All right, so the next thing that we are going to do is to calculate the present value for a series
of payment in finance, we call that annuity.
So what is annuity?
Annuity is basically a series of payment, series of annual payments.
I would say a series of annual equal payments.
So that is what an annuity is.
And exactly that is what we are going to calculate.
You may have used some long processes of calculating the present value of annuity or maybe a complicated
formula to calculate the annuity factor.
But here in Excel, it will be very easy.
But first, let us take a look at our traditional approach just to make a basic sense of what we are
trying to do.
So in our example here, we have the discount rate of 10 percent and the annual amount is one hundred
thousand dollars and that yours are basically five.
So for five years you will be receiving a payment of one hundred thousand dollars each year.
And for clarity, I will clarify this, that this each payment is at the end of each year.
So you have one, two, three, four and five.
So first of all, we have to know, how do we calculate the present value to calculate the present value?
We multiply that amount with the discount factor and with the second factor.
What we have been doing till now is that we have taken the amount and then we multiply that in with
one divided by one plus one.
Plus, our order is the rate of interest that is here 10 percent.
So I would make sure I'm using this as 100 percent.
And then we apply the power that can be power of one, two, three or five, whichever year we are working
for.
So in this case here, it will be power one only because we are in year one.
So you can see that I have included the present value, but rather than jumping directly on the answer,
what I'm trying to do is that I'm trying to calculate the discount factor thing first.
So I would I will do that.
I would say one divided by one plus R one, plus R an artist 10 percent here.
So I will make sure that my one is also 100 hundred percent.
And after that I will close the bracket and apply the power of one, which is only to apply actually.
So it just took up just to complete the formula, I will say power of this value over of this year here
and here as my discount factor for year one, and not if I copy paste and down at the cells below,
it will be calculating the discount petrol for all the years.
But first, let us make sure if we need to lock any cells and yes, we need to lock the cells to treat
the interest rate.
OK, now I will copy and paste these cells down and you can see that we have discount petrol for all
the years and now I will multiply the amount with discount factor and here we have our present value
of all five years.
And if I can sum all of that, I'm sorry.
If I can just calculate the sum of all of these, that will be the total present value for all of these
five payments.
Or alternatively, what you could do in accounting.
What we have learned normally is that we can also calculate the present value of series of payments
using Annuity Factor.
And where does Annuity Factor basically annuity factor?
Is the sum of all the different factors, so energy factor will be the sum of all the relevant factors,
which in my case are one to five.
So I'll just take the sum of all of these and now you can multiply the annuity.
That is basically one hundred thousand.
Just take it one time and effectively take the sum of all of them.
And now you can multiply the annuity factor with the with the amount that is coming each year and that
the present value, the same answer can be calculated this way.
But not the beautiful thing about Exel is that in exchange you won't have to work that long.
You can simply calculate the present value of energy using the same formula that we had been using and
previously.
So I will do it here.
I will say equals present value.
That is basically the formula and the rate.
First thing is rate.
That is 10 percent.
In my case, I will take 10 percent.
And then NPR is basically the number of payment periods, which is in my case, five and not be empty
while you're working.
In the previous lectures, I told you that BMT is a continuous payment each year.
So if if you can look here, the payment received up to.
Right.
So previously we were not receiving any payment each year.
But here is the case where you are.
So what I'm going to do is that I'm going to take the party of one hundred thousand and then I will
ignore the future value because there is no other amount than that.
All the money that are coming out, these five agreements.
And now I will ignore this last factor for a moment, but I will get back to this and I will close the
brackets and I will press enter.
And here you can see if I can resize it.
Here you can see that we have the same present value that you have calculated here or what since the
answer is negative.
What I should have done is that I should have taken a minus sign here, and in which case the answer
would be positive.
So let's ignore this negative thing for now and let's focus on the concept.
The concept is that the same present value of an annuity for a series of payments can just be calculated
by this simple formula.
But in this formula, we have ignored the future value and we have calculated that we have put the value
of one hundred thousand in BMT here.
So that was really easy.
Right now, before we wind up, I would like to show you something, and that is basically the last
thing that the type that we were ignoring.
So what is type?
Type is basically when payment is due.
As for the end of the payment, and one is for the beginning of the period, what that means is you
are supposed to tell Exel that when this amount is receiving, you are receiving at the end of each
year or at the beginning of each year.
So we were ignoring that in the previous calculations because that that that did not have made any difference.
But in this formula, then you are working for a series of payment.
This this will make a difference.
So what I'm going to do is that I'm going to calculate the same again, that is present value.
And then first of all, I have to take the rate I'm sorry equals present value and then read rate is
10 percent.
And then I have to take number of periods, which is five, and then I have to take the payment that
has this much.
I will ignore the future value and not type in the previous one.
We have ignored that.
And when you have ignored that by default, XL has taken the first one that was end of the year.
So I had assumed that all the payments are coming at the end of each year.
But now in our case, if I make at the beginning of the period see what will happen if I close the formula
and you can see that the answer is different and how the actual has calculated this answer, let me
show you, if I go back and change the payment procedure at the beginning of your end, Will sorry,
at the beginning of year one, beginning of year one is basically today, year zero.
So year one is 12 months from now.
And zero is basically before 12, 12 months from now.
That means today.
So I will make it is zero.
And you can see that factor has changed dramatically that year.
To begin means year one.
I have to wait for year one to get to that year to still standing should before you one that you're
three beginning should be year to that year for beginning.
Should be your three and five beginning.
Should be year for.
So you can see that we have reached at the same answer that Axl has given us.
So if we can just specify Exel that if the payments are at the end of the period or at the beginning
of the period extended according to the answer for you.
So that was the present value of annuity.
And I hope that you must have it now starting to see the value, the power that it brings to you in
finance.