Download Quantitative Techniques & Financial Mathematics

FINANCIAL MANAGEMENT
C A I I B
MODULE A
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
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
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 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 ON
SEMI-ANNUAL OR MONTHLY BASIS THE THE EFFECTIVE RATE
OF INTEREST CHANGES
n
EFFECTIVE INTEREST RATE = (1 + r) - 1
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).
TIME VALUE MONEY


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
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%.
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.
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.
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.
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 .
.
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
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 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.
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 √∑(X - µ)²
√N

WHERE X = OBSERVATION
µ = POPULATION MEAN
N = ELEMENTS IN POPULATION
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
SAMPLING METHODS

FORMULA FOR STANDARD DEVIATION:

S = √{(∑fx2÷ N) - ∑f2x2÷ N}

-- FOR POPULATION

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 METHODS

TERMINOLGY :\

µ

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
= MEAN OF THE POPULATION DISTRIBUTION
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
σx¯
WHERE Z HELPS TO DETERMINE THE DISTANCE
OF THE SAMPLE MEAN FROM THE POPULATION
MEAN.
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 FROM
SAMPLING ERROR DUE TO CHANCE. THUS THE DIFFERENCE
BETWEEN SAMPLES AND BETWEEN SAMPLE AND
POPULATION MEANS IS DUE TO CHOICE OF SAMPLES.

SAMPLING METHODS


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

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
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


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b) FOR MEAN X LYING BELOW 100
P( Z< 100 – 104 )
2.97
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.
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.
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¯
∑ X¯2 – n X¯2
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
.
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 CAN
FREELY GIVE VALUES TO n-1 VARIABLES.
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
√ r² = + 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
σxσy
TREND ANALYSIS



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


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
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.
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 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.
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
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
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.
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.
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.
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 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.
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.
PROBABILITY DISTRIBUTION

FORMULA:


ESTIMATE OF POPULATION : σ^= √ (x - x¯ )²
STD. DEVIATION
√(n – 1)

ESTIMATE OF STD. ERROR : σ^x¯ = σ^
√n

STANDARD ERROR OF THE : σp¯ = √p q
PROPORTION
√n
OR = σ^ √(N - n)
√ n √(N - 1)
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.
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
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.
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
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.
.
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 THE
SENSITIVITY TO
PRICE.

DEFAULT RISK: WHICH IS TRUE WITH PRIVATE BONDS
RATHER THAN GOVT. BONDS( GILT EDGED SECURITIES)
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.
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.
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.
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
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




.
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 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.
END
ANY QUERIES MAY BE ADDRESSED TO
[email protected]