Lesson Corporate Finance: Calculating PV - Which interest rate to use

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

One important input which needs to be given as an input for calculating the <A HREF=lesson_PV.lesson>Present Value </A>(PV) of a future cash flow is the <A HREF=interest_rate.lesson>interest rate</A> with which to discount the cash flows. This is known as the <A HREF=discount_rate.wikipedia>discount rate</A>. Let's understand it this way. Suppose I have $1000 today, which I invest in 2 different ways offering me 6% and 9% interest per annum respectively. After a year, I will have $1060 from the first investment and $1090 from the second one. The extra money I earn as interest in the second one is due to the extra <A HREF=Risk.wikipedia>risk</A> associated with it, compared to the first transaction.

Every time we invest money, we take some <A HREF=Risk.wikipedia>risk</A> of not getting the money back. This <A HREF=Risk.wikipedia>risk</A> is nearly zero in case of government bonds and savings accounts of government banks. The interest rate offered by them is thus called <A HREF=Risk_Free_Interest.wikipedia>Risk Free Interest</A>. However, other merchants offer a higher rate of interest, because of this risk of not getting the money back. The<A HREF=expected_value.wikipedia> expected value</A> of interest earned after taking into account the probability of default would be the same as that earned with risk free investment.

The same concept applies when we need to find the PV of a given future <A HREF=cash_flow.wikipedia>cash flow</A>. Given a future cash flow, we need to discount it with the discount rate applicable to the risk associated with the cash flow. Thus if the cash flow is certain, we discount it with risk free interest rate. If the cash flow has certain uncertainty associated, then it is discounted at a higher rate appropriate to the risk profile.

Lets take an example now. I will receive two amounts in the future: $2000 after 1 year and $2100 after 2 years. The discount rates applicable to the two cash flows are 12% and 10% respectively. Which cash flow has a higher PV?

Solution: The PV of first cash flow would be 
<center>
{{{PV1 = 2000/(1+12/100)^1}}} = 1785.714
</center>
and the PV of second cash flow will be 
<center>
{{{PV2 = 2100/(1+10/100)^2}}} = 1735.537
</center>
Thus the first cash flow has a higher PV. To understand the net benefit from a project, we need to understand the <A HREF="NPV.lesson">Concept of Net Present Value and its usage</A>.