Time value of Money Compounding and Discounting Techniques

1. S
Time value of Money
Prepared by:
Arvinder Kaur
Faculty of management

2. Concept of Time value of
Money
S A RUPEE TODAY IS WORTH MORE THAN A RUPEE
TOMORROW.
S One of the most fundamental concepts in finance is that
money has a time value, i.e. , Money in hand today is
worth more than money that is expected to be received in
the future.
S The REASON is straightforward, i.e. , A rupee that you
receive today can be invested such that you will have
more than a rupee at some future time.

3. Example
S ‘A’ wins a prize contest and he has got two options:
S Option 1: Receive Rupees 10,000 now.
S Option 2: Receive Rupees 10,000 in three years.
S WHICH OPTION SHOULD ‘A’ CHOOSE ?

4. Answer of Example
S If ‘A’ is a rational person he would choose to receive
Rupees 10,000 NOW.
S After all, three years is a long time to wait. Why would
any Rational person defer payment into the future when
he could have the same amount of money now?

5. S For most of us, taking the money in the present is just
natural. So at the most basic level, the time value of
money demonstrates the concept of time value as:
“A RUPEE TODAY IS WORTH MORE THAN A RUPEE
TOMORROW.”
Time value of money results somewhere from the concept
of Interest.

6. Reasons Behind the Concept
of Time Value of money
S There are four primary reasons why a rupee received in
the future is worth less than a rupee received now:
 INFLATION
 INTEREST EARNINGS
 UNCERTAIN FUTURE
 HUMAN PREFERENCES

7. INFLATION
S Presence of positive rate of inflation reduce the PURCHASING
POWER of rupees through time.
S FOR EXAMPLE:
 One year back ONE apple was available for Rupees 10 and a
dozen of apple cost Rupees 120.
 Now one apple costs Rupees 15 and a dozen of apples cost
rupees 180.
 Now with Rupees 120 we can buy only 8 apples instead of 12
apples.

8. INTEREST EARNINGS
S A rupee today is worth more today than in the future
because of the opportunity cost of the lost earnings, i.e. ,
It could have been invested and earned a return between
today and a point of time.

9. UNCERTAIN FUTURE
S Thirdly, all future values are in some sense only
PROMISES and contain some uncertainty about their
occurrence.
S As a result of the risk of default or non performance of an
investment, a rupee in hand is worth more than an
expected rupee in future.

10. HUMAN PREFERENCES
S Finally, human preferences typically involve impatience or
the preference to consume goods and services now
rather than in future.

11. USES OF TIME VALUE OF
MONEY
S The concept of time value of money is used to calculate
the values of various cash flows such as:
 Future value of cash flow (Compounding technique)
 Present value of cash flow (Discounting technique)

12. CALCULLATION OF FUTURE
VALUE OF A LUMP SUM
S FUTURE VALUE of a lump sum refers to the value after
a certain period of time at a given rate of interest.
S FORMULA:
FUTURE CASH FLOW = PV * (1+R)t
Here, ‘PV’ refers to Present value of cash flow, ‘R’ refers to
the rate of interest and ‘t’ refers to the numbers of years of
investment.

13. Example
S QUESTION: Find maturity value of Rupees 10,000 which has
been given on 15% interest for five years, while the required
rate of return is 10%.
S SOLUTION:
FUTURE VALUE = PV * (1+r)t
= 10,000 * (1+0.15)5
= 10,000 * (1.15)5
= 10,000 * 2.011357
FUTURE VALUE = Rupees 20,113.57

14. Question For Practice
S Question: Mr. B wants to have a sum of Rupees 5,800
after 2 years. He has two alternative investment options
to select one for his investment objective.
S Option 1: Rate of interest @ 8% p.a.
S Option 2: Rate of interest @ 6% p.a.
S If Mr. B has Rupees 5,000 to invest for 2 years, which
investment option will meet his objective?

15. Compounded value of an
Annuity
S An annuity is a series o equal payments lasting for some
specified duration. The premium payments of life insurance
company are annuity payments.
S Here, FUTURE VALUE = CASH FLOW * (ACFi,n)
S ACF refers to annuity compound factor taken from annuity
compound factor table.

16. CALCULATION OF PRESENT
VALUE
S PRESENT VALUE (PV) refers to the current worth of a
future sum of money or stream of cash flows given a
specified rate of return.
S FORMULA:
PV = FUTURE CASH FLOW
(1+r)t

17. Example
S Question: Find present value of Rupees 80,000 to be
received after five years when required rate of return is 10%
S Solution:
PV = Cash flow/(1+r)t
= 80,000/(1+0.10)5
= 80,000/1.61051
= Rupees 49,674

18. Present value of a cash flow
stream
S It refers to the present value of a series of cash flow occurred
in different years.
S For Example: Find the present value of a series of cash flows
occurred in different years when the required rate of return is
10%
PERIOD FUTURE CASH FLOWS
1 RUPEES 80,000
2 RUPEES 70,000
3 RUPEES 50,000
4 RUPEES 30,000

19. SOLUTION
S As we know, PV = Future cash flow/(1+r)t
S PV = {80,000/(1+0.10)1} + {70,000/(1+0.10)2} + {50,000/(1+0.10)3}
+ {30,000/(1+0.10)4}
= (80,000/1.10) + (70,000/1.21) + (50,000/1.331) +
(30,000/1.4641)
= 72727 + 57851 + 37566 +20490
= Rupees 1,88,634

20. Present value of an annuity
S An annuity is a series of equal payments lasting for some
specific period.
S PV = Future cash flow * (ADFi,n)
S ADF refers to annuity discount factor taken from annuity
discount factor table.

21. NET PRESENT VALUE
S NPV is the difference between the sum total of Present values of
all the future cash inflows and outflows.
S NPV = ( PRESENT VALUE OF CASH INFLOWS) – ( PRESENT
VALUES OF CASH OUTFLOWS)
S HERE, CASH INFLOW = CASH INFLOW + SALE OF SCRAP +
INFLOW FROM WORKING CAPITAL
S CASH OUTFLOW = INITIAL INVESTMENT + ADDITIONAL
OUTFLOW

22. QUESTION FOR PRACTICE
S A Co. has invested Rupees 8,00,000 in a business and expected a
series of cash flow as per under given details:
S At the end of the fourth year Co. made a sale of scrap for Rupees
2,40,000 and realized rupees 30,000 from working capital.
S Find NPV if the required rate of return is 10%.
YEAR CASH INFLOW ADDITIONAL
CASH OUTLOW
1 RUPEES 2,50,000 RUPEES NIL
2 RUPEES 4,20,000 RUPEES
1,05,000
3 RUPEES 3,50,000 RUPEES NIL
4 RUPEES 2,50,000 RUPEES 10,000

23. Thank you