FINANCIAL MANAGEMENTC A I I B PAPER-1 MODULE AQUANTATIVE TECHNIQUES&FINANCIAL MATHEMATICS

RAVI ULLALCONSULTANT

TIME VALUE OF MONEYMONEY HAS TIME VALUE

THIS IS BASED ON THE CONCEPT OF EROSION IN VALUE OF MONEY DUE TO INFLATION

HENCE THE NEED TO CONVERT TO A PRESENT VALUE

OTHER REASONS FOR NEED TO REACH PRESENT VALUE IS -- DESIRE FOR IMMEDIATE CONSUMPTION RATHER THAN WAIT FOR THE FUTURE

-- THE GREATER THE RISK IN FUTURE THE GREATER THE EROSION

TIME VALUE OF MONEYEXTENTOF EROSION IN THE VALUE OF MONEY IS AN UNKNOWN FACTOR. HENCE A WELL THOUGHT OUT DISCOUNT RATE HELPS TO BRING THE FUTURE CASH FLOWS TO THE PRESENT.

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

ALL THREE FACTORS THAT CONTRIBUTE TO THE EROSION IN VALUE OF MONEY HAVE AN INVERSE RELATIONSHIP WITH THE VALUE OF MONEY i.e. THE GREATER THE FACTOR THE LOWER IS THE VALUE OF MONEY

TIME VALUE OF MONEY

IF DESIRE FOR CURRENT CONSUMPTION ISGREATER THEN WE NEED TO OFFER INCENTIVES TO DEFER THE CONSUMPTION.

THE MONEY THUS SAVED IS THEN PROFITABLY OR GAINFULLY EMPLOYED . HENCE THE DISCOUNT RATE WILL BE LOWER.

INVESTMENT IN GOVERNMENT BONDS / SECURITIES IS LESS RISKY THAN IN THE PRIVATE SECTOR SIMPLY BECAUSE NOT ALL CASH FLOWS ARE EQUALLY PREDICTABLE AND WHERE THERE IS SOVEREIGN GUARANTEE THE RISK IS LESS.

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

TIME VALUE OF MONEY

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

THE DISCOUNT VARIES DIRECTLY WITH EACH OF THESE FACTORS.

THE DISCOUNT OF FUTURE FLOWS TO THE PRESENT IS DONE WITH THE NEED TO KNOW THE EFFICACY OF THE INVESTMENT.

TIME VALUE OF MONEY

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

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

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

IF 2 INVESTMENTS ARE TO BE COMPARED THEN THE INVESTMENT WITH HIGHER N P V IS SELECTED. THE DISCOUNTED RATES FOR EACH ARE THE RISK RATES ASSOCIATED WITH INVESTMENTS.

TIME VALUE OF MONEY

REAL CASH FLOWS ARE NOMINAL CASH FLOWS ADJUSTED TO INFLATION.

NOMINAL CASH FLOWS ARE AS RECEIVED WHILE REAL CASH FLOWS ARE NOTIONAL FIGURES

REAL CASH FLOWS = NOMINAL CASH FLOWS 1 INFLATION RATE

TIME VALUE OF MONEY THERE ARE 5 TYPES OF CASH FLOWS:-- SIMPLE CASH FLOWS-- ANNUITY-- INCREASING ANNUITY-- PERPETUITY-- GROWING PERPETUITY

THE FUTURE CASH FLOWS ARE CONVERTED TO THE PRESENT BY A FACTOR KNOWN DISCOUNT THE DISCOUNT RATE adjusted for inflation IS REAL RATE THIS REAL RATE IS AN INFLATION ADJUSTED RATE

TIME VALUE OF MONEYDISCOUNTING IS THE INVERSE OF COMPOUNDINGFINAL AMOUNT = A PRINCIPAL = PRATE OF INT. = r PERIOD = n n n A = P(1+r) WHERE (1 + r) = COMPOUNDING FACTOR n nP = A__ (1+ r) WHERE 1 (1 + r) = DISCOUNTING FACTOR

IF INSTEAD OF COMPOUNDING ON ANNUAL BASIS IT IS ON SEMI-ANNUAL OR MONTHLY BASIS THE THE EFFECTIVE RATE OF INTEREST CHANGES nEFFECTIVE INTEREST RATE = (1 + r) - 1 N WHERE N = NO. OF COMPOUNDING PERIODS

TIME VALUE OF MONEYANNUITY IS A CONSTANT CASH FLOW AT REGULAR INTERVALS FOR A FIXED PERIOD

THERE 4 TYPES OF ANNUITIES

A) END OF THE PERIOD n a) P V OF AN ANNUITY(A) = A [1-- {1 (1 + r)} ] r n b) F V OF AN ANNUITY(A) = A{(1 + r) -- 1} r

a) IS THE FORMULA OF EQUATED MONTHLY INSTALMENT(EMI).

TIME VALUE MONEY B) BEGINNING OF THE PERIOD n-1 - a) P V OF ANNUITY(A) = A + A[1- {1 (1 + r) }] r n - b) F V OF ANNUITY(A) = A(1+ r){(1 + r) - 1} r

IF g IS THE RATE AT WHICH THE ANNUITY GROWS THEN n nP V OF ANNUITY(A) = A(1 + g ){1 [(1 + g) (1 + r)] } (r + g)

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

TIME VALUE OF MONEYA PERPETUITY IS A CONSTANT CASH FLOW AT REGULAR INTERVALS FOREVER. IT IS ANNUITY OF INFINITE DURATION.

P V PERPETUITY(A) = A r

P V PERPETUITY(A) = A (r g) IF PERPETUITY IS GROWING AT g.

RULE OF 72: DIVIDING 72 BY THE INTEREST RATE GIVES THE NUMBER OF YEARS IN WHICH THE PRINCIPAL DOUBLES.

SAMPLING METHODSA SAMPLE IS A REPRESENTATIVE PORTION OF THE POPULATION

TWO TYPES OF SAMPLING:

--- RANDOM OR PROBABILITY SAMPLING

--- NON-RANDOM OR JUDGEMENT SAMPLINGIN JUDGEMENT SAMPLING KNOWLEDGE & OPINIONS ARE USED. IN THIS KIND OF SAMPLING BIASEDNESS CAN CREEP IN, FOR EX. IN INTERVIEWING TEACHERS ASKING THEIR OPINION ABOUT THEIR PAY RISE.

SAMPLING METHODSFOUR METHODS OF SAMPLING:

a) SIMPLE RANDOM

-- USE A RANDOM TABLE

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

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

OR LAST 2) FROM THE TABLE TO SELECT A SAMPLE

THE CHANCE OF ANY NUMBER APPEARING IS THE SAME FOR ALL.

SAMPLING METHODSb) SYSTEMATIC SAMPLING

-- ELEMENTS OF THE SAMPLE ARE SELECTED AT A UNIFORM INTERVAL MEASURED IN TERMS OF TIME, SPACE OR ORDER.

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

POPULATION ARE SEQUENTIAL OR THERE IS A CERTAINITY

OF CERTAIN HAPPENINGS . .

SAMPLING METHODSc) STRATIFIED SAMPLING -- DIVIDE POPULATION INTO HOMOGENOUS GROUPS

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

AND GIVE WEIGHTS TO THE GROUP/STRATA ACCORDING PROPORTION TO THE SAMPLE OR --SELECT AT RANDOM A SPECIFIED NO. OF ELEMENTS FROM

EACH STRATA CORRESPONDING TO ITS PROPORTION

TO THE POPULATION

-- EACH STRATUM HAS VERY LITTLE DIFFERENCE WITHIN

BUT CONSIDERABLE DIFFERENCE WITHOUT

SAMPLING METHODS d) CLUSTER SAMPLING

-- DIVIDE THE POPULATION INTO GROUPS WHICH ARE CLUSTERS

-- PICK A RANDOM SAMPLE FROM EACH CLUSTER

-- EACH CLUSTER HAS CONSIDERABLE DIFFERENCE WITHIN BUT SIMILAR WITHOUT

IMP: WHETHER WE USE PROBABILITY OR JUDGEMENT SAMPLING THE PROCESS IS BASED ON SIMPLE RANDOM SAMPLING .

SAMPLING METHODSEXAMPLES OF TYPES OF SAMPLING:

SYSTEMATIC SAMPLING : A SCHOOL WHERE ONE PICKS EVERY 15TH STUDENT.

STRATIFIED SAMPLING: IN A LARGE ORGANISATION PEOPLE ARE GROUPED ACCORDING TO RANGE OF SALARIES.

CLUSTER SAMPLING: A CITY IS DIVIDED INTO LOCALITIES.

SAMPLING METHODSSINCE WE WOULD USING THE CONCEPT OF STANDARD DEVIATION LET US UNDERSTAND ITS SIGNIFICANCE

IT IS A MEASURE OF DISPERSION.

GENERAL FORMULA FOR STD. DEV. IS (X - ) NWHERE X = OBSERVATION = POPULATION MEAN N = ELEMENTS IN POPULATION

SAMPLING METHODSDESPITE ALL THE COMPLEXITIES IN THE FORMULA THE STD. DEV. IS THE SAME IN STATE AS SUMMATION OF DIFFERENCES BETWEEN THE ELEMENTS AND THEIR MEAN.. --- IT IS THE RELIABLE MEASURE OF VARIABILITY .

. --- IT IS USED WHEN THERE IS NEED TO MEASURE CORRELATION COEFFICIENT, SIGNIFICANCE OF DIFFERENCE BETWEEN MEANS.

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

--- IT IS USED WHEN THE DISTRIBUTION IS NORMAL OR NEAR NORMAL

SAMPLING METHODSFORMULA FOR STANDARD DEVIATION: -- FOR POPULATION S = {(fx2 N) - f2x2 N}

THIS IS FOR GROUPED DATA, WHERE f IS THE FREQUENCY

OF ELEMENTS IN EACH GROUP AND N IS THE SIZE OF

POPULATION

SAMPLING METHODS IT IS IMPORTANT TO REMEMBER THAT EACH SAMPLE HAS

A DIFFERENT MEAN AND HENCE DIFFERENT STD.

DEVIATION. A PROBABILITY DISTRIBUTION OF THE

SAMPLE MEANS IS CALLED THE SAMPLING DISTRIBUTION OF THE MEANS. THE SAME PRINCIPLE

APPLIES TO A SAMPLE OF PROPORTIONS.

SAMPLING METHODS A STD. DEVIATION OF THE DISTRIBUTION OF THE SAMPLE

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

STD. ERROR INDICATES THE SIZE OF THE CHANCE ERROR BUT ALSO THE ACCURACY IF WE USE THE

SAMPLE STATISTIC TO ESTIMATE THE POPULATION STATISTIC

SAMPLING METHODSTERMINOLGY :\

= MEAN OF THE POPULATION DISTRIBUTION

x = MEAN OF THE SAMPLING DITRIBUTION OF THE MEANS

x = MEAN OF A SAMPLE

= STD. DEVIATION OF THE POPULATION DISTRIBUTION

x = STD. ERROR OF THE MEAN

SAMPLING METHODS

x= WHERE n IS THE SAMPLE SIZE. THIS FORMULA IS n TRUE FOR INFINITE POPULATION OR FINITE

POPULATION WITH REPLACEMENT.

Z = x - WHERE Z HELPS TO DETERMINE THE DISTANCE x OF THE SAMPLE MEAN FROM THE POPULATION

MEAN.

SAMPLING METHODSSTD. ERROR FOR FINITE POPULATION:

x = [N-n] WHERE N IS THE POPULATION SIZE n [N-1]

AND [N-n] IS THE FINITE POPULATION MULTIPLIER [N-1]THE VARIABILITY IN SAMPLING STATISTICS RESULTS FROM SAMPLING ERROR DUE TO CHANCE. THUS THE DIFFERENCE BETWEEN SAMPLES AND BETWEEN SAMPLE AND POPULATION MEANS IS DUE TO CHOICE OF SAMPLES.

SAMPLING METHODSCENTRAL LIMIT THEOREMTHE RELATIONSHIP BETWEEN THE SHAPE OF POPULATION DISTRIBUTION AND THE SAMPLNG DIST. IS CALLED CENTRAL LIMIT THEOREM.AS SAMPLE SIZE INCREASES THE SAMPLING DIST. OF THE MEN WILL APPROACH NORMALITY REGARDLESS OF THE POPULATION DIST.SAMPLE SIZE NEED NOT BE LARGE FOR THE MEAN TO APPROACH NORMAL WE CAN MAKE INFERENCES ABOUT THE POPULATION PARAMETERS WITHOUT KNOWING ANYTHING ABOUT THE SHAPE OF THE FREQUENCY DIST. OF THE POPULATION

SAMPLING METHODSEXAMPLE: n = 30, = 97.5, = 16.3a) WHAT IS THE PROB. OF X LYING BETWEEN 90 & 104ANS) x= , = 2.97 n P( 90 97.5 < x - < 104-97.5 ) 2.97 x 2.97

-2.52 < Z < 2.19

USE Z TABLE

P = 0.4941 + 0.4857 = 0.98

b) FOR MEAN X LYING BELOW 100 P( Z< 100 104 ) 2.97 0.50 0.4115 = 0.0885

REGRESSION AND CORRELATIONREGRESSION & CORRELATION ANALYSES HELP TO

DETERMINE THE NATURE AND STRENGTH OF RELATIONSHIP

BETWEEN 2 VARIABLES. THE KNOWN VARIABLE IS CALLED

THE INDEPENDENT VARIABLE WHEREAS THE VARIABLE WE

ARE TRYING TO PREDICT IS CALLED THE DEPENDENT

VARIABLE. THIS ATTEMPT AT PREDICTION IS CALLED

REGRESSION ANALYSES WHEREAS CORRELATION TELLS

THE EXTENT OF THE RELATIONSHIP.

REGRESSION AND CORRELATIONTHE VALUES OF THE 2 VARIABLES ARE PLOTTED ON A

GRAPH WITH X AS THE INDEPENDENT VARIABLE. THE

POINTS WOULD BE SCATTERED . DRAW A LINE BETWEEN

POINTS SUCH THAT AN EQUAL NUMBER LIE ON EITHER SIDE

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

POINTS ON THE LINE.

REGRESSION AND CORRELATIONONE CAN DRAW ANY NUMBER OF LINES BETWEEN THE POINTS. THE LINE WITH BEST FIT IS THE THAT WITH LEAST SQUARE DIFFERENCE BETWEEN THE ACTUAL AND ESTIMATED POINTS.IN THE EQN. Y = a + b Xb = SLOPE = XY n X Y X2 n X2SLOPE OF THE LINE INDICATES THE EXTENT OF CHANGE IN Y DUE TO CHANGE IN X. . a = Y - b X

WHERE X , Y ARE MEAN VALUES .

REGRESSION AND CORRELATIONSTD ERROR OF ESTIMATE Se = {(Y Ye ) (n -2)} or = { Y -a Y b (XY)} (n-2). WHERE Ye = ESTIMATES OF Y

n 2 IS USED BECAUSE WE LOSE 2 DEGREES OF FREEDOM IN ESTIMATING THE REGRESSION LINE.

IF SAMPLE IS n THE DEG OF FREEDOM = n-1 i.e. WE CAN FREELY GIVE VALUES TO n-1 VARIABLES.

REGRESSION AND CORRELATIONTHERE ARE 3 MEASURES OF CORRELATION

- COEFFICIENT OF DETERMINATION. IT MEASURES THE

STRENGTH OF A LINEAR RELATIONSHIP

COEFF. OF DET. = r2 = (Y Ye )2 1- ---------------- ( Y - Y )2

COEF. OF DETERMINATION IS r COEFF. OF CORRELATION IS r r = + r, HENCE FROM r2 TO r WE KNOW THE STRENGTH

BUT NOT THE DIRECTION.

.

REGRESSION AND CORRELATION-COVARIANCE. IT MEASURES THE STRENGTH &

DIRECTION OF THE RELATIONSHIP.

COVARIANCE = ( X - X )(Y - Y ) n -COEFFICIENT OF CORRELATION. IT MEASURES THE

DIMENSIONLESS STRENGTH & DIRECTION OF THE

RELATIONSHIP

COEFF.OF CORR. = COVARIANCE xy

TREND ANALYSIS4 TYPES OF TIME SERIES VARIATIONS:-- a) SECULAR TREND IN WHICH THERE IS FLUCTUATION BUT STEADY INCREASE IN TREND OVER A LARGE PERIOD OF TIME.

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

-- c) SEASONAL VARIATION WHICH SEE REGULAR CHANGES DURING A YEAR.

-- d) IRREGULAR VARIATION DUE TO UNFORESEEN CIRCUMSTANCES.

TREND ANALYSIS

IN TREND ANALYSIS WE HAVE TO FIT A LINEAR TREND BY

LEAST SQUARES METHOD. TO EASE THE COMPUTATION WE

USE CODING METHOD WHERE WE ASSIGN NUMBERS TO THE

YEARS FOR EXAMPLE. THEN WE CALCULATE THE VALUES OF

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

THE EQN. FOR FORECASTING.

TREND ANALYSISSTUDY OF SECULAR TRENDS HELPS TO DESCRIBE A

HISTORICAL PATTERN;

USE PAST TRENDS TO PREDICT THE FUTURE;

AND ELIMINATE TREND COMPONENT WHICH

MAKES IT EASIER TO STUDY THE OTHER 3 COMPONENTS.

TREND ANALYSISONCE THE SECULAR TREND LINE IS FITTED THE CYCLICAL & IRREGULAR VARIATIONS ARE TACKLED SINCE SEASONAL

VARIATIONS MAKE A COMPLETE CYCLE WITHIN A YEAR AND

DO NOT AFFECT THE ANALYSIS.

THE ACTUAL DATA IS DIVIDED BY THE PREDICTED DATA A RELATIVE CYCLICAL RESIDUAL IS OBTAINED

A PERCENTAGE DEVIATION FROM TREND FOR EACH VALUE IS FOUND

THE PAST CYCLICAL VARIATION IS ANALYSED

TREND ANALYSISSEASONAL VARIATION IS ELIMINATED BY MOVING AVERAGE METHOD . a) FIND AVERAGE OF 4 QTRS. BY PROCESS OF SLIDING

b) DIVIDE EACH VALUE BY 4

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

SLIDING METHOD

TREND ANALYSISd) CALCULATE THE PERCENTAGE OF ACTUAL VALUE TO

MOVING AVERAGE VALUE

e) MODIFY THE TABLE ON QTR. BASIS AND AFTER

DISCARDING THE HIGHEST AND LOWEST VALUE FOR EACH

QTR FIND THE MEANS QTR. WISE.

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

SEASONAL INDEX

g) USE THE INDEX TO GET DESEASONALISED VALUES.

PROBABILITY DISTRIBUTIONTHIS CHAPTER IS ON METHODS TO ESTIMATE POPULATION

PROPORTION AND MEAN:

THERE ARE 2 TYPES OF ESTIMATES:

POINT ESTIMATE: WHICH IS A SINGLE NUMBER TO ESTIMATE

AN UNKNOWN POPULATION PARAMETER. IT IS INSUFFICIENT

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

PROBABILITY DISTRIBUTIONINTERVAL ESTIMATE: IT IS A RANGE OF VALUES

USED TO ESTIMATE A POPULATION PARAMETER;

ERROR IS INDICATED BY EXTENT OF ITS RANGE

AND BY THE PROBABILITY OF THE TRUE

POPULATION LYING WITHIN THAT RANGE.

ESTIMATOR IS A SAMPLE STATISTIC USED TO ESTIMATE A

POPULATION PARAMETER.

PROBABILITY DISTRIBUTION

CRITERIA FOR A GOOD ESTIMATOR

a) UNBIASEDNESS: MEAN OF SAMPLING DISTRIBUTION OF

SAMPLE MEANS ~ POPULATION MEANS. THE STATISTIC

ASSUMES OR TENDS TO ASSUME AS MANY VALUES

ABOVE AS BELOW THE POP. MEAN

b) EFFICIENCY: THE SMALLER THE STANDARD ERROR, THE MORE EFFICIENT THE ESTIMATOR OR BETTER THE

CHANCE OF PRODUCING AN ESTIMATOR NEARER TO THE

POP.PARAMETER .

PROBABILITY DISTRIBUTIONc) CONSISTENCY: AS THE SAMPLE SIZE INCREASES, THE

SAMPLE STASTISTIC COMES CLOSER TO THE POPULATION

PARAMETER.

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

PROBABILITY Of 0.955 MEANS THAT 95.5 OF ALL SAMPLE

MEANS ARE WITHIN + 2 STD ERROR OF MEAN

POPULATION . SIMILARLY, 0.683 MEANS + 1 STD ERROR.

PROBABILITY DISTRIBUTIONCONFIDENCE INTERVAL IS THE RANGE OF THE

ESTIMATE WHILE CONFIDENCE LEVEL IS THE PROBABILITY THAT WE ASSOCIATE WITH INTERVAL

ESTIMATE THAT THE POPULATION PARAMETER IS IN IT.AS THE CONFIDENCE INTERVAL GROWS SMALLER, THE

CONFIDENCE LEVEL FALLS.

PROBABILITY DISTRIBUTIONFORMULA: ESTIMATE OF POPULATION : ^= (x - x ) STD. DEVIATION (n 1)

ESTIMATE OF STD. ERROR : ^x = ^ OR = ^ (N - n) n n (N - 1)

STANDARD ERROR OF THE : p = p q PROPORTION n

BOND VALUATIONBONDS ARE LONG TERM LOANS WITH A PROMISE OF SERIES

OF FIXED INTEREST PAYMENTS AND REPAYMENT OF

PRINCIPAL

THE INTEREST PAYMENT ON BOND IS CALLED COUPON RATE

IS COUPON RATE.

THEY ARE ISSUED AT A DISCOUNT AND REPAID AT PAR. GOVT. BONDS ARE FOR LARGE PERIODS

BONDS HAVE A MARKET AND PRICES ARE QUOTED ON

NSE/BSE.

BOND VALUATIONBOND PRICES ARE LINKED WITH INTEREST RATES IN THE MARKET.

IF THE INTEREST RATES RISE, THE BOND PRICES FALL AND

VICE VERSA.

PRESENT VALUE OF BONDS CAN ALSO BE CALCULATED

USING THE DISCOUNT FACTOR FOR THE COUPONS AS WELL

AS THE FINAL PAYMENT OF THE FACE VALUE

BOND VALUATIONSOME IMPORTANT STANDARD MEASURES:

CURRENT YIELD: IT IS THE RETURN ON THE PRESENT

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

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

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

BOND VALUATIONYIELD TO MATURITY: THIS MEASURE TAKES INTO ACCOUNT

CURRENT YIELD AND CHANGE IN BOND VALUE OVER ITS

LIFE . IT IS THE DISCOUNT RATE AT WHICH THE PRESENT

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

FACE VALUE = CURRENT PRICE. n. PRICE = C i + C n + F V WHERE C i = COUPON i =1 (1 + r) n-1 (1 + r) n INCOME F V = FACE VALUE n = LIFE OF BOND

BOND VALUATIONIF THE YIELD TO MATURITY (YTM) REMAINS UNCHANGED,

THEN THE RATE OF RETURN = YTM.EVEN IF INTEREST RATES DO NOT CHANGE, THE BOND

PRICES CHANGE WITH TIME;

AS WE NEAR THE MATURITY PERIOD, THE BOND PRICES

TEND TO THE PAR/FACE VALUE.

.

BOND VALUATIONTHERE ARE 2 RISKS IN BONDS INVESTMENT

a) INTEREST RATE RISK: WHERE THE BOND PRICES CHANGE

INVERSELY WITH INTEREST RATE. ALSO THE LARGER THE

MATURITY PERIOD OF A BOND, THE GREATER THE SENSITIVITY TO

PRICE.

DEFAULT RISK: WHICH IS TRUE WITH PRIVATE BONDS

RATHER THAN GOVT. BONDS( GILT EDGED SECURITIES)

BOND VALUATIONDIFFERENT TYPES OF BONDS:

ZERO COUPON BOND: NO COUPON INCOME.

FLOATING RATE BOND: INTEREST RATES CHANGE ACCORDING TO THE MARKET.

CONVERTIBLE BOND: BONDS CONVERTED TO SHARES AT A LATER DATE.

BONDS ON CALL: THE ISSUER RESERVES THE RIGHT TO CALL BACK THE BOND AT ANY POINT IN TIME GENERALLY OVER PAR.

BOND VALUATIONSOME THOUGHTS ON BONDSTHE INTEREST IS CALLED COUPON INCOME AS COUPONS ARE ATTACHED TO THE BONDS FOR INTEREST PAYMENTS OVER THE LIFE OF THE BONDBOND INTEREST REMAINS THE SAME IRRESPECTIVE OF THE CHANGES IN THE INT. RATES IN THE MARKETBOND PRICES ARE USUALLY QUOTED AT %AGE OF THEIR FACE VALUE i.e. 102.5.CURRENT YIELD OVERSTATES RETURN ON PREMIUM BONDS & UNDERSTATES RETURN ON DISCOUNT BONDS; SINCE TOWARDS THE END OF THE BOND PERIOD THE PRICE MOVES NEARER THE FACE VALUE. i.e. PREMIUM BOND AND DISCOUNT BOND .IF BOND IS PURCHASED AT FACE VALUE THEN Y T M IS THE COUPON RATE.

LINEAR PROGRAMMINGEVERY ORGANISATION USES RESOURCES SUCH AS MEN(WOMEN), MACHINES MATERIALS AND MONEY.

THESE ARE CALLED RESOURCES

THE OPTIMUM USE OF RESOURCES TO PRODUCE THE MAXIMUM POSSIBLE PROFIT IS THE ESSENCE OF LINEAR PROGRAMMING

EACH RESOURCE WOULD HAVE CONSTRAINTS

HENCE WORKING WITHIN THE CONSTRAINTS; MINIMIZING COST; MAXIMIZING PROFIT SHOULD BE THE CORPORATE PHILOSOPHY.

LINEAR PROGRAMMINGIN LINEAR PROGRAMMING PROBLEMS, THE CONSTRAINTS ARE IN THE FORM OF INEQUALITIES

LABOUR AVAILABLE FOR UPTO 200 HRS. < 200

MAXIMUM FUNDS AVAILABLE IS RS. 30,000/- < 30,000

MINIMUM MATERIAL TO BE USED IS 300 KGS > 300

SOLUTION TO THESE EQUATIONS ARE BY GRAPHICAL METHOD OR THE SIMPLEX METHOD

SIMULATIONSIMULATION IS A TECHNIQUE WHERE MODEL OF THE PROBLEM, WITHOUT GETTING TO REALITY, IS MADE TO KNOW THE END RESULTS

SIMULATION IS IDEAL FOR SITUATIONS WHERE SIZE OR COMPLEXITY OF THE SITUATION DOES NOT PERMIT USE OF ANY OTHER METHOD

IN SHORT, SIMULATION IS A REPLICA OF REALITY.

EXAMPLES OF PROBLEM SITUATIONS FOR SIMULATION ARE-- AIR TRAFFIC QUEUING-- RAIL OPERATIONS-- ASSEMBLY LINE SYSTEMS-- AND SO ON

.

SIMULATION THEREFORE IT IS CLEAR THAT WHEN USE OF REAL SYSTEM

UPSETS THE WORKING SCHEDULE IN THE SYSTEM OR IS

IMPOSSIBLE TO EXPERIMENT REAL TIME, AND IT IS

TOO EXPENSIVE TO UNDERTAKE THE EXERCISE, THEN

SIMULATION IS IDEAL.

. HOWEVER SIMULATION CAN BE A COSTLY EXERCISE, TIME

CONSUMING AND WITH VERY FEW GUIDING PRINCIPLES.

FINAL LEGTHANK YOU VERY MUCH FOR YOUR PATIENCE; I TRUST IT WAS USEFUL. BEFORE WE DISPERSE LET US GO THRU A SET OF QUESTIONS WITH MULTIPLE CHOICE ANSWERS,WHICH WILL COVER THOSE ASPECTS OF THE SUBJECT THAT MAY NOT BEEN TOUCHED UPON.

ENDANY QUERIES MAY BE ADDRESSED TO

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