8 CA Final Sfm Mafa Theory Notes by Aaditya Jain Covering 20 Marks
Target 100 % Marks Only For Nov CA Aaditya Jain In SFM ... · FORMULA bOOK STRATEGIC FINANCIAL...
Transcript of Target 100 % Marks Only For Nov CA Aaditya Jain In SFM ... · FORMULA bOOK STRATEGIC FINANCIAL...
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IMPORTANT PRACTICAL QUESTION
SFMFORMULA bOOK
STRATEGIC FINANCIAL MANAGEMENT
The Best CA Final OLD SYLLABUS
CA,MBA(FINANCE),CFA,NCFM,B.COM,M.COMAWARDED AS NSE CERTIFIED MARKET PROFESSIONAL
MASTER OF FINANCIAL ANALYSISPOST GRADUATE DIPLOMA IN FINANCIAL MATRKET
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IMPORTANT PRACTICAL QUESTION
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IMPORTANT PRACTICAL QUESTION
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 %
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IMPORTANT PRACTICAL QUESTION
Normal Company Ke =r Indifferent Indifferent
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 RATEWhen 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 :
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IMPORTANT PRACTICAL QUESTION
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
RELATIONSHIP BETWEEN KE & PE RATIO
Ratio P/E1
eK
ASSET TURNOVER RATIO (ATR)
Asset Turnover Ratio = Asset Total
Sales Net
Decision:Higher the better
RETURN 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 ) = ShareEquity OfNumber TotalFund sr'ShareholdeEquity 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
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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
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
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IMPORTANT PRACTICAL QUESTION
CURRENT YIELD / FLAT YIELD /CURRENT INTEREST YIELD/BASIC YIELD
Current Yield = OB 1I
Where 1I = Interest To Be Paid at Year End 1
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 Interest
p.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
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IMPORTANT PRACTICAL QUESTION
YIELD TO PUT ( YTP )
2oBValuePut
Years PutoB–ValuePutInterest
YTP
KD OF PERPETUAL BOND
Bo
Interest Annual Kd or Yield
DURATION OF NORMAL BOND OR FREDRICKMACAULAY '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 %.
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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.
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
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IMPORTANT PRACTICAL QUESTION
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
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 = UnitsOfNumber AssetNet
= UnitsOfNumber Liability 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 AveragePer Unit 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
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IMPORTANT PRACTICAL QUESTION
RELATIONSHIP BETWEEN RETURN OF MUTUAL FUND, RECURRING EXPENSES , INITIAL EXPENSES ANDRETURN DESIRED BY INVESTORS
InvestorsBy RequiredReturn Expenses) Initial(1 Expenses RecurringFund Mutual OfReturn
DIVIDEND YIELD METHOD OR DIVIDEND CAPITALIZATION VALUATION METHOD
Dividend Yield = (MPS)SharePerPriceMarket(DPS)SharePerDividend
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
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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 ]
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 and other 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 Loans
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Assets 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
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 Acquiring of ValueAsset Net Ltd) (B FirmTarget of ValueAsset 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
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IMPORTANT PRACTICAL QUESTION
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 :
= 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
Now by solving the above equation keeping Exchange Ratio constant we can find desired Exchange Ratio.
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
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IMPORTANT PRACTICAL QUESTION
ERBNANSynergyBEAE
BARatio P/EAMPS
Now by solving the above equation keeping Exchange Ratio constant we can find desired Exchange Ratio.
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 mergerwill be same )MPS Before Merger = Equivalent MPS after Merger BAMPSERBMPS
BARatio P/EBAEPSERBMPS
ERBNANSynergyBEAE
BARatio P/EERBMPS
Now by solving the above equation keeping Exchange Ratio constant we can find desired Exchange Ratio.
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
Now by solving the above equation keeping Exchange Ratio constant we can find desired Exchange Ratio.
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
Now by solving the above equation keeping Exchange Ratio constant we can find desired Exchange Ratio.
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
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IMPORTANT PRACTICAL QUESTION
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
=
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]
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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
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 22σ21w 21σ
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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
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
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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
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 RATIO
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This 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 themarket. 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
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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 SMLCHARACTERISTICS LINE (CL)
The Characteristic Line shows the relationship between the Return Of an Investment in Security and Return OfMarket Portfolio.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 be
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zero .COVARIANCE OF A SECURITY WITH THE SAME SECURITYA Of 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)
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 s,m2rs2σ 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
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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.
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
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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
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 POSITION
Position Actual Price On Expiration Profit/LossLong Increase ProfitLong Decrease Loss
GAIN OR LOSS UNDER FUTURE CONTRACT-SHORT POSITIONShort Increase LossShort Decrease Profit
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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: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.
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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 hedgingVALUE OF HEDGING FOR INCREASING & REDUCING BETA TO A DESIRED LEVEL(ASSUMING LONG POSITION)When Existing beta > Desired betaObjective: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 Premium
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Purchase 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 BUYERPay 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
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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 / 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 Short
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IMPORTANT PRACTICAL QUESTION
straddle 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
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 .
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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.
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
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IMPORTANT PRACTICAL QUESTION
PARTIES TO LEASE AGREEMENTThere are two parties under any lease agreement :(i) Lessor : Owner of the asset is known as Lessor .(ii) Lessee : The party who uses the asset is known as Lessee .
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.Under Lease Agreement it is the lessor who claims the depreciation andUnder Loan Agreement it is charged by the Borrower.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
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
PARTIES UNDER LOAN AGREEMENTThere are two parties under loan agreement1.Borrower :Borrower will take loanBorrower will be the user as well as the owner of the assetsBorrower will be entitled to Charge deptreciation and will receive Salvage value2.BankBank will give loanBank will be neither be a user or nor the owner of the assetsBank will be not Charge depreciation and will not receive Salvage value
LESSEE VS BORROWERCalculate Present Value Of Outflow under both the option separately by using the discount rate and choosesuch option which involves least outflow.LESSEE BORROWERNo Depreciation Charge Charge DepreciationUser User & Owner
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Not Entitled To Salvage Value Entitled To Salvage ValuePay Lease Rent No Lease Rent Is PaidNo Principal Repayment Principal RepaymentNo Payment Of Interest Interest Payment
EVALUATION FOR LESSEELessee should choose such option which will minimize its Outflow and maximize its Inflow . He should gener-ally undertake the following steps for taking decision :Step 1 : He should first evaluate its inflow and outflow under both the option given in questionMajor Outflow Under Leasing Option :(i) Lease Rent Paid Net Of TaxMajor Inflow Under Leasing Option :No major inflow for lesseeThere may be other inflow and outflow which, if given in question,must be also taken into account .Step 2 : Discount Rate : Kd = Interest Rate ( 1- Tax)Step 3 : Calculate Present Value Of Cash Outflow(PVCO) by using the discount rate
EVALUATION FOR BORROWERBorrower should choose such option which will minimize its Outflow and maximize its Inflow.He should gener-ally undertake the following steps for taking decision :Step 1 : He should first evaluate its inflow and outflow under both the option given in questionMajor Outflow Under Borrowing Option :(i) Interest Paid Net Of Tax(ii) Principal RepaymentMajor Inflow Under Borrowing Option :(i) Tax Saving On Depreciation(ii) Salvage Value Adjusted for Tax on Capital Gain/LossStep 2 : Discount Rate : Kd = Interest Rate ( 1- tax)Step 3 : Calculate Present Value Of Cash Outflow(PVCO) by using the discount rate.
BREAKEVEN LEASE RENTALS FROM THE VIEWPOINT OF LESSEE :The break even lease rental is the rental at which the lessee is indifferent to a choice between lease financingand borrowing option.At Breakeven Lease Rental :PV Of Cash OutflowUnder Loan Option = PV Of Cash Outflow Under Lease Option
HOW TO EVALUATE FROM THE POINT OF VIEW OF LESSOR- AN INVESTMENT DECISIONWhile deciding whether to give asset on Lease or not,Lessor should undertake following stepsStep 1 : He should first evaluate the inflows and outflowsMajor Outflow : Cost Of AssetMajor Inflow : Lease Rental Received Net Of Tax , Tax Saving on Depreciation , Salvage Value adjusted for tax.Step 2 : Discount Rate : Ko = Cost Of CapitalStep 3 : Calculate NPVDecision:If NPV is positive,then Lessor should give the asset on Lease otherwise he should not give.
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 :
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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.
PRESENT VALUE OF INTEREST NET OF TAX & PRINCIPAL REPAYMENT MUST BE EQUAL TO THE AMOUNT OFLOAN PROVIDED DISCOUNT RATE IS KD
When discount rate is Kd then-PV of Interest Net Of Tax + Present Value Of Principal Repayment = Amount OfLoan
NET ADVANTAGE OF LEASING (NAL)NAL = Outflow Under Loan Option - Outflow Under Lease OptionDecision : If NAL is positive,Lease Option is preferred,otherwise select Loan Option.
EQUAL MONTHLY INSTALMENT -WHEN INSTALMENT IS PAID AT THE END OF EACH MONTH
EMI = periods) 12 x n p.m, % (r PVAFDiffers) ItIf Taken Loan or ( AssetOf Cost
Where r = interest rate charged by bank before tax i.e Kd before
tax.
EQUAL MONTHLY INSTALMENT -WHEN INSTALMENT IS PAID AT THE BEGINNING OF EACH MONTH
EMI = 1)]-periods 12 x (n p.m, % [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..
RISK ADJUSTED DISCOUNT RATE (RADR)Under this technique we discount the Cash Flows by a rate higher than Risk Free Rate .Such rate is known asRisk Adjusted Discount Rate . Such rate is computed in the following mannerAlternative 1:(1 + Risk Adjusted Discount Rate )=(1 + Risk Free Discount Rate ) ( 1 + Risk Premium )Alternative 2: It can also be calculated by using CAPM : Discount Rate = Rf + Beta x ( Rm - Rf)
Note : The Net Present Value computed by using Risk Adjusted Discount Rate is known as Risk Adjusted NetPresent Value .Note : Higher Risk should be discounted by higher rate.
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IMPORTANT PRACTICAL QUESTION
CERTAINTY EQUIVALENT APPROACH (CEC)Certainty Equivalent Approach involves discounting of Certain Cash Flows instead of the Total Cash Flows.Steps In Certainty Equivalent ApproachStep 1 : Estimate the total future cash flows from the proposal. These cash flows have some degree of riskinvolved.Step 2 : Calculate the Certainty Equivalent Coefficient (CEC) factors for different years .The value of CEC can vary between 1 indicating no risk and 0 indicating the extreme risk. This means higher therisk, lower is the value of CEC. (This value is generally given in question )Step 3 : Multiply Total Cash Flows (Step 1) x CEC (Step 2) = Certainty Equivalent Cash FlowsStep 4 : Certainty Equivalent Cash Flows are discounted at Risk Free Rate to find out the NPV of the proposal.
EXPECTED NET PRESENT VALUE OR EXPECTED CASH FLOWS OREXPECTED VALUE
Expected NPV or Expected CF or Expected Value= Each possible outcome of an event Probability of that outcome occuringExample :Estimated Value Probability Estimated Value Probability1000 .1 1002000 .3 6004000 .3 12003000 .2 6005000 .1 500
1. Expected Value/NPV/Cash Flow =3000Note:Probability Of All Outcomes will always be equal to 1
PROFITABILITY INDEX (PI) / BENEFIT COST RATIO / PRESENT VALUE INDEX / DESIRABILITY FACTOR
Formula :Profitability Index (PI) OutflowsOf Value PresentInflowsOf Value Present
Accept/Reject Criterion :Where PI > 1 Accept the proposal ; PI = 1 Indifference point ; PI < 1 Reject theproposal
EFFECT ON CASH FLOW DUE TO INFLATIONThe future cash flows can be either expressed as(i) inclusive of inflation which are referred as Money Cash Flows(ii) exclusive of Inflation which are referred as Real Cash flowsConversion of Real Cash Flows into Money Cash Flows and Vice -versa :
Money Cash flows = Real Cash Flows (1+ Inflation Rate) or Real Cash Flows = Rate) Inflation(1Flows Cash Money
12.EFFECT OF INFLATION ON DISCOUNT RATEDiscount Rate can be expressed either as(i) inclusive of future inflation which is referred to as Money Discount Rate(ii) exclusive of future inflation which is referred to as Real Discount RateConversion of Money Discount Rate into Real Discount Rate and vice versa :(1+ Money Discount Rate ) = (1+Real Discount Rate ) ( 1+ Inflation Rate )
CALCULATION OF NPV WHEN INFLATION RATE IS GIVEN
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IMPORTANT PRACTICAL QUESTION
Present Value may be found either by(i) Discounting the Real Cash Flows at the Real Discount Rate or(ii) Discounting the Money Cash Flows at the Money Discount RateIn both cases resultant NPV would be sameNote : If question said that the value are given at "Current Prices " it means that these prices are given withouttaking the effect of inflation .
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.
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.
SENSITIVITY ANALYSIS / SCENARIO ANALYSIS - KEEPING NPV = 0Meaning : Sensitivity Analysis enables managers to assess how responsive the Net Present Value is to changesin the variables or factors which are used to calculate it .Importance : It directs the management to pay maximum attention towards the factor where minimum per-centage of adverse changes causes maximum adverse effect.Decision : If NPV were to become 0 with 2 % change in Initial Investment relative to 10 % change in CashInflows , Project is said to be more sensitive to Intial Investment than to Cash Inflows .
Symbolically : 100Base
Change(%) ySensitivit
Some factors to be used under Sensitivity Analysis are Size of the project, Cash flows, Life of the project,Discount rate.Under this analysis adverse effect of each input variable (parameters) is considered separately and all othervariables are held constant.Factor Adverse EffectInflow DecreaseDiscount Rate IncreaseOutflow IncreaseLife Decrease
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IMPORTANT PRACTICAL QUESTION
SENSITIVITY ANALYSIS USING % ADVERSE VARIATION IN FACTORSUnder this method Sensitivity is calculated by taking adverse changes by a specific % which will be indicatedin questionThe adverse factor for which % Fall In NPV is maximum is considered to be most sensitive.
% Fall In NPV = 100NPV Original
NPV Original-NPV Revised
PROBABILITY OF OCCURRENCE IF THE CASH FLOWS ARE (A) PERFECTLY DEPENDENT OVERTIME (B) INDE-PENDENT OVERTIME
The probability of occurrence of the worst or best case if the cash flows are(a) Perfectly Dependent Overtime is Required Probability (b) Independent Overtime is (Required Probability) n
Where n = Life Of The Project
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
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IMPORTANT PRACTICAL QUESTION
COST OF CAPITAL FOR UNLEVERED FIRMCost Of Capital = Cost Of Equity
OVERALL BETA FOR UNLEVERED FIRMOverall Beta For Unlevered Firm = Equity Beta
DEBT EQUITY RATIO
Debt Equity Ratio = EquityDebt
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
HILLER 'S MODELWhen Cash Flows are Dependent or correlated : Standard Deviation of the project as a whole :
)nPVFn(SD..................)2PVF2(SD)1PVF1(SD When Cash Flows are Independent or uncorrelated :Standard Deviation of the Project as a whole :
2)nPVFn(SD..................2)2PVF2(SD2)1PVF1(SD
BREAKEVEN UNITSBEP refers to that volume of sales where the profit or loss is zero. Break Even Units =
100Unit Per onContributi
Cost Fixed
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IMPORTANT PRACTICAL QUESTION
MODIFIED NPVThe Net Present Value calculated so far was based on an assumption that the cash inflow that is generatedover the years is invested at the same rate at which our cash flows are discounted . But this may not be true in allcases . It may so happen that the cash inflows of the project may be invested at different rates . In such case weshould compute Modified NPV as follows :Find the Future Value of cash inflows at the given rate of investment for the remaining years.So if the project isfor 5 years ,the cash inflow generated in first year end shall be compounded for 4 years.Similarly the cash inflowgenerated in second year end shall be compounded for 3 years and so on .Take the total of future values which may be termed as Future Value or Terminal Value
Find the Present Value Of Cash Inflows in the following manner : nCapital)Of Cost(1
Value Terminal
Modified Net Present Value = Present Value Of Cash Inflows Initial Cash Outfloww
MODIFIED IRRModified IRR is the rate at which Modified NPV is zero.
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
= 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
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IMPORTANT PRACTICAL QUESTION
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 - InterestMARKET 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
= 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.
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IMPORTANT PRACTICAL QUESTION
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.
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