1. Net Present Value
The next DCF application that we'll discuss together is called the Net Present
Value Framework or just NPV for short. Net present value is a financial
metric used to evaluate the profitability of an investment by comparing
the present value of its future cash flows to the initial investment cost.
It helps to determine whether an investment will generate positive or negative
returns, taking into account the time value of money.
To see how this works, consider a three year investment. The upfront cost
today is $1000. As we said the term of this investment is threw years,
and so each year this investment will return to us $400. We decide
that we need a 5% return for this investment so we'll use the
discount rate of 5%. This discount rate is used to find the discount
factor for each cash flow. In year zero or today, we invest $1000,
so we express this as a negative to show that it's a cash
outflow from our perspective. Also, the PV of $1000 today is just $1000
so we have no discounting to do for this negative $1000.
Using these variables, we calculate the discount factor for each of the
cash flows and multiply that by $400 to get the PV of each
cash flow. We then sum the expected PVs and subtract that from the
initial investment, which in this case gives us a positive NPV of 89.30.
Let's verify this result back in Excel. So here we are back on
the demo sheet of our discounted cash flows template workbook and I've scrolled
down to the last section called net present value NPV. Now,
thinking about the example that we were just discussing, the initial investment
was $1000. The annual cash flow that this is generating is $400 and
the required return that we have is 5%
and it's a three year investment. So let's think about the cash flows. What
do we pay today? Well, today, we pay the initial investment of $1000 but
because we pay it, we're going to make it a negative number.
And then each of the next three years, we receive $400 which I
will absolutely reference and then I can just fill right by hitting Ctrl+R.
So what about our discount factors? Well we know our discount factor formula.
The discount factor is one over bracket one plus the discount rate,
the required return which I'll absolutely reference again, all raised to
the power of n and in year zero today, the PV,
time is zero. And so our discount factor is one. And I can
highlight the row and then Ctrl+R to fill right to get our discount factors
really easily. And our present value equals our future value times the discount
factor. So unsurprisingly, $1000 today has a present value of $1000 and
I can highlight the row and Ctrl+R to fill right and we can
see what we've got there in terms of our cash flows. So what's
our net present value? Well, we can calculate that by
taking the sum of our present values including our initial investment today,
$89.30. But we can also use the NPV function in Excel to calculate the NPV.
Now the NPV function in Excel works in a funny old way or
there's a certain way that it works I should say. So before I
start typing NPV and open up the bracket, you can see that it
wants the rate but then it wants the values. But it assumes that
the first value happens one period from today.
So what that means is I have to go along, if I take
the rate, which is five and then the values are the values that
happen or start one period from today, which is 400.
Which means to get the actual NPV, I also have to add
the investment today. And because the investment today is a negative,
by adding it what I'm really doing is subtracting it from the NPV
calculation. And when I do that I get 89.3. Investors or companies may
look at the cost benefit of an investment or a project by using
the NPV decision rule. Investments or projects with a positive NPV add value.
They return enough cash to more than cover the cost of the investment,
all the project, based on the required return. So this is a good
indication to proceed with the investment or the project.
An investment or a project with a negative NPV does not cover the
upfront investment based on the required return. And they are sometimes
described as destroying value. They fail to return enough cash to cover
the cost of the investment or project. So this is a good indication
to reject the investment or project.
2. Let's practice!