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