1. Discounting a Single Cash Flow
In this example, we're expected to receive a cash flow of $100
five years from today. What should we pay today if we want a
return of 4% compounded annually? Working backwards or discounting from
the future value of $100 in five years time divided by open[one plus
4% close bracket, and do this five times for each of the five
years, and this results in a present value of 82.19.
We have just used DCF to find the present value.
Now, let's tidy the math up a little,
rather than discounting the future value five individual times to get the
present value, there's a quicker way of doing this, which is to simply
divide by bracket one plus 4% close bracket, all raised to the power
of five. Also, dividing by one plus 4% raise to the power of five is
the same as multiplying by one over bracket, one plus 4%]
raised to the power of five. Now, this term here is really important,
and it's called the discount factor. In this example, the discount factor
is equal to 0.8219. Now, we can link the future value with the
present value, 82.19 equals %100 multiplied by 0.8219. In other words,
the present value equals the future value multiplied by the discount factor.
Let's open up Excel and have a go.
But first, you'll need to go to that downloads section of this course
and download the next Excel workbook called Discounted cash flow template.
So I've opened up the Excel workbook called Discounted cash flow template,
and I've gone to the second sheet called Demo. Let's just walk through
those numbers that we were just discussing together. Remember, what we had
was a future value of 100, and it was five years from today.
And we want to know its present value if the discount rate was
4%. So then what we need to do calculate the year five discount
factor, the discount factor equals one over bracket one, plus a discount
rate, all raise to the power of n, which in this case is
five. So these are discount factor, 0.8219, and we can now calculate what
the present value is by taking the future value and multiplying it by
the discount factor. So the present value, if we had 100 in five
years time, and interest rates were at 4%, the present value would be
82.19. Now we can use the PV function to calculate the same thing.
So let's just put some of the inputs of the PV function down
below here, so what's the rate? The rate is 4%,
the discount rate. The number of periods is a five, NPER is 5.
There is no permits been made or received along the way,
and the future value, there's a 100, so those are the inputs for
the present value formula, which I'm just gonna type here in cell E13. Now,
I'm gonna start by typing a negative at the front, so the result
is a positive number, so the present values is in the right.
And the reason why I put them in this order is that we
can just go down and pick them up,
and the future value is 100 and the type is always,
as with these types of questions is zero, we get the same answer.
82.19. Now we can virtualize what's happening with this kind of timeline
down here. In five years time, we're going to have a 100,
so let's just pick that up. All right. Now, I can discount that
by one year to find the value in year four by multiplying by
a one year discount factor. So I'm going to start with the future
value and I'm going to multiply that by a one year discount factor,
one divided by bracket, one plus the discount rate of four,
and I'm going to absolutely reference that, and because I want a one
year discount factor, because I'm trying to find the present value one year
before that 100, I could raise that to the power of one,
but raising it to the power of one doesn't really change anything,
so actually, I'm just going to leave that out. And so I can
see that one year beforehand that you have $100 in year five, is actually
with 96.15. So what I can do is I can actually drag that back
to the present value by just taking my cursor and then just dragging back
till we get to the present value here. And you can see that
I've got a present value of 82.19. If I discount back each year,
one year at a time at a rate of 4%,
and of course, the present value of 82.19 is what we calculated earlier
in this demonstration.
2. Let's practice!