CHAPTER 4

CHAPTER 41TIME VALUE OF MONEY

CONTENTS

Time Value of Money- An introduction Compounding Discounting Annuity Future Value of Annuity Present Value of Annuity Continuous Compounding & Discounting Effective rate of Interest Equated Monthly Instalments

TIME VALUE OF MONEY

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CHAPTER 4

TIME VALUE OF MONEY (TVM)-AN INTRODUCTION

Value of money varies with time.

Not only is the amount of money important, equally important is the time when is it received or paid.

One of the most important concepts used in financial decision-making.

Applications include:

o Personal finance

o Capital budgeting

o Valuation

o Derivatives and risk management.

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CHAPTER 4

TIME VALUE OF MONEYAN INTRODUCTION

Value of money varies with time due to: • Presence of inflation

• Preference for current consumption

• Investment opportunities available

Does not account for the investment risks. Present cash flows are compounded to find

their Future value. Future Cash flows are discounted to arrive

at their Present value.

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CHAPTER 4

COMPOUNDING

Application of interest over interest is known as compounding.

Present cash flows, P are compounded to their future values, F for an estimated time period, n at an expected rate of interest, r.

Future value interest factor (FVIFr,n)

TIME VALUE OF MONEY

5

r) P x (F n 1nr) ( 1

CHAPTER 4

COMPOUNDING AND RATE

Effect of compounding increases with the increase in interest rates.

TIME VALUE OF MONEY

6

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 9Time (yrs)

Fu

ture

Val

ue

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

CHAPTER 4

COMPOUNDING AND TIME

Effect of compounding increases as the time lengthens.

TIME VALUE OF MONEY

7

(Rs. 1 at 12%)

1.1201.254

1.4051.574

1.7621.974

2.2112.476

2.773

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

Val

ue

CHAPTER 4

DISCOUNTING

Value of the money received or paid later is lesser than what it is today.

The process of reduction in value eliminating the interest that could have accrued is known as discounting.

Future cash flows (F) are discounted to their present values (P) for an estimated time period (n) at an expected rate of interest (r).

TIME VALUE OF MONEY

8

nr)(FP

1

1

CHAPTER 4

DISCOUNTING

Present value interest factor (PVIFr,n)

TIME VALUE OF MONEY

9

nr)(

1

1

CHAPTER 4

DISCOUNTING AND RATE

Severity of discounting increases with the increase in the rate of discounting.

TIME VALUE OF MONEY

10

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 9Time (yrs)

Pre

sen

t V

alu

e

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

CHAPTER 4

DISCOUNTING AND TIME

Effect of discounting increases as the time lengthens.

TIME VALUE OF MONEY

11

(Rs. 1 at 12%)

0.8930.797

0.7120.636

0.5670.507

0.4520.404

0.3610.322

0.00

0.100.20

0.300.40

0.50

0.60

0.70

0.800.90

1.00

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

Pre

sen

t V

alu

e

CHAPTER 4

ANNUITY

Equal amounts of cash flows spaced uniformly over time, normally a year.

Examples include:

• Premium of insurance policy

• EMI of a loan

• Deposits to a recurring deposit account.

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CHAPTER 4

FUTURE VALUE OF ANNUITY

Future value of annuity (FVAr, n) depends upon:• Amount of cash flow (i.e. annuity)• Rate of interest per period• Number of periods.

Future value interest factor for annuity

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r

r)( AnnuityFVA

n

r,n

11

r

r)(FVIFA

n

r,n

11

CHAPTER 4

PRESENT VALUE OF ANNUITY

Present value of annuity (PVA r,n) like its future value depends upon:• Amount of cash flow (i.e. annuity)• Rate of interest per period• Number of periods.

Present value interest factor for annuity

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14

n

n

nr rr

rAnnuityPVA

)1(

1)1(,

n

n

nr rr

rPVIFA

)1(

1)1(,

CHAPTER 4

CONTINUOUS COMPOUNDING

Value of compounding or discounting depends upon its frequency.

The value rises/falls exponentially in case of continuous compounding.

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-rtrt

rt

= F x ee

=F x e, Pesent Valu

eue, F=P x Future Val

1Pr

CHAPTER 4

EFFECTIVE RATE OF INTEREST

The effective rate may be found for a given annual rate (r)and frequency of compounding (m) in a year.

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11 =

m

m

rateInterest REffective

CHAPTER 4

EQUATED MONTHLY INSTALMENTS

Loans are repayable normally in Equated Monthly Installments (EMIs).

EMIs are a form of annuity.

Each EMI can be bifurcated into interest and principal repayment components.

The interest component of EMIs declines while the principal component increases with successive EMIs.

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CHAPTER 4

FINDING EMI IN ADVANCE

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CHAPTER 4

SEGREGATING EMIS

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CHAPTER 4