Corporate Finance

Time Value of Money 
 47

PV = 2

(1.08)

1500

.1 08

1000

500 ++

Notice that Rs 500 is in current rupees. So we are not finding its present value.

PV = Rs 2711.50

Try finding the present value of this series if the cash flow were to occur at the beginning of the year.

Types of Cash Flows

Cash flows can exhibit different patterns. In the given example, the periodic amounts are different and the
series had a finite life. A series of periodic flows of equal amounts is called an Annuity and a series of
periodic flows of equal amounts but with an infinite life is called perpetuity. Thus investing or receiving
Rs 500 as dividend forever is perpetuity.

Future Value of an Annuity

Consider this example: You require Rs 250,000 at the end of 5 years to buy a car. Assume that this is
the price that would prevail 5 years from now, for the model you have in mind. You wish to invest a
fixed (constant) sum every year to accumulate Rs 250,000 at the end of 5 years. The series of cash flows
would be:

The future value of an annuity for a period of ‘n’ years, at ‘r’ rate of interest, is given by:

FVAn= ⎥

⎦

⎤

⎢

⎣

⎡ −+

r

r

A

n 1) 1(

(3)

where A = amount invested at the end of every year for ‘n’ years,

r = rate of interest in decimal form, and

n = time period in years.