caiib_fm_mod_a

8/6/2019 caiib_fm_mod_a

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FINANCIAL MANAGEMENTFINANCIAL MANAGEMENT

C A I I BC A I I B

PAPERPAPER--11

MODULE AMODULE A

QUANTATIVE TECHNIQUESQUANTATIVE TECHNIQUES

&&

FINANCIAL MATHEMATICSFINANCIAL MATHEMATICS

RAVI ULLALRAVI ULLAL

CONSULTANTCONSULTANT


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TIME VALUE OF MONEYTIME VALUE OF MONEY

MONEY HAS TIME VALUEMONEY HAS TIME VALUE

THIS IS BASED ON THE CONCEPT OF EROSION IN VALUE OFTHIS IS BASED ON THE CONCEPT OF EROSION IN VALUE OFMONEY DUE TO INFLATIONMONEY DUE TO INFLATION

HENCE THE NEED TO CONVERT TO A PRESENT VALUEHENCE THE NEED TO CONVERT TO A PRESENT VALUE

OTHER REASONS FOR NEED TO REACH PRESENT VALUE ISOTHER REASONS FOR NEED TO REACH PRESENT VALUE IS ---- DESIRE FOR IMMEDIATE CONSUMPTION RATHER THANDESIRE FOR IMMEDIATE CONSUMPTION RATHER THAN

WAIT FOR THE FUTUREWAIT FOR THE FUTURE

---- THE GREATER THE RISK IN FUTURE THE GREATER THETHE GREATER THE RISK IN FUTURE THE GREATER THEEROSIONEROSION


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EXTENTOF EROSION IN THE VALUE OF MONEY IS ANEXTENTOF EROSION IN THE VALUE OF MONEY IS ANUNKNOWN FACTOR. HENCE A WELL THOUGHT OUTUNKNOWN FACTOR. HENCE A WELL THOUGHT OUTDISCOUNT RATE HELPS TO BRING THE FUTURE CASHDISCOUNT RATE HELPS TO BRING THE FUTURE CASHFLOWS TO THE PRESENT.FLOWS TO THE PRESENT.

THIS HELPS TO DECIDE ON THE TYPE OF INVESTMENT,THIS HELPS TO DECIDE ON THE TYPE OF INVESTMENT,EXTENT OF RETURN & SO ON.EXTENT OF RETURN & SO ON.

ALL THREE FACTORS THAT CONTRIBUTE TO THE EROSIONALL THREE FACTORS THAT CONTRIBUTE TO THE EROSION

IN VALUE OF MONEY HAVE AN INVERSE RELATIONSHIP WITHIN VALUE OF MONEY HAVE AN INVERSE RELATIONSHIP WITHTHE VALUE OF MONEY i.e. THE GREATER THE FACTOR THETHE VALUE OF MONEY i.e. THE GREATER THE FACTOR THELOWER IS THE VALUE OF MONEYLOWER IS THE VALUE OF MONEY


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IF DESIRE FOR CURRENT CONSUMPTION ISGREATER THENIF DESIRE FOR CURRENT CONSUMPTION ISGREATER THENWE NEED TO OFFER INCENTIVES TO DEFER THEWE NEED TO OFFER INCENTIVES TO DEFER THECONSUMPTION.CONSUMPTION.

THE MONEY THUS SAVED IS THEN PROFITABLY ORTHE MONEY THUS SAVED IS THEN PROFITABLY ORGAINFULLY EMPLOYED . HENCE THE DISCOUNT RATE WILLGAINFULLY EMPLOYED . HENCE THE DISCOUNT RATE WILLBE LOWER.BE LOWER.

INVESTMENT IN GOVERNMENT BONDS / SECURITIES IS LESSINVESTMENT IN GOVERNMENT BONDS / SECURITIES IS LESSRISKY THAN IN THE PRIVATE SECTOR SIMPLY BECAUSE NOTRISKY THAN IN THE PRIVATE SECTOR SIMPLY BECAUSE NOT

ALL CASH FLOWS ARE EQUALLY PREDICTABLE AND WHEREALL CASH FLOWS ARE EQUALLY PREDICTABLE AND WHERETHERE IS SOVEREIGN GUARANTEE THE RISK IS LESS.THERE IS SOVEREIGN GUARANTEE THE RISK IS LESS.

IF THE RISK OF RETURN IS LOWER AS IN GOVT. SECURITIESIF THE RISK OF RETURN IS LOWER AS IN GOVT. SECURITIESTHEN THE RATE OF RETURN IS ALSO LOWER.THEN THE RATE OF RETURN IS ALSO LOWER.


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THE PROCESS BY WHICH FUTURE FLOWS ARE ADJUSTEDTHE PROCESS BY WHICH FUTURE FLOWS ARE ADJUSTEDTO REFLECT THESE FACTORS IS CALLED DISCOUNTING &TO REFLECT THESE FACTORS IS CALLED DISCOUNTING &THE MAGNITUDE IS REFLECTED IN THE DISCOUNT RATE.THE MAGNITUDE IS REFLECTED IN THE DISCOUNT RATE.

THE DISCOUNT VARIES DIRECTLY WITH EACH OF THESETHE DISCOUNT VARIES DIRECTLY WITH EACH OF THESEFACTORS.FACTORS.

THE DISCOUNT OF FUTURE FLOWS TO THE PRESENT ISTHE DISCOUNT OF FUTURE FLOWS TO THE PRESENT IS

DONE WITH THE NEED TO KNOW THE EFFICACY OF THEDONE WITH THE NEED TO KNOW THE EFFICACY OF THEINVESTMENT.INVESTMENT.


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THE DISCOUNTING BRING THE FLOWS TO A NET PRESENTTHE DISCOUNTING BRING THE FLOWS TO A NET PRESENTVALUE OR N P V.VALUE OR N P V.

N P V IS THE NET OF THE PRESENT VALUE OF FUTURE CASHN P V IS THE NET OF THE PRESENT VALUE OF FUTURE CASHFLOWS AND THE INITIAL INVESTMENT.FLOWS AND THE INITIAL INVESTMENT.

IF N P V IS POSITIVE THEN WE ACCEPT THE INVESTMENTIF N P V IS POSITIVE THEN WE ACCEPT THE INVESTMENTAND VICE VERSA.AND VICE VERSA.

IF 2 INVESTMENTS ARE TO BE COMPARED THEN THEIF 2 INVESTMENTS ARE TO BE COMPARED THEN THEINVESTMENT WITH HIGHER N P V IS SELECTED. THEINVESTMENT WITH HIGHER N P V IS SELECTED. THEDISCOUNTED RATES FOR EACH ARE THE RISK RATESDISCOUNTED RATES FOR EACH ARE THE RISK RATES

ASSOCIATED WITH INVESTMENTS.ASSOCIATED WITH INVESTMENTS.


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REAL CASH FLOWS ARE NOMINAL CASH FLOWS ADJUSTEDREAL CASH FLOWS ARE NOMINAL CASH FLOWS ADJUSTEDTO INFLATION.TO INFLATION.

NOMINAL CASH FLOWS ARE AS RECEIVED WHILE REAL CASHNOMINAL CASH FLOWS ARE AS RECEIVED WHILE REAL CASHFLOWS ARE NOTIONAL FIGURESFLOWS ARE NOTIONAL FIGURES

REAL CASH FLOWS =REAL CASH FLOWS = NOMINAL CASH FLOWSNOMINAL CASH FLOWS

11 INFLATION RATEINFLATION RATE


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THERE ARE 5 TYPES OF CASH FLOWS:THERE ARE 5 TYPES OF CASH FLOWS: ---- SIMPLE CASH FLOWSSIMPLE CASH FLOWS ---- ANNUITYANNUITY ---- INCREASING ANNUITYINCREASING ANNUITY

---- PERPETUITYPERPETUITY ---- GROWING PERPETUITYGROWING PERPETUITY

THE FUTURE CASH FLOWS ARE CONVERTED TO THETHE FUTURE CASH FLOWS ARE CONVERTED TO THEPRESENT BY A FACTOR KNOWN DISCOUNTPRESENT BY A FACTOR KNOWN DISCOUNT

THE DISCOUNT RATE adjusted for inflation IS REAL RATETHE DISCOUNT RATE adjusted for inflation IS REAL RATE

THIS REAL RATE IS AN INFLATION ADJUSTED RATETHIS REAL RATE IS AN INFLATION ADJUSTED RATE


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DISCOUNTING IS THE INVERSE OF COMPOUNDINGDISCOUNTING IS THE INVERSE OF COMPOUNDING

FINAL AMOUNT = A PRINCIPAL = PFINAL AMOUNT = A PRINCIPAL = P

RATE OF INT. = r PERIOD = nRATE OF INT. = r PERIOD = n

n nn n

A = P(1+r) WHERE (1 + r) = COMPOUNDING FACTORA = P(1+r) WHERE (1 + r) = COMPOUNDING FACTOR

n nn n

P =P = A__ A__

(1+ r) WHERE 1(1+ r) WHERE 1 (1 + r) = DISCOUNTING FACTOR(1 + r) = DISCOUNTING FACTOR

IF INSTEAD OF COMPOUNDING ON ANNUAL BASIS IT IS ONIF INSTEAD OF COMPOUNDING ON ANNUAL BASIS IT IS ONSEMISEMI--ANNUAL OR MONTHLY BASIS THE THE EFFECTIVE RATEANNUAL OR MONTHLY BASIS THE THE EFFECTIVE RATEOF INTEREST CHANGESOF INTEREST CHANGES

nn

EFFECTIVE INTEREST RATE = (1 + rEFFECTIVE INTEREST RATE = (1 + r/n/n)) -- 11


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ANNUITY IS A CONSTANT CASH FLOW AT REGULARANNUITY IS A CONSTANT CASH FLOW AT REGULAR INTERVALS FOR A FIXED PERIODINTERVALS FOR A FIXED PERIOD

THERE 4 TYPES OF ANNUITIESTHERE 4 TYPES OF ANNUITIES

A) END OF THE PERIODA) END OF THE PERIODnn

a) P V OF AN ANNUITY(A) = Aa) P V OF AN ANNUITY(A) = A [1[1---- {1{1 (1 + r)} ](1 + r)} ] rrnn

b) F V OF AN ANNUITY(A) = A{(1 + r)b) F V OF AN ANNUITY(A) = A{(1 + r) ---- 1}1} rr


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TIME VALUE MONEYTIME VALUE MONEY

B) BEGINNING OF THE PERIODB) BEGINNING OF THE PERIOD

nn--11

-- a) P V OF ANNUITY(A) = A + Aa) P V OF ANNUITY(A) = A + A[1[1-- {1{1 (1 + r)(1 + r) }]}] rr

nn

-- b) F V OF ANNUITY(A) = A(1+ r){(1 + r)b) F V OF ANNUITY(A) = A(1+ r){(1 + r) -- 1}1} rr

IF g IS THE RATE AT WHICH THE ANNUITY GROWS THENIF g IS THE RATE AT WHICH THE ANNUITY GROWS THEN

n nn n

P V OF ANNUITY(A) = A(1 + g ){1P V OF ANNUITY(A) = A(1 + g ){1 [(1 + g)[(1 + g) (1 + r)] }(1 + r)] } (r + g)(r + g)

IMPIMP:: IN BANKS , TERM LOANS MADE AT X% REPAYABLE ATIN BANKS , TERM LOANS MADE AT X% REPAYABLE ATREGULAR INTERVALS GIVE A YIELD 1.85X%.REGULAR INTERVALS GIVE A YIELD 1.85X%.


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A PERPETUITY IS A CONSTANT CASH FLOW AT REGULARA PERPETUITY IS A CONSTANT CASH FLOW AT REGULARINTERVALS FOREVER. IT IS ANNUITY OF INFINITE DURATION.INTERVALS FOREVER. IT IS ANNUITY OF INFINITE DURATION.

P V PERPETUITY(A) = AP V PERPETUITY(A) = A rr

P V PERPETUITY(A) = AP V PERPETUITY(A) = A (r(r g) IF PERPETUITY IS GROWINGg) IF PERPETUITY IS GROWINGAT g.AT g.

RULE OF 72: DIVIDING 72 BY THE INTEREST RATE GIVESRULE OF 72: DIVIDING 72 BY THE INTEREST RATE GIVES

THE NUMBER OF YEARS IN WHICH THETHE NUMBER OF YEARS IN WHICH THE

PRINCIPAL DOUBLES.PRINCIPAL DOUBLES.


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SAMPLING METHODSSAMPLING METHODS

FOUR METHODS OF SAMPLINGFOUR METHODS OF SAMPLING::

a) SIMPLE RANDOMa) SIMPLE RANDOM

---- USE A RANDOM TABLEUSE A RANDOM TABLE

---- ASSIGN DIGITS TO EACH ELEMENT OF THEASSIGN DIGITS TO EACH ELEMENT OF THEPOPULATION(SAY 2)POPULATION(SAY 2)

---- USE A METHOD OF SELECTING THE DIGITS (SAY FIRST 2USE A METHOD OF SELECTING THE DIGITS (SAY FIRST 2

OR LAST 2) FROM THE TABLE TO SELECT A SAMPLEOR LAST 2) FROM THE TABLE TO SELECT A SAMPLE

THE CHANCE OF ANY NUMBER APPEARING IS THE SAMETHE CHANCE OF ANY NUMBER APPEARING IS THE SAMEFOR ALL.FOR ALL.


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b) SYSTEMATIC SAMPLINGb) SYSTEMATIC SAMPLING

---- ELEMENTS OF THE SAMPLE ARE SELECTED AT A UNIFORMELEMENTS OF THE SAMPLE ARE SELECTED AT A UNIFORM

INTERVAL MEASURED IN TERMS OF TIME, SPACE ORINTERVAL MEASURED IN TERMS OF TIME, SPACE OR

ORDER.ORDER.

---- AN ERROR MAY TAKE PLACE IF THE ELEMENTS IN THEAN ERROR MAY TAKE PLACE IF THE ELEMENTS IN THE

POPULATION ARE SEQUENTIAL OR THERE IS A CERTAINITYPOPULATION ARE SEQUENTIAL OR THERE IS A CERTAINITY

OF CERTAIN HAPPENINGS .OF CERTAIN HAPPENINGS ...


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c) STRATIFIED SAMPLINGc) STRATIFIED SAMPLING---- DIVIDE POPULATION INTO HOMOGENOUS GROUPSDIVIDE POPULATION INTO HOMOGENOUS GROUPS

---- FROM EACH GROUP SELECT AN EQUAL NO. OF ELEMENTSFROM EACH GROUP SELECT AN EQUAL NO. OF ELEMENTS

AND GIVE WEIGHTS TO THE GROUP/STRATA ACCORDINGAND GIVE WEIGHTS TO THE GROUP/STRATA ACCORDING

PROPORTION TO THE SAMPLEPROPORTION TO THE SAMPLE OROR

----SELECT AT RANDOM A SPECIFIED NO. OF ELEMENTS FROMSELECT AT RANDOM A SPECIFIED NO. OF ELEMENTS FROM

EACH STRATA CORRESPONDING TO ITS PROPORTIONEACH STRATA CORRESPONDING TO ITS PROPORTION

TO THE POPULATIONTO THE POPULATION

---- EACH STRATUM HAS VERY LITTLE DIFFERENCE WITHINEACH STRATUM HAS VERY LITTLE DIFFERENCE WITHIN


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d) CLUSTER SAMPLINGd) CLUSTER SAMPLING

---- DIVIDE THE POPULATION INTO GROUPS WHICH AREDIVIDE THE POPULATION INTO GROUPS WHICH ARE

CLUSTERSCLUSTERS

---- PICK A RANDOM SAMPLE FROM EACH CLUSTERPICK A RANDOM SAMPLE FROM EACH CLUSTER

---- EACH CLUSTER HAS CONSIDERABLE DIFFERENCE WITHINEACH CLUSTER HAS CONSIDERABLE DIFFERENCE WITHINBUT SIMILAR WITHOUTBUT SIMILAR WITHOUT

IMP:IMP:WHETHERWE USE PROBABILITY OR JUDGEMENTWHETHERWE USE PROBABILITY OR JUDGEMENTSAMPLING THE PROCESS IS BASED ON SIMPLE RANDOMSAMPLING THE PROCESS IS BASED ON SIMPLE RANDOM

SAMPLING .SAMPLING .


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SINCE WE WOULD USING THE CONCEPT OF STANDARDSINCE WE WOULD USING THE CONCEPT OF STANDARDDEVIATION LET US UNDERSTAND ITS SIGNIFICANCEDEVIATION LET US UNDERSTAND ITS SIGNIFICANCE

IT IS A MEASURE OF DISPERSION.IT IS A MEASURE OF DISPERSION.

GENERAL FORMULA FOR STD. DEV. ISGENERAL FORMULA FOR STD. DEV. IS (X(X -- )) N N

WHERE X = OBSERVATIONWHERE X = OBSERVATION

= POPULATION MEAN = POPULATION MEANN = ELEMENTS IN POPULATIONN = ELEMENTS IN POPULATION


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DESPITE ALL THE COMPLEXITIES IN THE FORMULA THEDESPITE ALL THE COMPLEXITIES IN THE FORMULA THESTD. DEV. IS THESTD. DEV. IS THE SAME IN STATESAME IN STATEAS SUMMATION OFAS SUMMATION OFDIFFERENCES BETWEEN THE ELEMENTS AND THEIR MEAN.DIFFERENCES BETWEEN THE ELEMENTS AND THEIR MEAN.

.. ------ IT IS THE RELIABLE MEASURE OF VARIABILITY .IT IS THE RELIABLE MEASURE OF VARIABILITY .

.. ------ IT IS USED WHEN THERE IS NEED TO MEASUREIT IS USED WHEN THERE IS NEED TO MEASURECORRELATION COEFFICIENT, SIGNIFICANCE OFCORRELATION COEFFICIENT, SIGNIFICANCE OFDIFFERENCE BETWEEN MEANS.DIFFERENCE BETWEEN MEANS.

------ IT IS USED WHEN MEAN VALUE IS AVAILABLE.IT IS USED WHEN MEAN VALUE IS AVAILABLE.

------ IT IS USED WHEN THE DISTRIBUTION IS NORMAL OR NEARIT IS USED WHEN THE DISTRIBUTION IS NORMAL OR NEARNORMALNORMAL


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FORMULA FOR STANDARD DEVIATION:FORMULA FOR STANDARD DEVIATION:

---- FOR POPULATIONFOR POPULATION SS == {(fx{(fx22 N)N) -- ff22xx22 N}N}

THIS IS FOR GROUPED DATA, WHERE f IS THE FREQUENCYTHIS IS FOR GROUPED DATA, WHERE f IS THE FREQUENCY

OF ELEMENTS IN EACH GROUP AND N IS THE SIZE OFOF ELEMENTS IN EACH GROUP AND N IS THE SIZE OF

POPULATIONPOPULATION


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A STD. DEVIATION OF THE DISTRIBUTION OF THE SAMPLEA STD. DEVIATION OF THE DISTRIBUTION OF THE SAMPLE

MEANS IS CALLED THE STD. ERROR OF THE MEAN.MEANS IS CALLED THE STD. ERROR OF THE MEAN. THETHE

STD. ERROR INDICATES THE SIZE OF THE CHANCESTD. ERROR INDICATES THE SIZE OF THE CHANCE

ERROR BUT ALSO THE ACCURACY IF WE USE THEERROR BUT ALSO THE ACCURACY IF WE USE THE

SAMPLE STATISTIC TO ESTIMATE THE POPULATION STATISTICSAMPLE STATISTIC TO ESTIMATE THE POPULATION STATISTIC


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TERMINOLGY :TERMINOLGY :\\

= MEAN OF THE POPULATION DISTRIBUTION = MEAN OF THE POPULATION DISTRIBUTION

xx = MEAN OF THE SAMPLING DITRIBUTION OF THE MEANS= MEAN OF THE SAMPLING DITRIBUTION OF THE MEANS

x = MEAN OF A SAMPLEx = MEAN OF A SAMPLE

= STD. DEVIATION OF THE POPULATION DISTRIBUTION= STD. DEVIATION OF THE POPULATION DISTRIBUTION

xx = STD. ERROR OF THE MEAN= STD. ERROR OF THE MEAN


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x=x= WHERE n IS THE SAMPLE SIZE. THIS FORMULA ISWHERE n IS THE SAMPLE SIZE. THIS FORMULA ISnn

TRUE FOR INFINITE POPULATION OR FINITETRUE FOR INFINITE POPULATION OR FINITE

POPULATION WITH REPLACEMENT.POPULATION WITH REPLACEMENT.

Z =Z = xx -- WHERE Z HELPS TO DETERMINE THE DISTANCEWHERE Z HELPS TO DETERMINE THE DISTANCExx

OF THE SAMPLE MEAN FROM THE POPULATIONOF THE SAMPLE MEAN FROM THE POPULATION

MEAN.MEAN.


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STD. ERROR FOR FINITE POPULATION:STD. ERROR FOR FINITE POPULATION:

x =x = [N [N--n]n] WHERE N IS THE POPULATION SIZEWHERE N IS THE POPULATION SIZE

n [Nn [N--1]1]

ANDAND [N [N--n]n] IS THE FINITE POPULATION MULTIPLIERIS THE FINITE POPULATION MULTIPLIER

[N [N--1]1]

THE VARIABILITY IN SAMPLING STATISTICS RESULTS FROMTHE VARIABILITY IN SAMPLING STATISTICS RESULTS FROMSAMPLING ERROR DUE TO CHANCE. THUS THE DIFFERENCESAMPLING ERROR DUE TO CHANCE. THUS THE DIFFERENCEBETWEEN SAMPLES AND BETWEEN SAMPLE ANDBETWEEN SAMPLES AND BETWEEN SAMPLE ANDPOPULATION MEANS IS DUE TO CHOICE OF SAMPLES.POPULATION MEANS IS DUE TO CHOICE OF SAMPLES.


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CENTRAL LIMIT THEOREMCENTRAL LIMIT THEOREM

THE RELATIONSHIP BETWEEN THE SHAPE OF POPULATIONTHE RELATIONSHIP BETWEEN THE SHAPE OF POPULATIONDISTRIBUTION AND THE SAMPLNG DIST. IS CALLED CENTRALDISTRIBUTION AND THE SAMPLNG DIST. IS CALLED CENTRALLIMIT THEOREM.LIMIT THEOREM.

AS SAMPLE SIZE INCREASES THE SAMPLING DIST. OF THEAS SAMPLE SIZE INCREASES THE SAMPLING DIST. OF THEMEN WILL APPROACH NORMALITY REGARDLESS OF THEMEN WILL APPROACH NORMALITY REGARDLESS OF THEPOPULATION DIST.POPULATION DIST.

SAMPLE SIZE NEED NOT BE LARGE FOR THE MEAN TOSAMPLE SIZE NEED NOT BE LARGE FOR THE MEAN TOAPPROACH NORMALAPPROACH NORMAL

WE CAN MAKE INFERENCES ABOUT THE POPULATIONWE CAN MAKE INFERENCES ABOUT THE POPULATIONPARAMETERS WITHOUT KNOWING ANYTHING ABOUT THEPARAMETERS WITHOUT KNOWING ANYTHING ABOUT THESHAPE OF THE FREQUENCY DIST. OF THE POPULATIONSHAPE OF THE FREQUENCY DIST. OF THE POPULATION


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EXAMPLE:EXAMPLE: n = 30,n = 30, = 97.5, = 97.5, = 16.3= 16.3 a) WHAT IS THE PROB. OF X LYING BETWEEN 90 & 104a) WHAT IS THE PROB. OF X LYING BETWEEN 90 & 104 ANS) ANS) x=x= , = 2.97, = 2.97 nn

P(P( 9090 97.597.5


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REGRESSION AND CORRELATIONREGRESSION AND CORRELATION

REGRESSION & CORRELATION ANALYSESREGRESSION & CORRELATION ANALYSES HELP TOHELP TO

DETERMINE THE NATURE AND STRENGTH OF RELATIONSHIPDETERMINE THE NATURE AND STRENGTH OF RELATIONSHIP

BETWEEN 2 VARIABLES. THE KNOWN VARIABLE IS CALLEDBETWEEN 2 VARIABLES. THE KNOWN VARIABLE IS CALLED

THE INDEPENDENT VARIABLE WHEREAS THE VARIABLE WETHE INDEPENDENT VARIABLE WHEREAS THE VARIABLE WE

ARE TRYING TO PREDICT IS CALLED THE DEPENDENTARE TRYING TO PREDICT IS CALLED THE DEPENDENT

VARIABLE. THIS ATTEMPT AT PREDICTION IS CALLEDVARIABLE. THIS ATTEMPT AT PREDICTION IS CALLED

REGRESSION ANALYSES WHEREAS CORRELATION TELLSREGRESSION ANALYSES WHEREAS CORRELATION TELLS

THE EXTENT OF THE RELATIONSHIP.THE EXTENT OF THE RELATIONSHIP.


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THE VALUES OF THE 2 VARIABLES ARE PLOTTED ON ATHE VALUES OF THE 2 VARIABLES ARE PLOTTED ON A

GRAPH WITH X AS THE INDEPENDENT VARIABLE. THEGRAPH WITH X AS THE INDEPENDENT VARIABLE. THE

POINTS WOULD BE SCATTERED . DRAW A LINE BETWEENPOINTS WOULD BE SCATTERED . DRAW A LINE BETWEEN

POINTS SUCH THAT AN EQUAL NUMBER LIE ON EITHER SIDEPOINTS SUCH THAT AN EQUAL NUMBER LIE ON EITHER SIDE

OF THE LINE. FIND THE EQN. SAY Y= a +b X ; PLOT THEOF THE LINE. FIND THE EQN. SAY Y= a +b X ; PLOT THE

POINTS ON THE LINE.POINTS ON THE LINE.


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ONE CAN DRAW ANY NUMBER OF LINES BETWEEN THEONE CAN DRAW ANY NUMBER OF LINES BETWEEN THEPOINTS. THE LINE WITH BEST FIT IS THE THAT WITH LEASTPOINTS. THE LINE WITH BEST FIT IS THE THAT WITH LEASTSQUARE DIFFERENCE BETWEEN THE ACTUAL ANDSQUARE DIFFERENCE BETWEEN THE ACTUAL ANDESTIMATED POINTS.ESTIMATED POINTS.

IN THE EQN. Y = a + b XIN THE EQN. Y = a + b X

b = SLOPE =b = SLOPE = XYXY n Xn X Y Y X X22 n Xn X22

SLOPE OF THE LINE INDICATES THE EXTENT OF CHANGE INSLOPE OF THE LINE INDICATES THE EXTENT OF CHANGE INY DUE TO CHANGE IN X.Y DUE TO CHANGE IN X.

. a = Y. a = Y -- b Xb X

WHERE X , Y ARE MEAN VALUESWHERE X , Y ARE MEAN VALUES

..


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STD ERROR OF ESTIMATESTD ERROR OF ESTIMATE

Se = {(YSe = {(Y YYee )) (n(n --2)}2)} oror == { Y{ Y --a Ya Y b (XY)}b (XY)}

(n(n--2)2)

. WHERE Y. WHERE Yee = ESTIMATES OF Y= ESTIMATES OF Y

nn 2 IS USED BECAUSE WE LOSE 2 DEGREES OF FREEDOM2 IS USED BECAUSE WE LOSE 2 DEGREES OF FREEDOM

IN ESTIMATING THE REGRESSION LINE.IN ESTIMATING THE REGRESSION LINE.

IF SAMPLE IS n THE DEG OF FREEDOM = nIF SAMPLE IS n THE DEG OF FREEDOM = n--1 i.e. WE CAN1 i.e. WE CANFREELY GIVE VALUES TO nFREELY GIVE VALUES TO n--1 VARIABLES.1 VARIABLES.


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THERE ARE 3 MEASURES OF CORRELATIONTHERE ARE 3 MEASURES OF CORRELATION

-- COEFFICIENT OF DETERMINATION. IT MEASURES THECOEFFICIENT OF DETERMINATION. IT MEASURES THE

STRENGTH OF A LINEAR RELATIONSHIPSTRENGTH OF A LINEAR RELATIONSHIP

COEFF. OF DET. = rCOEFF. OF DET. = r22 == (Y(Y YYee ))22

11-- --------------------------------( Y( Y -- Y )Y )22

COEF. OF DETERMINATION IS rCOEF. OF DETERMINATION IS rCOEFF. OF CORRELATION IS rCOEFF. OF CORRELATION IS r r = r = ++ r, HENCE FROM rr, HENCE FROM r22 TO r WE KNOW THE STRENGTHTO r WE KNOW THE STRENGTH

BUT NOT THE DIRECTION.BUT NOT THE DIRECTION.

..


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--COVARIANCECOVARIANCE. IT MEASURES THE STRENGTH &. IT MEASURES THE STRENGTH &

DIRECTION OF THE RELATIONSHIP.DIRECTION OF THE RELATIONSHIP.

COVARIANCE =COVARIANCE = ( X( X -- X )(YX )(Y -- Y )Y )nn

-- --COEFFICIENT OF CORRELATIONCOEFFICIENT OF CORRELATION. IT MEASURES THE. IT MEASURES THE

DIMENSIONLESS STRENGTH & DIRECTION OF THEDIMENSIONLESS STRENGTH & DIRECTION OF THE

RELATIONSHIPRELATIONSHIP

COEFF.OF CORR. =COEFF.OF CORR. = COVARIANCECOVARIANCE

xxyy


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TREND ANALYSISTREND ANALYSIS

4 TYPES OF TIME SERIES VARIATIONS:4 TYPES OF TIME SERIES VARIATIONS: ---- a) SECULAR TREND IN WHICH THERE IS FLUCTUATION BUTa) SECULAR TREND IN WHICH THERE IS FLUCTUATION BUT STEADY INCREASE IN TREND OVER A LARGE PERIOD OFSTEADY INCREASE IN TREND OVER A LARGE PERIOD OF TIME.TIME.

---- b) CYCLICAL FLUCTUATION IS A BUSINESS CYCLE THATb) CYCLICAL FLUCTUATION IS A BUSINESS CYCLE THAT SEES UP & DOWN OVER A PERIOD OF A FEW YEARS.SEES UP & DOWN OVER A PERIOD OF A FEW YEARS. THERE MAY NOT BE A REGULAR PATTERN.THERE MAY NOT BE A REGULAR PATTERN.

---- c) SEASONAL VARIATION WHICH SEE REGULAR CHANGESc) SEASONAL VARIATION WHICH SEE REGULAR CHANGES

DURING A YEAR.DURING A YEAR.

---- d) IRREGULAR VARIATION DUE TO UNFORESEENd) IRREGULAR VARIATION DUE TO UNFORESEEN CIRCUMSTANCES.CIRCUMSTANCES.


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IN TREND ANALYSIS WE HAVE TO FIT A LINEAR TREND BYIN TREND ANALYSIS WE HAVE TO FIT A LINEAR TREND BY

LEAST SQUARES METHOD. TO EASE THE COMPUTATION WELEAST SQUARES METHOD. TO EASE THE COMPUTATION WE

USE CODING METHOD WHERE WE ASSIGN NUMBERS TO THEUSE CODING METHOD WHERE WE ASSIGN NUMBERS TO THE

YEARS FOR EXAMPLE. THEN WE CALCULATE THE VALUES OFYEARS FOR EXAMPLE. THEN WE CALCULATE THE VALUES OF

CONSTANTS a & b IN THE EQN. Y = a + b X AND THEN USECONSTANTS a & b IN THE EQN. Y = a + b X AND THEN USE

THE EQN. FOR FORECASTING.THE EQN. FOR FORECASTING.


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STUDY OF SECULAR TRENDS HELPS TO DESCRIBE ASTUDY OF SECULAR TRENDS HELPS TO DESCRIBE A

HISTORICAL PATTERN;HISTORICAL PATTERN;

USE PAST TRENDS TO PREDICT THE FUTURE;USE PAST TRENDS TO PREDICT THE FUTURE;

AND ELIMINATE TREND COMPONENT WHICHAND ELIMINATE TREND COMPONENT WHICH

MAKES IT EASIER TO STUDY THE OTHER 3 COMPONENTS.MAKES IT EASIER TO STUDY THE OTHER 3 COMPONENTS.


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ONCE THE SECULAR TREND LINE IS FITTED THE CYCLICAL &ONCE THE SECULAR TREND LINE IS FITTED THE CYCLICAL &

IRREGULAR VARIATIONS ARE TACKLED SINCE SEASONALIRREGULAR VARIATIONS ARE TACKLED SINCE SEASONAL

VARIATIONS MAKE A COMPLETE CYCLE WITHIN A YEAR ANDVARIATIONS MAKE A COMPLETE CYCLE WITHIN A YEAR AND

DO NOT AFFECT THE ANALYSIS.DO NOT AFFECT THE ANALYSIS.

THE ACTUAL DATA IS DIVIDED BY THE PREDICTED DATATHE ACTUAL DATA IS DIVIDED BY THE PREDICTED DATA

A RELATIVE CYCLICAL RESIDUAL IS OBTAINEDA RELATIVE CYCLICAL RESIDUAL IS OBTAINED

A PERCENTAGE DEVIATION FROM TREND FOR EACH VALUEA PERCENTAGE DEVIATION FROM TREND FOR EACH VALUE

IS FOUNDIS FOUND


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SEASONAL VARIATION IS ELIMINATED BY MOVING AVERAGESEASONAL VARIATION IS ELIMINATED BY MOVING AVERAGE

METHODMETHOD

.. a) FIND AVERAGE OF 4 QTRS. BY PROCESS OF SLIDINGa) FIND AVERAGE OF 4 QTRS. BY PROCESS OF SLIDING

b) DIVIDE EACH VALUE BY 4b) DIVIDE EACH VALUE BY 4

c) FIND AVERAGE OF SUCH VALUES IN b) FOR 2 QTRS BYc) FIND AVERAGE OF SUCH VALUES IN b) FOR 2 QTRS BY

SLIDING METHODSLIDING METHOD


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d) CALCULATE THE PERCENTAGE OF ACTUAL VALUE TOd) CALCULATE THE PERCENTAGE OF ACTUAL VALUE TO

MOVING AVERAGE VALUEMOVING AVERAGE VALUE

e) MODIFY THE TABLE ON QTR. BASIS AND AFTERe) MODIFY THE TABLE ON QTR. BASIS AND AFTER

DISCARDING THE HIGHEST AND LOWEST VALUE FOR EACHDISCARDING THE HIGHEST AND LOWEST VALUE FOR EACH

QTR FIND THE MEANS QTR. WISE.QTR FIND THE MEANS QTR. WISE.

f) ADJUST THE MODIFIED MEANS TO BASE 100 AND OBTAIN Af) ADJUST THE MODIFIED MEANS TO BASE 100 AND OBTAIN A

SEASONAL INDEXSEASONAL INDEX

g) USE THE INDEX TO GET DESEASONALISED VALUES.g) USE THE INDEX TO GET DESEASONALISED VALUES.


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PROBABILITY DISTRIBUTIONPROBABILITY DISTRIBUTION

THIS CHAPTER IS ON METHODS TO ESTIMATE POPULATIONTHIS CHAPTER IS ON METHODS TO ESTIMATE POPULATION

PROPORTION AND MEAN:PROPORTION AND MEAN:

THERE ARE 2 TYPES OF ESTIMATES:THERE ARE 2 TYPES OF ESTIMATES:

POINT ESTIMATE:POINT ESTIMATE: WHICH IS A SINGLE NUMBER TO ESTIMATEWHICH IS A SINGLE NUMBER TO ESTIMATE

AN UNKNOWN POPULATION PARAMETER. IT IS INSUFFICIENTAN UNKNOWN POPULATION PARAMETER. IT IS INSUFFICIENT

IN THE SENSE IT DOES NOT KNOW THE EXTENT OF WRONG.IN THE SENSE IT DOES NOT KNOW THE EXTENT OF WRONG.


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CRITERIA FOR A GOOD ESTIMATORCRITERIA FOR A GOOD ESTIMATOR

a) UNBIASEDNESS:a) UNBIASEDNESS: MEAN OF SAMPLING DISTRIBUTION OFMEAN OF SAMPLING DISTRIBUTION OF

SAMPLE MEANSSAMPLE MEANS ~~ POPULATION MEANS. THE STATISTICPOPULATION MEANS. THE STATISTIC

ASSUMES OR TENDS TO ASSUME AS MANY VALUESASSUMES OR TENDS TO ASSUME AS MANY VALUES

ABOVE AS BELOW THE POP. MEANABOVE AS BELOW THE POP. MEAN

b) EFFICIENCY:b) EFFICIENCY: THE SMALLER THE STANDARD ERROR, THETHE SMALLER THE STANDARD ERROR, THE

MORE EFFICIENT THE ESTIMATOR OR BETTER THEMORE EFFICIENT THE ESTIMATOR OR BETTER THE

CHANCE OF PRODUCING AN ESTIMATOR NEARER TO THECHANCE OF PRODUCING AN ESTIMATOR NEARER TO THE

POP.PARAMETER .POP.PARAMETER .


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c) CONSISTENCY:c) CONSISTENCY: AS THE SAMPLE SIZE INCREASES, THEAS THE SAMPLE SIZE INCREASES, THE

SAMPLE STASTISTIC COMES CLOSER TO THE POPULATIONSAMPLE STASTISTIC COMES CLOSER TO THE POPULATION

PARAMETER.PARAMETER.

d) SUFFICIENCY:d) SUFFICIENCY: MAKE BEST USE OF THE EXISTING SAMPLE.MAKE BEST USE OF THE EXISTING SAMPLE.

PROBABILITY Of 0.955 MEANS THAT 95.5 OF ALL SAMPLEPROBABILITY Of 0.955 MEANS THAT 95.5 OF ALL SAMPLE

MEANS ARE WITHINMEANS ARE WITHIN ++ 2 STD ERROR OF MEAN2 STD ERROR OF MEAN

POPULATION .POPULATION .

SIMILARLY, 0.683 MEANSSIMILARLY, 0.683 MEANS ++ 1 STD ERROR.1 STD ERROR.


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FORMULA:FORMULA:

ESTIMATE OF POPULATION :ESTIMATE OF POPULATION : ^= = (x(x -- x )x )

STD. DEVIATION (nSTD. DEVIATION (n 1)1)

ESTIMATE OF STD. ERROR :D. ERROR : ^xx == ^ OROR == ^ (N(N -- n)n)

n n (N n n (N -- 1)1)

STANDARD ERROR OF THE :STANDARD ERROR OF THE : pp == p qp qPROPORTION nPROPORTION n


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Normal curveNormal curveMean

Median

Mode

Symmetrical around

a vertical line erected atthe mean

The tails extendIndefinitely but

never reac

h thehorizontal axis


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BOND VALUATIONBOND VALUATION

BONDS ARE LONG TERM LOANS WITH A PROMISE OF SERIESBONDS ARE LONG TERM LOANS WITH A PROMISE OF SERIES

OF FIXED INTEREST PAYMENTS AND REPAYMENT OFOF FIXED INTEREST PAYMENTS AND REPAYMENT OF

PRINCIPALPRINCIPAL

THE INTEREST PAYMENT ON BOND IS CALLED COUPON RATETHE INTEREST PAYMENT ON BOND IS CALLED COUPON RATE

IS COUPON RATE.IS COUPON RATE.

THEY ARE ISSUED AT A DISCOUNT AND REPAID AT PAR.THEY ARE ISSUED AT A DISCOUNT AND REPAID AT PAR.

GOVT. BONDS ARE FOR LARGE PERIODSGOVT. BONDS ARE FOR LARGE PERIODS

BONDS HAVE A MARKET AND PRICES ARE QUOTED ONBONDS HAVE A MARKET AND PRICES ARE QUOTED ON

NSE/BSE.NSE/BSE.


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BOND PRICES ARE LINKED WITH INTEREST RATES IN THEBOND PRICES ARE LINKED WITH INTEREST RATES IN THE

MARKET.MARKET.

IF THE INTEREST RATES RISE, THE BOND PRICES FALL ANDIF THE INTEREST RATES RISE, THE BOND PRICES FALL AND

VICE VERSA.VICE VERSA.

PRESENT VALUE OF BONDS CAN ALSO BE CALCULATEDPRESENT VALUE OF BONDS CAN ALSO BE CALCULATED

USING THE DISCOUNT FACTOR FOR THE COUPONS AS WELLUSING THE DISCOUNT FACTOR FOR THE COUPONS AS WELL

AS THE FINAL PAYMENT OF THE FACE VALUEAS THE FINAL PAYMENT OF THE FACE VALUE


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SOME IMPORTANT STANDARD MEASURES:SOME IMPORTANT STANDARD MEASURES:

CURRENT YIELD:CURRENT YIELD: IT IS THE RETURN ON THE PRESENTIT IS THE RETURN ON THE PRESENT

MARKET PRICE OF A BOND = (MARKET PRICE OF A BOND = (COUPON INCOMECOUPON INCOME)*100)*100CURRENT PRICECURRENT PRICE

RATE OF RETURN:RATE OF RETURN: IT IS THE RATE OF RETURN ON YOURIT IS THE RATE OF RETURN ON YOUR

INVESTMENTINVESTMENT

.RATE OF RETURN =.RATE OF RETURN = (COUPON INCOME+ PRICE CHANGE)(COUPON INCOME+ PRICE CHANGE)INVESTMENT PRICE.INVESTMENT PRICE.


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YIELD TO MATURITY:YIELD TO MATURITY: THIS MEASURE TAKES INTO ACCOUNTTHIS MEASURE TAKES INTO ACCOUNT

CURRENT YIELD AND CHANGE IN BOND VALUE OVER ITSCURRENT YIELD AND CHANGE IN BOND VALUE OVER ITS

LIFE . IT ISLIFE . IT IS THE DISCOUNT RATETHE DISCOUNT RATEAT WHICH THE PRESENTAT WHICH THE PRESENT

VALUE (PV) OF COUPON INCOME & THE FINAL PAYMENT ATVALUE (PV) OF COUPON INCOME & THE FINAL PAYMENT AT

FACE VALUE = CURRENT PRICE.FACE VALUE = CURRENT PRICE.nn

. PRICE =. PRICE = CC ii ++ C nC n+ F V+ F V WHERE CWHERE C ii = COUPON= COUPONi =1 (1 + r)i =1 (1 + r) nn--11 (1 + r)(1 + r) nn INCOMEINCOME

F V = FACEF V = FACEVALUEVALUE

n = LIFE OFn = LIFE OF

BONDBOND


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IF THE YIELD TO MATURITY (YTM) REMAINS UNCHANGED,IF THE YIELD TO MATURITY (YTM) REMAINS UNCHANGED,

THEN THE RATE OF RETURN = YTMTHEN THE RATE OF RETURN = YTM..

EVEN IF INTEREST RATES DO NOT CHANGE, THE BONDEVEN IF INTEREST RATES DO NOT CHANGE, THE BOND

PRICES CHANGE WITH TIME;PRICES CHANGE WITH TIME;

AS WE NEAR THE MATURITY PERIOD, THE BOND PRICESAS WE NEAR THE MATURITY PERIOD, THE BOND PRICES

TEND TO THE PAR/FACE VALUE.TEND TO THE PAR/FACE VALUE.

..


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THERE ARE 2 RISKS IN BONDS INVESTMENTTHERE ARE 2 RISKS IN BONDS INVESTMENT

a)a) INTEREST RATE RISKINTEREST RATE RISK: WHERE THE BOND PRICES CHANGE: WHERE THE BOND PRICES CHANGE

INVERSELY WITH INTEREST RATE. ALSO THE LARGER THEINVERSELY WITH INTEREST RATE. ALSO THE LARGER THE

MATURITY PERIOD OF A BOND, THE GREATER THEMATURITY PERIOD OF A BOND, THE GREATER THESENSITIVITY TOSENSITIVITY TO

PRICE.PRICE.

DEFAULT RISK:DEFAULT RISK: WHICH IS TRUE WITH PRIVATE BONDSWHICH IS TRUE WITH PRIVATE BONDS

RATHER THAN GOVT. BONDS( GILT EDGED SECURITIES)RATHER THAN GOVT. BONDS( GILT EDGED SECURITIES)


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DIFFERENT TYPES OF BONDS:DIFFERENT TYPES OF BONDS:

ZERO COUPON BOND:ZERO COUPON BOND: NO COUPON INCOME.NO COUPON INCOME.

FLOATING RATE BOND:FLOATING RATE BOND: INTEREST RATES CHANGEINTEREST RATES CHANGEACCORDING TO THE MARKET.ACCORDING TO THE MARKET.

CONVERTIBLE BOND:CONVERTIBLE BOND: BONDS CONVERTED TO SHARES AT ABONDS CONVERTED TO SHARES AT ALATER DATE.LATER DATE.

BONDS ON CALL:BONDS ON CALL: THE ISSUER RESERVES THE RIGHT TOTHE ISSUER RESERVES THE RIGHT TOCALL BACK THE BOND AT ANY POINT IN TIME GENERALLYCALL BACK THE BOND AT ANY POINT IN TIME GENERALLYOVER PAR.OVER PAR.


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SOME THOUGHTS ON BONDSSOME THOUGHTS ON BONDS THE INTEREST IS CALLED COUPON INCOME AS COUPONSTHE INTEREST IS CALLED COUPON INCOME AS COUPONS

ARE ATTACHED TO THE BONDS FOR INTEREST PAYMENTSARE ATTACHED TO THE BONDS FOR INTEREST PAYMENTSOVER THE LIFE OF THE BONDOVER THE LIFE OF THE BOND

BOND INTEREST REMAINS THE SAME IRRESPECTIVE OF THEBOND INTEREST REMAINS THE SAME IRRESPECTIVE OF THECHANGES IN THE INT. RATES IN THE MARKETCHANGES IN THE INT. RATES IN THE MARKET

BOND PRICES ARE USUALLY QUOTED AT %AGE OF THEIRBOND PRICES ARE USUALLY QUOTED AT %AGE OF THEIRFACE VALUE i.e. 102.5.FACE VALUE i.e. 102.5.

CURRENT YIELD OVERSTATES RETURN ON PREMIUM BONDSCURRENT YIELD OVERSTATES RETURN ON PREMIUM BONDS& UNDERSTATES RETURN ON DISCOUNT BONDS; SINCE& UNDERSTATES RETURN ON DISCOUNT BONDS; SINCE

TOWARDS THE END OF THE BOND PERIOD THE PRICETOWARDS THE END OF THE BOND PERIOD THE PRICEMOVES NEARER THE FACE VALUE. i.e. PREMIUM BONDMOVES NEARER THE FACE VALUE. i.e. PREMIUM BOND rrANDANDDISCOUNT BONDDISCOUNT BOND qq..

IF BOND IS PURCHASED AT FACE VALUE THEN Y T M IS THEIF BOND IS PURCHASED AT FACE VALUE THEN Y T M IS THECOUPON RATE.COUPON RATE.


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LINEAR PROGRAMMINGLINEAR PROGRAMMING

EVERY ORGANISATION USES RESOURCES SUCH ASEVERY ORGANISATION USES RESOURCES SUCH ASMEN(WOMEN), MACHINES MATERIALS AND MONEY.MEN(WOMEN), MACHINES MATERIALS AND MONEY.

THESE ARE CALLED RESOURCESTHESE ARE CALLED RESOURCES

THE OPTIMUM USE OF RESOURCES TO PRODUCE THETHE OPTIMUM USE OF RESOURCES TO PRODUCE THEMAXIMUM POSSIBLE PROFIT IS THE ESSENCE OF LINEARMAXIMUM POSSIBLE PROFIT IS THE ESSENCE OF LINEARPROGRAMMINGPROGRAMMING

EACH RESOURCE WOULD HAVE CONSTRAINTSEACH RESOURCE WOULD HAVE CONSTRAINTS

HENCE WORKING WITHIN THE CONSTRAINTS; MINIMIZINGHENCE WORKING WITHIN THE CONSTRAINTS; MINIMIZINGCOST; MAXIMIZING PROFIT SHOULD BE THE CORPORATECOST; MAXIMIZING PROFIT SHOULD BE THE CORPORATEPHILOSOPHY.PHILOSOPHY.


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LINEAR PROGRAMMINGLINEAR PROGRAMMING

IN LINEAR PROGRAMMING PROBLEMS, THE CONSTRAINTSIN LINEAR PROGRAMMING PROBLEMS, THE CONSTRAINTSARE IN THE FORM OF INEQUALITIESARE IN THE FORM OF INEQUALITIES

LABOUR AVAILABLE FOR UPTO 200 HRS.LABOUR AVAILABLE FOR UPTO 200 HRS. 300300

SOLUTION TO THESE EQUATIONS ARE BY GRAPHICALSOLUTION TO THESE EQUATIONS ARE BY GRAPHICAL

METHOD OR THE SIMPLEX METHODMETHOD OR THE SIMPLEX METHOD


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SIMULATIONSIMULATION

SIMULATION IS A TECHNIQUE WHERE MODEL OF THESIMULATION IS A TECHNIQUE WHERE MODEL OF THEPROBLEM, WITHOUT GETTING TO REALITY, IS MADE TOPROBLEM, WITHOUT GETTING TO REALITY, IS MADE TOKNOW THE END RESULTSKNOW THE END RESULTS

SIMULATION IS IDEAL FOR SITUATIONS WHERE SIZE ORSIMULATION IS IDEAL FOR SITUATIONS WHERE SIZE OR

COMPLEXITY OF THE SITUATION DOES NOT PERMIT USE OFCOMPLEXITY OF THE SITUATION DOES NOT PERMIT USE OFANY OTHER METHODANY OTHER METHOD

IN SHORT, SIMULATION IS A REPLICA OF REALITY.IN SHORT, SIMULATION IS A REPLICA OF REALITY.

EXAMPLES OF PROBLEM SITUATIONS FOR SIMULATION AREEXAMPLES OF PROBLEM SITUATIONS FOR SIMULATION ARE

---- AIR TRAFFIC QUEUINGAIR TRAFFIC QUEUING ---- RAIL OPERATIONSRAIL OPERATIONS ---- ASSEMBLY LINE SYSTEMSASSEMBLY LINE SYSTEMS ---- AND SO ONAND SO ON

..


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SIMULATIONSIMULATION

THEREFORE IT IS CLEAR THAT WHEN USE OF REAL SYSTEMTHEREFORE IT IS CLEAR THAT WHEN USE OF REAL SYSTEM

UPSETS THE WORKING SCHEDULE IN THE SYSTEM OR ISUPSETS THE WORKING SCHEDULE IN THE SYSTEM OR IS

IMPOSSIBLE TO EXPERIMENT REAL TIME, AND IT ISIMPOSSIBLE TO EXPERIMENT REAL TIME, AND IT IS

TOO EXPENSIVE TO UNDERTAKE THE EXERCISE, THENTOO EXPENSIVE TO UNDERTAKE THE EXERCISE, THEN

SIMULATION IS IDEAL.SIMULATION IS IDEAL.

.. HOWEVER SIMULATION CAN BE A COSTLY EXERCISE, TIMEHOWEVER SIMULATION CAN BE A COSTLY EXERCISE, TIME

CONSUMING AND WITH VERY FEW GUIDING PRINCIPLES.CONSUMING AND WITH VERY FEW GUIDING PRINCIPLES.


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FINAL LEGFINAL LEG

THANK YOU VERY MUCH FOR YOURTHANK YOU VERY MUCH FOR YOUR

PATIENCE; I TRUST IT WAS USEFUL.PATIENCE; I TRUST IT WAS USEFUL.

BEFORE WE DISPERSE LET US GOBEFORE WE DISPERSE LET US GOTHRU A SET OF QUESTIONS WITHTHRU A SET OF QUESTIONS WITH

MULTIPLE CHOICE ANSWERS,WHICHMULTIPLE CHOICE ANSWERS,WHICH

WILL COVER THOSE ASPECTS OF THEWILL COVER THOSE ASPECTS OF THESUBJECT THAT MAY NOT BEENSUBJECT THAT MAY NOT BEEN

TOUCHED UPON.TOUCHED UPON.


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