DATE : MINIMUM THEORETICAL PRICE OF PUT OPTIONTheoretical Minimum Value of Put Option:= Present Value of Strike Price– Current Market Price =Strike Price e–rt –Current Market Price

INTRINSIC VALUE AND TIME VALUE OF OPTION-CALLOption Premium is the component of two parts : Intrinsic Value + Time Value of MoneyIntrinsic Value of Call Option= Maximum of (0,Current Market Price As On Today-Exercise Price);Time Value of Option = Option Premium - Intrinsic Value

INTRINSIC VALUE AND TIME VALUE OF OPTION-PUTIntrinsic Value of Put Option=Maximum of (0,Exercise Price-Current Market Price).Time Value of Option = Option Premium - Intrinsic Value

STRADDLESStraddle can be of two types:1.Long Straddle :Buying a Call and a Put with the same strike price and the same exipry date. In Longstraddle the investor will have to pay premium on the call as well as on put option contract.2.Short Straddle :Selling a Call and a Put with the same strike price and the same exipry date.In Shortstraddle the investor will receive premium on the call as well as on put option contract.If question is silent always assume Long Straddle.

RISK NEUTRAL METHOD-FOR CALL

Value/Premium/Price Of Call As On Today = r)(1p)(12Cp1C

HOW TO CALCULATE PROBABILITY

Alt 1 : p Price Lower -Price HigherPrice LowerRate) Interest(1 Price Spot



In SFM



r = rate of interest adjusted as per option period . For example if annual rate of interest is 10 % and Option periodis 3 months then we will take .025 in the above formula .

CALCULATION OF OPTION PREMIUM FOR CALL UNDER BIONOMIAL MODEL-HEDGE RATIO TECHNIQUEOption Premium = Current Market Price - Amount Of Borrowing Where,e,

/ Hedge Ratio/Option Delta = Price LowPrice HighPrice Low At Expiry On CallOf ValuePrice High At Expiry On CallOf Value

= 2S–1S2C–1C

Amount Of Borrowings : B = )2C–2S(Δr1

1

CALCULATION OF AMOUNT OF BORROWING UNDER HEDGE RATIO TECHNIQUE

Amount Of Borrowings : B = )2C–2S(Δr1

1 or )1C–1S(Δ

r11

Where r = rate of interest adjusted for periods for example if rate of interest is 10% pa and we are asked tocalculate 6 month option premium,then we have to adjust 10% pa for 6 month i.e we will take 5%.

HEDGE RATIO OR DELTA FOR CALL

Asset Underlyingof Price in ChangePremium Option in ChangeΔ Delta

2S1S2C1C

Note : Delta of a Call Option is always positive and Delta of a Put Option is always negative

DELTA OF PUT OPTION

Delta = Price LowPrice HighPrice Low At Expiry On PutOf ValuePrice High At Expiry On PutOf Value

=2S–1S2C–1C

Note:It will always be negative.OPTIONS GREEKS

GAMMA Gamma ( Sensitivity to Change in Delta ) :It is a measure of the rate of change of the delta with respect tothe price of the underlying asset .

It is calculated as : Asset Underlyingof Price in ChangeDelta in ChangeGamma

VEGAVega( Sensitivity to Change in Volatility of Asset Price ):It is a measure of rate of change in option price withrespect to the percentage change in volatility.

It is calculated as : Priceof Volatility in ChangePremium Option in ChangeVega

THETATheta ( Sensitivity to Change in Time to Expiry ) : It is the rate of change in value of the option with respectto time to maturity.



In SFM



It is calculated as Expiry to Time in ChangePremium Option in ChangeTheta

RHORho ( Sensitivity to Change in Interest Rate ) : It is the rate of change in option price with respect to changein interest rate .

It is calculated as : Interestof Rate in ChangePremium Option in ChangeRho

PUT CALL PARITY THEORY (PCPT)Symbolically : As per PCPT we have :OP Of Call As On Today + Present Value of Strike Price = OP of Put As On Today + Current Market Price

BLACK & SCHOLES MODEL-FOR CALLValue or Premium Of Call Option = Spot Price N(d1) – Exercise Price e–rt N(d2)

HOW TO CALCULATE D1 & D2

tσ

t]2.50σ[rPrice Exercise

Price Market Currentln2d

; d2 = d1 – tσ

σ = Standard Deviation ;t = remaining life to expiration of the option in terms of year for example for a call option

of 6 months t = .5 , for a call option of 73 days t = 36573

;r = continuous compounded risk free annual rate of return

;ln = Natural Log

BLACK & SCHOLES MODEL-WHEN DIVIDEND AMOUNT IS GIVENAs per BSM Model : Value of Call Option = Adjusted Current Price N(d1) – Exercise Price e–r x t N(d2)

Where tσ

t]2.50σ[rPrice Exercise

Price Market Current Adjustedln1d

;d2 = d1 – tσ

Where Adjusted Current Market Price = Current Market Price - Present Value Of Dividend Income

TREATMENT OF DEPRECIATIONDepreciation can be calculated in the following manner :(i) Straight Line Method (SLM) (ii) Written Down Value (WDV)Depreciation is charged by the owner of the asset.Depreciation is not an item of Cash Outflow,hence it should not be considered for our analysis.However Tax Saving on depreciation is an item of inflow and hence must be recognized .Tax Saving On Depreciation = Amount Of Depreciation x Tax Rate

TREATMENT OF SALVAGE VALUE-WDV -IN CASE OF PROFITAdjusted Salvage Value = Salvage Value - Profit On Sale x Tax Rate

TREATMENT OF SALVAGE VALUE-WDV -IN CASE OF LOSSAdjusted Salvage Value = Salvage Value + Loss On Sale x Tax Rate



In SFM



TREATMENT OF SALVAGE VALUE-SLMSalvage Value is not adjusted for tax under SLM unless otherwise stated.

TREATMENT OF TAXATIONAll cash inflows and outflows which are a part of Profit and Loss account should be taken after tax.

TREATMENT OF TAXATION FOR ITEMS ARISING AT THE BEGINNING OF EACH YEAR :Tax Savings On Items Arising At the Beginning of each year can be takenAlt 1: Either at the end of each year [ Normally preferred in case of Leasing Chapter]Alt 2:At the beginning of each year

EQUAL ANNUAL LOAN INCLUSIVE OF INTEREST :-WHEN INSTALMENT IS PAID AT THE END OF EACH YEAR

For calculating Equal Annual Loan Inclusive Of Interest we will use following formula :

years) n %, (r PVAFDiffers) ItIf Taken Loan or ( AssetOf Cost

Where r = interest rate charged by bank before tax i.e Kd before tax.

EQUAL ANNUAL LOAN INCLUSIVE OF INTEREST :-WHEN INSTALMENT IS PAID AT THE BEGINNING OF EACH YEAR

For calculating Equal Annual Loan Inclusive Of Interest we will use following formula :

years) 1-n %, (r PVAF1Differs) ItIf Taken Loan or ( AssetOf Cost

Where r = interest rate charged by bank before tax i.e Kd before tax.

NET PRESENT VALUE (NPV)Formula :Net Present Value(NPV)= Present Value Of Cash Inflows - Present Value Of Cash OutflowsAccept/Reject Criterion :NPV > 0 Accept the proposal ; NPV = 0 Indifference point ; NPV < 0 Reject theproposalNote : If question has not said specifically that which evaluation technique should be used , we will alwaysprefer NPV Method..

COMPARISION IN CASE OF UNEQUAL LIFE / EQUATED ANNUAL VALUEIf two projects have unequal life ,then the two projects are not comparable . To make them comparable we willuse Equivalent Annual Value Concept for each project by applying the following formula :

Equation: years) n%, K PVAF(Inflow CashOf Value Present or Outflow CashOf Value Present or NPV

Where K % = Discount Rate and n = Total Life of the project

PAY BACK PERIOD / PAY OFF PERIOD / CAPITAL RECOVERY PERIOD :IN CASE OF EVEN CASH FLOWSPayback Period is the period within which the total cash inflows from the project equals the cost of theproject.

Formula :Payback Period = Inflows Cash Annual

Investment Initial

Decision : The project with the lower payback period will be preferred.



In SFM



PAY BACK PERIOD / PAY OFF PERIOD / CAPITAL RECOVERY PERIOD : IN CASE OF UNEVEN CASH FLOWS

Formula : Payback Period = Amount Available

Amount Remaining Years Completed

Decision : The project with the lower payback period will be preferred.

BETA OF A FIRM / FIRM BETA / OVERALL BETA OF FIRM / ASSET BETA / PROJECT BETA-IF TAX IS NILOverall Beta or Firm Beta or Asset Beta or Project Beta

=

EquityDebt

EquityBeta Equity +

EquityDebt

Debt Beta Debt

BETA OF A FIRM / FIRM BETA / OVERALL BETA OF FIRM / ASSET BETA / PROJECT BETA-IF TAX IS CONSID-ERED

Overall Beta or Firm Beta or Asset Beta or Project Beta =

Equitytax)–Debt(1Equity

Beta Equity

+ Equitytax)–(1Debttax)–(1Debt

Beta Debt

LEVERED AND UNLEVERED FIRMIf a company finances its investments and projects completely with Equity then the company is known asUnlevered FirmIf a company finances its investments and projects both with Equity and Debt then the company is known asLevered Firm

OVERALL COST OF CAPITAL ( KO)-IF TAX IS NILAlt 1 : Return] Free RiskReturn [Market Overall BetaRate Free RiskoK

Alt 2 : DebtOf WeightDebtOf CostEquityOf WeightEquityOf CostoK dWdKeWeK Where ,

) Rate Free RiskReturn Market ( Beta EquityRate Free RiskeK ) fRmR ( EquityBfR

) fRmR ( DebtBfRdK

OVERALL COST OF CAPITAL ( KO)-IF TAX IS CONSIDEREDDebtOf WeightDebtOf CostEquityOf WeightEquityOf CostoK dWdKeWeK

Where , ) Rate Free RiskReturn Market ( Beta EquityRate Free RiskeK ) fRmR ( EquityBfR

Tax)(1 InterestdK COST OF CAPITAL FOR UNLEVERED FIRM

Cost Of Capital = Cost Of Equity

OVERALL BETA FOR UNLEVERED FIRMOverall Beta For Unlevered Firm = Equity Beta

DEBT EQUITY RATIO

Debt Equity Ratio = EquityDebt



In SFM



DEBT RATIO

Debt Ratio = DebtEquityDebt

EFFECT IN OVERALL BETA DUE TO CHANGE IN CAPITAL STRUCTUREA school of thought led by Modigliani and Miller's theory believe thatOverall Beta of the firm is not affected by the Change in Capital Structure.Overall Beta of a firm will be same as other company belonging to the same industry(sector) and it will not beeffected by the Change in Capital Structure.

EFFECT IN EQUITY & DEBT BETA DUE TO CHANGE IN CAPITAL STRUCTUREEquity Beta and Debt Beta Changes with the change in Capital Structure

For example : Overall Beta of Idea Company will be same as Overall Beta of Airtel Company as both thecompany belong to the same industry .But there Equity Beta and Debt Beta may be different at different CapitalStructure .

TREATMENT OF WORKING CAPITALIn the absense of information the students are advised to assume :Introduction Of Working Capital at the beginning .This should be treated as Outflow.Release Of Working Capital at the end . This should be treated as InflowNote : Changes in items such as Working Capital do not affect taxes.Note : Any Increase in Working Capital should be treated as Outflow.Note : Any Decrease in Working Capital should be treated as Inflow

BREAKEVEN UNITSBEP refers to that volume of sales where the profit or loss is zero.

Break Even Units = 100Unit Per onContributi

Cost Fixed

THEORETICAL POST-RIGHTS (EX-RIGHT) PRICE PER SHARE

Theoretical Post-Rights (ex-right) or After Right Price Per Share =

Issued Share RightOf Number NewShareOf No. ExistingShares Rightof No.Price Share RightShareOf No. ExistingRight Cum MPS

THEORETICAL VALUE OF THE RIGHTS ALONEAlt 1:Value Of Right Per Share = MPS Before Right - MPS After Right

Alt 2:Value Of Right Per Share = Issued Are Shares Right One WhichOf Respect In SharesOf No.Price Offer-Right Ex MPS

MPS AFTER RIGHT ISSUE IN CASE OF SYNERGY(NPV)MPS of the Project After Right Issue



In SFM



= Issued Share RightOf Number NewShareOf No. ExistingNPV or SynergyShares RightPrice Share RightShare Existing MPS Existing

FRA : HOW TO CALCULATE PROFIT/LOSS

FRA(Net Settlement) = 365 or 360

rate underlying in Days x expiration at Rate + 1

365 or 360 rate underlying in DaysRate) Contract Forward - Expiration At (Rate

HOW TO CALCULATE EVASymbolically : EVA = Net Operating Profit After Taxes - Cost Of Capital EmployedWhere Net Operating Profit After Taxes [NOPAT] = EBIT(1 - Tax)Cost Of Capital Employed = Cost Of Capital Capital Employed

Cost Of Capital (Ko) or Weighted Average Cost of Capital(WACC) = PWpKdWdKrWrKeWeK

Note : In Calculating Operating Profit,interest is not deducted as interest is a non-operating items.Note : Total Funds / Capital Employed includes : Equity Share Capital + Reserves + Debentures +Preference ShareCapital +Long Term Loan - Profit and Loss Account ( Dr.) - Fictitious Asset

Note : Financial Leverage = [EBT] Tax Before Profit or Earning[EBIT] Tax and Interest Before Profit or Earning

Note : EBT = EBIT - Interest

MARKET VALUE ADDED(MVA)MVA is yet another concept which is used to measure the performance and value of the firm .Symbolically :From Equity Point Of ViewMVA =Current Value of the securities of the Company in the Market - Total Amount of Shareholder's Funds[BalanceSheet Fig. ]Note: Shareholder's Funds[Balance Sheet Fig.]includes Equity Share Capital + Retained Earning - AccumulatedLoss - P/L Account ( Debit Balance )From Overall Company's Point Of ViewMVA = Value of the Company Based On Free Cash Flows - Total Capital Employed or Amount Invested

INTEREST COVERAGE RATIO (ICR)A ratio used to determine how easily a company can pay interest on outstanding debt.

Interest Coverage Ratio = Expense InterestEBIT

The lower the ratio, the more the company is burdened by debt expense. An interest coverage ratio below 1indicates the company is not generating sufficient revenues to satisfy interest expenses.Decision: Higher the better

CAPITAL GEARING RATIO (CGR)Formula:Capital Gearing Ratio



In SFM



= Fund rs'Shareholde EquityFunds Bearing Income Fixed

= Losses)-Surplus & ReservesCapital Share (EquityLoan) Term LongDebenturesCapital Share e(Preferenc

Decision: Lower the better

FIXED INTEREST AND DIVIDEND COVERAGE

Interest and Fixed Dividend Coverage = Dividend PreferenceInterest Debenture

Interest Debenture PAT

Decision: Higher the better

EXPONENTIAL MOVING AVERAGE (EMA)Formula: EMA = EMA yesterday + a x [ Price Today - EMA Yesterday ] Where a = Smoothing Constant / Multiplier.Itwill be normally given in question .If not given than it can be calculated by using a = 2/(N+1) where N is thenumber of items in the average.

SHARPE'S OPTIMAL PORTFOLIO/APPLICATION OF CUT OFF POINT1.Find out the “excess return to beta” ratio for each stock under consideration.2.Rank them from the highest to the lowest.3.Proceed to calculate Cut Off Point Of Security (Ci) for all the stocks according to the ranked order using the

following formula:

N

1i ei2σ

2iβm2σ1

2eiσ

iβ)fR–i(RN

1im2σ

iC

Where ei2σ = variance of a stock’s movement that is not associated with the movement of market index i.e.stock’s unsystematic risk.The highest Ci value is taken as the cut-off point i.e. C*.It is the cut off rate.Security with C* value and thesecurities before this security are to be included in the portfolio and others are rejected.

4.The next step is to calculate weights.For this purpose we have to calculate Zi. :Zi =

*Ciβ

fRiR

ei2σiβ

By using Zi ,weights are calculated.

VALUE OF EQUITY AS PER RISK PREMIUM APPROACH

Value of Equity Share = Share Per Value PaidUpRisk To According Adjusted IndustryOf Yield Expected

Company TheOf Yield Actual

100Capital Share Equity

Shares On YieldShares(%) Equity On Yield Actual

BOND IMMUNIZATIONA portfolio is immunized when its duration equals the investor’s time horizon. In other words, if the averageduration of portfolio must be equals the investor’s planned investment period.A portfolio is immunized when it is “unaffected” by interest rate changes.



In SFM



TEST OF HYPOTHESIS/RUN TEST /DEGREE OF FREEDOMStep-1:First Calculate Mean Value of r & Standard Deviation in the following manner

Mean Value Of r 12n1n2n12n

; 1)2n1(n2)2n1(n

)2n1n2n1(2n2n12nDeviation Standard

Here n1 refers to total number of positive changes ;n2 refers to total number of negative changes.Step-2: Calculate Standard Lower & Upper Limit in the following manner :The Standard Lower limit = Mean Value Of r - Table Value x SDThe Standard Upper limit = Mean Value Of r + Table Value x SDStep-3: Decision:If our value of r lies within the standard lower limit and standard upper limit,the randomnessis there i.e the market is weakly efficient,otherwise it is not weakly efficient.Here r refers to number of times sign changesNote:Table Value or Degree Of freedom should be selected in following manner :n1+n2-1

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