Hi, welcome back to finance for non-finance professionals.

In this video, I'd like to talk to you about one of our capital budgeting tools,

net present value.

Net present value is going to be the standard bearer for

a lot of the capital budgeting stuff that we're going to talk about in week two.

It's one of our main capital budgeting tools, the net present value

pulls right out of the work that we've done in week one about compounding and

discounting and using rates of return.

The net present value, the basic idea,

is to add up the present value of all future cash flows and

like a lot of what we did with the annuity and bond examples in week one.

We're going to add up that present value, the future stream of all future cash

flows, and we're going to weigh that against the initial investment.

And we're going to ask a very simple question.

Does all the present value of the money coming in over the life of the project,

does it outweigh how much money we have to spend in order to do the project?

Net present value is just that, it's the net between the present value of these

two streams, money going out and money coming in.

We're going to ask a present values since whether that NPV is greater than zero.

If it's greater than zero, then the costs are less than the benefit.

The benefits exceed the costs we should do the project,

make the investment, that's our decision rule.

Is the NPV bigger than zero,

we can write down the formula for NPV very simply

as following along very closely with what we did in our discounting in week one.

The NPV is equal to the initial cost,

which has a minus sign in front of it.

Make that bigger.

Plus, what?

What's coming in off the project is cash flows.

Cash flow in period one, discounted one period back plus the cash flow

in period two, discounted to periods back.

You get the idea.

Plus maybe the cash flow in period three, discounted back.

Three periods plus maybe more cash flow's coming in.

What we're going to do is take that initial cost up here and

we're going to weigh that against the present value of all the cash coming in.

We're going to net the two.

There's a minus sign here.

Plus signs on all of these and

we're going to ask where they're sort of like a seesaw.

Whether all that money going out, ways against all the money coming and

ask whether that's bigger than zero or less than zero.

You can think of this sort of like seesaw.

If I think of that red minus sign over on the left being an initial investment and

that stream of green plus sign being the money coming in off the project

in the future, we can measure the NPV as the difference between the two,

the net between those two streams.

Right now you can see the seesaw's kind of balance against during the project because

the initial investment is sort of outweighing those positive plus signs.

But the larger those plus signs become, or the smaller that red negative becomes,

that balance tends to tip and the NPV becomes larger.

If that initial investment is much larger the NPV becomes smaller.

And you can see that the NPV whether it's bigger than zero or less than zero,

depends on sort of that balance between the money going out and

the money coming in.

Let's work a problem together and compute an NPV impractice.

So let's think of this table of cash flows that I've got and at a discount rate of

10%, let's think about whether it's worth it to do the project.

So what have I got?

I've got here in period 0 I'm going to spend how much?

$1,500.

And the question now is is it worth it to spend that $1,500?

Well, what's coming in off the project.

I've got a cash flow of $900 coming in at the end of year 1 and

I've got a cash flow of $750 coming in at the end of year 2.

And if I just sum up the cash flows, if I just say 15 minus

1,500 plus 900 plus 750, I get an answer of $150.

So this project is generating cash.