Page 28 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Unit 2: Time Value of Money

Present value after ‘n’ Years: Notes
Formula:
A
PV =
(1 + i) n
Where,
PV = principal amount the investor is willing to forego at present

i = Interest rate.
A = amount at the end of the period ‘n’.
n = Number of years.

With this formula, we can directly calculate the amount; any depositor would be willing to
sacrifice at present, with a time preference rate or discount rate of x%.

Example: If Mr. X, depositor, expects to get ` 100 after one year, at the rate of 10%, the
amount he will have to forego at present can be calculated as follows :

PV = A
( 1i ) + n
100
PV = =` 90.90
(1.10+ )
Similarly, the present value of an amount of inflow at the end of ‘n’ years can be computed.

2.4.1 Present Value of a Series of Cash Flows

In a business situation, it is very natural that returns received by a firm are spread over a number
of years. An investment made now may fetch returns a certain time period. Every businessman
will like to know whether it is worthwhile to invest or forego a certain sum now, in anticipating
of returns he expects to earn over a number of years. In order to take this decision he needs to
equate the total anticipated future returns, to the present sum he is going to sacrifice. The
estimate of the present value of future series of returns, the present value of each expected
inflow will be calculated.
The present value of series of cash flows can be represented by the following:

C C C C
PV = 1 1 + 2 2 + 3 3 + n n
(1 i+ ) (1i+ ) (1i+ ) (1i+ )
n C
PV = ∑ t n
+
T1 (1i )
=
Where,
PV = sum of individual present values of each cash flow : C , C , C ..........
1 2 3
C = Cash flows after period 1,2,3………….n.
n
i = Discounting rate.
However, a project may involve a series of cash inflows and outflows. The computation of the
present value of inflows by the above equation is a tedious problem. Hence, present value Table
is used.

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