1.9. The general NPV formula

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From the course by Moscow Institute of Physics and Technology

Principles of Corporate Finance – A Tale of Value

5 ratings

Moscow Institute of Physics and Technology

Principles of Corporate Finance – A Tale of Value

5 ratings

Course 2 of 5 in the Specialization Understanding Modern Finance

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.

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

Meet the Instructors

Konstantin Kontor
Director and Professor of Finance and Strategy
American Institute of Business and Economics (AIBEc)

Now, let's go back to the general NPV formula.

We know that it looks like this.

That NPV is equal to minus C sub 0 plus C1 or 1 plus

R1 plus CK or 1 plus RK to the K power and so on and so forth.

Well, what observations can we make?

One we already made,

we said that actually, C sub 0,

we can spread over time.

So that should not fall only here.

But like I said, we can sort of incorporate that into some components of C1,

CK, so and so forth.

So this is not so very difficult.

But for now, how can we proceed?

Well, there are basically two ways.

So let's look at this formula.

We have Cs unknown and Rs unknown.

Let's assume that Cs are known.

Then, we can afford to play with Rs that vary.

If however, Cs are not known,

we can't hardly afford the luxury of playing with variable Rs.

So we can say that R here is sort of constant.

Now, this way leads us to the analysis of

Bonds or better to say, the riskless bonds.

And this is more applicable for stocks.

Well indeed, for valuation of stocks,

Rs also are not constant.

But again, to deal with that is sort of a luxury because

the uncertainty in Cs are so great that to a first approximation we can't ignore it.

So that's how we proceed from here.

Our second week is devoted to specifically these two cases.

The first part is devoted to the analysis of again,

government bonds and we will see that although Cs will be fixed.

By the way, when Cs are known or fixed,

this is the overall sub universe

of so-called fixed income securities or fixed income instruments.

These are the ones for which the Cs are forked.

They are written down in a contract.

So they are forecasted with a significant degree of certainty.

That does not mean that the risky bond cannot default.

In this case, the investor does not get all the promised amount of money.

But we will limit our discussion when it comes to

the second or next week only to riskless bonds.

Here we will talk about the stocks.

We will indeed say,

well fine, we understand that this is a poor assumption.

But we will still hold our constant and then we will try to analyze all these stories of

growth or constant growth and we will see exactly

where the value of a stock really comes from.

So what is beyond?

Beyond, this is the huge area of cases in which,

first of all, everything is not constant.

But even worse, when some of these Rs and Cs tend

to change as a result of some changes in the environment.

So if indeed we have these choices when we

have the ability to make adjustments or forecasts,

that opens up collegially a new, let's say,

a paragraph or even a new chapter in valuation.

That is all associated with options and

other derivative securities that we study in

greater detail in the further weeks of this course.

So I'm wrapping up for now.

I wish you all good luck with your assignments.

There quite a few problems that although seem to be

very straightforward but do require some time and effort.

And it's very important that you solve these problems on your assignment because

otherwise it will be not that clear for you what we'll be doing starting next week.

So I wish you good luck again with these assignments and I see you next week.

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