TIME VALUE OF MONEY OF FINANCIAL MANAGEMENT

2. TIME VALUE OF MONEY
TOPIC :

3. THETIMEVALUE OF MONEY
Would you prefer to
have 10,000 rupees now or
10,000 rupees 2 years
from now?
Of course, we would all
prefer the money now!
This illustrates that there
is an inherent monetary
value attached to time.

4. TIMEVALUE OF MONEY
 Let ‘s assume someone is offering you rupees10,000 today or
rupees10,000 after 2 years.What would you prefer?
You would select rupees 10,000 today
because money today is worth more
than money a year later. But how?
Deposit in an interest bearing account
at 5% for next two years.You will have
10,000*1.05*1.05 = rupees11,025

5. WHYTIMEVALUE
A rupee today is more valuable than a rupee a year hence.
Why ?
• First, a rupee can be invested and earn interest over time, giving it
potential earning power.
•Money is subject to inflation, eating away at the spending power of
the currency over time, making it worth less in the future.
•Finally, there is always the risk of not actually receiving the money in
the future - if you hold the money now, there is no risk of this
happening.
Many financial problems involve cash flows occurring at different
points of time. For evaluating such cash flows, an explicit
consideration of time value of money is required

6. USES OFTIMEVALUE OF MONEY
 TimeValue of Money, orTVM, is a concept that is
used in all aspects of finance including:
 Loans
 Savings/ Retirement planning
 Investments
 Bond valuation
 Stock valuation
 Accept/reject decisions for project management
 Financial analysis of firms
 And many others!

7. FUTUREVALUE OF A LUMP SUM
You can think of future value as the opposite
of present value
Future value determines the amount that a
sum of money invested today will grow to in
a given period of time
The process of finding a future value is
called “compounding” (hint: it gets larger)

8. 1. EXAMPLE
 Suppose you put 5000 in bank for one year at 3%
interest rate per year. What is the value of your
money in one year?
 Interest = 5000(.03) = 150
 Value in one year = principal + interest
= 5000+5000(.03) = 5000 + 150 = 5150
= 5000(1 + .03) = 5150
 Suppose you leave the money in for another year.
How much will you have two years from now?
 FV = [5000(1.03)](1.03)
= 5000(1.03)2 = 5304.5

9. EXAMPLE (CONT..)
 1 year:Value = 5000(1+.03)
= 5000(1+.03)1
 2 years:Value = [5000(1+.03)](1+.03)
= 5000(1+.03)2
 3 years:
Value = {[5000(1+.03)](1+.03)} (1+.03)
= 5000(1+.03)3
 4 years:Value =
{{[5000(1+.03)](1+.03)} (1+.03)} (1+.03)
= 5000(1+.03)4

10. BASIC DEFINITIONS
FV = PV(1 + r)t
 PresentValue – earlier money on a time line
 FutureValue – later money on a time line
 Interest rate – “exchange rate” between earlier money
and later money
 Time- t
 Time value of money: A rupee in hand today is worth
more than a rupee promised at some time in the
future.

11. EXAMPLE OF FV OF A LUMP SUM
 How much money will you have in 5 years if you invest 1000
today at a 10% rate of return?
1. Draw a timeline
0 1 2 3
1000 ?
i = 10%
4 5

12. EFFECTS OF COMPOUNDING
 Compounding: the process of accumulating interest
over time to earn more interest.
 Compound interest: interest earned on both the initial
principal and the interest earned from prior periods.
 Compound interest (total interest)
=Simple interest+Interest on interest
 Simple interest: interest on principal

13. MULTIPLE COMPOUNDING
TECHNIQUE
 When interest has to be compounded more than
once in a year then this method is used.
 For ex- banks may allow interest on quarterly basis
or a company may allow compounding of interest
twice a year on 30th June and 31st December every
year.The future value of money can be calculated
as below.
 FV=PV(1+r/m)*mt ;m-no. of times of
compounding per year

15. PRESENTVALUE OF A LUMP SUM
 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” (hint: it gets smaller)
 The interest rate used to discount cash flows is
generally called the discount rate.
 Present value for future cost over multiple years
can be done by taking the summation of individual
years.

16. EXAMPLE OF PV OF A LUMP SUM
 How much would 100 rupees received five years from now be worth today if
the current interest rate is 10%?
1. Draw a timeline
The arrow represents the flow of money and the
numbers under the timeline represent the time period.
Note that time period zero is today.
0 1 2 3 4 5
100?
i = 10%

18. EXAMPLE OF PV OF A LUMP SUM
2. Write out the formula using symbols:
PV = FV/ (1+r)t
3. Insert the appropriate numbers:
PV = 100 / (1 + .1)5
4. Solve the formula:
PV = 62.09
5. Check using a financial calculator:
FV = 100
n = 5
i = 10%
PV = ?

19. GRAPH OF COMPOUNDING &
DISCOUNTING