FINANCIAL MANAGEMENT C A I I B MODULE A

1
FINANCIAL MANAGEMENTC 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
  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

3
TIME VALUE OF MONEY

• EXTENTOF 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

4
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.

5
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.

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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.

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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

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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 THE
  PRESENT 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(1r) 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
  ON SEMI-ANNUAL OR MONTHLY BASIS THE THE EFFECTIVE
  RATE OF INTEREST CHANGES
• 
  n
• EFFECTIVE INTEREST RATE (1 r) - 1
• 
  N
• WHERE N NO. OF COMPOUNDING PERIODS

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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 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).

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TIME VALUE MONEY

• B) BEGINNING OF THE PERIOD
• 
  n-1
• - a) P V OF ANNUITY(A) A A1- 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 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.

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SAMPLING METHODS

• A SAMPLE IS A REPRESENTATIVE PORTION OF THE
  POPULATION
• TWO TYPES OF SAMPLING
• --- RANDOM OR PROBABILITY SAMPLING
• --- NON-RANDOM OR JUDGEMENT SAMPLING
• IN 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.

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SAMPLING METHODS

• FOUR 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.

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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
• BUT CONSIDERABLE DIFFERENCE WITHOUT

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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
  WITHIN
• BUT 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 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.

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SAMPLING METHODS

• SINCE 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 v?(X - µ)²
• 
  v N
• WHERE X OBSERVATION
• µ POPULATION MEAN
• N 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
  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

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SAMPLING METHODS

• FORMULA FOR STANDARD DEVIATION
• -- FOR POPULATION S v(?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

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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
• s STD. DEVIATION OF THE POPULATION
  DISTRIBUTION
• sx STD. ERROR OF THE MEAN

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SAMPLING METHODS

• sx s WHERE n IS THE SAMPLE SIZE. THIS
  FORMULA IS
• vn
• TRUE FOR INFINITE POPULATION
  OR FINITE
• POPULATION WITH REPLACEMENT.
• Z x - µ WHERE Z HELPS TO DETERMINE THE
  DISTANCE
• sx
• OF THE SAMPLE MEAN FROM
  THE POPULATION
• MEAN.

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SAMPLING METHODS

• STD. ERROR FOR FINITE POPULATION
• sx s v N-n WHERE N IS THE POPULATION
  SIZE
• vn v N-1
• AND v N-n IS THE FINITE POPULATION MULTIPLIER
• v 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.

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SAMPLING METHODS

• CENTRAL LIMIT THEOREM
• THE 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

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SAMPLING METHODS

• EXAMPLE n 30, µ 97.5, s 16.3
• a) WHAT IS THE PROB. OF X LYING BETWEEN 90 104
• ANS) sx s , 2.97
• vn
• P( 90 97.5 lt x - µ lt 104-97.5 )
• 2.97 sx
  2.97
• -2.52 lt Z lt 2.19
• USE Z TABLE
• P 0.4941 0.4857 0.98
• b) FOR MEAN X LYING BELOW 100
• P( Zlt 100 104 )
• 2.97
• 0.50 0.4115 0.0885

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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 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 X
• b SLOPE ? XY n X Y
• ? X2 n X2
• SLOPE 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
• .

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REGRESSION AND CORRELATION

• STD ERROR OF ESTIMATE
• Se v?(Y Ye ) (n -2) or vv Y²
  -a vY b v (XY)
• 
  
  v(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.

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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. r2 ?(Y Ye )2
• 1-
  ----------------
• 
  ?( Y - Y )2
• COEF. OF DETERMINATION IS r²
• COEFF. OF CORRELATION IS r
• v r² r, HENCE FROM r2 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
• 
  sxsy

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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
• THE PAST CYCLICAL VARIATION IS ANALYSED

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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 s v (x - x )²
• STD. DEVIATION
  v(n 1)
• ESTIMATE OF STD. ERROR sx s OR
  s v(N - n)
• 
  v n v n v(N - 1)
• STANDARD ERROR OF THE sp vp q
• PROPORTION
  vn

47
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.

48
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

49
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.

50
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 COUPON
• i 1 (1 r) n-1 (1 r) n
  
  INCOME
• 
  
  F V FACE VALUE
• 
  
  n LIFE OF
• 
  BOND
  

51
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.
• .

52
BOND VALUATION

• THERE 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)

53
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 A
  LATER DATE.
• BONDS ON CALL THE ISSUER RESERVES THE RIGHT TO
  CALL BACK THE BOND AT ANY POINT IN TIME GENERALLY
  OVER PAR.

54
BOND VALUATION

• SOME THOUGHTS ON BONDS
• THE INTEREST IS CALLED COUPON INCOME AS COUPONS
  ARE ATTACHED TO THE BONDS FOR INTEREST PAYMENTS
  OVER 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 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.

55
LINEAR PROGRAMMING

• EVERY 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.

56
LINEAR PROGRAMMING

• IN LINEAR PROGRAMMING PROBLEMS, THE CONSTRAINTS
  ARE IN THE FORM OF INEQUALITIES
• LABOUR AVAILABLE FOR UPTO 200 HRS. lt
  200
• MAXIMUM FUNDS AVAILABLE IS RS. 30,000/- lt
  30,000
• MINIMUM MATERIAL TO BE USED IS 300 KGS gt
  300
• SOLUTION TO THESE EQUATIONS ARE BY GRAPHICAL
• METHOD OR THE SIMPLEX METHOD

57
SIMULATION

• SIMULATION 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
• .

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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.

59
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 THE SUBJECT THAT
  MAY NOT BEEN TOUCHED UPON.

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END

• ANY QUERIES MAY BE ADDRESSED TO
• chitturb_at_rediffmail.com