This document discusses the concept of time value of money, which refers to the idea that money received or paid in the future is worth less than the same amount today. It covers key concepts like compounding, discounting, annuities, and effective interest rates. Compounding means applying interest over interest to calculate future values, while discounting reduces future values to calculate present values. Annuities refer to equal periodic payments, and formulas are provided to calculate future and present values of annuities based on interest rates and time periods.

1. CHAPTER 4
CHAPTER 41TIME VALUE OF MONEY

2. 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
2
CHAPTER 4

3. 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.
TIME VALUE OF MONEY
3
CHAPTER 4

4. TIME VALUE OF MONEY
AN 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.
TIME VALUE OF MONEY
4
CHAPTER 4

5. 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
+= 1
n
r)( += 1
CHAPTER 4

6. 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 9
Time (yrs)
FutureValue
at 5% at 10% at 15% at 20% at 25%
CHAPTER 4

7. COMPOUNDING AND
TIME
 Effect of compounding increases as the time
lengthens.
TIME VALUE OF MONEY
7
(Rs. 1 at 12%)
1.120
1.254
1.405
1.574
1.762
1.974
2.211
2.476
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)
FutureValue
CHAPTER 4

8. 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
n
r)(
FP
+
×=
1
1
CHAPTER 4

9. DISCOUNTING
 Present value interest factor (PVIFr,n)
TIME VALUE OF MONEY
9
n
r)( +
=
1
1
CHAPTER 4

10. 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 9
Time (yrs)
PresentValue
at 5% at 10% at 15% at 20% at 25%
CHAPTER 4

11. DISCOUNTING AND TIME
 Effect of discounting increases as the
time lengthens.
TIME VALUE OF MONEY
11
(Rs. 1 at 12%)
0.893
0.797
0.712
0.636
0.567
0.507
0.452
0.404
0.361
0.322
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)
PresentValue
CHAPTER 4

12. 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.
TIME VALUE OF MONEY
12
CHAPTER 4

13. 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
TIME VALUE OF MONEY
13
r
r)(
AnnuityFVA
n
r,n
11 −+
×=
r
r)(
FVIFA
n
r,n
11 −+
=
CHAPTER 4

14. 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
TIME VALUE OF MONEY
14
n
n
nr
rr
r
AnnuityPVA
)1(
1)1(
,
+
−+
×=
n
n
nr
rr
r
PVIFA
)1(
1)1(
,
+
−+
=
CHAPTER 4

15. CONTINUOUS
COMPOUNDING
 Value of compounding or discounting
depends upon its frequency.
 The value rises/falls exponentially in case
of continuous compounding.
TIME VALUE OF MONEY
15
-rt
rt
rt
= F x e
e
=F xe, Pesent Valu
eue, F=P xFuture Val
1
Pr
CHAPTER 4

16. EFFECTIVE RATE OF
INTEREST
 The effective rate may be found for a
given annual rate (r)and frequency of
compounding (m) in a year.
TIME VALUE OF MONEY
16
11= −














+
m
m
r
ateInterest REffective
CHAPTER 4

17. 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.
TIME VALUE OF MONEY
17
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18. FINDING EMI IN ADVANCE
TIME VALUE OF MONEY
18
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19. SEGREGATING EMIS
TIME VALUE OF MONEY
19
CHAPTER 4