caiib fm moda cont
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FINANCIAL MANAGEMENT
C A I I B
MODULE A
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TIME VALUE OF MONEY
MONEY HAS TIME VALUE
THIS IS BASED ON THE CONCEPT OF EROSION IN VALUE OFMONEY 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
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TIME VALUE OF MONEY
EXTENTOF EROSION IN THE VALUE OF MONEY IS ANUNKNOWN FACTOR. HENCE A WELL THOUGHT OUTDISCOUNT RATE HELPS TO BRING THE FUTURE CASHFLOWS 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 WITHTHE VALUE OF MONEY i.e. THE GREATER THE FACTOR THELOWER IS THE VALUE OF MONEY
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TIME VALUE OF MONEY
IF DESIRE FOR CURRENT CONSUMPTION ISGREATER THENWE NEED TO OFFER INCENTIVES TO DEFER THECONSUMPTION.
THE MONEY THUS SAVED IS THEN PROFITABLY ORGAINFULLY EMPLOYED . HENCE THE DISCOUNT RATE WILLBE LOWER.
INVESTMENT IN GOVERNMENT BONDS / SECURITIES IS LESSRISKY THAN IN THE PRIVATE SECTOR SIMPLY BECAUSE NOT
ALL CASH FLOWS ARE EQUALLY PREDICTABLE AND WHERETHERE IS SOVEREIGN GUARANTEE THE RISK IS LESS.
IF THE RISK OF RETURN IS LOWER AS IN GOVT. SECURITIESTHEN THE RATE OF RETURN IS ALSO LOWER.
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TIME VALUE OF MONEY
THE PROCESS BY WHICH FUTURE FLOWS ARE ADJUSTEDTO REFLECT THESE FACTORS IS CALLED DISCOUNTING &THE MAGNITUDE IS REFLECTED IN THE DISCOUNT RATE.
THE DISCOUNT VARIES DIRECTLY WITH EACH OF THESEFACTORS.
THE DISCOUNT OF FUTURE FLOWS TO THE PRESENT IS
DONE WITH THE NEED TO KNOW THE EFFICACY OF THEINVESTMENT.
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TIME VALUE OF MONEY
THE DISCOUNTING BRING THE FLOWS TO A NET PRESENTVALUE OR N P V.
N P V IS THE NET OF THE PRESENT VALUE OF FUTURE CASHFLOWS 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 THEINVESTMENT WITH HIGHER N P V IS SELECTED. THEDISCOUNTED RATES FOR EACH ARE THE RISK RATES ASSOCIATED WITH INVESTMENTS.
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TIME VALUE OF MONEY
REAL CASH FLOWS ARE NOMINAL CASH FLOWS ADJUSTEDTO INFLATION.
NOMINAL CASH FLOWS ARE AS RECEIVED WHILE REAL CASHFLOWS ARE NOTIONAL FIGURES
REAL CASH FLOWS = NOMINAL CASH FLOWS
1 – INFLATION RATE
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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 THEPRESENT BY A FACTOR KNOWN DISCOUNT
THE DISCOUNT RATE adjusted for inflation IS REAL RATE
THIS REAL RATE IS AN INFLATION ADJUSTED RATE
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TIME VALUE OF MONEY
DISCOUNTING IS THE INVERSE OF COMPOUNDING
FINAL AMOUNT = A PRINCIPAL = P
RATE OF INT. = r PERIOD = n
n n
A = P(1+r) WHERE (1 + r) = COMPOUNDING FACTOR n n
P = A__
(1+ r) WHERE 1 ÷ (1 + r) = DISCOUNTING FACTOR
IF INSTEAD OF COMPOUNDING ON ANNUAL BASIS IT IS ONSEMI-ANNUAL OR MONTHLY BASIS THE THE EFFECTIVE RATEOF INTEREST CHANGES
n
EFFECTIVE INTEREST RATE = (1 + r) - 1
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TIME VALUE OF MONEY
ANNUITY IS A CONSTANT CASH FLOW AT REGULAR INTERVALS FOR A FIXED PERIOD
THERE 4 TYPES OF ANNUITIES
A) END OF THE PERIODn
a) P V OF AN ANNUITY(A) = A [1-- {1÷ (1 + r)} ]÷ rn
b) F V OF AN ANNUITY(A) = A{(1 + r) -- 1} ÷ r
a) IS THE FORMULA OF EQUATED MONTHLY
INSTALMENT(EMI).
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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 n
P 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%.
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TIME VALUE OF MONEY
A PERPETUITY IS A CONSTANT CASH FLOW AT REGULARINTERVALS 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.
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SAMPLING METHODS
A SAMPLE IS A REPRESENTATIVE PORTION OF THEPOPULATION
TWO TYPES OF SAMPLING:
--- RANDOM OR PROBABILITY SAMPLING
--- NON-RANDOM OR JUDGEMENT SAMPLING
IN JUDGEMENT SAMPLING KNOWLEDGE & OPINIONS AREUSED. IN THIS KIND OF SAMPLING BIASEDNESS CAN CREEPIN, FOR EX. IN INTERVIEWING TEACHERS ASKING THEIROPINION ABOUT THEIR PAY RISE.
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SAMPLING METHODS
FOUR METHODS OF SAMPLING:
a) SIMPLE RANDOM
-- USE A RANDOM TABLE
-- ASSIGN DIGITS TO EACH ELEMENT OF THEPOPULATION(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 SAMEFOR ALL.
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SAMPLING METHODS
b) 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 .
.
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SAMPLING METHODS
c) 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
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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 WITHINBUT SIMILAR WITHOUT
IMP: WHETHER WE USE PROBABILITY OR JUDGEMENT
SAMPLING THE PROCESS IS BASED ON SIMPLE RANDOM
SAMPLING .
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SAMPLING METHODS
EXAMPLES OF TYPES OF SAMPLING:
SYSTEMATIC SAMPLING : A SCHOOL WHERE ONE PICKSEVERY 15TH STUDENT.
STRATIFIED SAMPLING: IN A LARGE ORGANISATION PEOPLE ARE GROUPED ACCORDING TO RANGE OF SALARIES.
CLUSTER SAMPLING: A CITY IS DIVIDED INTO LOCALITIES.
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SAMPLING METHODS
SINCE WE WOULD USING THE CONCEPT OF STANDARDDEVIATION LET US UNDERSTAND ITS SIGNIFICANCE
IT IS A MEASURE OF DISPERSION.
GENERAL FORMULA FOR STD. DEV. IS √∑(X - µ)²√ N
WHERE X = OBSERVATION
µ = POPULATION MEANN = ELEMENTS IN POPULATION
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SAMPLING METHODS
DESPITE ALL THE COMPLEXITIES IN THE FORMULA THE
STD. DEV. IS THE SAME IN STATE AS SUMMATION OFDIFFERENCES 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
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SAMPLING METHODS
FORMULA FOR STANDARD DEVIATION:
-- FOR POPULATION S = √{(∑fx2÷ N) - ∑f 2x2÷ N}
THIS IS FOR GROUPED DATA, WHERE f IS THE FREQUENCY
OF ELEMENTS IN EACH GROUP AND N IS THE SIZE OF
POPULATION
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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.
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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
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SAMPLING METHODS
TERMINOLGY :\
µ = MEAN OF THE POPULATION DISTRIBUTION
µx¯ = MEAN OF THE SAMPLING DITRIBUTION OF THE MEANS
x¯ = MEAN OF A SAMPLE
σ = STD. DEVIATION OF THE POPULATION DISTRIBUTION
σx¯ = STD. ERROR OF THE MEAN
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SAMPLING METHODS
σx¯= σ WHERE n IS THE SAMPLE SIZE. THIS FORMULA IS√n
TRUE FOR INFINITE POPULATION OR FINITE
POPULATION WITH REPLACEMENT.
Z = x¯ - µ WHERE Z HELPS TO DETERMINE THE DISTANCE
σx¯
OF THE SAMPLE MEAN FROM THE POPULATION
MEAN.
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SAMPLING METHODS
STD. ERROR FOR FINITE POPULATION:
σx ¯ = σ √ [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 FROMSAMPLING ERROR DUE TO CHANCE. THUS THE DIFFERENCEBETWEEN SAMPLES AND BETWEEN SAMPLE ANDPOPULATION MEANS IS DUE TO CHOICE OF SAMPLES.
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SAMPLING METHODS
CENTRAL LIMIT THEOREM
THE RELATIONSHIP BETWEEN THE SHAPE OF POPULATIONDISTRIBUTION AND THE SAMPLNG DIST. IS CALLED CENTRALLIMIT THEOREM.
AS SAMPLE SIZE INCREASES THE SAMPLING DIST. OF THEMEN WILL APPROACH NORMALITY REGARDLESS OF THEPOPULATION DIST.
SAMPLE SIZE NEED NOT BE LARGE FOR THE MEAN TO APPROACH NORMAL
WE CAN MAKE INFERENCES ABOUT THE POPULATIONPARAMETERS WITHOUT KNOWING ANYTHING ABOUT THESHAPE OF THE FREQUENCY DIST. OF THE POPULATION
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SAMPLING METHODS
EXAMPLE: n = 30, µ = 97.5, σ = 16.3 a) WHAT IS THE PROB. OF X LYING BETWEEN 90 & 104 ANS) σx¯= σ , = 2.97 √n
P( 90 – 97.5 < x¯ - µ < 104-97.5 ) 2.97 σx¯ 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
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REGRESSION AND CORRELATION
REGRESSION & 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.
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REGRESSION AND CORRELATION
THE 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.
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REGRESSION AND CORRELATION
ONE CAN DRAW ANY NUMBER OF LINES BETWEEN THEPOINTS. THE LINE WITH BEST ’ FIT’ IS THE THAT WITH LEASTSQUARE DIFFERENCE BETWEEN THE ACTUAL ANDESTIMATED POINTS.
IN THE EQN. Y = a + b X b = SLOPE = ∑ XY – n X¯ Y¯
∑ X¯ 2 – n X¯ 2
SLOPE OF THE LINE INDICATES THE EXTENT OF CHANGE INY DUE TO CHANGE IN X.
. a = Y¯ - b X¯
WHERE X¯ , Y¯ ARE MEAN VALUES
.
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REGRESSION AND CORRELATION
STD ERROR OF ESTIMATE
Se = √{∑(Y – Ye ) ÷ (n -2)} or = √{√ Y² -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 CANFREELY GIVE VALUES TO n-1 VARIABLES.
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REGRESSION AND CORRELATION
THERE ARE 3 MEASURES OF CORRELATION
- COEFFICIENT OF DETERMINATION. IT MEASURES THE
STRENGTH OF A LINEAR RELATIONSHIP
COEFF. OF DET. = r 2 = ∑(Y – Ye )2
1- ----------------∑( Y - Y¯ )2
COEF. OF DETERMINATION IS r ²COEFF. OF CORRELATION IS r√ r² = + r, HENCE FROM r 2 TO r WE KNOW THE STRENGTH
BUT NOT THE DIRECTION.
.
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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
σxσy
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TREND ANALYSIS
4 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.
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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.
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TREND ANALYSIS
STUDY 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.
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TREND ANALYSIS
ONCE 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
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TREND ANALYSIS
SEASONAL 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
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TREND ANALYSIS
d) 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.
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PROBABILITY DISTRIBUTION
THIS 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.
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PROBABILITY DISTRIBUTION
INTERVAL 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.
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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 .
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PROBABILITY DISTRIBUTION
c) 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 µ.
SIMILARLY, 0.683 MEANS + 1 STD ERROR.
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PROBABILITY DISTRIBUTION
CONFIDENCE 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.
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PROBABILITY DISTRIBUTION
FORMULA:
ESTIMATE OF POPULATION : σ^= √ (x - x¯ )²
STD. DEVIATION √(n – 1)
ESTIMATE OF STD. ERROR : σ^x¯ = σ^ OR = σ^ √(N - n)
√ n √ n √(N - 1)
STANDARD ERROR OF THE : σp¯
= √p q PROPORTION √n
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BOND VALUATION
BONDS 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.
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BOND VALUATION
BOND 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
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BOND VALUATION
SOME 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.
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BOND VALUATION
YIELD 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 = COUPONi =1 (1 + r) n-1 (1 + r) n INCOME
F V = FACEVALUE
n = LIFE OF
BOND
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BOND VALUATION
IF 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.
.
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BOND VALUATION
THERE ARE 2 RISKS IN BOND’S 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 THESENSITIVITY TO
PRICE.
DEFAULT RISK: WHICH IS TRUE WITH PRIVATE BONDS
RATHER THAN GOVT. BONDS( GILT EDGED SECURITIES)
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BOND VALUATION
DIFFERENT 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 ALATER DATE.
BONDS ON CALL: THE ISSUER RESERVES THE RIGHT TOCALL BACK THE BOND AT ANY POINT IN TIME GENERALLYOVER PAR.
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BOND VALUATION
SOME THOUGHTS ON BONDS THE INTEREST IS CALLED COUPON INCOME AS COUPONS
ARE ATTACHED TO THE BONDS FOR INTEREST PAYMENTSOVER THE LIFE OF THE BOND
BOND INTEREST REMAINS THE SAME IRRESPECTIVE OF THE
CHANGES IN THE INT. RATES IN THE MARKET BOND 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; SINCETOWARDS THE END OF THE BOND PERIOD THE PRICEMOVES NEARER THE FACE VALUE. i.e. PREMIUM BOND ANDDISCOUNT BOND .
IF BOND IS PURCHASED AT FACE VALUE THEN Y T M IS THECOUPON RATE.
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LINEAR PROGRAMMING
EVERY ORGANISATION USES RESOURCES SUCH ASMEN(WOMEN), MACHINES MATERIALS AND MONEY.
THESE ARE CALLED RESOURCES
THE OPTIMUM USE OF RESOURCES TO PRODUCE THEMAXIMUM POSSIBLE PROFIT IS THE ESSENCE OF LINEARPROGRAMMING
EACH RESOURCE WOULD HAVE CONSTRAINTS
HENCE WORKING WITHIN THE CONSTRAINTS; MINIMIZINGCOST; MAXIMIZING PROFIT SHOULD BE THE CORPORATEPHILOSOPHY.
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LINEAR PROGRAMMING
IN 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
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SIMULATION
SIMULATION IS A TECHNIQUE WHERE MODEL OF THEPROBLEM, WITHOUT GETTING TO REALITY, IS MADE TOKNOW THE END RESULTS
SIMULATION IS IDEAL FOR SITUATIONS WHERE SIZE ORCOMPLEXITY 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
.
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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.
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FINAL LEG
THANK 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 THESUBJECT THAT MAY NOT BEEN
TOUCHED UPON.
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END
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