Chapter 4 Ppt[1]

8/2/2019 Chapter 4 Ppt[1]

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CHAPTER 4

TIME VALUE OF MONEY


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Chapter 4Time Value of Money

2

CONTENTS

Introduction

Basis of Time Value Compounding & Discounting Discounting & Present Value

Future Value of Annuity Present Value of Annuity Periodicity of Compounding &

discounting

Continuous Compounding & Discounting Equated Monthly Instalments

Finding EMIs Segregating EMIs into Interest and Principal


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TI ME VALUE OF MONEY

Time value of money is probably one

of the most important concepts thatforms the basis of decision making inalmost all areas of finance.

The applications range from personalfinance areas to corporate finance likecapital budgeting and valuation andderivatives and risk management.

The time value of money states thatnot only the amount of money isimportant but when is it received or

paid is equally important.


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TI ME VALUE OF MONEY

The reason for the time value of moneyis that it has capacity to increase invalue even when it is not put to anyuse.

3 causes creating time value of money. Presence of inflation, Preference for current consumption, and

Investment opportunities availableTime value of money does not account

for the risk associated with investment


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COMPOUNDI NG

Interest rate prevailing in the market

form the basis of finding the timevalue of money.The value of money increases with

time due to application of interest.It grows at a higher rate when

interest is applied on the interest.

Application of interest over interest isknown as compounding.

Future Value F = P x (1+r)n


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COMPOUNDI NG AND RATE

Effect of compounding/discounting is more

pronounced as time extends or the discountrate increases

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

1 2 3 4 5 6 7 8 9

Time (yrs)

FutureValue

at 5% at 10% at 15% at 20% at 25%


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COMPOUNDI NG AND TIME

Compounding/Discounting effect increases asthe time lengthens

(Rs. 1 at 12%)

1.1201.254

1.4051.574

1.762

1.974

2.211

2.4762.773

3.106

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

1 2 3 4 5 6 7 8 9 Time (yrs)

Fu

ture

Value


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DI SCOUNTI NG

Value of the money received or paid

later is less than what it is today bythe amount of interest for the time.The process of reduction in value

eliminating the interest that couldhave accrued is known as discounting.

n)r+1(

F

=P


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DI SCOUNTI NG AND RATE

Effect of discounting is more pronounced astime extends or the discount rate increases

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1 2 3 4 5 6 7 8 9

Time (yrs)

PresentValue

at 5% at 10% at 15% at 20% at 25%


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DI SCOUNTI NG AND TI ME

Compounding/Discounting effect increases asthe time lengthens

(Rs. 1 at 12%)

0.893

0.797

0.712

0.636

0.5670.507

0.4520.404

0.3610.322

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1 2 3 4 5 6 7 8 9

Time (yrs)

Pr

esentValue


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FUTURE VALUE OF ANNUI TY

Future value is simply the amount of

principal and the interest for a given time. Annuities refer to the equal amounts of cash

flows spaced uniformly over time, normally

a year. The value of equal amount of receivable or

payable at evenly spaced intervals of time

at a given rate of interest is called futurevalue of annuity.

n

1

nr)+(1=n)(r,FVA1,Rs.ofAnnuityofValueFuture


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FUTURE VALUE OF ANNUI TY

Mr. Warren Buffet decided to donate 85% of his $ 44 billionfortune to Bill & Melinda Gatess Foundation in instalments of $ 1.5

billion every year. Mr. Buffet stipulated that the annual paymentsmust be distributed to the beneficiaries within a year before thesubsequent payment is made. If Mr. Buffet did not stipulate thecondition and instead Gatess Foundation decided to invest annualcontribution at 8% and spend the aggregate sum only upon

receiving the entire contribution promised, what amount would thefoundation have at the end?

The donation of Mr. Warren Buffet would last for next 25 years(0.85 x 44/1.5). If Gatess Foundation invested $1.5 billion every

year for next 25 years at 8% the value received after 25 yearswould be

= $1.5 billion x FV of Annuity (8%, 25 yrs)

= 1.5 x 73.106 = $109.659 billion

r

1-r)+(1=n)FVA(r,years,nfo rr%a tFactorAnnuityValueFuture

n


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PRESENT VALUE OF ANNUI TY

Similarly for a sum receivable or payable at

a future date can be equated with the equalamounts evenly spaced over time at aknown rate of interest.

n

1nr)+(1

1=n)(r,PVA1,Rs.ofAnnuityofValuePresent

n

n

r)r(1

1-r)+(1=n)PVA(r,

years,nforr%atFactorAnnuityValuePresent

+


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PRESENT VALUE OF ANNUI TY

We found that Mr. Warren Buffet, decided to donate 85%

of his $ 44 billion fortune to Bill & Melinda GatessFoundation in instalments of $1.5 billion every year. Doyou think that Mr. Warren Buffet has really donated 85% ofthe wealth? If not what is the % of wealth is being reallydonated by him assuming that he earns 8% on his wealth?

The donation of Mr. Warren Buffet would last for next 25years (0.85 x 44/1.5).

If Gatess Foundation invested $1.5 billion every year fornext 25 years at 8% the value received after 25 yearswould be

= $1.5 billion x PV of Annuity (8%, 25 yrs)= 1.5 x 10.6748 = $16.0122 billion

The fraction of present wealth being donated= 16.0122/44= 36.39%


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CONTI NUOUS COMPOUNDI NG

Value of compounding or discountingchanges depending upon how often itis done. The value rises/falls

exponentially if we assume continuouscompounding.

rt-

rt

rt

exF=e

1xF=PValue,Present

exP=FValue,Future


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EFFECTI VE RATE OF I NTEREST

The effective rate may be found for agiven annual rate of r and m numberof compounding in a year by

For continuous compounding the

effective rate of interest may be foundfrom the expression

er 1.

1-}mr+1{=RateInterestEffective m


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EQUATED MONTHLY

I NSTALMENTS

Loans are repayable normally in Equated

Monthly Installments (EMIs), the computationof which uses the concept of time value ofmoney and annuity factors.

Each EMI can be bifurcated into interest andprincipal repayment. The proportion ofinterest declines and amount towardsprincipal increases with successive EMIs in

such a manner that the aggregate of the tworemains same.


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FI NDING EMI I N ADVANCE


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SEGREGATI NG EMIs

Principal Amount (Rs.) 20,000 Interest rate (%) 10%

Period (years) 3 EMI (Rs. Per month) 640.01

Instalment No.

Period

Cash Flow for

the period

Discount

Factor

Present

Value

Principal

outstandingat the

beginning of

period

Interest

Amount

Principal

Repaid

- - 19,359.99 1.0000 -19,359.99

1 640.01 0.9917 634.72 19,359.99 161.33 478.68

2 640.01 0.9835 629.48 18,881.31 157.34 482.67

3 640.01 0.9754 624.27 18,398.65 153.32 486.69

4 640.01 0.9673 619.11 17,911.96 149.27 490.74

5 640.01 0.9594 614.00 17,421.21 145.18 494.83

6 640.01 0.9514 608.92 16,926.38 141.05 498.96

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