Untitled-29

(^38) Financial Management
Still this leaves one problem unanswered: If the projects have different time spans
(which could be as far apart as 50 years or more) how do we use the results that we
get from here to compare. It becomes very difficult. Also we cannot be too sure of the
discounting rates and cash flows so getting comparable values would be difficult to say
the least. To solve this problem we solve for the present value.
Present Value
When we solve for the present value, instead of compounding the cash flows to the
future, we discount the future cash flows to the present value to match with the
investments that we are making today. Bringing the values to present serves two
purposes:

1. The comparison between the projects become easier as the values of returns of
   both are as of today, and


2. We can compare the earnings from the future with the investment we are making
   today to get an idea of whether we are making any profit from the investment or
   not.
   For calculating the present value we need two things, one, the discount rate (or the
   opportunity cost of capital) and two, the formula.
   The present value of a lump sum is just the reverse of the formula of the compound
   value of the lump sum:

in

FutureValue

esentValue

( 1 )

Pr

+

=

Or to use the tables the change would be:

Present Value = Future Value * (Present Value Interest Factor n,i)

where n = no of time periods and i is the interest rate.

Let us look at an example of how we calculate the future value:

Example

Rs.2,00,000 is the amount that you require after 20 years for your retirement. How

much should you invest now at 5% per annum compounded annually?

Solution

Here i = 0.05, FV = 2,00,000, and n = 20. Putting it in the formula we get:

( 1 0. 05 )^20

200000

Pr

+

esentValue=