Previously, we talked about future value, where we saw that if you invest 100 dollars today, you
will get more money in the future.
Correspondingly, if someone promises to give you hundred dollars in the future, the present value
of that is less than hundred dollars.
In this lecture, we are going to discuss the concept behind present value.
In this lecture and throughout this course will denote present value by Bebe.
Now, I can say that Bibi is that initial sum of money, which, if I invest today at the best possible
risk free investment rate, will then turn into hundred dollars.
Let me highlight the important times in the last line I just said.
BP is the initial investment.
And I'm putting it in the risk free, risk free means that I am certain that I will get that return.
I said best possible risk free, because there are several types of risk free opportunities, it could
be saving the money as a deposit in a bank.
It could be a fixed deposit or government bond and many more such opportunities.
But we are choosing the one with the highest rate of return.
So I suppose the best option available to you at the risk free rate is a fixed deposit, which is giving
you eight percent return.
Then the present value of this hundred dollar will be a hundred, divided by one plus zero point zero
eight, which is for the interest rate.
Then the present value comes to be ninety two point six.
This means that having hundred dollars after one year is like having ninety two point six dollars today
and making a fixed deposit out of it.
Now, why are we calculating the present value, we calculate the present value to evaluate the investment
opportunity.
Generally, if the present value of the future cash flows is more then the investment you are doing
today.
Then the investment option is considered as a good option.
And if you have two investment options with different amounts and periods of return.
You can compare them also using the present value.
For example, suppose you have these two investment options option and option B.
And both of them, you are investing a thousand dollars in the beginning.
And the first option, you are getting 250 dollars for the next five years.
And in the second option, you're getting 600 dollars, but for the next two years only.
The best possible interest rate that you can get is 10 percent.
Now, which of these two options is the better option for investing your thousand dollars?
For this, we will calculate the present value of the five future cash flows.
For the first year, it is 250, divided by one plus zero point one race to the Power-One.
Zero point one, because it is 10 percent interest and power, one because it is the first year.
For the second year, the power will be to 438, the power will be three and so on.
We add all these future cash flows and subtract the initial investment that we do in this investment
opportunity, the initial investment is done at year zero.
So there is no discounting of this money.
When we calculate this, the present value comes out to be negative to two point three.
This means that it is better to investors thousand dollars at 10 percent interest rate and the best
risk free opportunity that you have.
So whichever opportunity, for example, if it is a fixed deposit and it is giving you 10 percent interest
rate, it is better to put your thousand dollars there than investing in this option A.
Now, let us look at option B.
The calculation is same.
The only difference is that the payment is for two years and it is of six hundred dollars.
We discounted using the present value formulas and subtract the initial investment out of it, so the
net present value that we get is forty one point three.
This is positive, which means that this investment opportunity is better than the best risk free opportunity
that you have.
So this option is a good investment opportunity.
And out of option, and B, also, whichever option gives you a higher present value, that is the better
option.
Not that theoretically, there is no difference between present value or net present value.
But often in software tools, the pre function and the NPV function handle different types of scenarios.
So even though they are actually the same thing, softwares may use these terms differently.
So in the letters, we will be using Bibi and Bibi interchangeably.
NPV is a very important concept, and it is often used for the purpose of valuation, such as valuation
of a company or valuation of a customer and many such things.
So you must ensure that you understand the concept as well as learn its implementation in the software
tool.
I'll summarize the counterpart here.
So NPB or Pewee is the amount of money that if you invest today at the best available risk free rate.
Is equivalent to the expected future returns from the investment.
If NBP is positive, it means that it makes more sense to invest the money in that opportunity instead
of putting the money in the best available risk free option.
When you have two or more investment options, whichever has positive and higher NPV is the better option
available for investing.
Now, let's check out the implementation and modeling of NPB in our software.