Time value of money

2. OBJECTIVE
1. Understand what is meant by "the time value of
money."
2. Understand the relationship between present and
future value.
3. Describe how the interest rate can be used to adjust
the value of cash flows – both forward and backward
– to a single point in time.
4. Calculate both the future and present value of: (a) a
single amount; (b) a stream of equal cash flows (an
annuity); and (c) a stream of mixed cash flows.
5. Use interest factor tables and understand how they
provide a shortcut to calculating present and future
values.

3. Introduction
 Time value of money means value of a unit of money is
different in different time periods.
 Also known as ‘Time preference of money’ as a rupee
today is more valuable than a rupee hence.

4. Reasons for Time preference for
money
 Uncertainty
 Preference for present consumption
 Investment opportunities
 Inflation

5.  Would an investor want Rs. 100 today or after one year?
 Cash flows occurring in different time periods are not
comparable.
 It is necessary to adjust cash flows for their differences in
timing and risk.
 Example : If preference rate =10 percent
 An investor can invest if Rs. 100 if he is offered Rs 110 after one
year.
 Rs 110 is the future value of Rs 100 today at 10% interest rate.
 Also, Rs 100 today is the present value of Rs 110 after a year at
10% interest rate.
 If the investor gets less than Rs. 110 then he will not invest.
Anything above Rs. 110 is favorable.

6. Techniques
 To have logical and meaningful comparisons between cash
flows that occur in different time periods it is necessary to
convert the sums of money to a common point in time.
 There are two techniques for doing this
Compounding Technique
• To determine the future value of a current
amount.
Discounting Technique
• To determine the present value of a future
amount.

7. A. Compounding Technique or
Future Value
i)Future value of a single sum
e.g Mr. x invests Rs. 1000 in a saving bank account at 5%
interest compounded annually.
Year 1 2 3
Beginning
amount
1000 1050 1102.50
Amount of
interest
50 52.5 55.125
Amount at
the end
1050 1102.50 1157.625

8. General future value formula
A= P (1+r)t
FVn = PV (1+k)n
Where FVn = future value n years hence
PV = present value
k = interest rate per year
n = number of year for which compounding is done.
The factor (1+k)n is referred to as the compounding factor or the
Future Value Interest Factor (FVIFk,n)

10. Increased frequency of Compounding
e.g if Mr. X has invested Rs. 1,000 in a 2 year time deposit
bank scheme which offers 6% interest per annum
compounded semi-annually, then interest earned is as
shown in table
year 6
months
1 year 18 months 2 years
Beginning
amount
1000 1030 1060.90 1092.73
Amount of
interest
30 30.90 31.83 32.78
Amount at
the end
1030 1060.90 1092.73 1125.51

11. FV of a amount if compounded m times in a year
Formula:
FVn = PV (1 + k ) m*n
m
so in above example,
FVn = 1000 ( 1 + 6 ) 2*2
2
= 1000 (FV IF3, 4 )
= 1000 ( 1.126)
= 1126

12. iii)Future Value of an Annuity
Annuity refers to periodic flow of equal amount.
e.g Mr. Ram deposits Rs 2000 at the end of every year for five years in to his
account. Interest is being compounded annually at a rate of 5%.
Formula :
FVAn = A (1+k) n - 1
K
Where FVAn = future value of an annuity which has a duration of n Period
A = Constant periodic flow
K = Interest rate per period
n = duration of the annuity
The term (1+k) n - 1 is referred to as the future value interest factor for
K
an annuity . i.e. (FVIFAn)
By referring to tale for FVIF the value of
FVAn = 2ooo * FVIFA( 5%,5Y)
=2ooo * 5.526 = Rs 11052

13. B. Discounting Technique or
Present Value
i)Present value of a single future amount
e.g Suppose someone gives you Rs.1000 , six year hence. What is the
present value of this amount if the interest rate is 10%?
Formula :
PV = FVn
(1 + k )n
where 1 / ( 1+ k)n is Present Value Interest Factor (PVIF)
Thus PV = 1000 * PVIF( 10%, 6Y)
= 1000 * .5645
=564.50

14. ii)Present / Discounted value of a series of cash
flow
e.g If time value of money is 10 %, find the present value
of following series of Payments?
Rs. 500, Rs. 1000, Rs. 1500 , Rs. 2000, Rs. 2500 for 1st ,
2nd , 3rd ,4th ,and 5th year respectively.
Year End Cash Flows PVIF Present
Value
1 500 0.909 454.50
2 1000 0.826 826.00
3 1500 0.751 1126.50
4 2000 0.683 1366.00
5 2500 0.621 1552.50
Present value 5325.50

15. iii) Present Value of an Annuity
e.g. Present value of a 4 year annuity of Rs10000
discounted at 10%
Instead of using long method like previous example we can
use Present Value Interest Factor of an annuity
( PVIFA) Table.
PVA4 = 10000(PVIFA10%,4)
= 10000(3.170)
= 31700

16.  The time preference for money is generally expressed
by an interest rate. This rate will be positive even in the
absence of any risk. It may be therefore called the risk-
free rate.
 An investor requires compensation for assuming risk,
which is called risk premium.
 The investor’s required rate of return is:
Risk-free rate + Risk premium.
Required Rate of Return