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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
2
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.
TIME VALUE OF MONEY
3
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.
TIME VALUE OF MONEY
4
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.
TIME VALUE OF MONEY
12
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
TIME VALUE OF MONEY
13
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
TIME VALUE OF MONEY
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.
TIME VALUE OF MONEY
15
-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.
TIME VALUE OF MONEY
16
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.
TIME VALUE OF MONEY
17
CHAPTER 4
FINDING EMI IN ADVANCE
TIME VALUE OF MONEY
18
CHAPTER 4
SEGREGATING EMIS
TIME VALUE OF MONEY
19
CHAPTER 4