Lesson Corporate Finance: Present Value -Basics

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This Lesson (Corporate Finance: Present Value -Basics) was created by by Shruti_Mishra(0)

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

Lets start the lesson with a simple question. Suppose I give you an option to take $1000 from me today or two years from now. Which one will you choose? You would of course choose today. On the other hand, suppose I give you an option to take $1000 from me today or take $2000 two years from now. Now you might be confused. In the first case, the value of money today seems obviously more. Anything you can do with $1000 two years from now, you can also do by taking the money now and keeping it for two years. In the meanwhile you can also invest the same amount and get back more than $1000 in two years. The option for getting the money today is thus more valuable. In the second case the choice is however not so obvious.

Simply put, <A HREF=Present_value.wikipedia>Present Value </A>(PV) is the value today of a future <A HREF=Cash_flow.wikipedia>cash flow</A>. Money today is more valuable than money 5 years from now because it can be invested for the 5 years period and interest can be earned. The cost of waiting for the money is the <A HREF=Interest.wikipedia>interest</A> lost in that period. The present value of an amount in future is the equivalent amount today, which will yield the given amount in future, on being invested.

For e.g. if the interest rate is 10% per annum, $1000 invested today will become $1100 one year from now. Thus the present value of getting $1100 after a year is $1000. We can thus calculate the PV simply by reversing the <A HREF=Compound_interest.wikipedia>compound interest</A> calculation. The formula for calculating the total amount from a compound interest is

<center>
{{{Amount = Principal * (1 + Rate)^Time}}}
</center>
<br>
Thus the present value of the future amount will be

<center>
{{{PV = Amount/(1 + Rate)^Time}}}
</center>
<br>
Where Rate is the interest rate for the considered time period.

For calculating the PV of multiple cash flows at different times, we can simply sum the PVs of the individual cash flows. Thus the PV in this case would be

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{{{PV = sum( Ci/(1+r)^i, i=1, T )}}}
</center>
where Ci is the cash flow at time i and r is the applicable interest rate. The method to get the applicable interest rate can be seen in the lesson: <A HREF="PV_rate2use.lesson">Calculating PV: Which interest rate to use</A>.

Also see: <A HREF="PV_rate2use.lesson">Calculating PV: Which interest rate to use</A>, <A HREF="NPV.lesson">Concept of Net Present Value and its usage</A>.