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1.5. Introducing PV and NPV

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Principles of Corporate Finance – A Tale of Value

Moscow Institute of Physics and Technology

5 (6 ratings) | 1.4K Students Enrolled

Course 2 of 5 in the Understanding Modern Finance Specialization

The study of Corporate Finance seems to be a very generic part of business education. Still, it either falls in the trap of intimidating formulas or is superficially journalistic. Both extremes preclude the understanding of the core finance ideas, concepts, and models. This Course is an attempt to avoid the above extremes. We discuss the core basis and mechanisms of modern corporate finance in a learner-friendly way. We will analyze the market’s most fundamental problems, realize the intrinsic interests and preferences of investors, reveal the true meaning of specific financial terms, and uncover important issues that are so often ignored in choosing and valuing investment projects. The learners will gain insight into the essence of corporate finance. They will be able to use the obtained knowledge and skills to successfully advance in their career at a financial institution, as well as in the area of financial management at non-financial businesses.

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5 (6 ratings)

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From the lesson

Why Finance Matters? Net Present Value. How to Calculate NPV

In Week 1 we propose the game plan for our study of value. Then we analyze the key assumptions for the general valuation model. We focus on the understanding of the sources of value and the fundamental ideas of investor’s choice, the opportunity cost of capital, risk and return. We discuss the importance of time and expectations in determining value. Then we discuss the present value approach to studying the projects’ value and choice. We present the general PV formula and introduce the key concept of net present value (NPV) as a criterion of the choice of good investment projects. Then we study some most widely used shortcuts and apply the formulas to find the NPV’s of certain projects that play a special role in valuation. We end up with the general NPV formula and discuss the challenges in using it.

1.1. Introduction – the idea of value6:48

1.2. The game plan – a jumbo jet taking off5:09

1.3. The valuation model – key assumptions11:27

1.4. The opportunity cost of capital6:56

1.5. Introducing PV and NPV12:50

1.6. PV calculation shortcut (1) – perpetuities9:16

1.7. PV calculation shortcut (2) – annuities6:14

1.8. A fixed rate mortgage – an example of PV11:44

1.9. The general NPV formula4:57

Taught By

Konstantin Kontor
Director and Professor of Finance and Strategy

Now in this episode, the central episode of the first week,

we will introduce something that most of you have heard about and

that is very famous in corporate finance.

This is the approach that deals with the concepts of present value and

net present value.

Now first of all, let's start with an elementary project like this.

Again, my jumbo jet taking off metaphor was specifically

pronounced in order to show to the people that although I start

from the things that seem to be offensively easy to understand.

But, again, our jump from that to something much more advanced and

realistic will be very quick.

So let's take a look at the elementary project.

So we have one period, this is 0 when we make a decision.

This is point 1.

And we expect To receive $1 at point 1 here.

And we pose the question, what is the equivalent to

the receipt of that $1 at point 1 at point 0?

So that may seem like an answer to the following question.

If I invest in this project,

What is the equivalent of putting some money in my pocket right now,

or maybe taking some money out of my pocket?

Well, in order to tackle that, we have to realize how would we treat

this time flow, and how would we treat this project?

Because something happens from 0 to point 1.

And we say that this project has a rate of return of r, what does that mean?

That means that for any amount of money that you invest here,

you will get this amount multiplied by 1 plus r at point 1.

If this is the case, then we can easily get an answer to our question.

We'll say, if x is the equivalent of that at point 0,

then x multiplied by 1+r should be equal to our expected $1.

And we get the first famous formula that x is equal to present value of this $1,

and this 1 over 1+r, where r is the return for this project.

Now projects have different returns, projects have different lengths.

And as we understand projects have also different risks.

But for the first part of this course, in weeks one, two, and

three we will take risk and return as a given, and we'll study that all the later.

But for now, this is like I said an elementary project.

We can have clearly other projects, and now we can make some generalizations.

Now generalization one will be,

what if we expect to receive

C dollars?

Well, then free NPV will be

equal to C over 1 + r, great.

But look, what if by the way here we assume that

r is positive and C is positive, too.

If this is the case, then we can say that PV is positive which is kind of cool.

So the question is in order to receive that,

I have to enter this project.

I have to pay something to enter into this project.

Because I receive a positive amount right now.

Remember, I said that PV answers the following question.

How much money do I put in my pocket right now

that is equivalent to my investing in this project?

So if I put a positive amount in my pocket right now, that seems that I got a gift.

Well, again, this is a very clear idea that in general we have to pay

something for these projects.

And that leads us to the next formula.

If you paid, I put -C sub 0 for this project,

and then you receive this PV whatever it is, then this is called net present value.

So that basically answers the following question,

how much do I put in my pocket or do I take out of my pocket

after I entered in this project, after having paid C sub 0?

Well, all that is great.

But now if I know how to calculate NPVs,

then I have a fundamental criterion for valuation.

I can say remember I started out in the very first episode saying that we have to

find the criterion of affixing labels, what is good and what is bad.

And now we can say that clearly a black box is good.

When?

If its NPV is positive.

So this is the most fundamental valuation criteria.

So that basically means that I found a project

by having invested in which I put some money in my pocket right now.

Sort of from nothing.

Well, not exactly from nothing.

And we understand that if all projects in all this world they would have

been let's say absolutely clear to everyone, then as a result of competition,

it's unlikely that people would be able to find some some positive NPV projects.

We will indeed see that in some markets that are very liquid,

very close to being perfect, this is indeed the case.

For example, this is NPVs of most investments in

riskless bonds are very close to zero NPV projects.

But if you take up a lot risk, if you engage in something uncertain,

then it's very likely that if you are lucky, or

if you're successful, then you do indeed get a positive NPV.

So basically, this is the general thing.

And this process, as you know, is called discounting.

And from here we can proceed with some more generalizations,

because here I used a one period project.

Well, first of all,

I will show you some simplistic examples how business this discounting works.

Let's say that we analyze the following project.

So this is, again, 0 and 1.

I invest $1,000.

And then in the blue project, I expect to receive

$1,200.

And the return of that is 10%.

And in the black project, for which cash flows are exactly the same, so

this is minus 1,000 here and plus 12,000 here.

But the rate of return on black project is 30%.

Now you don't have to be a wiz to calculate that for

a blue project the NPV is equal to +91, while for

a black project the NPV is equal to -77.

So you can see that although in both projects you

are expected to make more money than you invested.

But the question is not only more but how much more.

How much more is enough to make the project good.

And now we can see that the threshold point is clearly 20%.

So if, for example, this project would require a 20% return,

then its NPV would be equal to 0.

All these things will happen very often in our future examples and studies, but for

now this is kind of thing that you have to keep in mind.

So this idea of how much more makes it good.

But then we can make generalization two.

We can say, well, projects Have different lengths.

And we know the different rs for all these lengths.

And so we can say that if, for example, this is 0, 1, and 2.

And this is C1, this is C2.

And then let's say that r1 is the correct

expected rate of return for this kind of investment.

And then r2, if we invest for two years,

then clearly this in general is going to be a different rate of return.

Not because of the length, but also because of the fact that maybe

the expectations for a two year investment are different.

We have to compare returns that are sort of normalized to the same period.

So here r2, in order to get the PV of that, you have to square that.

Then the NPV of this will be equal to -C sub 0 plus

C1 over 1 + r1 + C2 over 1 + r2 squared.

So we generalized for two periods.

But, again, now we can make the general formula.

We can say that the general NPV is equal to

-C sub 0 + C1 over 1+r1 + the general

term Ck over (1+rk) to the k-th power.

And then plus because that doesn't have to be finite.

So this is the general formula which we reached very quickly.

But the problem is that, in order to find MPV,

you have to know all the C sub 0, C1, Ck, and so forth.

And also you have to know r1 rk, and so on and so forth.

So, well, you can always say that In reality you can make investments not only

at point 0 but then later on 2.

But for the sake of simplicity, we can always think that these

investments can be treated sort of like costs at these points.

So we will not delve deeper into that for now.

We discuss these differences between capital expenditures and

some kinds of costs.

Not only in what follows in this course, but

also in some greater detail in our third course.

But for now, we've reached this formula and that all sounds great.

We know that unfortunately we posed more extensions than we have answers.

Because you say, great, if I only knew all Cs and all Rs, I would be great.

However, we do not always know them.

And starting from the next episode, we'll start to see how this formula works

if we do know some of these Cs, or we have a good forecast of them, or

if we make some special cases that will simplify the use of this formula.

Let me tell you right away that although some of the examples are, not only widely

known but seem to be very much made up to make the formula look simple.

But the key story is that actually people do use these simple

results in actual corporate evaluations and evaluations of some real assets.

So our examples from the next episodes will not be so irrelevant, if you will.

So starting the next episode, we will study these short cuts.

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