INTRODUCTION
TO CAPITAL BUDGETING 5-9
NET PRESENT VALUE
The concept of present value and its calculation should be familiar
to you from our discussion of the time value of money in Unit
Three. In this section, we extend the concept to show another way it
is used: to calculate the net present value of an investment.
Present Value of Cash Flows
Let's begin by reviewing the formula for calculating the present
value of a series of cash flows.
PV = CF
1
[ 1 / (1+R) ]
1
+ CF
2
[ 1 / (1+R) ]
2
+ ... + CF
T
[ 1 / (1+R) ]
T
Sum of a series
of discounted
cash flows
We discount the cash flow in the first period (CF
1
) for one period,
discount the cash flow received in the second period (CF
2
) for two
periods, and so forth until we have discounted all of the cash flows.
The present value is the sum of the discounted cash flows. We can
shorten this formula using the summation symbol
(pronounced
sigma) to represent the sum of a series.
T
PV =
CF
t
[ 1/ (1 + R) ]
t
t=1
These two equations are equal; they both represent the sum of a series
of discounted cash flows. In the shortened version, the T at
the top of the
means that we end with the T (last) cash flow, and the t
= 1 at the bottom means that we start the summation with the first cash
flow.