The Time Value of Money

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WHAT IS THE TIME VALUE OF MONEY.?
 A dollar received today is worth more than a dollar received
tomorrow
 This is because a dollar received today can be invested to
earn interest
 The amount of interest earned depends on the rate of
return that can be earned on the investment
 Time value of money quantifies the value of a dollar
through time

INTRODUCTION
 Understanding of Future Value and Present Value of money is
important for effective Financial Decision Making.
 Every Organization tries to invest in New Ideas, New Projects,
New Product or some Expansion and Modernization
Activities.
 It can be used to compare Investment alternatives and to solve
problems involving Loans, Mortgages, Leases, Savings and
Annuities.

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USES OF TIME VALUE OF MONEY
 Time Value of Money or TVM is a concept that
is used in all aspects of finance including:
 Bond valuation
 Stock valuation
 Accept/ Reject decisions for project management
 Financial analysis of firms
 And many others

SIMPLE INTEREST AND COMPOUND INTEREST
 What is the difference between simple interest
and compound interest.?
 Simple interest: Interest is earned only on the
principal amount.
 Compound interest: Interest is earned on both the
principal and accumulated interest of prior periods.
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EXAMPLE
 Suppose that you deposit Rs. 500 in your savings
account that earns 5% annual interest, How much
will you have in your account after two years
using
(a) simple interest and (b) compound interest?
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 Simple Interest
 Interest earned = 5% of Rs. 500
 = 500×.05 = Rs. 25 per year
 Total interest earned = Rs. 25×2 = Rs.50
 Balance in your savings account:
= Principal + accumulated interest
= Rs. 500 + Rs. 50 = Rs. 550
 Compound interest (assuming compounding once a year)
 Interest earned in Year 1 = 5% of Rs. 500 = Rs. 25
 Interest earned in Year 2 = 5% of (Rs. 500 + accumulated interest)
= 5% of (Rs. 500 + 25) = 525 ×.05 = Rs. 26.25
 Balance in your savings account:
= Principal + interest earned
= Rs. 500 + Rs. 25 + Rs.26.25
= Rs. 551.25
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TYPES OF TVM CALCULATIONS
 There are many types of TVM calculations
 The basic types will be covered in this review
module and include:
 Present Value of Single Amount
 Future Value of Single Amount
 Present and Future Value of Annuities

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BASIC RULES
 The following are simple rules that you should always use no
matter what type of TVM problem you are trying to solve:
1. Stop and think: Make sure you understand what the
problem is asking. You will get the wrong answer if you are
answering the wrong question.
2. Draw a representative timeline and label the cash flows and
time periods appropriately.
3. Write out the complete formula using symbols first and then
substitute the actual numbers to solve.
4. Check your answers using a calculator.

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FORMULAS
 Common formulas that are used in TVM
calculations:
 Present Value Of Single Amount:
PVIF= FV* 1 / (1+r)n
 Future Value Of Single Amount :
FVIF = PV * (1+r)n

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FORMULAS (CONTINUED)
 Present value of an annuity:
1
PVIFA =FV * 1- (1+r)n
r
 Future value of an annuity:
FVIFA = PV * (1+r)n -1
r

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VARIABLES
 Where,
 PV = Present Value
 PVIFA = Present Value of an Annuity
 FV = Future Value
 FVIFA = Future Value of an Annuity
 r = Rate of Return
 n = Number of Time Periods

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PRESENT VALUE OF SINGLE AMOUNT
 Present value calculations determine what the value of a cash
flow received in the future would be worth today (time 0)
 The process of finding a present value is called
“Discounting”
 The interest rate used to discount cash flows is generally
called the Discount Rate

PRESENT VALUES
Present Value
Value today of a
future cash
flow.
Discount Rate
Interest rate used
to compute
present values of
future cash flows.
Discount Factor
Present value of
a Rs.1 future
payment.

PRESENT VALUES
n
r)+(1
periodsnafterValueFuture
=PV
PV=ValuePresent

PRESENT VALUE
What will be the present value of Rs. 500 to be received
10 years from today if the discount rate is 6%.?
PV = Rs. 500 {1/(1+.06)10}
= Rs. 500 (1/1.791)
= Rs. 500 (.558)
= Rs. 279

FUTURE VALUE OF SINGLE AMOUNT
- Future Value is the value at some future time of a
present amount of money, or a series of payments,
evaluated at a given interest rate.
 Future Value can be increased by:
• Increasing number of years of compounding
• Increasing the interest or discount rate

FUTURE VALUES
Example - FV
What is the future value of Rs. 100 if interest is
compounded annually at a rate of 6% for 3 years.?
10.119.)06.1(100. 3
RsRsFV 
FV = Rs. 100 *(1+r)

PRESENT VALUE V/S FUTURE VALUE
 Present value factors are reciprocals of future value
factors
 Interest rates and future value are positively related
 Interest rates and present value are negatively
related
 Time period and future value are positively related
 Time period and present value are negatively
related

TIME LINES
 Show the timing of cash flows.
 Tick marks occur at the end of periods, so
Time 0 is today; Time 1 is the end of the first
period (year, month, etc.) or the beginning
of the second period.
CF0 CF1 CF3CF2
0 1 2 3
I%

TYPES OF ANNUITIES
Ordinary Annuity: Payments or receipts occur at
the end of each period.
Annuity Due: Payments or receipts occur at the
beginning of each period.
 An Annuity represents a series of equal payments
(or receipts) occurring over a specified number of
equidistant periods.

PRESENT VALUE OF AN ANNUITY
 Example:
 Mr. Alpesh deposit Rs. 2000 annually for 7 years and
this deposit compounded at 10%. Find the Future Value
Of Annuity.
FVIFA = PV x [(1+r)n -1/r]
= 2000 [(1+0.10)7 -1 / 0.10]
= 2000 [(1.1)7 – 1/ 0.10]
= 2000 x 9.4872
= 18, 974

FUTURE VALUE OF AN ANNUITY
 Example:
 Mr. Anil wants to purchase an apartment costing Rs. 30
Lakes. His employer is willing to give loan at 10% for 5
years. Calculate amount of installment paid every year.
PVIFA = A x [1- 1/(1+r)n/r]
30,00,000 = A x [1- 1/(1+0.10)5/0.10]
30,00,000 = A x [1- 1/(1.1)5/0.10]
30,00,000 = A x [3.791]
A = 30,00,000/ 3.791
= 7,91,348

The Time Value of Money

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