Well hello.

Matt here.

Thank you for watching this video on the net present value.

What we're going to do over the course of the next several minutes is I'm going to walk

you through the net present value formula.

And so we're going to talk about what really net present value is, what the purpose and

function of it is, and then we're actually going to go through a problem if you will

and I'm going to show you step-by-step actually how to calculate net present value.

And it really isn't that difficult although it can be depending upon the complexity of

the capital budgeting project that you're working on.

So really to start, the net present value, which is commonly abbreviated simply as NPV,

is simply a capital budgeting tool.

And NPV comes up a great deal in corporate finance and so if you've taken a class in

corporate finance one of the things that's generally covered is net present value.

And the whole purpose of NPV is to help a firm assess the level of importance certain

capital budgeting projects have.

So capital budgeting or capital expenditures usually are high dollar value items typically

referred to as cap x.

And those generally include purchasing large pieces of equipment.

Things that are very expensive.

Property, plants, things are going to be have a great deal of value.

Generally fixed assets that are long-term and they are generally very expensive.

And so what companies try to assess is I'm going to spend potentially tens of hundreds

if not millions of dollars on this item, whatever it is.

We can to have some reasonable assurance that the future cash flow, which is the money generated

from the project, is going to be enough to pay off that project within a reasonable amount

of time.

And it's up to the business to determine what a reasonable amount of time is.

And also the helpful thing to is that many businesses have probably half a dozen to a

dozen different projects or opportunities at their disposal.

Things that are they're seriously considering.

And a capital budgeting tool like NPV helps a firm evaluate those different options to

see what's going to be the best one of them.

They can weigh them essentially utilizing NPV to determine which one has the most likelihood

of success given all of the alternatives.

So that's kind of the purpose a little bit of the back story why we use NPV.

So lets walk you through kind of how to calculate NPV.

So the first thing is lets get a couple of examples going.

So first thing, just for sake of example, lets say that we're going to purchase a business.

We'll keep things fairly simplistic just so you kind of understand the process.

And lets say that we're going to purchase a business for ten thousand dollars.

And we want to determine if we're going to invest ten thousand dollars today, depending

upon how much money we feel is going to be generated by this business, is it going to

essentially kind of work itself out?

Is it going to kind of pan out?

And so we want to see if we're going to pay this off within three years.

If the money generated is going to make sense in three years.

And so what we're going to do is we're going to draw a timeline . And we're going to draw

some hash marks for each year.

And I'm going to give you just some projections in terms of cash flow.

And so lets say that we believe that in year one, which is going to be abbreviated up here,

we believe we can generate three thousand dollars in cash flow.

So this is not in sales this is actual cash generated from the company.

So after all expenses and takes have been paid.

In year two we believe we can generate four thousand dollars in cash flow.

And then in year three we believe that we can generate five thousand dollars in cash

flow.

So if you were to look at this very simplistically the first thing that you would think of right

off the bat is well I'm generated twelve thousand dollars a year or twelve thousand dollars

in three years rather.

So I have three thousand in year one, four thousand in year two, and then five thousand

in year three.

Add those up together and you get twelve thousand dollars.

Twelve thousand dollars is more than ten, so I'm obviously making out ahead there.

I'm done.

I don't have to do anything else.

But the problem is that we're not considering the time value of money.

And if you watched the earlier video that I recorded on the time value of money we know

that money changes in value over time.

It decreases.

So if I had ten dollars today, that ten dollars is going to be worth more than that same amount

of money, that ten dollars in a week, a month, or a year because of inflation money depreciates

obviously in value what I can do with it essentially is less my purchasing power erodes, and then

I also suffer from opportunity costs.

I don't have it in my possession I essentially give up everything that I can do with it.

And so because of the time value of money because this three thousand dollars here a

year from now is not the same thing as three thousand dollars today.

Because I can't do anything with it and inflation is going to erode the purchasing power of

that three thousand dollars I can't necessarily compare this ten thousand dollars with these

different values.

Because they're from different time periods.

And so what I have to do is I have to engage in a process known as discounting.

And discounting means we're going to take each of these values and we're going to discount

it back to today's dollars.

So essentially we're going to change the value and put it into the worth of today so that

we can compare essentially what we're getting in future cash flow to what it would be worth

if we had it presently in our possession.

So the way that we do that is we utilize a formula which is called the present value

formula.

And that is PV equals FV divided by one plus i to the nth power.

And so what these mean, let me define these real quick.

Is the PV is what we call the present value.

This is the value, the numerical value, of the money today.

So this is what the money is essentially today.

FV stands for future value.

This is the money at a future point in time.

So this is the value of that particular money the kind of numerical figure at some time

in the future.

i stands for an interest rate.

When we're calculating NPV we generally assume i to be a relatively risk free return.

It's essentially what we could do with it.

If we had this money presently in our possession what we could do?

What's a general safe rate of return if you will that we can gain from it?

So we discount it by that amount because if we had the money in our possession we could

earn lets say that amount on it.

And then n is the number of periods.

This can be expressed in months, years, weeks.

You know it could be on a semiannual basis.

You can change the actual unit of the periods.

We're going to use years simply because it's a little more simplistic.

It's not as complex to figure out, but you can generally do this on a month-to-month

basis.

You can do it on any other kind of system you wish to do so.

So just know that for future purposes.

So the first thing that we need to do is we need to solve each of these.

We have to discount each of these future cash flows into present value so we know what we're

doing here.

So lets go ahead and do that.

The reason that I went with three years is because if we're doing this by hand this is

going to take a little bit of time.

It can be somewhat tedious.

The process is very simple.

It just can be a little difficult.

You can use a financial calculator for this which makes it a lot easier.

And so if you're going to be doing this on a regular basis you'll probably figure out

how to do that.

So lets go ahead and do it for or determine the present value for year one.

So first we're trying to figure out what PV is.

And so we know that the future value is three thousand dollars because that's how much future

cash flow we have in year one.

That's the future value of that particular investment or sum of money if you will.

And we have one plus the interest rate.

So lets just go ahead and assume just for sake of simplicity that we believe we can

earn five percent so that's what we're going to discount this at.

And this is in year one right here so we're only discounting it one year.

And so we're going to do it to the first power.

Three thousand divided by one plus .05 actually comes out to two thousand eight hundred fifty

seven dollars and rounding fourteen cents.

And so three thousand dollars discounted at five percent for one year is worth two thousand

eight hundred and fifty seven dollars and fourteen cents.

And so what we're going to do is we're going to go ahead and write that figure right over

here.

And we're going to do the exact same thing and calculate the present value for year two.

So for year two.

Let me just put first year.

And here we'll do second year.

And so we have a future value of four thousand dollars in year two.

Same thing, we're dividing by one plus .05 and this time though it's going to be to the

second power.

And so one plus .05 to the second power actually comes out to one point one zero two five.

And we're going to divide that into our four thousand dollars, which is our future value.

Which gets us a numerical value of three thousand six hundred twenty eight dollars and once

rounding twelve cents.

And so once again lets go ahead and include this amount over here.

And so once again four thousand dollars discounted at five percent for after two years discounted

for two years is worth three thousand six hundred and twenty eight dollars and twelve

cents.

So last one, third year.

We have a five thousand dollar future value.

We're going to divide by one plus .05 this time to the third power.

So 1.05 to the third power comes out to one point one five seven six two five zero.

When you're dividing it's really important that you don't round this initial figure because

if you do that's really going to change the present value that you get.

You can round the end figure that's fine.

Meaning the end result like this number here, but try not to round something that you're

going to divide into because that's going to drastically change the end result.

Alright so five thousand divided by our one plus .05 to the third power ends up coming

out to four thousand three hundred nineteen dollars and nineteen cents.

So you can see that's drastically different than this five thousand dollars that we have

here because we're discounting it for three years at five percent.

So that five thousand dollars three years from now obviously we don't have access to

that.

That's going to be the same dollar amount, but what we can do with it in three years

is obviously less.

So in today's value that is four thousand three hundred nineteen dollars and nineteen

cents.

And so what we do now is we compare our investment of ten thousand dollars to the future cash

flow which is discounted into todays dollars and see what the difference is.

And so if you add all of these up, these actually come out to ten thousand eight hundred and

four dollars and forty five cents.

And so what you need to look at here is this figure, this ten thousand eight hundred and

five figure is greater than this ten thousand figure by eight hundred and four dollars and

forty five cents.

And so the way that the NPV works, we're going to go ahead and move over here, is a figure

that is greater than zero we usually accept the proposal.

And so that means that the present value of all the future cash flows is greater than

the actual investment in which case it's a good investment by NPV terms.

Now by how much greater it depends upon obviously the numbers that you have.

So if you're like a dollar over.

If your NPV is literally a dollar technically you accept the proposal, but it's really not

that strong.

And so then you're going to compare that to all of the other options that you have . It

may not be as optimal as some of the others.

Now if the NPV is less than zero then we reject the proposal.

And once again, that means that the future value or the present value of all the future

cash flows isn't enough to substantiate the investment.

We probably have other projects that are going to be more well suited for what we're trying

to accomplish.

Once again though, if it is below the zero by a dollar technically it's pretty close.

So that's really a judgement call.

That depends upon a number of different factors.

Now here we're just evaluating future cash flows.

So this figure is going to depend upon how accurate you calculate or project future cash

flows.

If you're overly optimistic you're probably going to get a wrong NPV.

If you're very very conservative maybe it will throw your NPV off a little bit.

So you have to weigh that as well.

In this case our NPV is eight hundred and four dollars and forty five cents.

Since that is greater than zero we would technically accept the proposal or project.

In which case it's a good idea.

Now there are a number of other capital budgeting tools that you can use.

NPV is simply just one of them.

So you can utilize a number of different alternatives.

You can utilize the payback period and a number of others to help get a more accurate picture

over whether this is a strong idea or not.

Whether this is something that you should pursue.

So you never should rely solely on one.

But as you can see here it's fairly simplistic.

It's not very difficult to actually calculate.

The important thing is maintaining a good sense of organization.

You're dealing with a lot of different numbers if you're drawing these things out by hand.

And so that makes it very difficult if you get one number mixed up you're going to throw

everything off.

So that what I would say is certainly be organized if you're going to utilize these for some

long projects.

This is only for three years, it's not uncommon for capital budgeting projects to have thirty

years in terms of a lifespan.

That would be very tedious to do this for thirty years so you probably want to use a

financial calculator for that.

It would make things much easier.

You can probably solve it in a matter of minutes and it would save you a lot of time.

But that's generally how NPV works and how to do the actual calculations.

So hopefully that was helpful.

If you have any questions comments feel free and leave a comment and I'll try and get back

to you as soon as I can.

Thanks for watching.